The field of nanoplasmonics has emerged as a vibrant and rapidly evolving area of research at the intersection of physics, chemistry, and materials science. At its heart lies the unique ability of metallic nanostructures to manipulate light far below the diffraction limit, leading to unprecedented control over electromagnetic fields, energy flow, and chemical reactivity at the nanoscale. The central protagonists of this field are surface plasmons—collective oscillations of conduction electrons at metal–dielectric interfaces—which, when excited by light, generate highly localized and enhanced electromagnetic fields. These effects underpin a broad spectrum of groundbreaking applications, from ultrasensitive biosensing and quantum information processing to advanced energy conversion and catalysis^[1–8].

The initial breakthroughs in nanoplasmonics were rooted in the discovery of surface-enhanced Raman scattering (SERS)^[9–15], which demonstrated that molecules placed near roughened metal surfaces could exhibit Raman signals magnified by many orders of magnitude. This remarkable enhancement was soon attributed to the strong local electromagnetic fields generated by localized surface plasmon resonances (LSPRs) in metallic nanostructures. Early research thus focused on exploiting the magnitude of these near fields to amplify light–matter interactions, enabling highly sensitive detection of molecules, control over luminescence^[16,17] and photothermal effects^[18,19], and the efficient generation of so-called hot carriers—nonequilibrium electrons and holes that drive new photoinduced chemistry and photodetection^[3,20,21].

Yet, as the field matured, it became clear that simply maximizing field intensity and absorption does not exhaust the potential of plasmonic systems. The ability to tailor and exploit the coherence of plasmonic excitations—meaning the control over phase, superposition, and quantum interference—has emerged as a decisive factor in determining the efficiency, selectivity, and new functionalities of nanoscale devices. For example, phase-sensitive effects such as Fano interference^[22–36] arise from the coherent superposition of spectrally broad and narrow resonances, resulting in sharp spectral features and windows of suppressed absorption. In particular, interference between coupled modes in metal–molecule hybrid systems can produce real-space phenomena such as energy transparency (ET), where excitation energy is transferred efficiently from metallic structures to molecular sites with surprisingly little dissipation, hinting at a novel way to mitigate damping effects^[29]. Furthermore, the hybridization of plasmonic modes with molecular or excitonic transitions gives rise to new hybrid states, known as plasmon–exciton polaritons. The quantum nature of these states enables both strong coupling and coherent energy transfer, radically altering the optical and electronic properties of the system^[37–46]. Strong coupling is often distinguished from Fano interference or ET by the appearance of anti-crossing behavior in spectra, although careful observation of molecular emission or other complementary measurements is required for unambiguous identification^[34,47].

As experimental methods continue to advance, the temporal aspect of plasmonic coherence has become increasingly important. Ultrafast pump–probe spectroscopy, two-dimensional electronic spectroscopy, and real-time single-molecule techniques now allow the direct observation of quantum beats, coherence lifetimes, and the dynamical evolution of hybrid states at femtosecond timescales^[48–51]. These time-resolved approaches not only provide deeper insight into the mechanisms of energy transfer and coherence decay, but also enable the dynamic control of quantum states for applications in quantum information processing, ultrafast optical switching, and light-driven chemical transformations.

The exploration of plasmonic coherence has also opened new frontiers in optical imaging and spectroscopy. Near-field techniques such as tip-enhanced Raman scattering (TERS)^[52–58], tip-enhanced photoluminescence (TEPL)^[59–61], and photoinduced force microscopy (PiFM)^[62–67] have leveraged the phase, symmetry, and spatial coherence of local plasmonic fields to surpass the diffraction limit and enable direct visualization of quantum states at the molecular and even atomic scale. Here, coherence is essential because it allows the selective excitation and detection of transitions that are otherwise hidden in the far field, by enforcing precise phase relationships and enabling control over spatial symmetry. Importantly, it has been theoretically predicted and experimentally demonstrated that such coherent and highly localized near-field environments can activate “forbidden” quantum transitions—those strictly suppressed in the far field due to symmetry, but rendered optically accessible through strong field gradients and local coherence^[68–71]. More recently, these advances have been complemented by studies in which forbidden transitions have been not only detected but also spatially resolved at the single-molecule level, providing direct real-space images of quantum states and transition pathways^[66,72]. This multidimensional access to quantum states is now driving breakthroughs in orbital tomography, symmetry-selective chemistry, and real-space mapping of molecular and electronic wavefunctions.

Another emerging theme is the recognition that coherence and collective effects among plasmonic nanostructures can be harnessed to achieve new regimes of energy transport and conversion. Recent studies have revealed that when multiple nanoparticles, antennas, or metasurface elements are coherently coupled, they form collective supermodes in which energy and information can be shared nonlocally across the array ^[73–76]. This delocalization leads to extended coherence domains, offering pathways to overcome the spatial bottleneck of classical hot spots and enabling nonlocal hot-carrier extraction, high-efficiency photodetection, and collective nonlinear optical responses. These insights have driven a growing interest in understanding how quantum coherence and modal hybridization can facilitate more efficient generation, transport, and extraction of hot carriers—nonequilibrium electrons and holes generated by plasmon decay—which are central to advanced photochemistry and optoelectronics^[3,4,21,77]. Building on these concepts, it has recently been demonstrated that quantum coherence within engineered plasmonic architectures can directly enhance hot-electron injection under conditions of modal strong coupling^[78,79]. By exploiting collective plasmonic supermodes and their coherent interaction with optical cavities, their studies reveal that hot electrons can be generated and transferred nonlocally across nanostructure arrays, breaking the limits of conventional localized excitation and offering a new paradigm for efficient energy harvesting and conversion at the nanoscale. This line of research underscores the central role of structural coherence and collective photonic effects in the design of next-generation plasmonic and quantum photonic devices.

The significance of coherence extends even further when considering the coupling between plasmons and electron–hole pairs within the metal itself. Earlier quantum mechanical approaches, including nonlocal response theories^[80,81] and ab initio simulations of plasmon decay^[82–84], have advanced our understanding beyond classical models by incorporating quantum-size effects, electron spill-out, and microscopic carrier dynamics. These studies have revealed the complexity of plasmon decay and hot-carrier generation (HCG), highlighting roles for both collective and single-particle excitations. However, they often focused primarily on longitudinal field components and largely treated damping and energy transfer in a phenomenological manner. Motivated by remaining discrepancies—such as the observed frequency dependencies and polarization anisotropies in HCG—recent work has introduced a new, self-consistent quantum framework^[85–87] that systematically accounts for the transverse field component and its role in mediating coherent, bidirectional energy exchange between plasmons and electron–hole pairs. This novel perspective reveals that phase-coherent interactions, mediated by the transverse field, can govern not only the efficiency but also the directionality and selectivity of carrier generation and relaxation in nanostructured metals. Such insights open the door to actively engineering quantum interference and coherence for advanced control over energy flow at the nanoscale.

The growing intersection of plasmonics with emerging fields such as quantum optics, topological photonics, and chiral nanoscience further amplifies the importance and reach of coherence-driven phenomena. Concepts such as topologically protected plasmonic edge states, enantioselective energy transfer, and quantum feedback control are being integrated into the plasmonic toolbox, pointing toward a future where deterministic manipulation of quantum states, robust information transport, and ultralow-loss energy flow are routinely achievable at the nanoscale^[88–92].

In this review, we provide a comprehensive and critical account of the evolution and current frontiers of plasmonic coherence, emphasizing how the understanding and control of coherence—beyond simple field enhancement—have transformed our grasp of nanoscale light–matter interactions. Beginning with the classical foundations and advancing through quantum mechanical and nonlocal models, we systematically cover the theoretical and experimental breakthroughs that underpin phenomena such as ET, strong coupling, and multipolar transition activation. Special attention is given to the interplay between plasmonic structures and both external and internal electron–hole pairs, the real-space visualization of forbidden transitions enabled by near-field coherence, and the emergence of collective supermodes in coupled nanostructures. By tracing these developments from fundamental principles to the latest advances in coherent HCG and real-space quantum imaging, our goal is to provide readers not only with a solid grounding in the physical mechanisms, but also with a clear perspective on the unresolved challenges and future directions in this rapidly developing field. (See Fig. 1 for a schematic overview of the conceptual trend from localized plasmonics to coherence-driven collective behavior.)

For clarity, a concise table summarizing the symbols and recurring abbreviations used throughout this review is provided in the next page.

The theoretical investigation of plasmonic coherence has evolved in parallel with advances in nanofabrication and spectroscopic techniques. Early studies were based on classical electrodynamics, followed by the development of semiclassical hybrid models, and more recently, fully quantum mechanical and ab initio approaches have been introduced. This progression in theoretical methods has both reflected and supported experimental efforts to understand and control coherence phenomena at the nanoscale. This section provides a brief overview of the major theoretical frameworks employed in the study of plasmonic coherence, spanning from classical electrodynamics to quantum optics and open quantum systems. The aim here is to establish a conceptual foundation that will help the reader navigate the coherence phenomena discussed in the subsequent sections. Specific theoretical treatments such as applications to concrete systems are revisited and elaborated upon in the corresponding later sections where such frameworks become directly relevant.

At the core of early plasmonics lies the classical treatment of metals as free-electron systems. The Drude model, formulated at the turn of the 20th century, provides a foundational description of the dielectric response of conduction electrons in metals: εD(ω)=ε∞−ωp2ω2+iγDω,(2.1)where ωp is the bulk plasma frequency characterizing the collective oscillation of free electrons, γD=1/τ is the Drude (electron scattering) damping rate with the momentum relaxation time τ, and ε∞ accounts for the high-frequency (interband) contributions^[93]. This simple model captures key aspects of metallic optical responses (e.g., the sign change of Reε across the visible) and explains why metals like gold and silver exhibit strong reflection and characteristic colors in the visible regime.

The concept of a bulk plasmon^[94–98] emerges naturally as a collective excitation in the form of a longitudinal wave of the electron gas, with the resonance condition given by the real part of εD(ω)=0. Taking into account the wavevector dependence then yields the plasmon dispersion relation in the metal. The presence of a boundary between a metal and a dielectric allows the emergence of a class of collective modes known as surface plasmons^[98–100]. These modes correspond to a longitudinal wave that is confined to the interface, with associated electric fields decaying exponentially into both media. In the classical framework, surface-bound solutions can be obtained by solving Maxwell’s equations with the Drude dielectric function for the metal.

As the geometry evolves beyond planar interfaces toward nanostructured materials, additional types of plasmonic excitations become accessible. One particularly important example is the LSPR, which arises in finite metallic structures such as nanoparticles. This resonance results from the confinement of surface plasmons within the boundaries of the particle, leading to discrete resonance conditions that are highly sensitive to the particle’s size, shape, and surrounding dielectric environment.

In the visible–near-infrared (NIR), interband transitions are non-negligible for noble metals. Practically, take the Drude permittivity εD(ω) given above and add the Lorentz interband term to the right-hand side: εDL(ω)=εD(ω)+∑jfjΩj2Ωj2−ω2−iΓjω.(2.2)

Here, Ωj, fj, and Γj denote the resonance frequency, strength, and damping of the jth interband oscillator. This compact refinement is widely used for LSPR and metasurface modeling in the visible–NIR^[101–103].

Besides Drude-like carriers, strong interband oscillators can themselves drive plasmon-like resonances in the visible–UV. In several p-block elements (e.g., Bi, Sb, and Ga), the real part of ε becomes negative over specific bands predominantly due to interband transitions, enabling LSPR-like responses without relying on free-carrier Drude terms; modeling is then naturally captured by Lorentz oscillators with appropriate strengths and onsets^[104,105]. Related interband-driven polaritonic resonances have also been realized in group-IV platforms, exemplified by deep-UV silicon metasurfaces engineered for spectroscopy and Raman enhancement^[106].

Having established both the electrodynamic setting and the material dispersion relevant to the visible–NIR, we now outline classical scattering formulations.

An exact analytical solution to Maxwell’s equations for electromagnetic wave scattering by a homogeneous sphere was provided by Mie in 1908^[107,108]. Although Mie’s original work predates the formal concept of plasmons, its application to metallic nanospheres, using experimentally determined complex refractive indices, enables a classical description of LSPR phenomena. This Mie-based framework has since been extended to describe more complex geometries, including ellipsoids, rods, nanoshells, and particle aggregates. To accurately capture the optical responses of such structures, one must consider additional effects such as depolarization fields, shape anisotropy, and electromagnetic retardation. For instance, Gans theory generalizes Mie theory to spheroidal particles, effectively capturing the polarization dependence and the tunability of LSPR with particle aspect ratio^[109–111].

While these analytical approaches provide deep insights into symmetric structures, they are inherently limited to idealized geometries. To overcome these limitations and treat arbitrary shapes and realistic environments, a suite of numerical methods has been developed. The discrete dipole approximation (DDA)^[112–115], the boundary element method (BEM)^[116–119], the finite-difference time-domain (FDTD) method^[120–123], and the finite-element method (FEM)^[124] have become standard for computing optical properties, local field distributions, and coupling effects in complex plasmonic systems. In addition, to handle systems composed of multiple spheres, theoretical frameworks such as the generalized Mie scattering theory^[125,126] and numerical approaches like the T-matrix method^[127–129] have been developed. These techniques allow for the modeling of multi-particle interactions, substrate effects, and dielectric inhomogeneity—bridging the gap between analytical theory and experimental reality.

The theoretical foundation of classical plasmonics has been built upon the Drude and Mie models, their analytical extensions, and the development of complementary numerical methods. These approaches have contributed to a detailed understanding and prediction of a broad range of optical phenomena in metallic nanostructures. This classical framework continues to provide essential insights and serves as a stepping stone toward quantum plasmonics and the exploration of more complex light–matter interactions at the nanoscale.

While the above numerical methods can, in principle, provide solutions to classical Maxwell’s equations for arbitrarily complex structures, they often obscure the underlying physical mechanisms. For developing a deeper understanding of light–matter interactions in plasmonic systems, theoretical and analytical approaches remain indispensable. This subsection outlines key conceptual frameworks—such as plasmon hybridization, Fano resonances, and lattice plasmons—that have been developed to elucidate collective phenomena arising from interactions between plasmonic nanostructures. Through these perspectives, we explore the emergence and significance of coherence in classical plasmonics.

The resonant characteristics of surface plasmons are highly sensitive to the geometric parameters of nanostructures, especially in the presence of nearby metallic structures. In nanoplasmonics, a wide variety of collective plasmonic modes has been explored to achieve spectral and spatial control over the optical response. Among these, Nordlander et al., inspired by the hybridization of atomic orbitals in molecular orbital theory, developed the concept of plasmon hybridization^{[73,74,130,131]}, which provides deeper insight into the interaction between induced polarizations arising from surface plasmon resonances. When two metallic nanoparticles are brought into close proximity, their individual dipolar plasmons couple to form hybridized modes: a bonding mode characterized by lower energy and in-phase oscillation, and an antibonding mode with higher energy and out-of-phase oscillation^{[74,132–134]}. This hybridization framework applies to a broad range of complex geometries, including nanoshells^{[73,130,135,136]}, nanorods^[137–143], and linear chains of nanoparticles. While numerous studies evaluating interactions between plasmons in metallic nanostructures predated the introduction of the term plasmon hybridization^{[132,144–149]}, the concept has provided a useful framework for interpreting plasmonic coupling phenomena and has significantly advanced the investigation of complex interactions in such nanostructures.

The optical response of a plasmonic nanostructure placed near a flat dielectric or metallic substrate can be effectively described using the traditional method of image charges. A basic example is the situation of a dipole near a planar interface, where the substrate’s influence is modeled by an image dipole located symmetrically across the boundary, where the original dipole and its image interact to form hybridized modes^{[74,150–152]}. Systems in which a molecular dipole interacts with its image dipole induced in a metallic substrate have been investigated, particularly in the context of SERS^[153]. In addition, in tip-enhanced microscopy, where a molecule couples to the locally enhanced field of LSPR between a tip and a substrate, image dipole interactions are often incorporated into theoretical models to analyze the resulting image^[154].

Fano resonances can emerge in plasmonic systems when a broad, radiative (bright) mode and a narrow, subradiant (dark) mode coexist due to surface plasmon interactions^{[26,27,155–158]}. These resonances exhibit characteristic asymmetric spectral line shapes, which have been observed not only in nanoplasmonics but also in a variety of physical systems across disciplines. The fundamental mechanism underlying Fano resonances is the interference between a continuum-like excitation and a discrete resonant state. Mathematically, the resulting line shape is described by the Fano formula^{[22,27,155,156,159]}F(ϵ)=(q+ϵ)21+ϵ2,(2.3)where q is the asymmetry parameter, and ϵ=ω−ω0γn/2denotes the normalized detuning from the narrow resonance. Here, γn is the full width at half-maximum (FWHM) linewidth of the narrow (dark) pathway; in our notation, γn=γ for a molecular exciton, whereas γn=Γdark for a subradiant plasmonic mode. The broadband continuum is characterized by the bright-mode linewidth Γ (Sec. 3.2). (We use ε for the material permittivity and ϵ for the reduced spectral variable in the Fano profile; the two are unrelated.) In plasmonic oligomers and metamolecules, the Fano effect enables the emergence of sharp spectral features and tunable transparency windows, which are highly sensitive to both structural geometry and the surrounding dielectric environment. The canonical line shape is shown in Fig. 2(a). [While Fig. 2(b) illustrates a coupling between an excitonic (molecular) level and a plasmonic mode, the same line shape formalism applies equally to plasmonic bright–dark interference.]

Lattice plasmon modes are formed in periodic metallic nanostructures. For instance, in arrays of gold or silver nanoparticles, resonances significantly narrower than the original LSPR emerge, accompanied by Fano-type spectral line shapes^[160–164]. In particular, the resonances are understood based on the band structure formed by the periodic arrangement of the nanostructures^[165–172]. Conceptually, plasmon hybridization in a minimal dimer yields gap-dependent bonding/antibonding splitting with bright/dark symmetry (Fig. 3).

In periodic arrays, the narrow features are commonly referred to as surface lattice resonances (SLRs) arising from the interplay of single-particle polarizability and the lattice Green’s function. Within the coupled-dipole picture, the collective mode condition reads α−1(ω)−S(k∥,ω)=0,(2.4)where α(ω) denotes the single-particle polarizability (including radiation reaction) and S is the lattice sum excluding the self term. Near a Rayleigh anomaly, ReS varies rapidly and, below the first diffraction threshold in a lossless background, ImS≈0, which suppresses radiative leakage and yields high-Q SLRs. For clarity, we refer to the total SLR linewidth as Γlat=Γlat,i+Γlat,r, with the former set by material absorption and the latter by out-coupling to open diffraction orders.

This has led to a wide range of studies, including applications to lasing^[173–176] and interpretations in terms of Bose–Einstein condensation^[177–179]. Similarly, periodic arrays of nanoholes in metallic films support distinctive modes, among which the extraordinary optical transmission (EOT) effect has attracted significant attention^[180–184]. Furthermore, topological edge states, as described by the Su–Schrieffer–Heeger (SSH) model^[185], have been demonstrated in periodic metallic nanostructures such as gratings^{[89,186–189]}, nanoparticle chains^[190–195], zigzag configurations^{[91,196–198]}, and various two-dimensional arrangements^[199–202]. The concept of topological plasmonics has taken shape and is gaining interest in nanophotonics^[203,204].

Periodic plasmonic arrays can also host quasi-bound states in the continuum (quasi-BICs), where an ideal symmetry-protected BIC becomes weakly leaky under a slight symmetry breaking of magnitude δ. Consequently, the radiative component of the lattice linewidth grows as Γlat,r∝δ2, leading to the well–known scaling Q∝δ−2 in the radiatively limited regime; when intrinsic loss dominates, Q saturates at ω0/(2Γlat,i). Such quasi-BICs provide sharp dispersive line shapes advantageous for sensing, nonlinear conversion, and low-threshold lasing^[205–209].

These frameworks illustrate how electromagnetic interactions between nanostructures give rise to rich and tunable collective optical behaviors. By providing physically intuitive models that link geometry, mode interference, and optical response, these approaches have become essential tools for both interpreting experimental observations and guiding the design of advanced plasmonic systems. As we move toward increasingly complex and quantum-informed regimes, these classical insights continue to offer a valuable foundation for exploring coherence and coupling phenomena in nanophotonics.

A key development in the theoretical description of plasmonic coherence has been the integration of quantum mechanical frameworks. When the size of metal nanoparticles is reduced to a few nanometers, or when the separation between metal surfaces falls below a few nanometers, quantum mechanical effects such as spatial nonlocality, electron spill-out, and quantum tunneling become non-negligible. This subsection introduces theoretical approaches, including time-dependent density functional theory (TDDFT) and hydrodynamic models, that have been developed to describe such effects in nanoscale plasmonic systems.

TDDFT, originally developed by Runge and Gross^[210], provides a powerful first-principles method for describing the dynamic electronic response of molecules, nanoparticles, and hybrid plasmonic systems. In TDDFT, the time-dependent Kohn–Sham equations are solved self-consistently for the time-evolving electron density ρ(r,t): iℏ∂∂tψj(r,t)=[−ℏ22m∇2+veff[ρ](r,t)]ψj(r,t),(2.5)where veff[ρ] incorporates both external and exchange-correlation potentials. TDDFT has been widely used to predict quantum plasmon resonances, charge-transfer excitations, and spectral shifts in realistic metallic clusters and hybrid systems^[211–219]. Moreover, hybrid methods that couple TDDFT with Maxwell’s equations have been proposed^[220,221], allowing for a self-consistent treatment of quantum mechanical effects in the optical response of LSPRs.

Hydrodynamic Drude models have been discussed since the early days of plasmonics^[222,223], but they began to attract increasing attention around two decades ago, when advances in the precise fabrication of colloidal nanoparticle systems enabled detailed experimental studies^[224–226]. With such developments, the hydrodynamic approach was found to provide both quantitative and qualitative agreement with experimental results, further highlighting its relevance to nanoscale plasmonic systems. In this model, which captures spatially nonlocal effects beyond the standard Drude model, conduction electrons are treated as a compressible fluid characterized by the electron density n(r,t) and velocity v(r,t). Their dynamics are governed by the following equation of motion^[224,226]: me(∂∂t+v·∇+γHD)v=−e(E+v×B)−∇δG[n]δn,(2.6)where G[n] is the energy functional of the electron fluid and γHD=1/τHD is the phenomenological collision rate in the hydrodynamic model. (In the linear, homogeneous limit, γHD reduces to the Drude damping γD introduced in Sec. 2.1.) This hydrodynamic behavior is incorporated into Maxwell’s equations through the polarization response. This approach has been applied to a wide range of systems, from simple wire geometries^[227–229] and dimer structures^{[80,213,230–233]} to geometries with various situations^[234–238]. In addition to its broad applicability, it has enabled the exploration of distinct nonlocal effects, such as blue shifts of resonant wavelength and the smearing of field enhancement in nanogaps^{[225,229,239]}. TDDFT and hydrodynamic models have been compared and used in a complementary manner to interpret plasmonic responses^[217,240]. Moreover, because the hydrodynamic model inherently incorporates retardation effects, the development of a more accurate formulation opens the way to analyzing larger metallic nanostructures beyond the practical limits of TDDFT^[229].

In the context of theoretical studies on systems where molecules are positioned near metallic nanostructures, such as in SERS and TERS, several classical methods have been developed to describe the optical response of the nanostructures under external fields by mimicking atomic arrangements using discrete charges (and dipoles), similar to the DDA. For instance, the discrete interaction model^[241–246], the frequency-dependent fluctuating charges model^[247–252], and similar methods^[253,254] are capable of evaluating the enhanced electric field in nanogap configurations such as dimers and tip–substrate systems, while explicitly considering atomic-scale structure. In particular, extensions of these methods that incorporate a quantum mechanical description of target molecules have enabled their application to the simulation of TERS imaging^[244,245].

With these theoretical advancements, it is now becoming possible not only to simulate larger-scale metal–molecule systems, but also to accurately incorporate quantum effects, reproduce experimental results both qualitatively and quantitatively, and even predict new physical phenomena.

The integration of quantum optics concepts with plasmonics has led to new physical insights and applications in nanoscale light–matter interaction. Theoretical models now incorporate quantized electromagnetic fields, cavity quantum electrodynamics (QED), and open quantum system techniques to describe spontaneous emission, photon statistics, coherence control, and HCG. This subsection also introduces electromagnetic Green’s function methods, which enable a rigorous and parameter-free description of emitter–plasmon interactions in both simple and complex nanostructures, as well as cooperative effects such as superradiance and energy transfer.

A prototypical quantum optical Hamiltonian for plasmonic strong coupling can be described by the Jaynes–Cummings-type model, which is widely used to predict vacuum Rabi splitting, and photon blockade in nanocavities^[43,255,256]. Metallic dimer nanoparticle systems, due to their simple geometry and strong field confinement, have been explored both theoretically and experimentally as prototypical platforms for studying strong coupling^{[255,257–259]}. In particular, strong and ultrastrong coupling in plasmonic nanocavities has confirmed quantum coherent energy exchange even at room temperature^[42,260,261]. Furthermore, two-dimensional transition metal dichalcogenides (TMDs) have attracted attention to realize strong coupling^{[44,262–266]}.

Dissipation and decoherence, intrinsic to metallic nanostructures, are described using open quantum system approaches, including Lindblad master equations: dρdt=−iℏ[H,ρ]+∑jLj[ρ],(2.7)with Lindblad terms Lj[ρ] capturing decay, dephasing, and coupling to the environment. Such treatments allow the quantification of quantum efficiency, photon indistinguishability, and the transition from coherent to incoherent energy flow^[267–274]. Techniques such as quantum-trajectory and stochastic Schrödinger approaches^[275–277] unravel Lindblad dynamics into stochastic pure-state trajectories, enabling simulations of dissipative plexciton, i.e., hybrid states of plasmons and excitons. Hot carriers have also attracted considerable attention due to their broad range of applications^[4]. Based on theoretical models of hot-carrier dynamics involving Landau damping, carrier injection into semiconductors has been extensively discussed^{[79,278–282]}. A recent study has highlighted cases in which the coherence between surface plasmon polaritons (SPPs) and electron–hole pairs plays an important role^[85].

Another approach treats the plasmon-generated electric field as the solution of Maxwell’s equations expressed through the electromagnetic Green’s function, and then uses this field to model interactions with nearby emitters^[283–285]. For simple geometries (e.g., spheres and cylinders), analytic Green’s functions are available, whereas for arbitrarily shaped metallic structures they can be obtained numerically. The quantum mechanical behaviors of emitters in the vicinity of nanometals, such as strong coupling^{[71,286–290]}, enhancement of the Purcell effect^[291–294], and antibunching^[295–297], can be described without relying on phenomenological coupling constants, and this approach provides direct access to quantum optical properties including spontaneous emission rates, and the local density of states. Extension to multiple quantum emitters reveals cooperative phenomena such as superradiance^[298–303] and resonance energy transfer^[303,304]. This integration has opened new avenues for investigating nanoscale molecular sciences such as SERS^[305,306] and TEPL^[307–309].

Many of the phenomena discussed above can be placed on a single map by treating the system as two coupled modes, for example, a radiative (bright) plasmonic resonance coupled to a weakly radiative (dark) resonance, or a plasmonic resonance coupled to a matter resonance. By varying only a few parameters—the coherent coupling g, the losses γ1,2, the detuning Δ, and the asymmetry of external drive—the response evolves continuously between interference-induced transparency, asymmetric Fano line shapes, and strong-coupling splitting. When a narrow resonance overlaps a broad radiative background and the drive predominantly excites the latter, destructive interference carves a transparency window that is commonly termed plasmon-induced transparency (PIT) (platform-specific implementations are treated in Sec. 5.2; see Sec. 3.2 for the ET counterpart in plasmon–matter hybrids); this is naturally understood within the general Fano picture of a narrow resonance embedded in a broad continuum^[27,310,311]. When the resonances are nearly aligned and the coherent coupling overcomes losses, the hybrid modes split and an avoided crossing appears, as widely reported for plasmonic strong coupling^[34,258]. Reports referred to as ET can be located on the same map as an interference regime in which the plasmonic pathway is suppressed and input power is funneled predominantly into the matter channel (see Sec. 3.2)^[29]. In this sense, interference-dominated responses and resolvable splitting are not disjoint mechanisms but two limits of a single hybridization landscape spanned by (Δ,γ1,2,g) and the drive asymmetry.

This perspective is useful because design trends become immediate without committing to a specific platform: to enhance interference-based windows, one lowers the radiative loss of the narrow resonance and increases drive asymmetry; to make splitting resolvable, one suppresses total loss while increasing g and tuning toward Δ≃0. At the same time, the map has clear limits. Strong spatial gradients that activate higher multipoles or symmetry-forbidden channels cannot, in general, be compressed into a single bright plus single dark mode without losing essential physics. Coupling to internal electron–hole continua in metals or semiconductors introduces energy- and momentum-resolved carrier dynamics and phonon pathways that exceed a two-mode reduction. Likewise, nonlocal response, lattice-mediated radiative coupling, and continuum baths can imprint memory and multi-mode interference beyond a Markovian 2×2 model. In those regimes, the coupled-oscillator view remains a compact entrance that organizes intuition, while quantitative predictions call for the field-theoretic and multipolar frameworks developed in the following sections.

This section has provided a conceptual overview of the theoretical frameworks that underpin our understanding of plasmonic coherence. Rather than presenting exhaustive details, we have focused on outlining the roles and capabilities of each framework, which are further revisited and elaborated upon where relevant in the subsequent sections. A brief coupled-oscillator map was appended at the end of this section to indicate how interference-dominated responses, Fano line shapes, and strong-coupling splitting connect; formal terminology and contrasts are deferred to Sec. 3.

Together, these diverse theoretical frameworks provide a set of tools applicable to various regimes for the analysis and design of plasmonic coherence across multiple length, time, and energy scales. Classical models offer insight and intuition for large structures and weak coupling conditions, while semiclassical and quantum mechanical approaches are indispensable for nanoscale systems, strong coupling, and the emergence of quantum phenomena.

Advances in quantum optics and open quantum system theory have enabled the description of coherent energy exchange, dissipative dynamics, and statistical properties of photons in complex nanostructures. Techniques based on electromagnetic Green’s functions have further provided a rigorous, parameter-free route to modeling emitter–plasmon interactions in both simple and structured environments.

As experimental techniques continue to probe smaller, faster, and more complex systems, the integration of these frameworks is expected to advance our understanding of coherent plasmonic behavior, with implications for applications such as HCG, energy flow control, and quantum information processing.

The study of coherent interactions between localized surface plasmons (LSPs) and external electron–hole excitations, such as excitons in molecules or quantum dots, represents a central pillar of contemporary nanophotonics and quantum optics. These interactions enable the control and manipulation of energy flow at the nanometer scale, with profound implications for both fundamental science and device applications.

Initially, the utility of metallic nanostructures was founded on their capacity to localize and enhance optical fields via the excitation of LSPRs. The foundational Drude model, Eq. (2.1), captures the essential frequency response of conduction electrons, providing both the resonance condition and the scaling laws for field concentration^[1]. This led to iconic effects such as SERS^[9–15], where the Raman cross-section of a molecule can be enhanced by more than 106 times.

However, as plasmonic research progressed into the nanoscale and hybrid era—where metallic structures are interfaced with quantum emitters—anomalous optical phenomena began to emerge. Experimental spectra revealed asymmetric line shapes, antiresonances, and transparency windows in hybrid plasmon–molecule systems—features that could not be explained by classical enhancement alone^{[23,24,28–34]}. These findings signaled a fundamental shift in understanding—from classical field enhancement to a more sophisticated framework incorporating quantum interference, coherent energy transfer, and strong light–matter coupling.

In this section, we provide a detailed, multi-layered review of the physical mechanisms, theoretical models, and experimental discoveries that underpin this transition. Special attention is paid to the deep physical insight behind Fano resonance, ET, strong coupling, and Rabi splitting in hybrid plasmon–electron-hole pair systems. While transparency effects between plasmonic resonators have been widely explored, platform-specific implementations are deferred to Sec. 5.2; here we concentrate on plasmon–matter hybrids and their interference physics, including ET.

Fano resonance, originally formulated to explain asymmetric spectral lines in atomic autoionization, arises from the quantum interference between a discrete state and a continuum^[22]. In the context of plasmon–e-h pair hybrid systems, the discrete state is provided by the exciton (e-h pair in a molecule or quantum dot), while the plasmon resonance acts as a broad continuum. When these two systems are brought into close proximity, the excitation of one channel modifies and interferes with the excitation of the other, resulting in an optical response that is far from a simple superposition: it reflects a nontrivial quantum superposition with hallmark asymmetric spectral profiles.

Mathematically, the Fano profile emerges by considering the total transition amplitude as the sum of a broad continuum channel and a discrete resonance: Atotal(ω)=Apl(ω)+Vω−ω0+iγn/2,(3.1)where Apl(ω) is the plasmon (continuum) amplitude, V is the coupling strength, ω0 is the discrete state energy, and γn is the FWHM linewidth of the narrow (discrete) pathway. (In our notation, γn=γ when the discrete state is a molecular exciton, whereas γn=Γdark for a subradiant plasmonic mode.) This expression captures the physical picture of interference between two excitation pathways. To explicitly describe the line shape arising from such interference, the normalized Fano profile is given by F(ϵ) in Eq. (2.3). As presented in Sec. 2.2, q in F(ϵ) is the asymmetry parameter that encapsulates the strength and phase of the interference^[27]. F(ϵ) can be derived from |Atotal(ω)|2 under specific assumptions, such as a Lorentzian background and frequency-independent coupling. In this context, q effectively corresponds to the ratio of the amplitudes and phases of the two interfering pathways. Figure 2(a) shows schematic energy diagrams of a broad plasmonic continuum and a narrow discrete state, while Fig. 2(b) displays simulated Fano profiles using Eq. (2.3) for various values of q.

Physically, this means that at certain frequencies, the two amplitudes are out of phase, producing destructive interference and a pronounced antiresonance (dip) in the spectrum. At other frequencies, constructive interference enhances the response. Although this mechanism is quantum in origin, much of the underlying physics can be captured by coupled oscillator models, which are widely used in plasmonics to provide intuition and analytical tractability^[28,29]. These models can capture the qualitative evolution from isolated molecular or plasmonic resonances to hybrid, interference-dominated features, and form the basis for interpreting a wide variety of observed phenomena. For a theoretical perspective that bridges weak, intermediate, and strong coupling regimes, as well as their spectroscopic signatures, see the recent review in Ref. [34].

A rigorous understanding of Fano-type interference in plasmon–electron-hole pair hybrid systems requires quantum mechanical treatments that can capture both coherence and dissipation. Two principal approaches are widely used: the quantum master equation and the electromagnetic Green’s function formalism. The master equation describes the evolution of the system’s reduced density matrix, enabling the calculation of not only steady-state spectra but also the time-resolved dynamics of population and coherence^[29,34,312]. This framework systematically incorporates coherent coupling, radiative and non-radiative decay, and pure dephasing, and has been pivotal for elucidating the transition from interference-dominated, asymmetric Fano profiles to the emergence of polaritonic modes in the strong-coupling regime as the coupling strength or detuning is tuned. Complementing this, the Green’s function formalism provides a general method to quantify how the nanophotonic environment modifies the spontaneous emission rate and quantum yield of an emitter through the local density of optical states (LDOS)^[313,314]. While this approach establishes the foundation for describing the photonic environment, the specific asymmetric line shapes of Fano resonances arise only when the quantum mechanical superposition of direct (excitonic) and indirect (plasmonic) excitation pathways is included.

Microscopically, the interference originates from coherent coupling between a discrete excitonic transition and a broad plasmonic continuum. The resulting spectral asymmetry, antiresonance depth, and linewidth depend sensitively on the emitter–plasmon detuning, coupling strength, and dissipative rates in both subsystems^[28–30,32]. Advanced theoretical studies combining these methods have clarified how system geometry, dielectric environment, and material properties govern the occurrence and tunability of sharp antiresonances, ET, or strong-coupling-induced Rabi splitting in such hybrid nanostructures.

Recent experimental progress has brought into sharp focus the phenomenon of Fano-type quantum interference arising from direct coupling between localized plasmons and external excitonic states, such as those in quantum dots, two-dimensional semiconductors, or organic molecules, embedded within or positioned close to metallic nanostructures. In these systems, the strong near-field of the plasmon resonance can coherently interact with the discrete electronic transitions of the emitter, giving rise to characteristic asymmetric line shapes and antiresonance dips in the optical spectrum. A particularly compelling and representative demonstration of this effect was reported by Lee et al.^[32], who systematically investigated Fano resonances in hybrid systems consisting of monolayer MoS2 integrated with plasmonic nanoantenna arrays. The left two panels in Fig. 4(a) illustrate the physical structure of the hybrid system (a plasmonic nanoantenna array on monolayer MoS2). The right three panels present the experimentally measured optical spectra as the resonance condition between the plasmon and exciton is systematically varied. As the plasmonic resonance approaches the excitonic transition, the reflection spectra evolve from symmetric profiles to pronounced asymmetric Fano line shapes with distinct antiresonance dips; as the detuning increases from a-3 via a-4 to a-5, the Fano line shape weakens, consistent with the reduced spectral overlap between plasmon and exciton. Their work established not only the direct experimental observability of plasmon–exciton Fano interference in real nanostructures, but also clarified the tunability and underlying mechanisms of these quantum interference features.

A complementary example is provided by hybrid systems in which J-aggregate dye molecules self-assemble around individual silver nanoprism antennas. Zengin et al.^[41] demonstrated that the plasmon–exciton coupling can be tuned by varying the nanoprism size (effective mode volume Veff) and the number of coupled molecules N; detuning Δ and spatial overlap are adjusted via geometry and environment. In Figs. 4(b-1)–4(b-6), representative spectra are arranged by effective coupling g∝N/Veff: Figs. 4(b-1)–4(b-3) trace a gradual evolution from weak coupling to an asymmetric Fano profile and toward the onset of mode splitting. This progression is governed by a reduction of Veff (smaller prisms, tighter fields) and an increase of N, together with detuning control; larger particles also increase the radiative rate of the bright plasmonic mode, broadening the background. Figure 4(b-5) shows a typical Fano line shape, while Fig. 4(b-4) highlights scattering suppression at the J-band and Fig. 4(b-6) provides the corresponding coupled-oscillator simulations (see the figure caption). These trends underscore the critical importance of geometric and molecular configuration in governing the degree of plasmon–exciton hybridization in such platforms. Here we emphasize the Fano characteristics; additional strong-coupling examples are summarized in Sec. 3.3.

Further highlighting the richness of this field, Wang et al.^[33] explored tunable Fano resonances in systems where a gold nanotriangle was coupled to a monolayer WS2 flake. By precisely controlling the separation distance between the nanotriangle and the two-dimensional semiconductor, they modulated the plasmon–exciton interaction strength, achieving a clear progression in the extinction spectra: from a single Fano dip in the weak-coupling limit to more complex asymmetric structures as the coupling was increased. Sample images [Figs. 4(c-1) and 4(c-2)], WS2 spectra [Fig. 4(c-3)], q-parameter dependence [Fig. 4(c-4)], and experimental and theoretical extinction spectra under various coupling conditions [Figs. 4(c-5)–4(c-7)] are presented in Fig. 4(c), clearly illustrating the crossover from interference-dominated to hybridized regimes. Such tunable and switchable Fano resonances have also been demonstrated in various other hybrid plasmonic and metamaterial (not electron–hole pairs) platforms, including bidirectional Fano switching in plasmonic metamaterials^[35] and non-dispersive Fano resonances in plasmonic-distributed Bragg reflector structures^[36]. This experimental control allows for the systematic mapping of the crossover between interference-dominated and hybridized regimes, capturing the nuanced interplay between quantum coherence and dissipation.

These experimental studies together establish several fundamental principles. The appearance of a Fano-type antiresonance serves as a direct signature of quantum interference between a discrete excitonic state and a plasmonic continuum, emerging only under conditions of optimal spectral and spatial overlap. The capacity to precisely tune the position, depth, and asymmetry of this spectral feature by manipulating detuning, gap width, or emitter placement provides a powerful degree of control for both fundamental investigation and practical application. Notably, the pronounced sensitivity of the Fano antiresonance to its local environment enables detection of single molecules or small changes in the dielectric function, offering a route to ultra-sensitive nanoscale sensors^[315]. Moreover, the concentration of electromagnetic energy within the nanogap not only amplifies nonlinear optical phenomena such as two-photon absorption^[316,317] but also lays the groundwork for integrated quantum photonic devices^[255].

In this subsection we focus on the mechanism of ET in plasmon–matter hybrids. ET shares a common interference origin with the optical transparency often termed PIT in the literature, in the sense that both can be framed within the same coupled-oscillator and Fano interference picture^[27]. However, it is important to recognize a practical distinction in the readout: PIT is identified as a window carved in the optical spectrum by destructive interference between a broad radiative mode and a narrow weakly radiative mode (classical implementations in plasmonic resonators were established early^{[310,318,319]} and platform-specific aspects are deferred to Sec. 5.2), whereas ET is identified by energy repartition into the matter channel under interference conditions.

More specifically, by ET we mean regimes in which destructive interference suppresses the plasmonic pathway (a near-zero in the plasmon amplitude or loss channel) while a discrete molecular or excitonic resonance coupled to the plasmon sustains a finite excitation. Microscopically, ET can be analyzed as interference between a plasmonic continuum and a discrete matter excitation; under appropriate spectral alignment and phase conditions, the incident energy is redirected from the metal into the molecular subsystem^[29,320]. Thus, while ET and PIT share the same interference backbone and are continuously connected to the asymmetric Fano line shape as detuning and coupling are varied^[26,27], their observables and intended readouts differ: optical transparency in the photonic channel versus energy redistribution into the matter channel. Keeping this distinction in mind avoids conflating plasmon–plasmon implementations (treated in Section 5.2) with the plasmon–matter physics emphasized here.

Building on Sec. 3.1 and the above distinctions, the canonical theoretical model for ET considers a two-level system (molecule or quantum dot) coherently coupled to a single-mode plasmonic antenna, both subject to optical driving. Under asymmetric drive, destructive interference produces a near-zero in the plasmonic channel while sustaining a finite excitation in the matter system. The Hamiltonian is given by $$\begin{gathered} H=ℏωanta†a+ℏω0σ+σ−+ℏg(a†σ−+aσ+) \\ −(dmol·E0σ++dant·E0a†+h.c.), \end{gathered}$$(3.2)where a (a†) is the annihilation (creation) operator for the plasmon mode, σ+ (σ−) is the raising (lowering) operator for the two-level emitter, and g is the coupling constant. The plasmon and the molecule each have their characteristic frequencies (ωant,ω0), and are subject to damping rates Γ and γ (for the antenna and molecule, respectively).

The dynamics of this system, including loss, are captured by the equations of motion: ddt⟨a⟩=−(iωant+Γ/2)⟨a⟩−ig⟨σ−⟩−iΩant,(3.3)ddt⟨σ−⟩=−(iω0+γ/2)⟨σ−⟩−ig⟨a⟩−iΩmol,(3.4)where the driving terms Ωant and Ωmol correspond to the external field coupling to the plasmon and molecular dipoles.

Critically, in realistic nanostructures, only the plasmonic antenna couples directly to the incident light (Ωmol≈0), while the molecule is excited only through near-field interaction with the antenna. One might thus expect that the molecule absorbs only a minor fraction of the incident power. However, under specific conditions, the system exhibits the opposite behavior: nearly all the energy is transferred to the molecule, and absorption in the metal is strongly suppressed. This effect is most pronounced when the following regime is realized: Γ≫g≫γ,that is, the antenna’s radiative decay is much faster than the coupling, which itself dominates over the molecular decay.

The underlying physical mechanism of ET is quantum interference between two excitation pathways: direct excitation of the plasmonic antenna and indirect excitation of the molecule via the antenna. When the coupling strength g is sufficiently large compared to the molecular decay rate γ, but smaller than the plasmonic decay rate Γ (Γ≫g≫γ), the interaction produces two hybridized modes whose spectral overlap is significant. Near the transparency (resonance) frequency, the relative phase between these modes shifts by 180 deg, so that the plasmonic components destructively interfere and cancel, while the molecular components constructively interfere and are enhanced. This results in a pronounced dip in the antenna’s absorption spectrum (Pant) and a maximum in molecular absorption (Pmol), enabling efficient energy transfer to the molecule even without direct illumination.

Ishihara et al.^[29] employed both analytic solutions and DDA simulations to visualize the spatial distribution of electromagnetic energy at the transparency frequency. These calculations reveal that the excitation is highly localized on the molecule, while the surrounding metal remains nearly unexcited. The real-space maps provide intuitive evidence for the “energy funneling” effect predicted by the quantum theory. Reference [320] similarly presents analytic and computational results demonstrating the pronounced suppression of antenna dissipation and the concentration of absorbed power in the molecular subsystem. Figure 5 shows the schematic of the DDA model, calculated absorption spectra, and real-space absorption maps, where the energy is concentrated in the molecule in the ET conditions.

This quantum coherent effect is fundamentally different from classical field enhancement, where both molecular and metal absorption increase simply due to stronger local fields. Here, hybridization of the plasmon and molecular exciton creates bright (symmetric) and dark (anti-symmetric) collective eigenmodes. At the transparency point, the system’s excitation predominantly occupies the dark mode, characterized by a nearly zero net dipole moment and minimal radiation loss. As a result, energy dissipation in the antenna is strongly suppressed, while the molecule efficiently absorbs the incident energy. A remarkable aspect of ET is that its occurrence and magnitude depend sensitively on system parameters—particularly the coupling strength g, the radiative loss rate Γ, the molecular decay rate γ, and the resonance detuning Δ=ωant−ω0. Reference [320] provided a comprehensive analysis showing that maximal energy transfer to the molecule is achieved for an optimal ratio of g/Γ. Counterintuitively, making the coupling arbitrarily strong does not guarantee complete transparency; if g becomes comparable to or exceeds Γ, the condition for destructive interference is no longer satisfied, and the metal begins to absorb again. Thus, there exists a “sweet spot” in parameter space where the quantum pathways perfectly cancel antenna excitation while maximizing molecular absorption. Figure 6 shows the calculated results of the master equation, showing the mechanism of ET and its optimum condition.

Having established the mechanism and the optimality map in Fig. 6, we next summarize how to reach the transparency sweet spot in practice. Within the coupled-oscillator picture, the depth and coherence of the transparency window are governed by an effective cooperativity C=4g2/(Γγ) together with the detuning Δ=ωant−ω0. Destructive interference requires comparable amplitudes and a π phase shift between the broad plasmonic pathway and the narrow excitonic pathway; in practice, the window is deepest yet single-peaked when C∼1 and |Δ| is small, whereas C≪1 yields only a shallow dispersive distortion and C≫1 with Δ≈0 tends to evolve toward normal-mode splitting rather than a Fano notch. Experimentally, the knobs map onto these ratios are as follows. First, g∝(μcosθ)N/Veff, where θ is the angle between the emitter transition dipole μ and the local polarization of the antenna mode. Increasing the number of coupled molecules N, improving dipole-field alignment (larger cosθ), and reducing the mode volume Veff all increase g. In practice, Veff can be reduced using smaller gaps D, tighter hotspots, and higher-index spacers that confine the field. Second, the antenna loss Γ=Γrad+Γnr is set mainly by geometry and materials: larger particles and brighter multipoles raise Γrad, while intrinsic loss and roughness raise Γnr; arrays or quasi-dark designs (e.g., SLRs or quasi-BICs) can suppress Γrad to narrow the continuum, though making the mode too dark reduces out-coupling and signal. Third, the excitonic width γ is minimized using narrow-band emitters (e.g., J-aggregates with small inhomogeneous broadening), improving chemical stability and host rigidity, and, when compatible, lowering temperature; aggregation and photobleaching increase γ. Finally, Δ is tuned by particle size and aspect ratio, by the dielectric environment (overcoats, solvents, polymer matrices), or by selecting molecular species; a small, deliberate Δ also lets the Fano asymmetry parameter q tailor the line shape without crossing into the splitting regime. In practice, one increases g via Veff reduction and optimized N and orientation, reduces Γ just enough to sharpen the continuum, chooses emitters and hosts that keep γ small, and then uses geometry or refractive index to place a small Δ at the desired wavelength; this situates the device near the C∼1 sweet spot that maximizes transparency and coherence while avoiding full normal-mode splitting.

The theoretical framework further predicts a variety of nonlinear and time-dependent effects as the system is driven more strongly or extended to multi-emitter regimes^[320]. At high excitation intensities, the hybrid system can exhibit population inversion, collapse of transparency, and even coherent Rabi oscillations—features reminiscent of few-level atomic physics but now realized in engineered nanostructures. These effects point to the possibility of all-optical switching and ultrafast quantum state control using plasmon–exciton platforms. Furthermore, Uryu et al.^[69] theoretically demonstrated a similar ET spectrum in a coupled system of gap plasmons and excitons with a finite axial wavevector (denoted here as k∥, equivalent to the 1D Bloch momentum K in Ref. [69]) along the nanotube axis. The condition k∥≠0 (off the Γ point) enables phase matching between the gap plasmon and an exciton branch propagating along the tube, which is essential for realizing the transparency feature in this 1D geometry.

ET in plasmon–exciton systems thus represents a paradigmatic example of how quantum interference and strong light–matter coupling can be engineered in nanoscale devices. It enables efficient and selective energy transfer to molecular subsystems, offers extreme environmental sensitivity, and provides new tools for manipulating light at the single- or few-photon level.

The realization of strong coupling between plasmons and excitons in hybrid nanostructures represents one of the most profound achievements in contemporary nanophotonics and quantum optics. In contrast to the weak-coupling or Fano interference regime, where the hybrid system is characterized by an asymmetric line shape or ET reflecting quantum interference between discrete and continuum states, the strong-coupling regime is reached when the coherent energy exchange between a plasmon and an exciton becomes faster than the combined decay rates of the constituent modes. This condition is typically expressed as g>(γpl+γex)/2, where g denotes the coupling strength and γpl, γex are the linewidths of the plasmon and exciton, respectively^[40,43].

The physical mechanism underlying strong coupling is captured by a quantum mechanical model in which the plasmonic and excitonic degrees of freedom hybridize to form new eigenstates known as upper and lower polaritons, or “plexcitons”^[30]. The coupled system is described by the Hamiltonian: H=ℏωpla†a+ℏωexb†b+ℏg(a†b+ab†),(3.5)where a (a†) and b (b†) are the bosonic annihilation (creation) operators for the plasmon and exciton, respectively. Diagonalizing this Hamiltonian yields the characteristic energy splitting: E±=ℏωpl+ℏωex2±12(ℏωpl−ℏωex)2+4ℏ2g2.(3.6)

The two branches correspond to the new polaritonic states, with an energy gap—the Rabi splitting—that provides a direct experimental signature of the onset of strong coupling.

In the weak-coupling regime, the system’s spectrum exhibits a single resonance peak whose width and shape are determined by the interplay of coherent and incoherent processes. As the coupling strength g increases, the single resonance gradually broadens and distorts, until at the strong-coupling threshold, it splits into two well-resolved peaks. This transition is often visualized by plotting the resonance energies as a function of detuning between the plasmon and exciton; an avoided crossing or “anticrossing” appears as the hallmark of strong coupling. This feature, sometimes referred to as the “vacuum Rabi splitting”, is a direct manifestation of reversible energy exchange between the plasmon and exciton^{[40–43,321]}.

A hallmark of strong coupling is the appearance of modified emission dynamics and lifetimes. In the strong-coupling regime, emission no longer arises from a simple exponential decay but instead exhibits nontrivial dynamics, including oscillations, non-exponential tails, and, in some cases, photon antibunching behavior. Such effects are indicative of the hybrid nature of the polaritonic states and their delocalization across the plasmonic and excitonic components.

The experimental realization of strong plasmon–exciton coupling was initially achieved in ensemble systems, where large numbers of organic dye molecules, J-aggregates, or quantum dots interact collectively with surface plasmonic modes or metallic nanostructure arrays^[37,38]. See Fig. 7(A) for the observation reported in Ref. [37]. Generally, the magnitude of the Rabi splitting in such systems increases with the square root of the number of emitters, as expected from the Dicke model of collective coupling. Ensemble-based strong coupling was rapidly adopted for applications in polaritonic chemistry, lasing, and energy transfer. However, these collective effects obscure the quantum nature of individual excitations and limit the ability to study coherent quantum phenomena at the single-particle level.

Time-resolved spectroscopy has fundamentally transformed the investigation of hybrid plasmon–exciton systems. Ultrafast pump–probe spectroscopy provides direct access to the quantum dynamics of plexcitons, allowing researchers to map the buildup and decay of hybrid states, resolve Rabi oscillations and quantum beats, and extract coherence times and dephasing rates. For example, Vasa et al.^[39,48] observed the ultrafast manipulation of strong coupling and quantum beats in metal–molecular aggregate hybrid nanostructures, revealing the interplay between coherent coupling, dissipation, and environmental effects. These techniques have enabled the direct observation of population transfer, ultrafast energy flow between modes, and transient transparency phenomena or their collapse under intense excitation.

The field subsequently moved toward the realization of strong coupling at the ultimate quantum limit—the single-emitter regime. Notably, Chikkaraddy et al.^[42] demonstrated room-temperature strong coupling between a single dye molecule and a gold nanogap cavity with an effective mode volume less than 103nm3. In this system, the extremely small gap and precise positioning of the molecule led to a Rabi splitting of approximately 90 meV, clearly resolving the upper and lower polariton peaks in the extinction and emission spectra. This experiment marked a milestone in quantum plasmonics, confirming that strong coupling can be achieved and studied at the single-molecule level under ambient conditions {see Fig. 7(B), adapted from Ref. [42]}. The realization of strong coupling with single quantum dots was also achieved using similar nanogap architectures. Liu et al.^[323] and Hu et al.^[46] have recently reported deterministic and robust strong coupling in gold nanogap cavities with individual quantum dots, enabling reproducible hybridization and the possibility of scaling such systems for photonic quantum information processing {see Fig. 7(C), adapted from Ref. [46]}.

Another significant advance in this direction was achieved by Park et al.^[322], who developed tip-enhanced strong coupling spectroscopy to probe single quantum emitters with high spatial and spectral resolution. Using a plasmonic scanning probe to form a tunable nanogap with a single molecule or quantum dot, they could directly observe Rabi splitting in the optical spectrum and precisely manipulate the coupling strength by controlling the probe position in real time {see Fig. 7(D), adapted from Ref. [322]}. This approach enabled the study and control of hybrid plexciton states at the ultimate quantum limit, opening up new possibilities for nanoscale coherent light–matter interaction.

An exciting direction in strong coupling research has been the integration of two-dimensional materials with plasmonic structures. For example, Wang et al.^[33] demonstrated strong coupling between the exciton resonance in a monolayer WS2 and the LSP mode of a gold nanotriangle. By carefully controlling the spatial separation and orientation, they could tune the system continuously from weak (Fano-type) to strong (Rabi-split) coupling. The transition was mapped out by monitoring the evolution of the extinction spectra, with clear anticrossing behavior as the plasmon and exciton resonances were brought into resonance. Two-dimensional materials such as TMDs are particularly promising for such studies due to their high oscillator strengths, atomically thin profiles, and strong excitonic effects, which persist even at room temperature.

Beyond the fundamental interest, hybridized polaritonic states have opened a wide range of technological possibilities, including polariton lasing, low-threshold light sources, room-temperature Bose–Einstein condensation of polaritons, quantum information storage, and control of chemical reactivity—not only in plasmonic systems but also in photonic and dielectric cavity platforms^{[43,254,324,325]}. Plasmon–exciton hybrid states are expected to enable similar functionalities, owing to their extremely small mode volumes and strong field confinement. In particular, the possibility of modifying ground-state chemical landscapes and reactivity through the formation of hybrid light–matter states (polaritonic chemistry) has attracted growing attention, suggesting new approaches to catalysis and molecular control at the quantum level. Strong coupling can also fundamentally alter energy transport and relaxation pathways in nanostructures, providing new routes for efficient energy harvesting, exciton routing, and the generation of long-lived quantum coherence. The demonstration of room-temperature strong coupling with single emitters and in atomically thin materials points to the feasibility of integrating such systems into scalable, chip-based quantum photonic platforms.

In summary, the progression from weak to strong coupling in plasmon–exciton hybrid systems represents a true quantum phase transition in the optical properties of nanoscale materials. The ability to control and exploit this transition at the level of single molecules, quantum dots, and two-dimensional materials, as well as to probe the ultrafast quantum dynamics of the resulting polaritons, has fundamentally broadened our understanding of light–matter interaction. It has also set the stage for the next generation of quantum photonic and optoelectronic devices, where tailored quantum coherence and hybridization are harnessed for novel functionalities.

In the experimental investigation of hybrid plasmon–exciton systems, the crossover between Fano interference and strong coupling (Rabi splitting) remains a central and subtle topic. Several theoretical and experimental studies have pointed out that there are situations in which spectral features alone—most notably, the appearance of avoided crossing or “anticrossing” in extinction or scattering spectra—may not be sufficient to unambiguously distinguish genuine strong coupling from effects such as Fano-type interference or collective coupling involving multiple emitters. While Pelton et al.^[34] emphasized that two-peak structures in scattering spectra can arise from interference effects even below the strong-coupling threshold, explicit caution that observed spectral splitting does not necessarily prove the formation of true polaritonic hybrid states is relatively limited in the current literature. Thus, careful analysis beyond spectral line shapes is often necessary to confirm strong coupling in these systems.

Following Refs. [41,71], a practical way to discriminate genuine strong coupling from Fano-type interference in plasmon–exciton hybrids is to fit the spectra with a coupled-oscillator model to extract the coupling rate g, the plasmon linewidth Γ, and the exciton linewidth γ, and to verify an avoided crossing under detuning control Δ=ωant−ω0. A commonly used threshold is 2g>(Γ+γ)/2, while a stricter single-particle diagnostic 2g>Γ has also been adopted for datasets of the type shown in Fig. 3(b) in Ref. [41]. In contrast, Fano/ET can yield apparent doublets in extinction without genuine eigenmode repulsion; to disambiguate this, Ref. [71] emphasizes probing the emitter channel (excitation/PL), where a split PL from the emitter itself appears only under genuine strong coupling. This is consistent with the theoretical criterion that strong coupling entails splitting in both plasmonic and molecular transitions, whereas multi-emitter Fano produces splitting only in the antenna channel (Ref. [47]).

One major source of this difficulty is that when multiple molecular or quantum dot excitons with slightly different resonance energies (due to inhomogeneous broadening or positional disorder) are coupled to a single plasmonic mode, the ensemble of discrete states can collectively interact with the plasmonic continuum. As shown the in report of Murata et al.^[47], the resulting optical spectrum may exhibit a splitting reminiscent of the vacuum Rabi splitting typically associated with strong coupling. However, in this “multi-emitter Fano” regime, the observed spectral features arise from the superposition of many overlapping Fano resonances rather than from the formation of true polaritonic states (see Fig. 8). This ambiguity was further addressed in experimental and theoretical investigations by Antosiewicz et al.^[326], who used classical and quantum models to show that an apparent splitting can be observed even when the coupling strength is below the threshold for strong coupling, provided the emitter ensemble is sufficiently broad.

Reference [47] provided a clear and experimentally testable theoretical criterion for discriminating between these two regimes by examining not only the plasmonic (antenna) extinction spectra but also the spectral response associated with the molecular (emitter) subsystem. Their analysis showed that, in the case of genuine strong coupling (Rabi splitting), both the plasmon and the molecular exciton acquire new eigenstates, resulting in a splitting of both the plasmonic and the excitonic transitions. In contrast, when the observed splitting is the result of overlapping Fano resonances in a multi-emitter system, only the plasmonic transition shows an apparent splitting, while the molecular excitonic states do not. This theoretical insight leads to an important experimental protocol: by selectively probing the emission or excitation spectrum from the molecular component, one can decisively determine whether true strong coupling is present. In their recent study^[71], Tomoshige et al. systematically calculated both extinction and photoluminescence spectra for model hybrid systems, illustrating that while the extinction (scattering) spectrum can display an anticrossing even in the absence of strong coupling, only the photoluminescence associated with the emitter exhibits a genuine polariton splitting when the strong coupling threshold is exceeded. The key message is that monitoring both the plasmonic and molecular spectral channels is essential for correctly identifying the regime of light–matter interaction.

This distinction is not merely of academic interest: the ability to unambiguously identify strong coupling has profound consequences for the interpretation of nonlinear effects, energy transfer, quantum coherence, and potential applications in quantum information and polaritonic chemistry.

In summary, while the spectral anticrossing observed in extinction or scattering measurements is a striking signature, it must be interpreted with caution. A compact diagnostic combines coupled-oscillator fitting with detuning-dependent mapping to test for genuine eigenmode repulsion (Ref. [41]) and emitter-channel probes (excitation/PL) that reveal polariton splitting only under true strong coupling (Refs. [47,71]). As rigorously demonstrated in Refs. [47,71], this two-pronged, experimentally grounded protocol provides a robust method for discriminating true strong coupling from the collective illusion generated by many weakly coupled Fano resonances, thereby clarifying a long-standing ambiguity in the field and helping to set a practical standard for the reliable identification of strong coupling in hybrid nanostructures.

Chirality, defined as the absence of mirror symmetry, plays a crucial role in chemistry, biology, and materials science. In plasmonics, chiral nanostructures have attracted significant attention due to their ability to generate strong optical activity and manipulate light–matter interactions far beyond what is possible in achiral systems^{[88,330–332]}. The strong near fields of metallic nanostructures can greatly enhance circular dichroism (CD) signals, leading to ultrasensitive chiral sensing and selective optical manipulation. This enhancement relies on breaking mirror symmetry, as realized in twisted metal rods, nanohelices, or DNA-origami-guided assemblies of gold nanoparticles^{[327,333–335]} [see Fig. 9(A), for example]. The optical chirality density formalism^[331] provides a quantitative measure of the local handedness of the electromagnetic field and is essential for describing chiral-selective light–matter interactions.

The physical basis of chiral light–matter interaction in plasmonic systems is often described by a Hamiltonian including both electric and magnetic dipole contributions: Hchiral=−d·E+λ(m·B),(3.7)where d and m are the electric and magnetic dipole moments, E and B are the local electric and magnetic fields, and λ quantifies the strength of the magnetic contribution^[330]. The optical chirality density Cχ is a useful measure of the local handedness of the electromagnetic field^[331]: Cχ=ε02E·(∇×E)+12μ0B·(∇×B).(3.8)

A major recent advance is the demonstration of enantioselective strong coupling between chiral plasmonic nanostructures and external molecular excitons or electron–hole pairs. In these hybrid systems, the interaction between the electric and magnetic dipole transitions of chiral molecules and the local chiral near field produces new hybridized states—often referred to as chiral plexcitons. Recent studies have begun to rigorously define and experimentally realize this concept, elucidating their physical mechanisms, tunable spectral features, and chiroptical responses in strong coupling regimes^[336,337]. These chiral plexcitons exhibit mode splitting and CD characteristics that are highly sensitive to the handedness of both the nanostructure and the molecule, and can be actively tuned by structural or environmental parameters. This emerging understanding provides a theoretical and experimental foundation for the ultrafine control of chiral light–matter interactions in complex hybrid systems.

Lan et al.^[338] were among the first to realize DNA-assembled chiral gold nanoparticle–chromophore hybrids, reporting highly resonant plasmon–exciton coupling that resulted in CD signals several orders of magnitude larger than those of the constituent molecules alone.

Wu et al.^[328] subsequently used J-aggregate dye molecules with strong chiral optical activity, coupled to structurally chiral gold nanoparticle assemblies. The authors observed clear mode splitting in both extinction and CD spectra, corresponding to the formation of chiral plexcitonic states [see Fig. 9(B)]. The Rabi splitting magnitude and the selectivity of the CD response depended strongly on the geometric chirality of the plasmonic structure and the handedness of the molecular excitons, providing direct evidence of enantioselective coupling at the nanoscale.

Guo et al.^[339] further investigated strong coupling between chiral emitters and plasmonic surface modes, finding that the optical chirality of the resulting hybrid states could be precisely manipulated via the handedness of the plasmonic field. Their experiments confirm that chiral-selective energy splitting and light absorption can be engineered at the nanoscale by carefully matching the handedness of both the plasmonic and molecular components.

Zhu et al.^[340] assembled hybrid systems using DNA origami to position chiral gold nanoparticles and dye molecules with nanometer accuracy. They observed unusually strong CD signals and clear evidence of strong exciton–plasmon coupling, confirming that DNA-origami-enabled precision in positioning enables efficient enantioselective hybridization of molecular and plasmonic states.

Most recently, Cheng et al.^[329] demonstrated the ability to tune the plexcitonic optical chirality by engineering the spatial arrangement and handedness of chiral gold nanostructures and J-aggregate molecules. They achieved controlled anti-crossing behavior in the CD spectra, with the energy gap and the strength of chiral selectivity adjustable via the structure’s handedness and coupling strength [see Fig. 9(C)]. This tunability enables precise control over the chiral light–matter interaction and provides a platform for chiral photonic devices.

These studies collectively demonstrate that the enantioselective coupling of external electron–hole pairs to chiral plasmonic nanostructures produces hybrid states with tunable chiroptical properties: the magnitude and selectivity of CD response, the size of the Rabi splitting, and the efficiency of energy transfer can all be adjusted by the relative handedness and coupling strength. Building on established theoretical frameworks and design strategies^{[88,327,330–334]}, combining chiral plasmonic fields with the intrinsic optical activity of chiral molecules now enables highly selective and controllable light–matter interactions.

Because the experimentally measured CD is a macroscopic observable that averages over the illuminated area, incidence, and ensemble orientations, sensitivity should be addressed at both microscopic and macroscopic levels. We adopt two complementary figures of merit: the dissymmetry factor g=2(IL−IR)/(IL+IR) in the optical channel and the differential slope dΔA/dc with respect to analyte concentration. In practice, these scale with (i) areal filling and the number of coherently contributing unit cells, (ii) lattice-mediated radiative narrowing (including quasi-BIC modes) that increases field dwell time, (iii) orientational order of chiral inclusions or alignment layers to reduce ensemble averaging, and (iv) polarization modulation with lock–in detection to suppress baseline drift. From a design standpoint, co-optimize microscopic and macroscopic factors: spectrally align the molecular transition with the antenna or hybrid mode that maximizes the chiral near-field (Sec. 3.2), then promote long-range phase coherence via periodic lattices or quasi-BIC modes to sharpen the resonance (Sec. 5.2); at the device scale, increase the effective collecting area and areal fill factor under the illumination numerical aperture, and match the detection bandwidth to the narrowed linewidth and collection optics. These choices preserve the local mechanism while ensuring that the ensemble-averaged CD remains large at the device scale.

Taken together, these advances and the practical guidelines above pave the way for applications in molecular photonics, stereoselective catalysis, and quantum information technologies.

Building upon the foundations of strong coupling and polariton formation discussed in the previous sections, recent efforts have expanded the scope of plasmon–exciton research toward new materials, ultrafast dynamics, and device-oriented functionalities. Notably, atomically thin semiconductors, perovskite nanocrystals, and single quantum emitters have emerged as versatile platforms for coherent hybridization with plasmonic modes.

One of the earliest experimental demonstrations of strong exciton–plasmon coupling in hybrid systems was reported by Liu et al.^[341], who investigated monolayer MoS2 integrated with silver nanodisk arrays. Through angle-resolved reflectance spectroscopy at both 77 K and room temperature, they observed clear anticrossing behavior with a Rabi splitting of up to 58 meV, providing direct evidence for the formation of plasmon–exciton polaritons. This study also showed that the coupling strength and polariton dispersion could be systematically tuned by modifying the nanodisk lattice geometry. Shortly thereafter, the evolving landscape of plasmon–exciton interactions was comprehensively reviewed by Luo and Zhao^[342], who emphasized the critical roles played by local field enhancement, dielectric environment, and nanostructure engineering in shaping the coherence properties and coupling strength of hybrid systems. Their review also highlighted the increasing importance of rational material and device design to enable not only strong coupling but also collective effects, nonlinear optical phenomena, and efficient single-photon emission—thus outlining future directions for the field. More recently, Tang et al.^[343] advanced the field by employing femtosecond pump–probe spectroscopy to probe ultrafast dynamics in CsPbBr3 perovskite nanocrystals coupled with silver nanostructures. Their measurements revealed sub-picosecond (approximately 540 fs) energy transfer resulting from resonant exciton–plasmon coupling, accompanied by a 5.7-fold enhancement in photoluminescence and a marked acceleration in carrier relaxation. This time-resolved study provided unambiguous evidence of coherent energy exchange and dynamical processes at femtosecond timescales, thereby extending the understanding of hybrid plasmon–exciton systems beyond steady-state observations. Together, these works mark a clear progression in the field—from the foundational demonstrations of strong coupling and polariton formation, through theoretical and experimental systematization of coupling mechanisms, to the direct observation of ultrafast coherence dynamics—laying the groundwork for the development of next-generation quantum nanophotonic devices.

In parallel with these foundational studies, the field has recently witnessed the emergence of new directions focusing on collective coherent effects under engineered symmetry and topology. Shiraki, et. al.^[302] have introduced the concept of chirality-selective superfluorescence in plasmon–emitter hybrid systems, representing a frontier that connects quantum coherence, collective emission, and chiral environments. Their theoretical model demonstrates that the development of quantum correlations—and hence the intensity and dynamics of collective superfluorescence—can be selectively controlled by matching or mismatching the handedness of spiral-configured quantum emitters and spirally stacked chiral metallic nanostructures. The study reveals that superfluorescence is maximized in the “parallel” (matched chirality) configuration, even when the plasmonic field enhancement is equivalent between cases. This mechanism, fundamentally distinct from field enhancement or the Purcell effect alone, opens the door to chirality-controlled cooperative phenomena and offers new perspectives for chiral sensing and quantum photonics.

Despite these advances, a number of key challenges remain unresolved. Achieving long coherence times at room temperature, suppressing inhomogeneous broadening and disorder, and developing scalable, reproducible fabrication routes for complex hybrid nanostructures are all ongoing issues. The interplay between disorder, decoherence, and strong coupling is particularly subtle and represents an important area for further theoretical and experimental study. Moreover, the field is now pushing toward multi-mode and multi-emitter hybridization, collective effects such as superfluorescence and superradiance, and the exploration of ultrastrong coupling regimes, where the interaction energy becomes comparable to the transition energies of the constituent systems. Active control of hybrid states—via electrical gating, mechanical modulation, or all-optical feedback—is an increasingly prominent goal, and the emergence of chirality as a new tuning parameter may prove decisive in guiding both device functionality and fundamental understanding.

Looking forward, the synergistic integration of emerging material systems, state-of-the-art spectroscopic techniques, and advanced theoretical frameworks is rapidly expanding the frontier of coherent plasmon–exciton physics. These developments not only deepen our understanding of light–matter interaction at the nanoscale but also pave the way for transformative applications in quantum information, ultrafast optoelectronics, biosensing, nonlinear spectroscopy, and energy conversion. The resolution of present challenges—and the full exploitation of chirality-controlled cooperative emission—will be decisive in realizing the full potential of hybrid plasmonic–quantum photonic devices in next-generation quantum and classical technologies.

In this section, we have explored the coherent interaction between LSPs and external electron–hole excitations, such as excitons in molecules and quantum dots. Beginning with the historical development from classical field enhancement to quantum interference, we have shown how the hybridization of plasmonic continua with discrete excitonic states gives rise to rich spectral phenomena including Fano resonances, PIT, and strong coupling.

We have reviewed the key theoretical frameworks underpinning these effects—from simple interference models to coupled oscillator formalisms and quantum master equations—and illustrated how such models capture the emergence of hybrid states and Rabi splitting in the optical spectra. Particular emphasis was placed on the role of interference between radiative and non-radiative channels, the asymmetry parameter q in Fano line shapes, and the coupling-dependent spectral response.

Experimentally, these phenomena have been observed in a variety of systems, including metallic nanoparticles coupled to dye molecules, J-aggregates, and quantum dots. The ability to coherently couple plasmons and excitons has enabled the modulation of light–matter interaction strength at the nanoscale, paving the way toward low-threshold nanolasers, enhanced nonlinear processes, and quantum photonic devices.

Looking ahead, future challenges include achieving coherent coupling at the single-exciton level with high fidelity, reducing dephasing due to environmental noise, and engineering systems with tunable or switchable coupling regimes. Integration with atomically thin materials, deterministic nanofabrication, and real-time control of hybridization strength will likely play key roles in advancing both fundamental understanding and technological applications of plasmon–electron-hole coherence.

The ability to visualize and manipulate quantum states at the nanometer scale has been revolutionized by advances in nanophotonics and plasmonics. Conventional far-field optical measurements are constrained by selection rules set by the point-group symmetry of molecular or solid–state wavefunctions, so that electric-dipole transitions dominate while higher-order multipoles are strongly suppressed; this reflects both the spatially uniform far-field profile and the underlying electronic/vibrational symmetry. There are two main routes to bypass these constraints: (i) multiphoton excitation (e.g., two-photon absorption), which follows different selection rules and can access nominally forbidden manifolds; and (ii) a localized near-field route, where the intense, highly inhomogeneous, and coherent fields of LSPs act over molecular length scales. The latter mechanism is fundamentally spatial: steep field gradients and large in-plane wavevector components locally break symmetry and reweight higher multipoles within the extent of the relevant states, so that “forbidden” transitions become visible even with linear readouts. In reciprocal space, the strongly confined gap field also carries large in-plane components (k∥), enabling optical activation of finite-momentum and multipolar excitations.

Since the dawn of SERS, the appearance of “forbidden” transitions has been discussed^[12] for vibrational (Raman) transitions. Strong field gradients near rough metal surfaces break molecular symmetry, allowing infrared-active modes or multipolar Raman components (electric quadrupole, magnetic dipole) to appear in the spectrum. The possibility that the spatial derivative of the electric field excites higher derivatives of the Raman polarizability was already recognized. This theoretical insight was later examined systematically by tip-enhanced spectroscopies. In the late 1990s, optimization of surface-plasmon resonance wavelengths and improvements in laser technology pushed SERS into the single-molecule regime. Nie and Emory^[344], and Kneipp et al.^[13] achieved enhancement factors of about 1014, making it possible to detect forbidden modes at extremely low concentrations. At that stage, however, the spatial resolution of the electric-field distribution was still limited by optical diffraction, so the exact location of selection-rule breaking was unknown, and the relative roles of field-gradient and chemical enhancement remained unresolved.

More recently, selection-rule breaking has also been extended to electronic transitions. Theoretical work by Iida et al. first pointed out the possibility of optically activating finite-momentum excitations in molecules near metallic nanostructures^[345], and the concept was further developed for coupled plasmon–molecule systems^[68], semiconductor nanorods by Jain et al.^[346], and carbon nanotubes by Uryu et al.^[69]. As a representative case, it has been theoretically proposed that in single-walled carbon nanotubes (SWNTs)^[69], high-k∥ components of gap plasmons can coherently drive excitons with finite momentum along the tube axis. In parallel, Takase et al. observed clear signatures of otherwise forbidden (Δn=±2) electronic transitions in a plasmon-enhanced Raman study of an isolated SWNT^[70]. These k-space insights paved the way for real-space visualization with TERS.

During the past two decades, near-field imaging techniques have not only surpassed the diffraction limit but have also opened routes to activate and control transitions that are forbidden or dark in standard optics. Among them, TERS, PiFM, and TEPL have emerged as powerful probes capable of interrogating molecular and material structures down to the single-molecule or sub-nanometer scale. All three techniques exploit the spatial gradient, coherence, and symmetry properties of plasmonic near fields. They now enable direct imaging of quantum states, mapping of orbital symmetry, and observation of hidden or multipolar excitations, fundamentally reshaping our understanding of light–matter interaction at the smallest length scales.

To unravel these questions at the true nanometer scale, the concept of combining scanning probes with plasmonic enhancement was introduced as TERS^[52–54]. A metal-coated atomic force microscope (AFM) tip is placed inside the laser focus, and the nanoplasmon resonance at the tip apex locally amplifies the Raman cross-section. The original demonstration broke the diffraction limit (∼200nm) and achieved chemical imaging with a spatial resolution of about 50 nm. TERS reached its full potential with the single-molecule chemical mapping of Zhang et al.^[57]. By matching the nanogap plasmon resonance of a Ag scanning tunneling microscope (STM) tip and a Ag(111) substrate to both the excitation and Raman-scattered photon energies (dual resonance), they visualized the internal structure of a single H2 TBPP molecule with ∼0.5nm resolution, identifying chemical species, orientation, and vibrational modes.

An additional order-of-magnitude improvement in resolution was provided by “picocavities,” reported by Benz et al., in which the light-activated single-gold-atom protrusions on the gold nanoparticle surface localize the optical near field to about 0.3 nm by enhancing the optomechanical coupling of single molecules by a factor of ∼106^[347]. Under such extreme confinement, strong optomechanical coupling (g/κ∼0.1) enables anti-Stokes pumping and vibrational Stark shifts. Lee et al. maintained a tip–molecule distance of 0.2 nm at 6 K in an STM environment, formed coherent tunneling plasmons, and mapped C−H stretching modes with angstrom-level resolution^[348]. The resulting atomic-scale Raman images directly show which bonds and along which directions forbidden transitions are activated. Recently, cryogenic STM–TERS has visualized intramolecular vibrational nodes with angstrom resolution and tracked charge–transfer excitons by tuning the gap–plasmon resonance^[349].

PiFM, developed in 2010 by Rajapaksa et al.^[63], detects the optical gradient force acting on an AFM tip caused by the plasmonic field localized between the probe, sample, and substrate. PiFM operates from the UV to the far infrared and can be extended to pump–probe nonlinear measurements, enabling chemical-selective mapping and ultrafast dynamics^[350]. Its first demonstration achieved ∼10nm spatial resolution. By measuring the vertical optical gradient force with lock-in techniques rather than scattered light, PiFM now combines sub-nanometer [and under ultra high voltage (UHV), angstrom] resolution with high surface sensitivity^[351]. Theoretical work has shown that picocavity formation is again critical for such high resolution^[352]. Forbidden electric-quadrupole and magnetic-dipole transitions, as well as dark modes that are invisible in the far field, have been imaged at the nanometer scale; at the single-molecule level, vibrational nodes and multipolar excitations have been observed directly^[66,352].

In monolayer TMDs, strong spin–orbit coupling and valley selection rules create “dark excitons” whose radiative decay is strongly suppressed. Park et al. placed a nano-optical antenna tip (AFM–TEPL) near WSe2 and, with a Purcell factor of ∼2×103, enhanced the dark-exciton emission by 106 and observed it at room temperature^[353]. In this case, the Purcell-induced modification of the radiative rate dominates over the field-gradient mechanism and breaks the “temporal” selection rule that keeps the dark state non-emissive, pointing to realistic device applications based on exciton–plasmon strong interaction.

A pioneering study that experimentally separated and quantified higher-order multipolar terms with TERS was reported by Wang et al.^[90]. By computing the electric field and its gradient in a gap-mode geometry and fitting single-molecule Raman intensities to electric-dipole–magnetic-dipole and electric-dipole–quadrupole mixed terms, they showed that magnetic-dipole modes can dominate at specific wavelengths, quantitatively confirming Moskovits’s early hypothesis. This enables “mapping” of forbidden-transition strengths and feedback to theoretical parameters.

Hasz et al. combined TEPL with AFM-induced local strain to image dark-exciton emission in monolayer WSe2 with a few-nanometer resolution^[354]. They demonstrated that both compressive and tensile strain can continuously tune the emission intensity and peak energy of dark and bright excitons.

To deploy atomic-scale measurements in applications, reproducible and batch-fabricated probes are essential. Zhou et al. used nano-imprint technology to mass-produce fiber probes that maintain a gap-mode Purcell factor above 103 and achieved 50 nm resolution dark-exciton imaging^[355]. The measurement time is less than one-third of conventional AFM–TEPL, enabling large-area mapping and statistical analysis.

Together, these studies have enabled direct imaging of quantum states, mapping of orbital symmetry, and observation of hidden or multipolar excitations, fundamentally refreshing our understanding of light–matter interaction at the nanometer scale. In this section, we systematically review the theoretical and experimental frameworks that underpin this paradigm shift.

In conventional far-field optics, the light–matter interaction is governed by the electric dipole approximation, assuming the driving field is spatially uniform over a molecule. Under this assumption, the oscillator strength is feg=2me(Ee−Eg)3ℏ2|⟨Ψe|r|Ψg⟩|2,(4.1)which vanishes for transitions between states of the same parity. Hence, electric quadrupole and magnetic dipole transitions are typically forbidden.

However, this approximation breaks down in plasmonic nanogaps, where the spatial gradient of the near field is steep. In such strongly confined fields, forbidden transitions become optically active due to nonlocal and multipolar interactions.

To account for these effects, the polarization must be expressed in a nonlocal form: P(r,ω)=ε0∫χ(r,r′;ω)E(r′,ω)dr′,(4.2)where the nonlocal susceptibility tensor χ(r,r′;ω) describes the spatially distributed response of the medium.

Within linear response theory, the susceptibility can be written as a sum over quantum transitions: χαβ(r,r′;ω)=∑e[dαβ(e)*(r,r′)ω−ωe0+iη−dβα(e)(r′,r)ω+ωe0+iη],(4.3)where ωe0=(Ee−E0)/ℏ, and dαβ(e)(r,r′)=⟨0|μα(r)|e⟩⟨e|μβ(r′)|0⟩/(ε0ℏ)represents the spatially resolved correlation between transition dipole densities. Here, η is a positive infinitesimal ensuring causality.

Substituting Eq. (4.2) into Maxwell’s equations yields a self-consistent integral equation for the total electric field: E(r,ω)=Einc(r,ω)+μ0ω2∫G(r,r′;ω)P(r′,ω)dr′,(4.4)where G(r,r′;ω) is the dyadic Green’s function incorporating the full electromagnetic response of the nanostructure (for details of nonlocal response theory and its applications, see Refs. [356,357]).

The breakdown of inversion symmetry in near-field interactions can also be understood via the multipolar expansion of the light–matter interaction Hamiltonian Hint=−d·E−m·B−∑ijQij∂jEi+⋯,(4.5)where d is the electric dipole moment, m is the magnetic dipole moment, and Qij is the electric quadrupole tensor. In strongly confined fields, large field gradients ∂jEi and high in-plane wavevectors k∥ (the Bloch wavevector parallel to the interface) break the selection rules derived under uniform-field approximations.

These effects can be quantitatively captured using the extended DDA (eDDA)^[70], which combines: •first-principles-derived polarizability tensors for sub-Ångström molecular regions, and•classical Drude dipoles for plasmonic nanostructures.

Self-consistent solution of Eq. (4.4) yields spatially resolved excitation spectra, including dipole-forbidden and multipolar transitions.

This nonlocal electrodynamic framework leads to several key physical insights: •forbidden quantum transitions (e.g., parity-even states) are activated where ∂jEi overlaps with nodal structures in the wavefunction;•gap geometry and plasmonic mode design can be used to control transition strengths via field gradients and spatial phase matching;•radiative quenching near metals is reduced for dark states due to weak far-field coupling.

By incorporating spatially nonlocal response and quantum current correlations, the susceptibility formalism described above enables accurate modeling of light–matter interaction beyond the dipole limit. This approach provides the theoretical foundation for interpreting forbidden transitions, symmetry breaking, and real-space imaging of quantum states in tip-enhanced and plasmonic near-field systems.

As an example of near-field-induced breakdown of optical selection rules for electronic transitions, Iida et al.^[68] considered a model molecule consisting of five quantum cells placed in a 2.8 nm gap between two gold blocks and solved, in a self-consistent manner, the metal response and the molecular polarizability using DDA. As shown in Fig. 10, the fourth (even-parity) excited state—optically dark in the far field—exhibits an induced polarization more than two orders of magnitude larger than that of the lowest dipole-allowed state when the molecule is centered in the gap. The key mechanism is the steep local field gradient ∇E, which overlaps the nodal structure of the molecular wavefunction.

Uryu et al.^[69] focused on SWNTs and constructed a self-consistent k-space model in which gap plasmons possessing large in-plane wavevector components (k∥) drive otherwise forbidden finite-longitudinal-momentum excitons. By embedding the nonlocal conductivity of the SWNT into the Green-function form of Maxwell’s equations and sweeping the gap width and plasmon resonance conditions, they predicted that plasmon components whose |k∥| match the excitonic longitudinal momentum of the Eii series (such as E22) couple strongly and create a Fano-type dip in the gold absorption spectrum (see Fig. 11 for details.) Because |k∥|=2πn/T, tuning the block periodicity T allows control over exciton momentum selectivity, thereby introducing the concept of selection-rule engineering via momentum compensation.

In parallel, Takase et al.^[70] fabricated a Au nanodimer–SWNT hybrid and achieved experimental observation of forbidden electronic transitions by plasmon-enhanced Raman spectroscopy. Transmission electron microscopy confirmed a gap of ∼1nm between the dimer tips. Under 785 nm excitation, a pronounced enhancement of the E12 band (Δn=+1)—normally absent in Raman scattering—was observed only when the nanotube resided inside the dimer gap (see Fig. 12 for details.) Polarization-dependent measurements showed that the forbidden peak reaches maximum intensity for light polarized along the dimer long axis (where |k∥| is largest) and decreases sharply for the orthogonal polarization. When the same geometry was fed into an eDDA calculation, the experimental intensity ratio IE12/IG≈0.1−0.2 agreed quantitatively with theory, confirming that the combined action of the field gradient and momentum compensation controls the breakdown of the selection rule.

Takase’s work is therefore seminal: it demonstrates, at the single-molecule level, that near-field coherence can activate dark electronic states in a predictable manner. By implementing the two keys proposed by Iida and Uryu—spatial field gradients and momentum compensation—it established a new paradigm in which optical selection rules themselves can be engineered on the nanometer scale.

TERS and TEPL have enabled the direct detection and imaging of forbidden and multipolar transitions. Zhang et al.^[57] used TERS to chemically map single molecules and observed vibrational modes that are symmetry-forbidden in conventional Raman spectroscopy. The emergence and intensity of these modes depended sensitively on the tip position and polarization, suggesting their origin in the local symmetry breaking caused by the plasmonic near-field. This development allowed for the direct observation of forbidden transitions within molecules, including multipolar excitations that had been inaccessible by conventional means.

Regarding forbidden molecular excitations, Zhang et al.^[154] directly visualized intermolecular exciton coupling with sub-nanometer resolution using scanning tunneling microscope-induced luminescence (STML). This study overcame the diffraction limit of conventional optical microscopy by combining local excitation from tunneling electrons with radiative enhancement from nanocavity plasmons, making it possible to observe coherent dipole–dipole interactions that had previously been unresolvable in real space. In the experiment, zinc phthalocyanine (ZnPc) molecules were electronically decoupled by placing them on three monolayers of NaCl on a Ag(100) substrate, and fluorescence from the molecules was strongly enhanced by the localized plasmon field in the tip–sample gap, enabling imaging with sub-nanometer spatial resolution. By manipulating the tip, a dimer of two ZnPc molecules was constructed, and spatially resolved STML spectra revealed five excitonic emission peaks as in Fig. 13(a). Photon images corresponding to each peak showed distinctly different nodal and antinodal patterns, which, when compared with theoretical simulations, were assigned to five types of dipolar coupling modes: in-line in-phase (sigma type), in-line out-of-phase, and parallel configurations in Fig. 13(b). Notably, the in-line in-phase mode exhibited the strongest emission as a superradiant state, while the out-of-phase mode, originally a dark subradiant state, was weakly detected because the steep localized plasmon is induced around by the tip. The system was shown to support coherent excitonic coupling. Moreover, the authors extended the ZnPc array to trimers and tetramers, demonstrating the concept of single-molecule superradiance through electrical excitation. However, in the tetramer, deviation from the ideal N-fold enhancement was observed, leading to discussions on the spatial extension of the plasmon field and the influence of nonradiative decay. This study represents a pioneering example of real-space imaging of forbidden excitonic transitions induced by electronic excitation.

Park et al.^[353] experimentally visualized the mechanism for brightening dark excitons in monolayer WSe2 at room temperature using TEPL with a scanning plasmonic antenna tip, as shown in Fig. 14. Figure 14(c) shows TEPL spectra acquired at a tip–sample separation of about 1 nm. When the incident polarization was out-of-plane, a peak appeared around 1.621 eV corresponding to the dark exciton (XD), while the in-plane polarization favored the bright exciton (X0). The energy difference between dark and bright modes, derived from Lorentzian fitting, was approximately 46 meV, consistent with low-temperature magneto-spectroscopy and coupling experiments using SPPs, indicating that the near-field method preserves the intrinsic exciton splitting. FDTD simulations showed that the out-of-plane electric field intensity |Ez|2 inside the nanogap reached at least 3×102 times the incident field, quantitatively demonstrating that this strong vertical field resonantly couples with the out-of-plane transition dipole of the dark exciton and converts it into a radiatively allowed state. In this way, efficient excitation through local field enhancement and accelerated spontaneous emission via the Purcell effect work together to enable bright nanoscale imaging of dark excitons that are forbidden in the far field.

While forbidden vibrational transitions have long been discussed in the context of SERS, the STM-TERS study by Lee et al.^[348] provided the first direct real-space visualization of such modes at atomic resolution, extending the reach of near-field optics to vibrational symmetry breaking with angstrom-scale mapping. They succeeded in imaging vibrational normal modes at atomic resolution using tip-enhanced techniques, revealing spatial patterns corresponding to nonlocal and multipolar transitions. When a Ag tip approached a Co(II)–tetraphenyl porphyrin(CoTPP) molecule, Raman signals that were undetectable at a 0.3 nm gap became strongly enhanced at 0.2 nm. In the quantum tunneling regime, tunnel plasmons became dominant over cavity fields, leading to a two-order-of-magnitude enhancement instead of the decay predicted by conventional models. Figure 15 presents decisive data: six vibrational modes (388, 864, 1047, 1413, 3199, and 3213cm−1) of a single CoTPP molecule were imaged at angstrom-scale resolution. The simulated images in the middle row reproduced the experimental contrasts and nodal structures almost perfectly. The lower row shows schematic diagrams of the corresponding vibrational normal modes based on density functional theory (DFT) calculations. These results demonstrate that vibrational normal modes of a single molecule, including high-frequency C−H stretches and low-frequency skeletal modes, can be visualized in real space with angstrom-scale resolution under sub-angstrom tip–sample distances. The excitation and scattering are mediated by atomically confined tunnel plasmons, enabling access to vibrational polarizations that are otherwise weakly probed in far-field Raman. This atomistic near-field regime offers a new framework for direct mapping of intra-molecular polarization responses down to nodal structures.

Jaculbia et al.^[349] decoupled single copper naphthalocyanine molecules on trilayer NaCl/Ag(111) and drove STM-TERS under molecular resonance conditions (738 nm) to image vibrational symmetry modes that are inactive even in far-field Raman spectroscopy. The key factor was a relatively large tip–substrate gap of 5.8 Å, which allowed the transverse electric field components (Ex, Ey) of the near field to reach the molecular plane, enabling excitation in the x–y plane that is weak in far-field Raman collected along the surface normal. In Fig. 16, TERS spectra acquired on a 1 Å grid showed three mode images at 680cm−1 (A1g), 1182cm−1 (B2g), and 1389cm−1 (B1g), each displaying distinct patterns: circular, plus-shaped, and cross-shaped, respectively. While the A1g image was isotropic and centered on the tip, the B2g and B1g patterns showed alternating intensity depending on the tip’s lateral position, demonstrating the activation of symmetry-forbidden in-plane vibrational modes via multipolar components of the local field. The authors explained that, without introducing any “new selection rules,” these images could be reproduced by incorporating contributions from transverse electric fields into the standard expression for the induced dipole moment, pρ=αρσEσ.

Wang et al.^[358] used gold nanocubes functionalized with 4-thiobenzonitrile (TBN) as samples and visualized local electric fields with ∼3nm spatial resolution via gap-mode TERS, as shown in Fig. 17. While the spatially averaged spectrum was dominated by conventional dipolar Raman peaks (1078, 1179, 1206, 1586, 2225cm−1), a weak shoulder appeared between 1225 and 1500cm−1 [Fig. 17(d), gray highlight], suggestive of forbidden transitions. By analyzing single-pixel spectra at the edges of the nanocubes, they identified peaks at 1326, 1382, and 1501cm−1 that were strongly enhanced at specific positions. Comparison with DFT-calculated generalized multipolar polarizabilities attributed these to electric-dipole–magnetic-dipole (G2) and electric-dipole–electric-quadrupole (A2) transitions, which differ from the conventional dipole Raman (α2) selection rules [Fig. 17(e), blue and yellow spectra]. This directly demonstrated that steep electric field gradients in the tip–sample junction can activate transitions forbidden under dipole selection rules. Although these multipolar Raman lines were weak on average, they were locally comparable or even superior to dipole lines, and their appearance was confined to regions where both electric field and its gradient were simultaneously strong. The authors ruled out the formation of photochemical byproducts as the origin of the observed peaks, supporting their assignment to multipolar Raman transitions. These transitions, nominally forbidden under dipole selection rules, were detected selectively at tip positions where strong local fields and field gradients coexist.

Two recent TEPL studies demonstrated real-space imaging of dark excitons in monolayer WSe2. In Ref. [354], Fig. 18(A) presents near-field photoluminescence maps of bright and dark excitons over a 200nm×200nm scan area. When overlaid with AFM topography, the dark exciton emission was significantly enhanced in strain-induced bubble regions of tens of nanometers in size, contrasting with the bright exciton distribution. This example illustrates that forbidden out-of-plane dipole transitions (dark excitons) are strongly localized by gap-mode Purcell enhancement and can be imaged with four times better spatial resolution than bright excitons. Meanwhile, Zhou et al.^[355] developed a robust fiber-coupled gap-mode TEPL using Au-coated pyramidal tips and obtained hyperspectral maps of dark and bright excitons on WSe2 flakes with oxidation defects as shown in panel B of Fig. 18. The dark exciton map clearly resolved oxide patches and flake edges with <50nm spatial resolution, while these features were largely smeared out in the bright exciton map due to diffraction-limited excitation and collection. Figure 18(B-a) shows an 800nm×800nm shear-force topography of a monolayer WSe2 flake, where local oxidation creates nonemissive patches (dark contrast). Hyperspectral TEPL data acquired using a gold-coated pyramidal probe were decomposed into contributions from the bright exciton (XB) and the out-of-plane dark exciton (XD). Figure 18(B-b) displays the PL spectra at oxidized and unoxidized regions. For XD, the emission appears approximately 50 meV below XB. Figures 18(B-c) and 18(B-d) display intensity maps of XD and XB, respectively. The nonemissive oxidized features and the flake edge are clearly identified in the XD map at the corresponding positions in the topography image, whereas these features are less distinct in the XB map. These results demonstrate that the fiber-integrated picocavity selectively activates and enhances out-of-plane dark excitons and enables imaging with approximately four times better spatial resolution than for bright excitons, without requiring mechanical strain tuning. Both studies are representative demonstrations that forbidden out-of-plane dipole transitions (dark excitons) can be converted into radiatively allowed states by picocavity electromagnetic fields and imaged in real space with better resolution than bright states.

PiFM detects the near-field-induced optical gradient force acting on the probe—on the order of piconewtons or below—as a frequency shift of an AFM cantilever, thereby converting the optical response into a mechanical signal. Because it requires no scattered-light channel, PiFM can be applied to samples with low quantum yield or to systems that exhibit strong substrate scattering, and the signal is proportional not to the electric-field intensity itself but to ∇|E|2 or E·∇P. It is therefore intrinsically highly sensitive to higher-order multipolar processes, such as electric quadrupoles and magnetic dipoles. Since the proof of concept in 2010, PiFM has progressed from atomic resolution vector tomography to single-molecule observation of forbidden transitions using picocavity fields.

The basic idea of using photoinduced force for scanning probe microscopy was first theoretically proposed by Iida and Ishihara^[62,359]. The principle of PiFM, based on the AFM technique, was first demonstrated in 2010 by Rajapaksa et al.^[63]. By illuminating the sample with visible light and monitoring the resonance frequency shift of an AFM cantilever, they detected contrast corresponding to the absorption resonance within dye islands (approximately 10 nm in diameter). Although the lateral resolution at that time was limited to ∼10nm, the three-step transduction process—“optical resonance → induced force → mechanical signal”—was experimentally verified, and the possibility of near-field spectroscopy without a scattering channel was presented for the first time.

The major challenge for early PiFM was that photothermal expansion and non-conservative forces contaminated the cantilever frequency shift, limiting the spatial resolution and quantitative accuracy. In 2017, Yamanishi et al.^[65] introduced a heterodyne side-band PiFM scheme in FM-AFM, in which the optical intensity is modulated at a low frequency fm. Mixing with cantilever oscillation at f1 generates a side-band at f1+fm, which is selectively detected, enabling a 99.975% suppression of photothermal artifacts. In 2018, the same group further developed a heterodyne frequency modulation (FM) method, theoretically and experimentally, in which the incident laser power is modulated at 2f1+fm while the cantilever is driven only at its fundamental resonance f1; the photoinduced force is extracted from the frequency-shift component at fm^[360]. Because frequency noise is one to two orders of magnitude lower than amplitude noise, the minimum detectable gradient force was reduced to the piconewton level, and the probe–sample gap could be stably maintained at <1nm without the signal being buried in thermal noise.

By integrating the heterodyne FM scheme into a vacuum chamber and optimizing the probe amplitude and lock-in phase, Yamanishi et al. achieved a lateral resolution of 0.7 nm for the local electromagnetic field on quantum dots^[351]. The quantum dots, shown schematically in Figs. 19(a) and 19(b), have a dumbbell shape: the two elliptical lobes and the central rod differ in composition and therefore in optical response. Simultaneous PiFM measurements at different excitation wavelengths allowed imaging of the optical contrasts arising from these compositional differences [see Figs. 19(d)–19(k)]. By sweeping the cantilever height in fine increments, photoinduced force curves versus z were recorded at each pixel and used to reconstruct a three-dimensional map. Numerical differentiation of the resulting interaction potential yielded the full vector components Fx, Fy, and Fz, enabling visualization of both the orientation and anisotropy of the local electric field with sub-nanometer precision [see Figs. 19(l)–19(o)]. The spatial width of the signal is smaller than the probe–apex radius, and theoretical analysis indicates a dominant contribution from a picocavity formed by the protruding front atom(s) of the tip.

Following this achievement, the near-field enhancement in the picocavity region was analyzed using a hybrid quantum–electromagnetic model that combines an eDDA description of the plasmonic nanogap with first-principles molecular wavefunctions^[352]. For example, in the case of phthalocyanine, the intramolecular polarization distribution was calculated and related to the PiFM imaging contrast for both dipole-allowed and -forbidden transitions as shown in Fig. 20(A). This clarified how forbidden modes—arising from higher-order multipoles—can be selectively activated and visualized, providing a guideline for interpreting molecular polarization patterns via PiFM. Yamamoto et al.^[66] subsequently mapped the optical response of a pentacene bilayer on Ag at 78 K in UHV with 0.6 nm spatial resolution using the heterodyne–FM method and a Au tip. The resulting image, reproduced in the figure, shows a strong signal at the ends of each pentacene molecule and cancellation at the center, as shown in Fig. 20(B). According to the preceding theory^[352], this pattern corresponds to a multipolar (forbidden) excitation within the molecule. Analysis based on the measured contact potential difference revealed that the forbidden transition involves charge transfer among the tip, molecule, and substrate, demonstrating that PiFM can render changes in electronic structure, including forbidden transitions, in an imaging mode.

In this section, we surveyed recent theoretical and experimental advances in real-space imaging of multipolar and forbidden transitions, which have remained inaccessible in conventional far-field optics, by exploiting coherence and spatial gradients of localized electromagnetic fields. We first organized the fundamental mechanism of selection rule breakdown due to inhomogeneous plasmonic fields at atomic and molecular scales, in terms of multipole expansion and high in-plane momentum components k∥. The concepts of field gradient–wavefunction overlap and the momentum compensation model laid the theoretical groundwork for later experimental breakthroughs^[68,69,345].

On the experimental side, TERS, TEPL, and PiFM each have visualized the breakdown of selection rules via distinct detection channels—scattered photons, photoluminescence, and photoinduced force, respectively—achieving a leap in spatial resolution from tens of nanometers to the angstrom scale^{[57,154,348,349,351,353,355]}. In particular, Purcell enhancement and quantum tunneling within picocavities proved essential for high-contrast readout of single-molecule vibrations and dark excitons. The activation of resonant-forbidden modes via transverse field components by Jaculbia et al.^[347–349], and the ∼50nm-scale imaging of dark excitons in monolayer WSe2 by Hasz et al. and Zhou et al. exemplify these advances^[354,355]. Furthermore, Wang et al. quantitatively identified electric quadrupole and magnetic dipole transitions via generalized multipolar polarizability analysis, experimentally validating the Moskovits hypothesis^[358]. Complementarily, PiFM converts near-field optical gradient forces into mechanical frequency shifts of an AFM cantilever, requiring no scattered-light channel and thus remaining effective even for low-yield or strongly scattering samples. With the heterodyne FM detection introduced by Yamanishi et al., the spatial resolution advanced from the 10-nm proof of concept to the sub-nanometer regime, enabling vector-resolved mapping of quantum-dot fields. Building directly on this progress, Yamamoto et al. achieved sub-nanometer imaging of pentacene bilayers and revealed multipolar forbidden transitions activated by picocavity fields. These developments firmly establish PiFM as a uniquely powerful complement to photon-based near-field probes^[66,351,352].

On the theoretical front, quantum-corrected electromagnetic models that go beyond classical electrodynamics—incorporating electron tunneling, nonlocal dielectric response, and plasmon quantization—have become essential^[361,362]. These models are effective for accurately predicting plasmonic resonances based on gap size and conductivity, and are expected to facilitate applications involving electro-optic modulation and strong coupling in nanogap modes. Moreover, its potential applications are suggested in sensing, nonlinear optics, and integrated quantum devices^[363].

Near-field imaging has already pushed the spatial resolution limit down to the angstrom scale, but further breakthroughs are anticipated along three dimensions: “temporal,” “volumetric,” and “autonomous” control. First, the work by Luo et al.^[364] demonstrated stable operation of femtosecond-pulsed TERS via femtosecond excitation integrated into STM–TERS, paving the way for time-resolved measurements. This would allow direct mapping of early-stage processes such as photoinduced charge transfer or coherent phonon generation in real space—beyond the capabilities of conventional pump–probe spectroscopy.

The adaptive wavefront shaping by Lee et al.^[365], using spatial light modulators and feedback algorithms, enabled real-time optimization of the nanolocalized field at the probe tip, doubling TEPL signal intensity. Such “computational nanoscopy” makes imaging feasible even under unstable conditions such as liquid or high-temperature environments, and enables dynamic visualizations via autonomous path optimization and in situ symmetry switching.

To address the analytical challenges posed by high-dimensional data, machine learning is becoming indispensable, as exemplified by the work of Kajendirarajah et al.^[366], who demonstrated rapid reconstruction of TERS images using deep learning. Nonlinear spectral unmixing and automated clustering of multipolar fingerprints^[367], and even real-time implementation into experimental control systems, are leading toward “self-driven imaging”^[368], capable of extracting optimal image quality while avoiding photon saturation.

As a final remark, the multiphoton route mentioned in Sec. 4.1 is complementary to the near-field approach: combining tip-enhanced nonlinear spectroscopies with linear, gradient-assisted readouts can increase tensor selectivity and coherence contrast without sacrificing spatial resolution. Advancing such hybrid methodologies—including stable ultrafast excitation, polarization/phase control, and background suppression—constitutes an important challenge and opportunity for the next generation of experiments.

Plasmonic nanostructures have ushered in a new era of light manipulation at nanometer scales, offering extraordinary opportunities to engineer electromagnetic fields, optical response, and energy flow in ways that are impossible in bulk or weakly confined systems. Beyond enabling intense field localization and spectral selectivity, a rapidly growing frontier involves the realization and exploitation of coherent coupling among multiple plasmonic elements. In this regime, collective behavior emerges from the quantum or electromagnetic coherence established between resonant modes in spatially separated metallic nanostructures, which profoundly alters both the physical mechanisms and technological potential of HCG, energy conversion, photodetection, and catalysis.

The foundation of classical plasmonics lies in the realization that metallic nanostructures can concentrate electromagnetic fields into subwavelength volumes, enabling extraordinarily enhanced light–matter interactions within nanoscopic regions. In the 1970s, theoretical studies predicted that when two metallic nanoparticles are brought into close proximity, a strong and highly localized electromagnetic field—known as a “hot spot”—forms in the narrow interparticle gap^[369,370]. This mechanism of field enhancement provided the theoretical underpinning for landmark techniques such as SERS and TERS, which allow for molecular detection with single-molecule sensitivity^[12,13,52].

In recent years, hot spots have been recognized as playing a central role not only in Raman enhancement, but also in nonlinear optics^[2] and plasmonic metamaterials^[371]. A particularly significant development was the understanding that hot spots serve as efficient sites for HCG—the production of non-equilibrium electrons and holes—through the nonradiative decay of LSPs. This process, known as Landau damping, involves the conversion of collective plasmonic oscillations into electron–hole pair excitations and has been identified as a key mechanism in plasmon-assisted photothermal, photoelectric, and photochemical energy conversion^{[3,4,21,77,278,372,373]}.

Moreover, attempts to further enhance field strength through geometrical refinement eventually encounter diminishing returns. As structures are pushed into the sub-nanometer regime, quantum mechanical effects—such as nonlocal response, electron spill-out, and tunneling—become significant^[374,375], often acting to suppress the very field localization that the design seeks to maximize.

While classical models do consider electromagnetic interactions between neighboring plasmonic structures, they typically fall short of describing quantum-coherent coupling effects—such as phase-coherent mode hybridization, spectral interference, and spatially extended collective behavior. These phenomena require a quantum mechanical picture in which coherence is treated as an essential and tunable parameter, and the superposition states formed among coupled plasmons are explicitly taken into account. The transition to such a picture had become essential for understanding the full potential of coupled plasmonic systems.

The transition from the conventional view of plasmonic interactions—developed in the late 20th century and centered on local field enhancement in nanogap regions—to a quantum picture, where plasmons excited in individual metallic nanostructures couple coherently to form hybridized superposition modes, reshaped our understanding of light–matter interactions in metallic nanosystems throughout the early 2000s and 2010s. Particularly, the emergence of coherent coupling among spatially distinct plasmonic elements has shifted the focus from local field enhancement to nonlocal, mode-level hybridization phenomena. This paradigm shift redefines plasmonic devices as optically addressable resonator networks where phase coherence and mode symmetry govern the response functions. In this section, we highlight three cornerstone concepts that illustrate these quantum aspects: plasmon hybridization, Fano resonance, and lattice plasmon resonances.

The notion of plasmon hybridization was first formalized by Nordlander et al.^[73,74], drawing direct analogy to the hybridization of atomic orbitals in molecules. In this picture, the plasmon modes of individual metallic nanostructures interact via near-field coupling to form bonding and antibonding supermodes. These new eigenmodes display altered spectral positions, field distributions, and symmetry properties, offering a designable platform for manipulating optical response at the nanoscale.

This concept is schematically depicted in Fig. 21(A), where two spherical nanoparticles exhibit dipolar (l=1) and quadrupolar (l=2) modes that split upon hybridization. The energy splitting, which depends on interparticle spacing and mode symmetry, is quantitatively calculated in Fig. 21(B) for the m=0 and m=1 azimuthal quantum number modes^[74]. Strong splitting is observed at small gaps (e.g., D<30nm), illustrating the increasing mode coupling strength. This theoretical foundation enables researchers to predict and control hybridization in arbitrarily shaped nanostructures.

The physical mechanism of plasmon hybridization, in which the electromagnetic modes of coupled metallic nanostructures reorganize into collective bonding and antibonding states, has been decisively demonstrated by several experimental approaches that reveal both spectral and spatial signatures of these hybrid modes (see Fig. 22).

In the study by Huang et al.^[376], hybridized plasmonic modes were investigated in gold nanoantennas using a combination of numerical simulations and two-photon photoluminescence (TPPL) microscopy. Near-field spectra calculated for dimers with varying feed-gap distances show that decreasing the gap leads to a clear spectral splitting of the dipolar mode into bonding and antibonding resonances, indicative of strong near-field coupling [see Figs. 22(I-A)]. To explore mode-selective excitation, near-field intensity spectra were calculated for antennas of increasing length, revealing a systematic redshift of the resonances. As the antenna length increases, the spectral overlap with the excitation window shifts from the bonding to the antibonding mode, enabling selective excitation of different hybridized states depending on geometry [see Figs. 22(I-B)]. Further experimental evidence was obtained via spatially resolved TPPL imaging, which visualized the spatial profiles of the hybridized modes [see Figs. 22(I-C)]. Bonding modes manifest as centralized emission along the antenna pair, while antibonding modes appear as two-lobed distributions with nodal planes. These images were recorded for a systematic antenna array, and selected antennas show clear transitions in modal symmetry, confirming spatial coherence and delocalization of the hybridized states.

Coenen et al.^[377] explored plasmon hybridization in a gold dolmen structure composed of a nanorod monomer and a perpendicularly arranged dimer, using cathodoluminescence (CL) and electron energy-loss spectroscopy (EELS). A high-energy electron beam was scanned across the structure to locally excite plasmon modes, while both emitted light and energy loss were recorded [see Fig. 22(II-A-a)]. The bonding and antibonding mode formation is conceptually illustrated in Fig. 22(II-A-b), and the actual excitation positions are shown in the TEM image in Fig. 22(II-A-c). Spectra acquired at position A (monomer side) predominantly reveal bonding-mode features [Fig. 22(II-B-a)], whereas excitation at position B (dimer side) enhances the antibonding mode [Fig. 22(II-B-b)]. Reference spectra from isolated components confirm that these signals arise from hybridized states. Field maps at selected wavelengths [Fig. 22(II-B-c)] display distinct modal distributions, providing spatial evidence of the hybridization.

Yu et al.^[75] further investigated hybridized plasmon modes in a periodic gold dolmen array [see Figs. 22(III-a) and 22(III-b)] by employing photoemission electron microscopy (PEEM) alongside numerical simulations. The extinction spectra under orthogonal linear polarizations [see Fig. 22(III-c)] reveal clear resonance splitting, indicative of bonding and antibonding mode formation. These spectral features are corroborated by FDTD simulations, which also reproduce the near-field photoemission intensity spectra [Fig. 22(III-d)]. Surface charge distributions at the resonance energies [Fig. 22(III-e)] reveal the spatial symmetry of each hybridized mode. Notably, PEEM images obtained under femtosecond laser excitation [Fig. 22(III-f)] exhibit close correspondence with the calculated near-field intensity patterns, providing direct experimental confirmation of modal symmetry and coherence.

Beyond canonical dimers and dolmen motifs, stacked rod pairs and rod dimers provide a minimal platform where hybridization yields clear bonding/antibonding splitting; the gap and aspect ratio tune the splitting, while the near-field phase relation distinguishes bright (in-phase) and dark (out-of-phase) combinations. Such prototypes also connect to magnetic plasmonics, in which antisymmetric current loops form an effective magnetic dipole and enable interference-based narrow features such as magnetic plasmon-induced transparency (PIT)^[378,379]. Related hybridization with optical cavities gives mode splitting and Purcell-assisted control of emission and directionality^[380].

Collectively, these studies provide robust and convergent evidence that plasmon hybridization is a universal mechanism for mode formation in coupled nanostructures. By employing TPPL, CL/EELS, and PEEM, the experiments reveal not only the energy splitting but also the spatial and phase structure of the resulting hybrid modes. This unified understanding is essential for engineering nanoscale systems with tailored optical properties, high field localization, and advanced functionalities in nonlinear optics and quantum plasmonics.

For detailed visualizations and data supporting these findings, see the subpanels of Fig. 22.

A central quantum phenomenon in plasmonic systems is the Fano resonance, which originates from the interference between a spectrally broad, superradiant (bright) mode and a narrow, subradiant (dark) mode. This interference leads to distinctly asymmetric line shapes in the optical response, which can be sensitively tuned by geometry, coupling strength, and symmetry breaking^{[25,26,157,381–384]}. Fano resonances are not only fundamental signatures of coherent modal interactions at the nanoscale, but also offer powerful means for tailoring optical spectra, enabling sharp transparency windows, spectral switching, and giant enhancement of nonlinear processes. In plasmonic resonator platforms, PIT (as briefly noted in Sec. 3.2) is a practical implementation of the same bright–dark Fano interference: by aligning a subradiant mode with a broad radiative background and controlling drive asymmetry, a narrow transmission window emerges in accordance with the Fano profile in Eq. (2.3); classical metamaterial realizations appeared early^{[26,310,318,319,378]}.

The universality and tunability of Fano resonances in plasmonic structures have been clarified by a series of seminal studies. Verellen et al.^[25] first showed that even individual metallic nanocavities can exhibit pronounced Fano-like line shapes, demonstrating that the effect is not limited to extended systems. Luk’Yanchuk et al.^[26] provided a comprehensive theoretical framework, elucidating how Fano resonances arise from the coherent interaction of discrete and continuum-like plasmonic states, and highlighting the role of symmetry and environment. Giannini et al.^[381] and Yang et al.^[382] extended this picture to coupled nanoparticles and nanorod dimers, revealing that dipole–quadrupole and higher-order couplings can generate Fano interference with strong spectral tunability. More recently, Zhang et al.^[384] demonstrated that coherent Fano interference in nanoclusters can significantly boost nonlinear optical effects, such as four-wave mixing, and Lovera et al.^[157] systematically classified the physical origins and excitation conditions for Fano resonances in plasmonic assemblies.

Direct experimental visualization of Fano-resonant mode structures has been achieved using advanced near-field techniques. In a landmark study, Alonso-González et al.^[383] employed scattering-type scanning near-field optical microscopy to map the amplitude and phase distributions of plasmonic modes in a gold heptamer cluster, consisting of six nanodisks surrounding a central one. This highly symmetric geometry supports both bright (radiative) and dark (non-radiative) collective modes, whose coherent interference gives rise to the asymmetric Fano line shape. The experimental setup enables interferometric detection of tip-scattered light, yielding spatially resolved amplitude, phase, and topography data [see Fig. 23(I-A-a)]. Simulated extinction spectra [Fig. 23(I-A-b)] show a Fano minimum that arises from destructive interference between superradiant and subradiant charge distributions. Insets illustrate the contrasting surface charge configurations responsible for bright and dark modes. By systematically varying the disk radius in the heptamer, the spectral position of the Fano resonance was tuned across the mid-infrared regime [Fig. 23(I-B-a)]. Crucially, both calculated and experimentally acquired near-field maps [Figs. 23(I-B-b) and 23(I-B-c)] confirm that the Fano minimum corresponds to a dark mode with a π phase shift and nodal structure, in stark contrast to the in-phase field of the bright mode. These results provide direct real-space evidence for the modal symmetry and phase behavior underlying Fano interference in plasmonic metamolecules.

Alongside in-plane coupling, out-of-plane (vertical) coupling offers a complementary pathway to engineer the same interference phenomena discussed above. Prototypical platforms include multilayer metasurface stacks and nanoparticle-on-mirror geometries separated by a nanometric spacer, where capacitive gap fields mediate strong vertical hybridization between a radiative bright mode and a subradiant gap or image mode. Depending on spacer thickness and symmetry, vertical coupling yields bonding/antibonding splitting that continuously connects to the Fano profile of Eq. (2.3), realizes PIT-like transparency when drive asymmetry and spectral alignment are met, and converts symmetry-protected BICs into quasi-BICs with large but finite Q. Beyond line shape control, the vertical field squeeze enhances LDOS and dwell time in the gap, with implications for hot-carrier extraction, nonlinear upconversion, and chiroptical responses^[385–387].

Taken together, these studies underscore the importance of modal symmetry, spatial coherence, and controlled coupling in engineering Fano resonances. By leveraging near-field techniques, it is now possible to design and tune plasmonic nanostructures for targeted spectral features, active switching, or enhancement of nonlinear processes—capabilities that are central to the development of advanced nanophotonic devices and sensors. For detailed spectral and field maps illustrating these concepts, see the subpanels of Figs. 23(I-A) and 23(I-B).

Lattice plasmon resonances (LPRs) emerge from the diffractive coupling of localized plasmons in periodic arrays of nanoparticles. The theoretical basis was established by Zou and Schatz^[388,389], who showed that periodic order introduces new narrow spectral features beyond those of individual particles, while Auguié and Barnes^[163] experimentally verified the existence of such collective resonances. Subsequent studies by Vecchi et al.^[390] and Meinzer et al.^[391] highlighted the role of diffractive surface modes and provided a metasurface perspective, whereas Väkeväinen et al.^[392] extended the regime to strong coupling with quantum emitters. The ability to tune LPRs by geometry and arrangement was further elucidated by Guo et al.^[168], with comprehensive reviews of the field provided by Kravets et al.^[76] and Cherqui et al.^[393].

A particularly elegant demonstration of subradiant LPRs was provided by Zhou and Odom^[394], who engineered periodic arrays of gold nanodisks embedded in flexible polyurethane (PU) substrates. Their fabrication scheme [Fig. 23(II-A-a)] enabled precise and independent control of both the disk height and the array periodicity, a key advance for exploring three-dimensional plasmonic interactions. Scanning electron microscopy confirmed the high fidelity and uniformity of the array [Fig. 23(II-A-b)], with a well-defined pitch and disk diameter.

Optical measurements revealed that the reflectance and transmittance spectra exhibit sharp, narrow resonances superimposed on a broader background [Figs. 23(II-B-a) and 23(II-B-b)]. Under TM-polarized light, both in-plane and out-of-plane dipolar modes are excited, while TE polarization isolates the in-plane response. The emergence of these spectrally sharp, subradiant features is a hallmark of diffractive lattice plasmon resonances, resulting from coherent coupling and radiative interference among the arrayed nanoparticles. These resonances are highly sensitive to structural parameters, excitation polarization, and environment, making them exceptionally useful for precision sensing and active photonic devices.

A critical finding by Zhou and Odom was that increasing the disk height systematically tunes the resonance wavelength, as verified by comparing measured and FDTD-simulated spectra for arrays with different heights [Figs. 23(II-C-a) and 23(II-C-b)]. The strong agreement between experiment and simulation confirms that vertical dipolar coupling plays a decisive role in determining the LPR characteristics. Modal analysis further revealed that the narrowest resonances correspond to collective, subradiant states with suppressed radiative loss and enhanced spatial coherence across the array.

These results demonstrate that LPRs represent a powerful and highly tunable platform for engineering coherent plasmonic phenomena at the nanoscale. By leveraging periodicity, structural control, and polarization selectivity, it is possible to create nanostructured materials with extremely sharp spectral features and large local field enhancements. Such systems are already enabling advances in plasmonic sensing, low-threshold lasing, and nonlinear optics, and are poised to provide a versatile toolkit for future developments in quantum and topological photonics. For fabrication, structural, and spectral details, see Figs. 23(II-A) through 23(II-C).

As discussed in Sec. 5.2, the quantum interference and coherent coupling between LSPRs in spatially separated metallic nanostructures offer a powerful mechanism for tailoring optical response, enhancing field localization, and enabling collective phenomena such as Fano resonances and lattice plasmon modes. However, there exists an inherent limitation to these coherence-driven strategies: the coherence of LSPRs is fundamentally constrained by rapid nonradiative damping, which severely shortens their dephasing time and restricts the spatial extent of coherent interactions. This short coherence time has long posed a barrier to achieving extended, phase-coherent interactions or cooperative phenomena in plasmonic systems.

Recent studies^[78,79,395], which extend the methods introduced in Refs. [396,397], have embedded metallic nanostructures within optical cavities by precisely controlling the spacer layer thickness. This approach enables access to the regime of strong light–matter coupling, leading to the emergence of delocalized hybridized modes with enhanced coherence and novel functionalities not achievable in conventional plasmonic systems.

A representative system is the vertically stacked Au nanoparticles/TiO2/Au film (ATA) structure, consisting of Au nanoparticles (Au-NPs) randomly (or periodically) distributed on a TiO2 dielectric spacer layer atop a gold film. In this configuration, the TiO2 layer serves as a high-index spacer, forming a Fabry–Pérot (FP) optical cavity between the nanodisk array and the Au film. The interaction between the LSPR of the Au-NPs and the FP cavity mode leads to hybridized optical states characterized by Rabi splitting, as reflected in both absorption and emission spectra^[78,79]. The essential features and experimental results for such cavity-coupled plasmonic systems are summarized in Fig. 24.

Shi et al.^[78] first proposed the ATA (Au-TiO2-Au) structure, in which Au nanoparticles (Au-NPs) are randomly distributed on a TiO2 dielectric spacer layer. The key experimental results are summarized in Fig. 24(I). A schematic of the ATA architecture (Au-NPs are randomly distributed) is shown in Fig. 24(I-A), highlighting the vertical arrangement that supports both LSPR and FP cavity mode. The energy-level diagram in Fig. 24(I-B) illustrates the formation of upper and lower polaritonic branches (P+ and P−) resulting from strong coupling between the LSPR and cavity mode, with the Rabi splitting Espl serving as a direct measure of the coupling strength. Experimentally, the thickness of the TiO2 layer can be tuned to bring the two modes into resonance, resulting in the characteristic anti-crossing behavior observed in the absorption spectra in Fig. 24(I-C) and the dispersion relation in Fig. 24 (I-D). This anti-crossing is a hallmark of the strong coupling regime, as it occurs when the energy splitting exceeds the linewidths of the individual modes.

The impact of this hybridization on photocarrier generation is evident in the internal quantum efficiency (IQE) measurements in Fig. 24(I-E): the ATA structure exhibits not only enhanced absorption and incident photon-to-current efficiency (IPCE) compared to reference samples, but also a significant increase in IQE (i.e., the efficiency normalized for absorption). This enhancement indicates that cavity-mediated hybridization promotes more efficient hot-carrier extraction, beyond what can be explained by optical field enhancements alone.

Further insight is gained by Liu et al.^[79], systematically varying the particle number density (PND) in periodic versions of the AT and ATA structures, as shown in Fig. 24(II). In non-cavity systems (AT), increasing PND leads to spectral broadening and redshift [Fig. 24(II-C)]. In contrast, in the cavity-coupled ATA structures, the modal strong coupling between the plasmons and FP cavity leads to a pronounced increase in peak absorbance splitting and nonlinear response as PND increases [Fig. 24(II-D), Figs. 24(II-E-a) and 24(II-E-c)]. The apparent quantum efficiency (AQE), shown in Fig. 24(II-E-d), also exhibits a dramatic enhancement with increasing PND under strong coupling conditions between the plasmons and FP cavity. This phenomenon can be clearly explained by the existence of a spatial region over which plasmonic elements collectively share the electromagnetic field, i.e., the coherence area (defined below).

In this work, the term “coherence area” does not merely refer to the geometric footprint of an individual plasmonic element or its spatial overlap with a cavity mode. Rather, it denotes the finite spatial domain over which distinct plasmonic nanostructures coherently share a common optical mode—typically mediated by an optical cavity—such that they exhibit collective, phase-synchronized behavior. To quantify this, we consider the plasmonic near fields Epl,i(r,ω) and Epl,j(r,ω) induced at nanostructures i and j (including cavity-mediated modifications to the local field distribution), and define a pairwise coherence factor: $$\begin{gathered} Ci,j(ω)=|∫Vε(r)Epl,i(r,ω)·Epl,j*(r,ω)d3r|2(∫Vε(r)|Epl,i|2d3r)(∫Vε(r)|Epl,j|2d3r) \\ (0≤Ci,j≤1), \end{gathered}$$(5.1)which captures both spatial and phase coherence between the two fields. This mode-overlap approach is widely used in coupled-mode theory to estimate modal interactions and coupling parameters, providing physically meaningful insight into hybridization and coherence phenomena^[398]. The coherence area Acoh is then defined as Acoh=πrcoh2,(5.2)where rcoh is the maximum pairwise distance between nanostructures i and j for which Ci,j(ω)≥Cth holds, with Cth being a predefined coherence threshold (e.g., 0.5). This definition implies that within Acoh, nanostructures remain phase-locked via the shared cavity mode.

Importantly, the coherence factor Ci,j(ω) not only characterizes the degree of collective synchronization but also determines the strength of light–matter interaction via its influence on LDOS. Specifically, higher Ci,j implies stronger spatial and phase alignment of the plasmonic and cavity fields, which reduces the effective mode volume Veff and enhances the Purcell factor Fp∝Q/Veff. This enhancement in LDOS leads to increased radiative decay rates Γrad, thereby directly impacting quantum efficiency metrics. The concept of coherence area is schematically illustrated in Fig. 25, where its role in governing device performance is emphasized. As discussed in Sec. 5.4, this coherence area significantly affects not only the external quantum efficiency (EQE), which is primarily dictated by optical absorption, but also the IQE and AQE, which reflect carrier extraction and energy conversion efficiency.

As an additional remark, beyond uniform FP stacks, gradient-thickness distributed Bragg reflector (DBR) cavities realize a spatially programmable detuning landscape, Δ(x,y), for the same coupled-mode physics discussed above. By imparting a controlled thickness wedge to the DBR, the local cavity resonance is swept in-plane, enabling on-chip mapping of anti-crossings, continuous tuning of the phase-sensitive overlap C, and multi-resonant high-Q responses without device-to-device variation. Such gradients therefore offer a complementary route to engineer coherence area, dwell time, and extraction pathways in cavity-assisted plasmonic systems^[399].

Taken together, these results demonstrate that embedding plasmonic nanostructures in an optical cavity fundamentally transforms their coherence properties and enables collective phenomena that greatly improve energy conversion efficiency. The interplay of cavity-induced delocalization, modal hybridization, and spatial coherence provides new avenues for the design of plasmonic devices for enhanced HCG, sensing, and nonlinear optics.

To interpret the experimental findings presented in the previous subsection—particularly the nontrivial dependence of quantum efficiency and spectral response on structure and density—it is essential to develop a microscopic theory capturing the effects of coherent mode hybridization and nonlocal energy redistribution. Recent theoretical frameworks^[79,282] account for both near-field dipole–dipole interactions and long-range cavity-mediated coupling among plasmonic nanodisks.

Figure 25 summarizes the key concepts and computational results. In the absence of a cavity [Fig. 25(A)], only short-range near-field coupling exists, which restricts Acoh to a very small spatial extent. Introducing an FP cavity [Fig. 25(B)] creates an additional delocalized photonic mode, which couples to more nanodisks and extends Acoh. This results in new hybridized modes with spatially extended phase coherence, providing a pathway for cooperative energy conversion and more efficient HCG.

The coupled system can be described by a Hamiltonian that includes localized plasmon, cavity, and electron–hole excitations, as well as their interactions (see Eqs. (1)–(4) in Ref. [282]). Dissipative dynamics and quantum efficiency are modeled using a quantum master equation formalism. The calculated absorption spectra with and without cavity [Figs. 25(C) and 25(D)] reproduce spectral shifts and key experimental and FDTD trends, showing the deviation from the conventional N-scaling of Rabi splitting widths [Figs. 25(E-a) and 25(E-b)]. Notably, the mechanism of AQE enhancement [Fig. 25(E-c)] can be interpreted as follows. In the absence of a metal film, the cavity cannot support extended coherence areas, resulting in uniformly low AQE regardless of nanodisk density. In contrast, when a metal film is present, the cavity facilitates the formation of a large coherence area. At high densities, where multiple Au nanodisks fall within a single coherence area, a quantum “antenna effect” emerges: the collective mode can concentrate the population on specific Au nanodisks that, due to structural fluctuations, happen to exhibit both strong damping and high hot-carrier injection efficiency [Figs. 25(E-d) and 25(E-e)]. This coherence-assisted population concentration leads to a marked increase in AQE.

These results provide a microscopic rationale for how cavity-mediated coherence and collective plasmonic effects can overcome the intrinsic limitations of isolated nanostructures. Indeed, several recent studies have reported novel applications of plasmon–cavity strong coupling systems. Examples include the realization of ultrastrong coupling between plasmonic nanoparticles and cavity photons under ambient conditions^[260], aiming at room-temperature operation of quantum photonic devices; the enhancement of water oxidation reactions via plasmon–nanocavity coupling^[400]; and the demonstration of spatially uniform and quantitative surface-enhanced Raman scattering that overcomes structural inhomogeneity^[401]. These advances highlight the rapid expansion of strongly coupled plasmonic systems across diverse fields, ranging from quantum science to chemical reactivity. Furthermore, they suggest that coherent engineering of light–matter interactions is a promising strategy for advancing plasmonic energy conversion, photodetection, and nonlinear optical technologies.

Beyond the limitations of classical near-field enhancement, a growing body of applied research has focused on controlling quantum interference and coherent coupling of LSPRs in spatially separated metallic nanostructures. These advances have expanded the functional scope of plasmonic devices and established plasmonics as a widely discussed theme across multiple academic disciplines. Recent theoretical and experimental efforts have increasingly integrated core concepts from modern condensed matter physics—such as topology, chirality, and moiré superlattices—drawing significant attention from the broader nanophotonics community. In what follows, we highlight three major categories of these developments: topological plasmonics, chiral plasmonic crystals, and plasmons in moiré superlattices. Figure 26 offers a visual summary of representative state-of-the-art experimental achievements in each domain and serves as a guide to the subsequent discussion.

Topological plasmonics has established that engineered plasmonic nanostructures can emulate the behavior of electronic topological insulators by supporting symmetry-protected edge states. Early theoretical work by Ling et al.^[190] introduced a diatomic chain of metallic nanoparticles based on the SSH model, in which inversion symmetry breaking opens a bandgap that supports topological edge modes. Subsequent works, including Gao et al.^[402], demonstrated robust edge mode propagation in designer plasmonic lattices, revealing their resilience to disorder due to topological protection. Downing and Weick^[403] and Pocock et al.^[191] clarified the persistence of topological gaps and edge states under collective quantum and electrodynamic interactions. More recently, Ghosh et al.^[404] proposed plasmonic “meron” lattices with nontrivial near-field winding, and Moritake et al.^[91] developed far-field imaging techniques to directly visualize topological edge resonances.

Two experimental realizations that exemplify these principles are presented [see Figs. 26(I-A) and 26(I-B)]. Sinev et al.^[405] demonstrated the near-field visualization of a plasmonic topological edge mode in a zigzag chain of gold nanodisks [see Fig. 26(I-A)]. A schematic of the structure under linearly polarized illumination is shown [see Fig. 26(I-A-a)], with the corresponding SEM image inset. The broken inversion symmetry of the chain enables the formation of a localized edge state. Near-field maps under x- and y-polarized light are presented [Figs. 26(I-A-b) and 26(I-A-c)], showing clear localization of the edge mode only for x-polarization. This selective excitation is corroborated by the spectral intensity profiles at the chain edge [Figs. 26(I-A-d) and 26(I-A-e)], where a sharp resonance appears under x-polarization but is suppressed under y-polarization. These results provide spatially and spectrally resolved evidence for topological edge mode formation in plasmonic systems.

Saito et al.^[406] proposed a distinct platform for detecting such edge modes in the far field [see Fig. 26(I-B)]. This structure—termed a valley plasmonic crystal—consists of an array of alternating-diameter aluminum nanopillars on a SiO2 spacer above a silver substrate [see Fig. 26(I-B-a)]. The designed inversion asymmetry supports valley-polarized edge modes at the boundary of the structure. To enable far-field observation, a grating coupler (GC) is introduced to convert otherwise nonradiative modes into radiative ones [see Fig. 26(I-B-b)]. Experimental CL kx–energy maps measured without and with the GC are presented [see Fig. 26(I-B-c)], revealing that the edge mode becomes observable only when the GC is present. This design underscores the importance of momentum matching and structural engineering in making topological plasmonic states accessible in the far field.

Chirality in plasmonic systems has emerged as a powerful strategy to break mirror symmetry and enable enantioselective or polarization-sensitive control of light–matter interactions. Gansel et al.^[411] introduced gold helical metamaterials that act as broadband circular polarizers by virtue of their structural chirality. Fan and Govorov^[412] demonstrated that chiral plasmonic assemblies can exhibit giant CD through near-field electromagnetic enhancement. Hentschel et al.^[413] realized three-dimensional chiral oligomers with tunable optical activity, while Valev et al.^[332] systematically reviewed the relationship between symmetry and optical chirality.

Li et al.^[407] leveraged hot-electron generation in chiral metamaterials for direct CPL detection, demonstrating a functionality that couples structural chirality with carrier extraction. More recently, Manoccio et al.^[414] introduced chiral surface lattice metacrystals with sharp, tunable CD features, and Guo et al.^[415] generalized the mechanisms of CD in periodic metallic structures via Bloch-like SPPs.

Beyond far-field chiroptical scattering, a representative hot-carrier-assisted CPL detector is shown in Fig. 26(II-A), following Li et al.^[407]. The device integrates a chiral plasmonic metamaterial, a dielectric spacer, and a metallic back reflector [Figs. 26(II-A-a) and 26(II-A-b)], so that nonradiative plasmon decay generates nonthermal electrons that surmount (or tunnel through) the interfacial barrier into the semiconductor. Because the near fields are chirality enhanced, the handedness of illumination sets both the sign and magnitude of the photocurrent dissymmetry. Consistent with this mechanism, Figs. 26(II-A-c)–26(II-A-e) shows CD spectra and polarization–resolved photoresponsivity under left- and right-circularly polarized (LCP/RCP) light, confirming selective HCG linked to optical chirality. Related demonstrations report robust CPL discrimination without external polarizers^[407,416]. Typical devices achieve sizable g-factors and high responsivity at room temperature, underscoring device-level viability of hot-electron chiral photodetection.

Spin-sensitive SLRs in 3D chiral metasurfaces were reported by Goerlitzer et al^[408] [Fig. 26(II-B)]. The unit cell, a 3D chiral crescent, is shown in Fig. 26(II-B-a) and assembled into a periodic lattice in Fig. 26(II-B-b). Side-view SEM images [Fig. 26(II-B-c) and 26(II-B-d)] confirm fabrication fidelity, and differential transmission (ΔT) under LCP/RCP illumination [Fig. 26(II-B-e)] reveals opposite spectral signatures corresponding to distinct chiral SLRs.

A third frontier in coherent plasmonics arises from the interplay between moiré superlattices and plasmonic excitations in two-dimensional (2D) materials, especially graphene. Grigorenko et al.^[417] first established the potential of graphene for deep subwavelength plasmon confinement, leveraging its tunable conductivity and atomic thinness. Building on this, Yeung et al.^[409] demonstrated that lithographically patterned graphene can support far-infrared plasmonic crystals, introducing periodic modulation to engineer plasmon dispersion.

Yeung et al.^[409] realized graphene plasmonic crystals (GPCs) by patterning periodic nanostructures into monolayer graphene, enabling far-infrared spectral modulation. Their experimental setup [see Fig. 26(III-A-a)] consists of multiple patterned regions with different lattice constants on a SiO2/Si substrate. The extinction spectra measured by FTIR spectroscopy [see Fig. 26(III-A-b)] show that while unpatterned graphene exhibits a broad absorption profile, the patterned GPCs display sharp, periodic plasmonic resonances. These features originate from plasmonic band formation driven by spatial modulation, demonstrating the viability of using patterned 2D materials to engineer dispersive plasmonic modes.

Xiong et al.^[410] developed a graphene photonic crystal by placing a graphene monolayer, encapsulated in hexagonal boron nitride (hBN), atop a periodic array of SiO2 nanopillars. The resulting periodic strain and doping modulations create hexagonally modulated carrier-density domains separated by artificial domain walls [see Fig. 26(III-B-a)]. A gold antenna launches plasmons across this modulated landscape [Fig. 26(III-B-b)]. Simulated LDOS maps reveal the presence of distinct upper and lower plasmonic bands [see Fig. 26(III-B-c)], which are spatially resolved in near-field imaging under various gate voltages [see Fig. 26(III-B-d)]. These real-space images highlight the emergence of gate-tunable domain-wall plasmons and the reconfiguration of plasmonic states under electrostatic control.

Together with related developments—including miniband plasmon observations in twisted bilayers^[418], photonic crystal band engineering ^[419], nonreciprocal transport from band hybridization^[420], and chiral or topological plasmon states in twisted systems^[421–423] —these studies mark a shift from conventional local-field-based designs toward phase-encoded, symmetry-protected, and miniband-engineered plasmonic functionalities. The moiré-based approaches illustrate the versatility of 2D materials in sculpting quantum coherence at the nanoscale. Whether through topological design, chirality, or superlattice-induced minibands, they offer a new paradigm for nanoscale light manipulation, quantum sensing, and reconfigurable plasmonic circuitry.

In summary, recent advances in topological, chiral, and moiré-engineered plasmonic systems collectively point toward a paradigm shift from traditional local-field-based plasmonics to coherence-driven, symmetry-protected, and band-structured architectures. By harnessing topological invariants, structural chirality, and miniband engineering, these approaches provide powerful new degrees of control over light at the nanoscale. This evolution not only deepens our fundamental understanding of quantum coherence and nonlocal effects in nanophotonics, but also opens promising avenues for reconfigurable photonic devices, quantum sensing, and energy-efficient signal processing based on designer plasmonic states.

This section has traced the conceptual and technological evolution of coherence in plasmonic nanostructures, emphasizing its central role in shaping next-generation nanophotonics. Section 5.1 recapitulated the classical picture where field enhancement in subwavelength hot spots underpins nonlinear optics and HCG via Landau damping. However, such enhancement is fundamentally limited by geometric constraints and nonlocal quantum effects.

To overcome these limitations, Sec. 5.2 introduced the quantum framework of plasmon hybridization and Fano interference. These mechanisms enable tunable spectral control and engineered mode structures that go beyond classical dipolar interactions, allowing coherence to manifest through interference and modal symmetry. Lattice plasmon resonances further extended coherence into spatially ordered arrays with narrow linewidths and collective behaviors.

Section 5.3 highlighted how embedding metallic nanostructures in optical cavities transitions plasmonic modes into a regime of strong light–matter coupling. The resulting polaritonic modes exhibit extended phase coherence and modified radiative properties, opening avenues for room-temperature quantum optics and enhanced energy conversion.

Building on this, Sec. 5.4 revealed a crucial and previously underappreciated role of cavities: not only enabling plasmon–exciton coupling, but also mediating coherent interactions between plasmonic elements themselves. This cavity-induced amplification creates coherence domains spanning multiple nanostructures, leading to nonlocal excitation energy redistribution and efficiency enhancements in HCG. These insights underscore the importance of treating the cavity as an active mediator in collective plasmon dynamics.

Section 5.5 surveyed recent frontiers that leverage such coherence domains, including superradiant emitter arrays, topological edge states, chiral plasmonic crystals, and moiré superlattices. These platforms utilize symmetry-protected or geometrically controlled coherence to achieve robust photonic functionalities and novel regimes of light–matter interaction.

Taken together, the studies presented in this section establish a unified narrative: plasmonic coherence is no longer confined to isolated structures or local field enhancements. Instead, it emerges as a tunable, spatially extended, and cavity-amplified property that enables cooperative phenomena and quantum functionalities. This transformation in understanding lays the groundwork for subsequent sections, where we systematically examine how coherence between plasmons and internal excitations can be harnessed for efficient hot-carrier extraction, energy transport, and quantum photonic device architectures.

The quest to understand and harness HCG in plasmonic systems has been one of the most vigorously pursued topics in nanophotonics and optoelectronics. Traditionally, the standard framework has been based on the concept of Landau damping, where the decay of LSPRs in metallic nanostructures results in the generation of energetic, non-equilibrium electron–hole pairs, i.e., “hot carriers”. This process, dominated by the longitudinal (L) electric field components, has formed the foundation for interpreting phenomena in plasmon-assisted photovoltaics, photodetection, photocatalysis, and quantum devices. However, this canonical picture assumes a one-way, incoherent transfer of energy from collective plasmonic oscillations to individual electron–hole excitations.

Historically, the photon-energy dependence of IQE—the number of hot carriers generated per absorbed photon—has been interpreted using internal photoemission theory, particularly Fowler’s analysis^[424,425]. This classical theory considers the thermionic emission of electrons over a Schottky barrier and leads to the scaling IQE(ℏω)∝Θ(ℏω−ΦB)(ℏω−ΦB)2ℏω,(6.1)where ℏω is the photon energy and ΦB is the Schottky barrier energy.

White et al.^[426] and Zhang et al.^[427] extended this framework by incorporating plasmonic effects. Specifically, they combined Fowler’s photoemission model with carrier generation via Landau damping to interpret IQE in plasmonic nanostructures. White adopted a phenomenological approach in which plasmon decay acts as a non-equilibrium excitation source for hot electrons, and applied a modified Fowler model to fit experimental IQE spectra. In contrast, Zhang et al. developed a more microscopic, material-specific theory based on energy- and momentum-resolved carrier distributions arising from plasmonic Landau damping. Zhang’s model accounts for band structure, transition probabilities, and interfacial transport, enabling quantitative prediction of IQE limits across different metals and device geometries.

However, recent experiments have revealed systematic deviations from this classical picture. In many systems, the observed IQE spectra cannot be explained by models based solely on Landau damping driven by L fields. These findings point to the limitations of the conventional view and suggest that additional mechanisms—possibly involving more fundamental, coherent coupling between plasmons and internal electron–hole pairs, i.e., carrier excitations in the metal—may be involved. They underscore the need for a conceptual shift toward a new framework that goes beyond Landau damping.

Before turning to the main subject of this section—coherent coupling between plasmons and internal electron–hole pairs—we first provide a brief overview of the conventional understanding of HCG, along with its associated techniques and applications, as well as the theoretical framework based on Landau damping, which will be discussed in more detail in the following section.

Plasmon-induced HCG was first demonstrated by Tian and Tatsuma in 2004^[428], who showed that plasmon excitation in gold nanoparticles supported on TiO2 can drive interfacial photoelectrochemical reactions. Since then, a broad range of applications have emerged that exploit the ability of plasmons to convert visible to near-infrared photons into energetic charge carriers.

In recent years, substantial efforts have been directed toward deepening the microscopic understanding of HCG processes. A central objective of these foundational studies is to clarify the mechanisms of carrier excitation, relaxation, and transport, which underpin the macroscopic energy conversion functionalities observed in plasmonic systems. For instance, Yu et al.^[429] quantitatively analyzed the energy distributions of hot carriers at metal–semiconductor interfaces, revealing how interfacial design influences carrier injection efficiency and spectral selectivity. Tagliabue et al.^[430] employed ultrafast spectroscopy to demonstrate that hot-hole injection dynamically modulates the behavior of hot electrons, emphasizing the critical role of carrier–carrier interactions. In parallel, Hattori et al.^[431] identified phonon-assisted indirect transitions as a significant contributor to HCG in plasmonic semiconductors, highlighting the role of lattice dynamics in non-equilibrium carrier excitation. Recognizing the growing complexity of the underlying physics, Lee et al.^[373] provided a comprehensive framework summarizing the key mechanisms for HCG and detection, helping to bridge experimental and theoretical perspectives. Advances in time- and energy-resolved probing methods have further enriched the field. Kim and Yoon^[432] introduced a photoelectrochemical approach capable of extracting both spectral and temporal characteristics of hot carriers with high precision. Finally, Lee et al.^[433] demonstrated that hot-hole transport in plasmonic Schottky junctions can be dynamically reconfigured by electrical polarity control, paving the way for tunable HCG-based electronic functions.

These studies illustrate that HCG remains an active area of fundamental research, with many microscopic aspects of carrier excitation and transport still under investigation. Ongoing efforts continue to refine our understanding of HCG and to establish its relevance across diverse material systems and device architectures. Importantly, these foundational insights are not purely academic—they increasingly inform applied strategies for harnessing hot carriers in practical contexts.

In what follows, we survey four major application domains in which plasmon-induced HCG plays a central role, each corresponding to a distinct energy conversion pathway: photon emission, phonon generation, electron extraction, and chemical reaction. For each category, we present representative studies that demonstrate how progress in fundamental understanding has facilitated advancements in device concepts and functionalities—from early proof-of-principle demonstrations to more recent realizations that exploit increasingly refined physical mechanisms.

Plasmonic nanostructures can generate light through radiative recombination of hot carriers, either optically or electrically excited. Cho et al.^[438] investigated photon emission in silicon-coupled plasmonic architectures, observing near-infrared luminescence. Cai et al.^[439] systematically characterized spontaneous emission from gold nanorods, while Ostovar et al.^[440] emphasized the role of intraband transitions in enhancing upconverted photon yield. A particularly notable development was reported by Cai et al.^[441], who demonstrated anti-Stokes photon emission driven by hot carriers in a plasmonically active system. In addition to optical excitation, Cui et al.^[434] demonstrated that hot-carrier luminescence can be driven entirely by electrical bias in a plasmonic tunnel junction. The device consists of a gold nanowire electromigrated to form a narrow tunneling gap, across which inelastic tunneling electrons excite LSPs [Fig. 27(I-A)]. These plasmons decay into nonthermal populations of hot electrons and holes, which can radiatively recombine, producing photon emission even without optical pumping [Fig. 27(I-B)]. The emission characteristics under different bias conditions are summarized in Figs. 27(I-C-a)–27(I-C-c). In the high-conductance regime, the spectrum exhibits a smooth broadband tail that extends below the energy threshold defined by eV [Fig. 27(I-C-b)], while in the low-conductance case, a sharp cutoff appears at eV, consistent with energy-conserving hot-carrier recombination [Fig. 27(I-C-c)]. The measured broadband spectrum under 1.0 V bias confirms the nonthermal nature of the luminescence process [Fig. 27(I-C-a)].

These findings, taken together, demonstrate that hot-carrier-mediated photon emission constitutes a versatile and evolving modality within plasmonic nanostructures. By enabling broadband, nonthermal, and even upconverted light emission, these mechanisms offer promising routes toward integrated nanoscale light sources, quantum emitters, and spectrally tunable photonic components. As understanding of carrier dynamics and energy transfer improves, such systems are poised to play an increasingly central role in active nanophotonic device architectures.

Plasmon-induced heat generation, or photothermal conversion, typically results from the nonradiative decay of plasmons and can drive lattice vibrations (phonons) in nanostructured systems. In the early stages of HCG research, El-Sayed et al.^[442] explored photothermal effects in the biomedical domain, employing Au nanoparticles to achieve localized heating for targeted cancer therapy. Kamarudheen et al.^[443] quantitatively distinguished between the contributions of photothermal heating and hot-carrier effects during nanoparticle synthesis. Chen et al.^[444] provided a comprehensive review of plasmonic platforms designed for efficient light-to-heat conversion across a broad range of materials and geometries.

More recently, a distinctive application of plasmon-induced heat has been reported by Linghu et al.^[435], who demonstrated that hot-carrier-mediated photothermal gradients can launch lattice vibrations (phonons), which in turn drive mechanical motion. Their system consists of gold nanowires placed on suspended silica microfibres, where pulsed laser illumination excites SPPs along the nanowire, resulting in localized temperature gradients [Fig. 27(II-A-a)]. These gradients generate surface acoustic waves (SAWs)—coherent phonons—that propagate along the microstructure, ultimately inducing directional displacement of the nanowire. Optical images in Figs. 27(II-A-b)–27(II-A-d) reveal that this motion is wavelength-dependent: under 532 nm excitation, weak SPP coupling leads to leftward drift, while 1064 nm excitation, which better matches the SPP resonance, causes rightward motion due to enhanced thermal asymmetry. Simulations in Fig. 27(II-B-a) show that this asymmetry originates from strongly confined electric fields. The driving mechanism is modeled in Fig. 27(II-B-b): localized thermal expansion at the nanowire front increases contact friction, enabling a peristaltic crawling motion. This motion is confirmed experimentally in Fig. 27(II-B-c), where time-lapse images reveal repetitive displacement synchronized with the laser repetition rate.

Collectively, these studies establish phonon generation via plasmon-induced photothermal processes as a functional energy conversion pathway in nanostructured systems. By coupling localized heating with lattice vibrations, such mechanisms enable precise thermal control and mechanical actuation at the nanoscale. Continued exploration of this phonon-mediated channel holds promise for applications in nanoscale heat regulation, acoustic wave engineering, and opto-mechanical transduction.

Plasmon-induced hot carriers can be extracted across metal–semiconductor interfaces to generate photocurrent, enabling direct electrical readout of plasmonic energy conversion. Knight et al.^[445] reported hot-carrier photodetection using plasmonic optical antennas. Narrowband detection with spectral selectivity was achieved by Knight et al.^[446]. Sistani et al.^[447] demonstrated hot-electron transfer at atomically sharp metal–semiconductor nanojunctions.

Konov et al.^[436] proposed a novel photodetector architecture that leverages Tamm plasmon polaritons (TPPs), hybrid interface modes between a metal and a Bragg mirror, to enhance hot-electron generation in the near-infrared region. The device consists of a titanium thin film deposited on a semiconductor multilayer stack, designed to support TPP modes at specific wavelengths [Fig. 27(III-A)]. Simulated absorption maps show how the difference between absorptance and transmittance depends on the metal layer thickness and incident photon energy [Fig. 27(III-B)], revealing optimal geometric parameters for maximizing absorption at the TPP resonance. The resulting optical properties of the structure are summarized in calculated reflectance, transmittance, and absorptance spectra using transfer matrix methods [Fig. 27(III-C)]. A pronounced absorption peak emerges at the TPP frequency, indicating strong field confinement and enhanced interaction with hot carriers. Importantly, this enhanced absorption translates into improved photodetection performance, as evidenced by the photosensitivity spectrum [Fig. 27(III-D)], which shows a narrowband peak aligned with the TPP resonance and is supported by both transfer-matrix simulations and temporal coupled-mode theory. These results highlight the utility of engineered plasmonic resonances in creating spectrally selective hot-carrier photodetectors that go beyond conventional broadband designs.

These results exemplify how resonant field confinement and interface optimization can significantly enhance hot-electron generation and extraction. Such strategies enable narrowband, spectrally selective photoresponse, and offer a general design framework for developing wavelength-tunable photodetectors and on-chip energy harvesting elements in plasmonic optoelectronic systems. For clarity, the efficiency gains discussed here do not imply reduced intrinsic electron–electron or electron–lattice scattering rates; with the dielectric function of the resonators unchanged, these material scattering rates are treated as fixed. Rather, improvements arise from optical and transport engineering—redistributing absorption into nonradiative channels near the extraction interface, increasing local field intensity and dwell time at the hotspot, and optimizing barrier/contact geometry to shorten the extraction path and raise the transmission probability before rethermalization.

As an outlook linking electrical readout to chemical function, we note that hot carriers in plasmonic/semiconductor (or plasmonic/catalyst) hybrids support two representative application lines. First, chiral photodetection: circularly polarized light can produce differential hot-electron extraction through chiral near fields, yielding handedness-dependent responsivity (cf. Fig. 26(II–A)). Second, photochemistry under weak, broadband illumination: nonradiative plasmon decay injects energetic carriers that drive surface reactions, enabling earth-abundant catalysts and steering selectivity beyond thermal limits; for example, LED-driven plasmonic photocatalysis achieves efficient H2 generation from NH3 using nonprecious materials^[448]. From a design standpoint, key control parameters are the interfacial alignment (Schottky barrier height), the mode volume Veff that governs hot-carrier yield, and the balance of dissipation channels that sets thermal vs. nonthermal contributions; see recent reviews for materials choices and metrics to identify true hot-carrier action^[449].

Plasmon-induced hot carriers can drive chemical transformations, forming the basis for photocatalysis and photoelectrochemistry. Mubeen et al.^[450] developed an autonomous plasmonic photosynthetic device. Ueno et al.^[451] provided a broad overview of plasmon-induced photocatalysis and photoelectrochemistry. DuChene et al.^[452] focused on hot-hole collection for CO2 reduction.

Dey et al.^[437] developed a plasmon-assisted photoelectrocatalytic platform that harnesses hot electrons for hydrogen evolution. The device architecture integrates a plasmonic gold layer with a NiO extraction layer and a co-catalyst, forming a heterostructure optimized for hot-carrier transfer and catalytic efficiency [Fig. 27(IV-A)]. Chronoamperometric measurements under visible-light illumination demonstrate a clear enhancement in photocurrent during light exposure [Fig. 27(IV-B)]. The inset highlights further improvement upon the addition of acetic acid as a hole scavenger, verifying that hot-hole removal enhances net electron-driven catalysis. To probe the temporal response, the photocurrent was measured under modulated illumination [Fig. 27(IV-C)]. The observed decay in signal amplitude ΔI at higher modulation frequencies reflects the finite lifetime of the involved carriers and the timescale of interfacial transfer processes. Transient absorption spectroscopy data collected after plasmon excitation reveals differences among Au, NiO/Au, and NiO/Au/co-catalyst systems [Fig. 27(IV-D)]. The full heterostructure exhibits the slowest decay, indicating prolonged carrier retention. This demonstrates that the combination of plasmon excitation and selective charge extraction leads to more efficient utilization of hot carriers in driving chemical reactions.

Taken together, these studies highlight the growing potential of hot-carrier-driven chemical transformations as a versatile platform for light-assisted catalysis and charge-transfer chemistry. By combining plasmonic field enhancement with tailored interfacial architectures, researchers have demonstrated both autonomous and externally biased systems capable of driving redox reactions, including CO2 reduction and hydrogen evolution. As control over carrier dynamics and extraction pathways continues to advance, plasmon-enhanced catalytic strategies are expected to play an increasingly central role in sustainable energy conversion, environmental remediation, and nanoscale synthetic chemistry.

In this subsection, we briefly review the theoretical foundations of HCG rooted in the Landau damping framework. Figure 28 provides a structured overview of the theoretical approaches developed to understand HCG in plasmonic systems. It is divided into three columns corresponding to (I) phenomenological relaxation models, (II) hydrodynamic theories incorporating nonlocal effects, and (III) first-principle simulations based on DFT and TDDFT. Each subfigure, labeled from Fig. 28(I-A) to Fig. 28(III-C-c), corresponds to representative findings from key studies, which are discussed below.

The mechanism proposed by Govorov et al.^{[278,279,461]} is based on a phenomenological relaxation picture. In this framework, optically excited LSPs generate electron–hole pairs incoherently through a nonradiative decay channel characterized by a relaxation constant γhot−electrons, corresponding to Landau damping. Other loss mechanisms such as interband transitions and Drude damping are excluded from this specific channel. This conceptual model forms the basis for describing HCG via plasmon decay in early theoretical studies [Fig. 28(I-A)]. The numerical foundation for this mechanism was developed by Zhang and Govorov in 2014^[461] and later extended by Besteiro et al. in 2017^[279]. The calculated hot-electron generation rates for Au nanospheres of different diameters show how spectral features depend on both energy and particle size [Fig. 28(I-B-a)]. A comparison between low- and high-energy electron generation in Au and Ag nanocrystals reveals that material composition strongly influences carrier distributions [Fig. 28(I-B-b)]. The associated energy dissipation for each spectral component shows that high-energy carrier generation entails greater plasmonic losses [Fig. 28(I-B-c)]. These results collectively highlight that both carrier yield and energetic efficiency are enhanced by larger plasmonic volumes, although subject to material-dependent limitations. In 2019, Chang et al.^[462] further demonstrated that such trends are fundamentally limited by the underlying band structure of the metal, where interband transitions impose intrinsic constraints on hot-carrier energy extraction.

The second column (II) introduces hydrodynamic and nonlocal theoretical approaches for describing spatially dispersive dielectric responses in plasmonic systems. In 2013, Luo et al.^[463] demonstrated that introducing spatial dispersion into the dielectric function leads to size-dependent blueshifts in plasmon resonance energies, particularly in nanoparticles with sub-10-nm dimensions. In 2014, Mortensen et al.^[80] and Christensen et al.^[464] formalized this behavior by establishing a generalized nonlocal optical response (GNOR) model that incorporates charge diffusion into the hydrodynamic Drude framework. This approach is illustrated in schematic form [Fig. 28(II-A-a)], where a metallic nanoparticle of radius R exhibits experimentally observed resonance shifts and damping as its size decreases. Nonlocal effects in coupled systems are depicted via nanowire dimers separated by a gap g, which exhibit gap-dependent spectral broadening and hybridized resonance shifts [Fig. 28(II-A-b)]. To account for these trends, the GNOR model introduces a diffusion mechanism for surface charge redistribution, as represented by the temporal spreading of an initial surface charge B0 into the particle volume [Fig. 28(II-A-c)]. Experimental validation of nonlocal optical effects was demonstrated by Shen et al.^[453]. A 2D monolayer superlattice composed of ultrasmall Au nanoparticles on a quartz substrate is schematically shown [Fig. 28(II-B-a)]. The resonance positions of the experimental transmission spectrum (black dots) are overlaid on a simulated color map based on the Drude–Lorentz model, plotted as a function of particle diameter [Fig. 28(II-B-b)]. Transmission spectra derived from experiment (top), classical theory (middle), and a nonlocal model (bottom) reveal that only the nonlocal theory captures the observed shifts in spectral dip position across nanoparticle sizes [Fig. 28(II-B-c)]. Until recently, hydrodynamic theories primarily addressed macroscopic manifestations of nonlocality—such as resonance blueshifts and damping—arising from spatially dispersive permittivity. However, more recent developments have extended this framework toward microscopic carrier dynamics relevant for HCG. In 2023, Zhou et al.^[454] proposed the quantum hydrodynamic model (QHDM), a quantum mechanically extended variant of the traditional hydrodynamic Drude theory. QHDM incorporates gradient-corrected kinetic energy functionals and Bohm-like quantum pressure terms, enabling spatially resolved modeling of electron density oscillations near interfaces. Ground-state conduction electron density n0(x) near the surface of a 5-nm-thick metallic slab is plotted using both DFT (dashed line) and QHDM with varying λw,g parameters (solid lines) [Fig. 28(II-C)]. The deviation between QHDM and DFT results near x=0 highlights how surface-localized quantum pressure alters electron distribution. Such modulation is critical for accurately capturing the spatial profile and efficiency of HCG in confined plasmonic systems.

The third column (III) presents insights gained from first-principle simulations based on DFT and TDDFT. In 2014, Sundararaman et al.^[465] introduced a DFT-based approach to compute HCG rates using Fermi’s golden rule, establishing a foundational framework for electronic-structure-driven predictions. In the same year, Manjavacas et al.^[455] used real-time TDDFT to simulate carrier generation dynamics in silver nanoparticles modeled as finite spherical potential wells. The schematic configuration is shown [Fig. 28(III-A-a)], where the particle diameter D defines the spatial confinement of conduction electrons. Energy-resolved hot-carrier distributions are presented for electrons (red) and holes (blue) under different nanoparticle sizes (D=15 and 25 nm), revealing that both the carrier yield and spectral width depend sensitively on size and assumed lifetime parameters [Figs. 28(III-A-b) and 28(III-A-c)]. Jin et al.^[456] extended these analyses by computing hot-carrier spectra for a D=32nm silver nanoparticle under various illumination energies. Their results [Fig. 28(III-B)] show energy-resolved distributions of electrons and holes with two peaks: interband d→sp transitions at the d-band edge (yellow arrows) and surface-assisted intraband sp→sp transitions near the Fermi level (green arrows). This demonstrates that both bulk and surface channels contribute to HCG, with spectral features tunable by excitation energy. In 2015, Ma et al.^[457] employed real-time TDDFT to study the interplay between collective (plasmonic) and individual (single-particle) excitations in metallic nanoclusters. They considered a well-defined icosahedral Ag55 cluster, whose atomic structure and electronic levels are shown [Fig. 28(III-C-a)]. Their simulations revealed substantial differences between absorption spectra computed using TDDFT and ground-state DFT, underscoring the role of dynamical screening and configuration interaction [Fig. 28(III-C-b)]. Furthermore, the energy transfer from collective plasmon modes to single-particle excitations was explicitly tracked in time, highlighting distinct decay rates and nontrivial coherent dynamics across excitation channels [Fig. 28(III-C-c)].

In summary, the three approaches shown in Fig. 28 have each contributed uniquely to our understanding of hot-carrier physics. Phenomenological models enabled early predictions of size and shape effects; hydrodynamic models introduced the importance of spatial dispersion and successfully explained experimental deviations from local theory; first-principles simulations provided energy- and time-resolved insights grounded in quantum mechanics. However, with the partial exception of Ma et al.^[457], who went beyond the standard Landau damping picture but still restricted the analysis to longitudinal field interactions, all these theories treat HCG as a decay process mediated by the longitudinal electric field. As we discuss in the next section, this conventional paradigm is increasingly challenged by experimental results showing spectral anomalies that cannot be reconciled with Landau damping alone, suggesting the emerging need to consider new HCG mechanisms beyond the standard decay-based framework.

Section 6.3 discusses recent experimental studies on plasmon-assisted HCG, which have revealed spectral behaviors that cannot be explained by the conventional theory based on Landau damping. As a starting point, we draw attention to the results by Shi et al.^[78], previously discussed in Sec. 5.3 and shown in Figs. 24(I-E-a)–24(I-E-c). These panels compare the absorption spectrum [Fig. 24(I-E-a)], the incident photon-to-current efficiency (IPCE) spectrum [Fig. 24(I-E-b)], and the IQE spectrum [Fig. 24(I-E-c)], defined as IPCE normalized by absorption, for two structures: the cavity-coupled ATA configuration (green line) and the cavity-free AT configuration (black line). Remarkably, in both systems, the IQE spectrum exhibits a peak near the plasmonic absorption maximum—even in the strongly coupled ATA system, where the absorption splits due to cavity-plasmon hybridization. Such behavior was also observed in a similar experiment conducted by the same group using an Au-nanorods/TiO2 system^[466]. The fact that the IQE spectrum retains this peak structure, despite being normalized by absorption, cannot be explained by a Landau damping mechanism in which hot carriers are generated incoherently and independently of the excitation energy. The mystery of IQE underscores the need for a conceptual shift toward a new framework that goes beyond Landau damping.

In the following, we review a series of related experiments across different platforms, which report similar anomalies and reinforce this emerging picture.

Fang et al.^[395] investigated plasmon-enhanced internal photoemission (IPE) using an antenna–spacer–mirror (ASM) structure consisting of Au nanodisks on a TiO2 spacer and Au mirror [Fig. 29(I)]. The electrochemical cell schematic used to extract photocurrent under quasi-monochromatic excitation is shown [Fig. 29(I-A)]. The reflectance and IQE spectra for three different TiO2 spacer thicknesses are displayed. [Figs. 29(I-B-a)–29(I-B-c)] As the thickness increases, the spectral position of Fabry–Pérot cavity resonances (light blue dashed line) shifts, modulating both reflectance and IQE. These results indicate that the IQE response is not governed solely by the plasmonic absorption cross section but is instead shaped by the optical cavity environment. To probe the underlying mechanisms, near-field simulations were performed for structures with and without the Au mirror [Fig. 29(I-C)]. The presence of the mirror leads to standing-wave patterns and enhanced field localization, especially at cavity resonance wavelengths, resulting in a significant increase in absorption. This interference-driven enhancement demonstrates the role of hybridized optical modes in modulating carrier generation. Experimentally measured IQE spectra (black and green) are compared with two theoretical predictions: one based on DFT for a Au–TiO2 slab (red), and another using a modified Fowler law (thin line)^[424–427] [Fig. 29(I-D)]. The observed IQE exhibits spectral features that deviate significantly from both predictions, particularly near the hybridized resonance energies. Such deviations from Fowler’s law have also been observed in the IQE of plasmon-induced photoemission^[467]. These findings highlight the inadequacy of conventional photoemission models based solely on energy barriers and incoherent electron emission.

Tagliabue et al.^[458] emphasized the importance of quantitatively disentangling plasmonic absorption from the generation of hot carriers by analyzing the IQE in Au nanostripe arrays on GaN substrates [Fig. 29(II)]. The device architecture designed to probe hot-electron injection across the Schottky barrier is shown [Fig. 29(II-a)]. Under resonant excitation, the photocurrent increases linearly with incident power [Fig. 29(II-b)]. The EQE spectrum exhibits a clear resonance peak [Fig. 29(II-c)]. Spatial absorption maps reveal strong field localization at resonance [Fig. 29(II-d)]. As the stripe width increases, the plasmon resonance and EQE peak redshift accordingly, indicating structural tunability [Figs. 29(II-e) and 29(II-f)]. The IQE spectra, normalized by absorption, exhibit pronounced differences depending on stripe width [Fig. 29(II-g)]. This implies that the efficiency of hot-electron injection is not determined solely by absorption but is strongly modulated by modal field distribution and device geometry. In particular, the observed IQE spectra deviate from the predictions of conventional Fowler theory, especially near the visible regime. Tagliabue et al. identified that these deviations arise from the intrinsic electronic band structure of Au, which governs the energy-dependent generation and injection of hot electrons. Using parameter-free modeling based on DFT and Boltzmann transport calculations, they showed that for photon energies below the interband threshold (1.8 eV), hot electrons are predominantly generated via intraband transitions and can be ballistically injected across the Schottky barrier. Above this threshold, interband transitions dominate, leading to fewer high-energy electrons and a suppressed IQE, in stark contrast to Fowler’s parabolic-band predictions. Thus, the metal’s band structure, not plasmon resonance, fundamentally determines the spectral profile of the IQE. As a direct extension of this work, Tagliabue et al.^[468] investigated hot-hole versus hot-electron injection in Cu/GaN heterostructures.

Taken together, their series of studies underscores a broader message: for the rational design of efficient hot-carrier devices, it is essential to move beyond plasmon resonance alone and consider the type of carrier being injected (electrons or holes), the underlying band structure of the metal, and the chemical and electronic nature of the metal–semiconductor interface.

Rodio et al.^[459] examined a different system: Au nanoparticles (NPs) deposited on ITO electrodes [Fig. 29(III)]. The AuNP/ITO architecture used for photoelectrochemical measurements is depicted [Fig. 29(III-A)]. Simulations based on Mie theory yield the absorption cross section and surface-averaged field enhancement for a single nanoparticle, taking into account the dielectric environment [Fig. 29(III-B)]. Importantly, the inset shows the near-field intensity enhancement normalized by absorption, reinforcing the point that near-field strength and absorption are not trivially linked. Experimental photocurrent spectra normalized by absorbed power for two electrolytes are shown, with the dashed line indicating the corresponding optical absorption [Fig. 29(III-C-a)]. The discrepancy in spectral profiles again indicates that absorption alone cannot explain the photocurrent behavior. Photocurrent versus absorbed power for several excitation wavelengths is shown, with linear fits revealing distinct slopes—i.e., distinct internal efficiencies [Fig. 29(III-C-b)].

A recurring theme that emerges from these experimental results is that the spectral characteristics of IQE in HCG do not follow classical Fowler theory, yet consistently exhibit peak structures near the plasmon resonance wavelengths, as clearly shown in Figs. 29(I-D), 29(II-g), and 29(III-C-a). If HCG were governed solely by incoherent Landau damping—that is, the irreversible decay of plasmons into electron–hole pairs—then the resulting IQE spectra would tend to lack sharp, resonance-locked features, as in minimal Fowler-type descriptions that neglect band-structure and interface-specific transport. In practice, band structure and interfacial transmission already imprint moderate energy dependence; however, these effects alone generally do not enforce resonance-tracking peaks. This discrepancy underscores the growing limitations of treating carrier generation exclusively through longitudinal-field-mediated Landau damping. Of particular importance is the fact that in systems studied by Fang et al.^[395] and Shi et al.^[78], where plasmons strongly couple to optical cavity modes and exhibit energy splitting, the IQE spectra also display corresponding split peaks that track the split absorption modes. This behavior is not readily captured by band-structure-only interpretations such as that by Tagliabue et al.^[458], and instead suggests a framework—involving quantum interference between plasmons and charge carriers, mode hybridization and wavelength-selective generation/transport may play an important role. These considerations motivate theoretical frameworks that explicitly track mode-resolved, potentially coherent energy exchange between plasmons and internal electron–hole pairs, beyond a purely decay-based picture. In the next subsections, we propose a hypothesis that coherent coupling between collective excitations (plasmons) and individual excitations (electron–hole pairs), mediated by transverse (T) fields, may hold the key to resolving this puzzle of IQE spectrum.

As discussed in Sec. 6.2, conventional theories of HCG in metallic systems typically compute the electromagnetic field using a macroscopic dielectric function—such as the Drude model—which assumes a local response. (In contrast, hydrodynamic models do incorporate macroscopic nonlocality.) These models generally assume that the classical electromagnetic field externally modifies the energy distribution of internal excitations. However, such formulations neglect the microscopic nonlocality of the electronic response and fail to self-consistently capture the feedback between internal excitations and the electromagnetic field.

To overcome these limitations, Yokoyama et al.^[85] and Iio et al.^[86,87] developed a fully microscopic theory that treats both longitudinal and transverse components of the electromagnetic field, as well as individual electron–hole excitations, on equal footing. Their framework goes beyond the Drude approach by including nonlocal current responses and solving Maxwell’s equations self-consistently with the microscopic polarization response. This allows for the emergence of spontaneous radiative coupling between collective plasmon modes and individual excitations via transverse fields—a phenomenon inaccessible in conventional models.

Their analysis reveals that transverse-field coupling between plasmons and individual electron–hole excitations can lead to a pronounced redshift in the resonance energy of the coupled system under specific nanoscale geometries and interface conditions. This spectral shift signifies the emergence of new hybridized modes between plasmon and individual excitations, clearly demonstrating that transverse fields can mediate coherent coupling between collective and individual excitations—an effect that becomes particularly significant in nanoscale systems with interfaces.

This mechanism should be distinguished from Landau damping^[469], which describes energy transfer from plasmons to individual excitations through residual longitudinal Coulomb interactions. In the decay-based picture, hot carriers originate primarily from longitudinal interactions, whereas transverse radiative fields mainly set the optical excitation pathways; at the nanoscale and in hybrid cavities, however, transverse-field-mediated coherent coupling can feed back into the generation channels and reshape the spectra. Yamada^[470] rigorously confirmed that in bulk metals, Landau damping arises from longitudinal interactions not involved in plasmon formation. However, in systems with interfaces—such as nanoscale structures—plasmons can couple to external fields, and the role of transverse electromagnetic fields becomes non-negligible. This enables a new channel of interaction in which plasmons couple to individual excitations via transverse radiative fields, resulting in energy-level reorganization not captured by bulk theories. Such radiative coupling offers a fundamentally different pathway for HCG.

A related class of radiative phenomena—where coupling between different quantum states within a single material gives rise to spontaneous resonance—has been demonstrated in excitonic systems by Kinoshita et al.^[460]. Figures 30(A-a) and 30(A-b) show the wavefunctions of a bound exciton and delocalized excitonic states, respectively. Figure 30(B-a) presents the exciton energy levels as a function of film thickness without radiative correction, while Fig. 30(B-b) includes radiative effects. A significant shift in resonance levels due to radiative corrections is clearly observed. Figure 30(C) shows the absorption spectra of the bound exciton as a function of thickness. Although bound excitons inherently possess weak optical absorption, the results show that their absorption is significantly enhanced through spontaneous resonance with delocalized excitons. Figure 30(D) displays the reflectance ΔR and transmittance ΔT as functions of the nonradiative damping constant Γ for a fixed film thickness of d=452nm, providing further evidence of spontaneous resonance.

Such radiative resonance is also highly likely to occur in metallic systems. If experimentally validated, it would not only revolutionize our understanding of HCG mechanisms but also offer new design strategies for a wide range of plasmonic applications.

It is important to note, however, that in the formulation by Yokoyama et al., the electronic system is expanded solely on the basis of individual excitations, and plasmons are not treated as explicit, quantized internal degrees of freedom. As a result, while plasmons appear as resonance features in the spectral response, the coupling strength between plasmons and individual excitations cannot be explicitly separated into longitudinal and transverse components. This makes it difficult to directly compare with the longitudinal coupling responsible for Landau damping, and also hinders the strategic control of coupling enhancement via transverse fields—a key challenge in optimizing HCG.

To fully capture the physics of spontaneous resonance and to assess energy transfer between collective and individual excitations, it is essential to formulate a theoretical framework in which plasmons are treated as quantized internal modes, rather than merely spectral features. Such a framework would allow for explicit identification of the coupling components—longitudinal and transverse—and enable systematic comparisons with established mechanisms like Landau damping. The development of this approach represents a fundamental step toward a deeper, mode-resolved understanding of light–matter interactions in plasmonic systems. In what follows, we outline the physical motivation behind this strategy and describe its conceptual implications.

The importance of quantum mechanical treatment for the plasmonic degrees of freedom was highlighted in the preceding subsection. Historically, this quantum formulation of plasmons dates back to Bohm and Pines, who in 1953 formulated a theory of collective excitations in a degenerate “bulk” electron gas without considering coupling to transverse fields^[471]. Their seminal work demonstrated that the Coulomb interactions among conduction electrons give rise to quantized collective excitations—later named “plasmons” by Pines^[94]. Notably, Bohm and Pines constructed the electron Hamiltonian in a basis of both plasmonic and single-particle excitations, allowing for the treatment of residual interactions between these modes. This formalism paved the way for Yamada’s identification of Landau damping^[470] as a consequence of the residual coupling between plasmons and electron–hole pairs, rooted in the foundational work by Landau^[469].

However, subsequent developments in classical plasmonics departed from this microscopic framework. By assigning a macroscopic and local Drude dielectric function to the metal, and combining it with Maxwell or Poisson equations, collective modes were discussed without accounting for single-particle degrees of freedom^[472,473]. This effectively erased the quantum origins of plasmons, reverting them into coarse-grained macroscopic modes. Consequently, most classical treatments neglected electron–hole excitations and their nonlocal optical responses.

In recent years, discontent with this oversimplified treatment has fueled renewed interest in the quantum nature of plasmons. The emergence of “quantum plasmonics”^[474] marked a revival of this perspective, aiming to uncover genuinely quantum effects such as photon antibunching, plasmon blockade, and quantum interference. These studies are based on QED frameworks, where plasmonic modes are quantized analogously to cavity photons, albeit using macroscopic permittivities with losses. Some efforts have further pursued quantization of longitudinal fields alone, yielding “pure” plasmonic modes^[475], though the Drude model remains the underlying basis. In both cases, single-particle electronic degrees of freedom and their spatially nonlocal response are not explicitly incorporated.

To overcome the limitations of classical and semi-classical models, recent theoretical efforts have pointed to the need for a fully quantum framework in which both plasmons and electron–hole pair excitations are treated as quantized internal degrees of freedom. Within such a framework, the interaction between these modes is mediated not only by longitudinal Coulomb fields—responsible for conventional Landau damping—but also by transverse electromagnetic fields that enable frequency-dependent, coherent coupling. Unlike longitudinal interactions, which result in irreversible energy dissipation, transverse-field-mediated coupling introduces resonant and bidirectional energy exchange between collective and individual modes. This mechanism naturally accounts for the enhancement of IQE near plasmon absorption peaks, as observed in various experimental results discussed in Sec. 6.3. Furthermore, because the transverse coupling inherits the frequency selectivity of the radiative field, the spectral shape of IQE is predicted to faithfully follow changes in the plasmonic resonance structure. Therefore, in systems where LSPs strongly couple with optical cavities—such as those discussed in Sec. 5.3, where the absorption spectrum exhibits mode splitting—this theoretical framework implies that the IQE spectrum should exhibit a corresponding splitting.

Moreover, this unified theory allows the prediction and control of spontaneous resonances between plasmonic and individual modes^[85,460]. It thus opens new directions in the design of quantum plasmonic devices for efficient HCG and light–matter interaction engineering.

Recent experimental progress has further revealed the broad diversity and applicability of HCG. As summarized in Sec. 6.1, the functionalities enabled by plasmon-induced hot carriers can be categorized into four representative domains: (i) photoluminescence, (ii) photothermal effects, (iii) photoelectric conversion, and (iv) photochemical reactions. These representative systems demonstrate that the generation, transport, and extraction of hot carriers depend sensitively on device architecture, material interfaces, and excitation conditions. Moreover, factors such as mode selectivity, temporal response, and energy filtering emerge as essential considerations for both fundamental understanding and practical design of plasmonic energy conversion devices.

Theoretical models based on Landau damping have succeeded in capturing size-dependent behaviors and spatial nonlocality by employing phenomenological, hydrodynamic, or first-principles approaches. However, these models remain fundamentally limited by their reliance on longitudinal-field-mediated dissipation. As such, they cannot describe mode-resolved or coherent energy exchange between collective and individual excitations.

To overcome these limitations, recent microscopic theories have introduced transverse electromagnetic fields as mediators of coherent coupling between plasmons and electron–hole excitations. Notably, the self-consistent model developed by Yokoyama et al. revealed the possibility of spontaneous resonance restructuring through radiative feedback. However, this formulation relies exclusively on polarization expansions based on individual excitation modes and does not explicitly include plasmons as independent quantized degrees of freedom. As a result, it becomes difficult to disentangle the coupling constants between collective and individual modes, making quantitative comparison with Landau damping and precise analysis of energy transfer or coherence effects inherently problematic.

These theoretical limitations have led to the emergence of a unified quantum framework based on an extended Bohm–Pines theory that incorporates radiative interactions. In this formulation, both plasmonic and electron–hole pair excitations are treated as quantized internal degrees of freedom, and both longitudinal and transverse couplings are included self-consistently in a single Hamiltonian. This approach not only recovers Landau damping in the appropriate limit but also enables the description of coherent transverse-field-mediated phenomena such as spectral reshaping, spontaneous resonances, and energy-selective HCG.

Taken together, the experimental and theoretical developments surveyed in this section highlight the importance of a quantum-consistent treatment of plasmonic systems. The ability to describe collective and individual excitations on equal theoretical footing provides a robust foundation for analyzing non-equilibrium carrier dynamics and coherence phenomena at the nanoscale. Moving forward, the integration of this quantum framework with next-generation experimental techniques—featuring high temporal, spectral, and spatial resolution—is expected to advance the design of efficient energy conversion devices that harness plasmon-induced hot carriers through tailored quantum functionalities.

Over the past two decades, the field of plasmonics and nanophotonics has undergone a remarkable transformation, evolving from an early focus on field enhancement and local electromagnetic hotspots to a sophisticated, interdisciplinary discipline centered on quantum coherence, nonlocal coupling, and the hybridization of diverse excitations. This review has charted the maturation of both experimental and theoretical methodologies, elucidating how coherence now stands as a central organizing principle in nanoscale light–matter interactions.

Initially, advances in plasmonics were largely driven by the exploitation of intense local fields near metallic nanostructures, enabling breakthroughs in surface-enhanced Raman scattering, photothermal conversion, and molecular detection. As research entered the quantum and ultrafast domains, it became evident that maximizing field intensity or absorption alone could not account for, nor fully optimize, the rich phenomena emerging in nanostructured systems. Instead, recent years have revealed that coherence—encompassing both classical and quantum regimes—enables fundamentally new behaviors inaccessible to local-field or semiclassical models.

A major focus of recent work has been on hybrid and strongly coupled systems, wherein plasmonic modes interact with molecular excitons, quantum dots, or cavity photons to form new quasiparticles—including polaritons and plexcitons—with mixed light–matter character. These hybrid states exhibit Rabi splitting, ET, nonlinear optical response, and the potential for manipulating chiral and topological properties at the nanoscale. Chiral plasmonics and topological photonic bands, in particular, are extending the reach of coherent control into enantioselective chemistry, robust energy transport, and quantum information protection against disorder and decoherence.

Complementing this development is the emergence of advanced near-field imaging techniques—such as TEPL and PiFM—which have unlocked the ability to directly visualize quantum state symmetries and forbidden transitions at sub-nanometer resolution. Real-space quantum-state mapping provides experimental access to orbital, vibrational, and electronic structures, and highlights the critical roles of symmetry breaking, multipolarity, and coherence in nanophotonic phenomena. These capabilities have enabled both new discoveries in fundamental science and the design of functional molecular-scale devices for quantum information, catalysis, and ultrasensitive sensing.

A key conceptual advance has also been the demonstration that engineered plasmon–plasmon coupling among nanostructures gives rise to collective, delocalized modes and spatially extended coherence domains. These domains support nonlocal energy transport, facilitate efficient hot-carrier extraction, and enable phenomena such as modal interference, hybridization, and phase synchronization—all of which drive enhanced performance in photochemical and optoelectronic applications. Metasurfaces and nanostructure arrays, through precise modal engineering, have been shown to achieve robust quantum interference and collective effects that surpass the capabilities of isolated systems.

Finally, this review has highlighted the emerging theoretical and experimental understanding of plasmon–electron–hole pair coupling. Traditionally, HCG was interpreted via Landau damping, where collective plasmonic oscillations decay into incoherent electron–hole excitations. However, recent theoretical work based on quantum models—including transverse-field-mediated coupling between plasmons and electron–hole pairs—has revealed coherent aspects of this interaction, providing explanations for frequency-dependent anomalies in quantum efficiency and offering new strategies for energy conversion. These insights are being increasingly validated by ultrafast spectroscopy and energy-resolved imaging.

Looking ahead, several frontiers promise to accelerate progress. Advances in nanofabrication—achieving atomic precision and deterministic placement of quantum emitters—are paving the way for designer coherence domains and programmable nanophotonic circuits. Ultrafast laser and multidimensional spectroscopies are enabling real-time monitoring and active control of hybridized modes at femtosecond timescales. Integration with machine learning, quantum computation, and topological photonics is anticipated to yield transformative platforms for on-chip quantum optics, high-efficiency energy conversion, and molecular-scale sensing.

Importantly, a distinctive trend in this field is the synthesis of diverse conceptual and methodological frameworks—bridging classical local-field theories, semiclassical oscillator models, and fully quantum mechanical treatments. This cross-fertilization is exemplified by the increasingly close interplay between theory and experiment, which is essential for addressing challenges such as controlling dephasing at ambient temperatures, extending coherence lifetimes, and scaling coherent effects toward practical device implementations.

As research advances, the strategic use of quantum coherence is poised to shift from a theoretical curiosity to a foundational tool for optimizing light–matter interactions in nanoscale systems. The deliberate creation, manipulation, and detection of coherent states underpin many of the most significant recent breakthroughs, and point toward a future in which such control becomes routine and robust.

Beyond plasmon–matter hybrids, the coherence mechanisms emphasized in this review—coupled–oscillator interference (Fano/PIT/ET), detuning control Δ, phase-sensitive mode overlap C, and cavity-assisted strong coupling with favorable Q/Veff—are being actively developed in ostensibly different platforms. In particular, dielectric and hyperbolic microcavities and multiple-quantum-well metasurfaces implement the same engineering principles to boost dwell time, LDOS, and nonlinear conversion efficiencies; recent examples include deep-UV hyperbolic metacavity lasers and all-dielectric MQW metasurfaces achieving giant second-harmonic generation^[476,477]. Studying these directions alongside plasmonic systems helps distinguish what is platform-specific (loss channels and extraction pathways) from what is universal (interference control, phase matching, and out-coupling), thereby deepening the significance of the physics and engineering surveyed here.

In summary, the evolution of plasmonics and nanophotonics is marked by a transition from the pursuit of maximal field enhancement to a new paradigm grounded in the orchestration of coherence, hybridization, and quantum control. The growing diversity of phenomena, the development of novel experimental and theoretical techniques, and the convergence of fundamental and applied goals collectively define this as a highly dynamic and promising area of science and technology. By synthesizing the progress achieved by the broader community, as well as contributions highlighted throughout this review, it is hoped that this summary will serve not only as a record of advances, but also as a catalyst and guide for the next generation of discoveries in coherent nanoscience and technology.

Acknowledgment. We thank T. Inaoka, H. Misawa, K. Sasaki, T. Yokoyama, and K. Miwa for the fruitful discussions. This work was supported by the JSPS KAKENHI (Nos. JP21H05019, 24K21196, JP24K08282, and JP25H01627).