Plasmons represent the collective oscillations between incident electromagnetic waves and the free electrons in metal, facilitating the breakthrough of the optical diffraction limit and enhancing the electromagnetic field significantly [1]. Under the influence of the external electric field, oscillations of conduction electrons within each metallic unit initiate localized surface plasmon resonances (LSPRs). These resonances enable the local field enhancement and regulate the optical response to ambient light fields. When the period of the array aligns with the resonance wavelength of its individual unit, the interplay between the diffractive order (DO) modes of the array and the LSPRs of each unit culminates in collective surface lattice resonances (SLRs) and exhibits a more pronounced field enhancement effect [2]. Notably, the honeycomb lattice corresponds to a hexagonal lattice with two particles per unit cell, leading to six equivalent lowest DOs of (1, 0), (0, 1), (−1, −1), (1, 1), (−1, 0), and (0, −1) [3]. The SLRs, emerging from the synergy between the DOs of the periodic array and the LSPRs induced by an external electromagnetic field, boast angle-dependent dispersions and considerably narrower linewidths [4,5]. These characteristics render the plasmonic array a superior alternative in comparing with conventional cavity modes.

In general, the chemical structural formula of a typical perovskite cell is represented as ABX3, constituting a cubic structure with five atoms. “A” typically represents organic or inorganic cation, which maintains charge balance within the lattice, with its composition being pivotal in regulating the bandgap width [6]. The metal ion “B” is predominantly a lead ion known for its stability. Regarding the halide group “X,” iodine, bromine, or chlorine are commonly chosen. Distinctly, a red shift occurs when transitioning the halide element from chlorine to iodine [7], enabling optical absorption and emission spectra to encompass the entire visible region. Recently, lead halide perovskites not only have exceptional photovoltaic performance and superior light-emitting characteristics but also feature ease of fabrication, extensive spectral tunability, and versatile dimensionality, ranging from three-dimensional to two-dimensional (2D) layered materials [8,9]. This versatility renders them suitable for quantum emitters within a coupling system. Moreover, as Frenkel exciton materials with small Bohr radii, the substantial binding energy and oscillator strength of lead halide perovskites facilitate the generation of organic exciton-polaritons at room temperature [10]. Distinctively, three-dimensional perovskite materials have garnered attention for their prolonged lifetime, low trap density, and reduced charge carrier recombination rate [11], while their susceptibility to moisture and heat challenges the application a lot [12]. Consequently, quasi-2D variants are yielded by integrating bulk organic cations into three-dimensional perovskites, exhibiting enhanced robustness and exciton binding energy [13].

By integrating perovskite into a resonant cavity, excitons generated through the recombination of electrons and holes exhibit Coulomb interaction within the perovskite, and cavity photons can engage in reversible energy exchange. This interaction culminates in the formation of a novel hybrid system characterized by coherent oscillations in the time domain [14]. The system enters the strong coupling regime when the rate of energy exchange, known as the Rabi frequency, exceeds the decay rates of both the cavity photon and the exciton. The phenomenon gives rise to a novel quasi-particle termed as exciton-polariton, and due to the hybrid light-matter nature, nonlinearity and optical coherence can be enhanced significantly [15,16]. As bosonic particles with a small effective mass, polaritons are instrumental in the exploration of macroscopic quantum phenomena [17]. Furthermore, the unique interplay between bosonic and excitonic properties fulfills achieving the room-temperature Bose-Einstein condensate, offering a platform for investigating low-threshold lasing [18–23]. In addition, advancements in quantum emitter and optical structures, as well as the understanding of polariton dynamics, coherence, and nonlinearity have propelled the rapid progression of sophisticated polaritonic applications. These applications with high-power efficiency [24,25] encompass a spectrum of technologies from ultrafast polariton switches [26,27] and quantum simulators [28], to optical sensing devices [29].

In this study, we report the observation of strong coupling from a centimeter-scale, periodically arranged plasmonic aluminum nanocone array embedded with a quasi-2D perovskite, evidenced by a 243 meV Rabi splitting at zero detuning. As a plasmonic nanocone array, this nanostructure can strongly suppress radiative loss through a Bloch surface wave, and the large sample area provides sufficient collective diffraction modes, resulting in high-quality resonances with narrow linewidths. Most importantly, the nanocone structure can confine photons at the tip, resulting in an exceptionally small Vm. Therefore, the plasmonic nanocone array achieves a commendable Q/Vm ratio, enhancing light-matter interaction. The enhanced signals and faster relaxation are discovered by transient absorption (TA) measurement. Subsequently, a comprehensive quantum mechanical model was employed to elucidate the distribution of the cavity and quantum emitter in terms of fractions, and the dynamics as Rabi oscillations. Such detailed modeling significantly argues the understanding of the interaction processes within the hybrid system.

The honeycomb plasmonic nanocone array (NCA), enjoying a long-term order, is meticulously fabricated using the electrochemical anodic oxidation process, characterized by a period of 400 nm and an approximate height of 100 nm. The generated NCA is vividly captured in the scanning electron microscope (SEM) image presented in Fig. 1(a). The concave shape of the cones, a result of pre-imprinting and oxide layer removal, can not only improve the field localization effect but also facilitate the subsequent material filling.

A numerical 2D Fourier transform of the NCA depicted in Fig. 1(b), distinctly showcases a six-fold symmetry inherent to the honeycomb lattice in reciprocal space. Each pair of contiguous cells within the honeycomb NCA lattice configuration in real space equates to one lattice site in reciprocal space, maintaining a hexagonal pattern and a period of 400 nm. The first Brillouin zone of the lattice is delineated in the inset, accentuated by a shade area with high-symmetry points Γ, K, and M. Given the pronounced extinction along high-symmetry orientations and the wavelength matching, light sources employed in subsequent measurements are consistently oriented parallel to the Γ−K direction on the x−y plane throughout the experiment [30]. The six lowest-order reciprocal lattice vectors, indicated by white arrows, exhibit identical magnitude in direct proportion to the dispersion energy [31]. When incident light aligns with the ky, the (0,−1) and (−1, −1) modes attain equivalent magnitudes, culminating in a degenerate state [32,33]. Consequently, when the in-plane wavevector k propagates along the y-direction, three degenerated states emerge, corresponding to the (1,1)/(0,1), (1,0)/(−1,0), and (−1,−1)/(0,−1) mode (as detailed in Appendix A). It can be observed that the resonant wavelengths of the dispersion increase significantly as the period increases from 300 to 600 nm in the lattices, while the band structure varies only slightly. After comparison, the honeycomb lattice with a period of 400 nm is identified as an optimal candidate for matching with perovskite in this work.

Figure 1(c) illustrates the reflectance of the NCA at varying incident angles, with SLRs in the NCA obtained through the adjustment of incident and reflex angles. The reflection spectra are meticulously measured from 10° to 50° at a fixed azimuthal angle (aligned with the direction of Γ−K). The white dashed lines in the figure denote the DOs calculated using the empty lattice approximation (ELA) model, corresponding to kDO in the inset of Fig. 1(b). Notably, the observed SLRs exhibit strong concordance with the theoretical DOs. In Fig. 1(d), the reflection peaks of NCA exhibit a red shift with increasing incident angles; when the incident angles range from 20° to 40°, the modes with the resonant wavelength range from 450 to 600 nm, whose spectra overlap with the emission of perovskite at 520 nm. Furthermore, the SLRs of NCA exhibit narrow full width at half-maximum (FWHM) as 22 nm. The quality factor (Q) of the NCA can be calculated as Q=λ/Δλ=24.61, which is related to the ratio of the energy stored in the cavity and energy dissipated per oscillation cycle. Here, λ represents the resonant wavelength, and Δλ denotes the linewidth. Combined with the Purcell factor (F) calculated via FDTD, the mode volume is obtained as Vm=(3Qλ3)/(4π2Fn3)=0.92×10−4μm3. The absorption and photoluminescence characteristics of the perovskite are presented in Appendix A. Distinctly, an absorption plateau is observed prior to 520 nm, revealing a strong excitonic resonance from the number (n) of four inorganic layers, while the peak of luminescence manifests at 527 nm [34]. This observation suggests a substantial energy requirement for mode formation of the quasi-2D perovskite.

The FA0.25Cs0.75PbBr3 perovskite (where FA denotes formamidine) is synthesized on the NCA using a spin-coating technique, with phenylethylamine incorporated into it. During the process, isopropanol was employed as an anti-solvent. The SEM image presented in Fig. 2(a) illustrates the morphology of the newly formed system. The thickness of packaged perovskite particles onto the Al nanocone array is approximately 60 nm, with the effective refractive index of 2.45.

Figure 2(b) displays the sample of the NCA with the perovskite; the area demarcated by the dotted line encompasses the NCA structure, confirming that the effective sample area can extend to a centimeter scale. Upon exposure to ultraviolet light, the perovskite emits green light, which is visually detectable and corresponds to the luminescence wavelength near 520 nm. To illustrate the field localization effect of the NCA, a simulation model is established using the finite-difference time-domain (FDTD) method to monitor the distribution of the electrostatic field, as displayed in Fig. 2(c) and Appendix A. At the wavelength of 520 nm with the incident angle of 30°, it is evident that the intensity of the electric field is predominantly localized at the tip of the cone.

There are multiple light-matter interactions in the perovskite-coated NCA. The first interaction occurs between the incident light and the perovskite, while the second involves the emission from the perovskite, resulting from exciton recombination, and the cavity mode of the plasmonic lattice. Additionally, there is an interaction between the incident light and the cavity itself. Although the exciton absorption and exciton recombination spectra of the perovskite are quite similar, the cavity mode only interacts with modes that satisfy both the energy and spatial overlap conditions. Figures 2(d) and 2(e) present the reflection dispersion and the corresponding spectrum along the Γ−K direction of the hybrid system. Two reflection dips, shifting with increasing angle near 520 nm, imply the possible interaction between the quasi-2D perovskite and the NCA. But due to the significant absorption of energy from the perovskite for wavelengths shorter than the band edge, the formation of the strong coupling is not distinctly visible under steady state. The energy splitting of the hybrid system is depicted in Fig. 2(f), characterized by an upper polariton (UP) and a lower polariton (LP). The discrepancy between the upper and lower polariton branches quantifies the coupling strength. Strong coupling is typically manifested as an anti-crossing in the spectrum, with an energy gap denoted as known as Rabi splitting: 2ℏω>γ+κ,or,g>(γ2+κ2)/2,(1)where ω is the frequency, γ and κ are losses of the cavity mode and quantum emitter, respectively, and g is the coupling strength.

Since the steady state measurements are not distinct enough to confirm the strong coupling, the hybrid system is further analyzed using transient state measurements. Figure 3(a) shows the TA spectra of quasi-2D perovskite-coated NCA under a 435 nm pump laser pulse. The inset presents the TA spectra of the perovskite-coated Al flat substrate, which exhibits a negative ground state bleaching (GSB) signal at 520 nm and a positive photoinduced absorption signal at 500 nm. In the case of the perovskite-coated NCA at an emission angle of 30°, the TA spectra reveal some interesting characteristics. The emerging LP mode at 536 nm is a multiple mode peak that includes a weak negative signal at 517 nm. This signal spectrally aligns with the eigenmode of the Al flat but exhibits much weaker intensity at 30°, while it remains prominent at 20° [Fig. 3(c)] and 40° [Fig. 3(d)]. Additionally, a clear UP mode at 485 nm is only observed at 30°, and the measured signals satisfy the relation ELP<Ee≈Ec<EUP. Interestingly, a signal at 549 nm [Fig. 3(c)] red shifts to 616 nm [Fig. 3(d)] as the emission angle varies from 20° to 40° that aligns well with SLR mode. Therefore, the strong coupling phenomenon can only be identified in the TA measurement and not in the steady state spectrum.

Concerning the relaxation process of the hybrid system in Fig. 3(b), the interaction between the modes can be extensively explored. Interestingly, the TA dynamics of UP and LP branches of perovskite-coated NCA are shorter than that of perovskite-coated Al flat substrate, because the relaxation of hybrid states is expedited by the attendance of plasmon. Particularly, the vibration of TA curves arises from the metal breathing mode [35].

To gain deeper insight into the contributions of sub-modes in polaritons, as well as the dynamics of hybrid states, a comprehensive quantum mechanical model is employed. This model is rooted in cavity quantum electrodynamics (CQED) and treats the cavity and quantum emitter modes as bosonic modes [36], operating within the Heisenberg picture. This approach facilitates a detailed analysis of energy exchange and damping in the frequency domain. Notably, the Hamiltonian of the strong coupling regime is categorized into three distinct components [37]: H^=H^c+H^qe+H^i,(2)where the terms H^c=ℏωca^†a^, H^qe=ℏωqeb^†b^, and H^i=ℏg(a^†b^+b^†a^) respectively signify the cavity mode, the quantum emitter mode, and the interaction Hamiltonian. It is worth mentioning that such processing of H^i refers to the rotating wave approximation [38,39].

Exhibit it as the matrix form and solve the equation to obtain the eigen-energies: H^=(a^†b^†)(ℏωcℏgℏgℏωqe)(a^b^),(3)(ℏωcℏgℏgℏωqe)(αβ)=E±(αβ).(4)

The photon energies of upper polariton and lower polariton states in the hybrid system can be represented as the eigenvalues E±=ℏ(ωc+ωqe)±Δ2+4(ℏg)22,(5)where Δ=ℏωc−ℏωqe is the detuning, and the Hopfield coefficients of cavity and quantum emitter components in UP/LP states can be represented as |α|2 and |β|2.

Applying the Heisenberg equation of motion O^˙=i/ℏ[H^,O^] to Eq. (3) and introducing the loss of cavity γc and quantum emitter γqe, the optical pumping to the two modes Γc,in and Γqe,in, we have {a^˙=−iωca^−igb^=−(iωc+γc2)a^−igb^+Γc,ina^in,b^˙=−iωqeb^−iga^=−(iωqe+γqe2)b^−iga^+Γqe,inb^in,(6)where a^in=a^in(0)eiωpumpt, b^in=b^in(0)eiωpumpt, and ωpump is the frequency of the optical pump.

Set Γc,in=0 and Γqe,in=1 and replace the operator O^(t) as O^eiωpumpt to get rid of the time-varying terms: {a^˙=−(iΔc+γc2)a^−igb^,b^˙=−(iΔqe+γqe2)b^−iga^+b^in(0),(7)where Δc=ωc−ωpump and Δqe=ωqe−ωpump.

When O^˙=0, the steady-state solutions can be solved as {a^(t→∞)=|0igb^in(0)iΔqe+γqe2||iΔc+γc2igigiΔqe+γqe2|,b^(t→∞)=|iΔc+γc20igb^in(0)||iΔc+γc2igigiΔqe+γqe2|.(8)

And the total emission is S(ωpump)=γc⟨a^†a^⟩t→∞+γqe⟨b^†b^⟩t→∞.(9)

By solving Eq. (8) to get a^(t,ωpump) and b^(t,ωpump), the populations of the cavity mode and quantum emitter mode can be signified as ⟨a^†a^⟩(t,ωpump) and ⟨b^†b^⟩(t,ωpump).

By evaluating the Hopfield coefficients, the dominant mode within each polariton branch can be discerned. As the foregoing, the contributions of the cavity and quantum emitter are quantified by |α|2 and |β|2, respectively. As shown in Fig. 3(e), for incident angles less than 30°, the UP subsystem is primarily influenced by the cavity mode, whereas the LP is dominated by the quantum emitter mode. With an increase of the incident angle, the mode comprising a larger fraction diminishes gradually, while the less predominant contribution increases, reaching equilibrium at zero detuning. This trend is consistent with the anticipated results of coupling. Beyond an incident angle of 30°, a reversal in detuning occurs, the quantum emitter mode becomes predominance in the UP, while the cavity mode becomes the dominant influence in the LP. The emergence of mode fractions within subsystems underscores the tunability of hybridization through detuning manipulation. In Fig. 3(f), the dynamics of polariton is stated through the quantification of energy exchange between cavity and quantum emitter modes. It is derived from the spectral splitting strength in Fig. 3(a) and in terms of photon numbers. The oscillation period of eigenstates maintains a consistent value of 17.13 fs for both UP and LP, which exhibits the coherent energy exchange.

In summary, this study experimentally demonstrates a room-temperature strong coupling between a plasmonic lattice and a quasi-2D perovskite, as evidenced by a Rabi splitting of 243 meV. The quasi-2D perovskite-coated Al NCA creates an ideal platform for polariton formation. Additionally, the hybrid system enjoys enhanced TA signals and faster relaxation in the time domain. Employing a comprehensive quantum mechanical model, the components of polariton branches and the temporal dynamics of energy exchange are delved into with an oscillation period as 17.13 fs. The insights gained from this work are instrumental in advancing the exploration of strong coupling applications, particularly in the realm of quantum information processing.

The aluminum flake with the diameter of 2.5 cm is acquired by tailoring and electrochemical polishing. Imprinting the nickel film with the structure arranged as hexagonal on the flake at 5 MPa for 2 min to obtain the elliptical holes, the period of the array is 400 nm. Anodization at 160 V and 4°C for 40 min is applied to fabricate an anodic alumina oxide membrane of the hexagonal lattice. The oxidation solution is composed of phosphoric acid and ethylene glycol, corresponding to a volume ratio of H3PO4:(CH2OH)2:H2O of 1:200:400. To acquire the bottom aluminum substrate with the shape of a concave cone, put the sample after oxidating in chromic acid solution for 8 h, which is blended by H3PO4 and CrO3. After slight dousing, the honeycomb plasmonic nanocone array is obtained.

There is a corona treatment for NCA before coating. Finishing the preprocessing, 200 μL of the FA0.25Cs0.75PbBr3 with PEA precursor solution is spin-coated on the lattices at the speed of 4000 r/min for 40 s, adding the anti-solvent isopropanol during the spinning.

There is an automated rotational stage to place the sample; a collimated white deuterium halogen light source from a halogen lamp (50 W iDH2000, Idea Optics) is used to illuminate the sample. The zeroth-order reflection spectra are measured from 10° to 50° in increments of 1° for the fixed azimuthal angle (along the Γ−K direction for NCA throughout the work).

The size of the illumination spot casting on the sample is about 2 mm. The reflected light is collected and coupled into an optical fiber connected to a fiber spectrometer (PG 2000, Idea Optics). After gathering background light and environmental light, the reflection data are normalized by the software automatically.

Simulate the system by FDTD calculations based on commercial software (FDTD Solution, Ansys). The optical constants of Al are taken from Palik with the spectrum ranging from 400 to 1000 nm, while those of CsPbBr3 are taken from Ermolaev. A 5 nm uniform mesh in the Al nanocone is used. The plane wave (BFAST) and Bloch (x, y)-PML (z) boundary conditions are installed. The shape of the concave cone is achieved by aluminum and etching ellipsoids. The perovskite with thickness of 60 nm is simulated as the main component CsPbBr3 designed among the cones. The 2D monitor is placed on the axis of the cone.

The transient spectroscopy system is manufactured by Dalian TIME-TECH SPECTRA. The output laser has a wavelength of 1030 nm, a power of 10 W, and a pulse energy of 67 μJ. The fundamental pulse (800 nm, 150 kHz, 39 fs) generated by a titanium sapphire laser system (PH1, Light Conversation) is split into two laser beams by a splitter. The stronger beam transmits through the optical parametric amplifier (ORPHEUS-F, Light Conversation) to generate the desired excitation light source, while the weaker one passes through a YAG crystal to provide continuous white light for detection as a probe laser. The light reflected from the sample is collected and sent to the femtosecond transient absorption spectrometer; the delay time between the pump and the probe light is manipulated by the mechanical delay stage. The reflex angle can be adjusted by rotating the sample stage. And the dispersion of the data is compensated for by the chirp correction algorithms from the TAS ANALYSER software.