Optical topological quasiparticles with nontrivial topological textures, such as skyrmions and meron lattices, have attracted considerable attention due to their potential applications in high-dimensional optical data storage and communications. Most previous studies of optical topological quasiparticles have focused on the formation of topological structures in isotropic media, whereas in our work, we perform a comprehensive investigation into the formation, topological stability, and phase transitions of optical meron lattices at the metal/uniaxial crystal interface. Our theoretical studies show that by rotating the optical axis orientation of the uniaxial crystal, meron lattices constructed by electric-field vector undergo phase transitions from a topologically nontrivial to a topologically trivial state, whereas the skyrmion number of the spin meron lattices remains robust against such rotations. The findings offer new insights into the topological stability and phase transitions of topological quasiparticles under light–matter interactions and hold promise for applications in optical data storage, information encryption, and communications.

Non-Hermitian chiral coalescence associated with polarization in optical scattering systems has been routinely realized and applied. However, the scattering exceptional points (EPs) associated with polarization obtained by modes with broadband response and high dissipation constrain its further application in narrowband optics. Here, as a scheme, distinct from the implementation pathway of traditional EPs, we introduce a quasi-bound state in the continuum based on a quadrupole mode as the response environment for EP generation, achieving an EP with high-quality-factor characteristics on a metasurface. Furthermore, we demonstrate the robustness of EPs as intrinsic features of non-Hermitian systems, independent of specific parameter choices. Finally, we present an example of direct chirality detection and display, showcasing the maximum spin-selective property induced by EPs. Our approach unveils the potential of scattering chiral EPs for applications in narrowband optics.

We propose an approach for generating the enhanced superchiral needle by matching electromagnetic components of the combined field, which is the superposition of a radially polarized vortex Bessel–Gaussian beam (RPVBGB) and an azimuthally polarized Bessel–Gaussian beam (APBGB). In the tightly focused combined field, the longitudinal magnetic component provided by the APBGB, together with the longitudinal electric component provided by the RPVBGB, induces an additional contribution to the optical chirality and thereby significantly improves the enhancement factor of the superchiral needle. It is revealed that the characteristics of the superchiral needle are mainly influenced by the ring aperture, the phase difference, and the amplitude ratio. Under proper parameters, the enhancement factor can reach from 22.9 to 32.9, and the needle width can reach from 0.0151λ to 0.0043λ and from 0.0182λ to 0.0058λ in the x- and y-directions, respectively. The results would be of interest for the chirality measurement of individual molecules.

Electromagnetic metasurfaces exhibit considerable potential for generating high-purity vortex beams and enabling high-resolution imaging and information encryption. However, traditional GHz devices face challenges, including reduced efficiency due to bulky size and material losses. Herein, we designed a multilayer structure and demonstrated through simulations that this configuration served as an efficient transmissive meta-atom. We designed arrays in multiple sizes and finally determined that the optimal minimal unit was the meta-quaternion vortex array, which was subsequently used as the pixel basis for the target image. A digitally patterned GHz metadevice was fabricated and experimentally characterized with right-handed circularly polarized (RCP) light. The experimental results were in excellent agreement with the simulations. We combined the classical nine-grid encryption method (Luoshu) with metasurfaces and introduced the weighted superposition computation technique (WeightLock) to achieve multilayer encryption of target characters. Our research offered novel strategies for the next-generation 5G/6G communication systems, radar detection, and information encryption fields, demonstrating broad application prospects in intelligent communication and advanced radar technologies.

Planar metasurfaces with both chirality and high quality (Q) factors have important applications in many fields. A chiral metasurface empowered by a bound state in the continuum (BIC) can provide a perfect solution to this problem. However, the metasurface design method based on physical intuition requires a substantial amount of computational resources, and the limited design parameters of meta-atoms restrict metasurfaces from achieving optimal optical performance. Here, we apply an inverse design method based on adjoint topological optimization to automatically alter the refractive index distribution of the metasurface, thereby maximizing the chirality of the BIC metasurface. Through this inverse design approach, chiral BIC metasurfaces with 3D intrinsic chirality at the target wavelength are designed and fabricated. To demonstrate the versatility of the proposed inverse design method, the metasurfaces with specific elliptic polarization states are designed. The inverse design method we propose provides an effective solution for the efficient design of chiral BIC metasurfaces.

Backflow is a counterintuitive phenomenon that is widely predicted in the fields of quantum physics and optics. In contrast to quantum backflow, which is challenging to be observed, optical backflow is prevailing in structured lights. For instance, the azimuthal backflow has been recently observed experimentally in optics via the superposition of two beams carrying different orbital angular momentum topological charges. In this paper, we investigate the spin-momentum characteristics of the superimposed orbital angular momentum beams to confirm the optical azimuthal backflow, which is closely related to off-axis vortex flow and super-oscillations. Furthermore, we extend our study to axial backflow, characterized by a reversed axial energy flow in tightly focused cylindrical vector vortex beams. Then, we explore the application of optical backflow in the manipulation of dipolar nanoparticles. By optimizing material parameters, we achieve on-demand control of optical forces in both azimuthal and axial backflow scenarios. Our findings provide in-depth insights into the optical backflow phenomena with potential applications in optical manipulations.

Engineering ultrashort laser pulses is crucial for advancing fundamental research fields and applications. Controlling their spatiotemporal behavior, tailored to specific applications, can unlock new experimental capabilities. However, achieving this control is particularly challenging due to the difficulty in independently structuring their intensity and spatial phase distributions, given their polychromatic bandwidth. This article addresses this challenge by presenting a technique for generating flying structured laser pulses with tunable spatiotemporal behavior. We developed a comprehensive approach to directly design and govern these laser pulses. This method elucidates the role jointly played by the pulse’s spatiotemporal couplings and its prescribed phase gradient in governing the pulse dynamics. It evidences that the often-overlooked design of the phase gradient is indeed essential for achieving programmable spatiotemporal control of the pulses. By tailoring the prescribed phase gradient, we demonstrate the creation of, to our knowledge, novel families of flying structured laser pulses that travel at the speed of light in helical spring and vortex multi-ring forms of different geometries. The achieved control over the dynamics of their intensity peaks and wavefronts is analyzed in detail. For instance, the intensity peak can be configured as a THz rotating light spot or shaped as a curve, enabling simultaneous substrate illumination at rates of tens of THz, far exceeding the MHz rates typically used in laser material processing. Additionally, the independent manipulation of the pulse wavefronts allows local tuning of the orbital angular momentum density carried by the beam. Together, these advancements unveil advantageous capabilities that have been sought after for many years, especially in ultrafast optics and light-matter interaction research.

Recently, spatiotemporal optical vortices (STOVs) with transverse orbital angular momentum have emerged as a significant research topic. While various STOV fields have been explored, they often suffer from a critical limitation: the spatial and temporal dimensions of the STOV wavepacket are strongly correlated with the topological charge. This dependence hinders the simultaneous achievement of high spatial accuracy and high topological charge. To address this limitation, we theoretically and experimentally investigate a new class of STOV wavepackets generated through the spatiotemporal Fourier transform of polychromatic Bessel–Gaussian beams, which we term as perfect spatiotemporal optical vortices. Unlike conventional STOVs, perfect STOVs exhibit spatial and temporal diameters that are independent of the topological charge. Furthermore, we demonstrate the generation of spatiotemporal optical vortex lattices by colliding perfect STOV wavepackets, enabling flexible manipulation of the number and sign of sub-vortices.

The enantiospecific detection of the chirality of substances at the nanoscale has attracted significant attention due to its importance in materials science, chemistry, and biology. This study presents, to our knowledge, a novel method for chirality detection based on transverse optical torque (OT), which leverages the transverse rotation of achiral particles induced by the transfer of chirality from the chiral particle within interference fields formed by the incident light without spin angular momentum (SAM). We demonstrate, both numerically and analytically, that by modulating the chirality of the chiral particle within a dimer system, it is possible to achieve the transfer of local SAM to the gold particle, thereby generating a transverse OT perpendicular to the light propagation direction. Furthermore, by adjusting the orientation of linear polarization in the excitation field, the respective contributions of electric and magnetic responses to the chirality-transfer-induced transverse OT can be exclusively observed separately, providing deeper insights into the underlying physical mechanisms. More importantly, the transverse OT exhibits an approximately linear dependence on the chirality parameter of the chiral particle, enabling enantiospecific detection of nanosamples. By replacing gold nanoparticles with suitable high-refractive-index dielectric materials such as germanium, the induced transverse magnetic dipolar OT can be further enhanced by more than two orders of magnitude, significantly improving the sensitivity of chirality detection and making it possible to detect weak chiral signals with exceptional precision. This work broadens the application scope of OTs in chirality detection and highlights the potential of chirality transfer mechanisms for advanced optical manipulation and the identification and analysis of chiral substances.

Single-shot multi-frame phase imaging plays an important role in detecting continuous extreme physical phenomena, particularly suitable for measuring the density of media with non-repeatable changes and uncertainties. However, traditional single-pattern multiplexed imaging faces challenges in retrieving amplitude and phase information of multiple frames without sacrificing spatial resolution and phase accuracy. In this study, we demonstrate single-shot common-path encoded coherent diffraction imaging with orbital angular momentum (OAM) multiplexing. It employs a sequence of vortex illumination fields, combined with encoding wavefront modulation and a vortex multiplexing phase retrieval algorithm, to achieve the retrieval of complex amplitudes from dynamic samples in single shots. Our experimental validation demonstrated the capability to achieve 9-frame high-resolution phase imaging of the dynamic sample in a single diffraction pattern. The spatial resolution and phase accuracy improve to 9.84 μm and 4.7% with this lensless multiplexed imaging system, which is comparable to single-mode imaging. This technology provides a multiplexed dimension with orbital angular momentum and holds potential in the study of transient continuous phenomena.

In recent years, optical skyrmions have garnered increasing attention for their ability to introduce new degrees of freedom in manipulating optical fields. While most research has focused on creating innovative optical topological states such as merons and hopfions, there has been limited exploration into their manipulation, which hinders practical applications in this field. In this study, we utilize a hybrid multi-zone filter to induce a Hall effect-like splitting of optical Stokes skyrmions (HESSs), enabling effective separation and manipulation. By manipulating the horizontal phase gradient parameter, we independently control the separation angle of skyrmions. Additionally, we demonstrate control over the topological charge parameter to achieve symmetric and asymmetric HESSs. This effect not only enhances the manipulation capabilities of optical fields but also opens up potential applications for high precision displacement measurements and preservation quantum information.

Optical skyrmions, as quasiparticles with non-trivial topological structures, have garnered significant attention in recent years. This paper proposes a method for customized spin angular momentum (SAM) distribution in highly localized focal fields, thereby enabling the generation of SAM skyrmion and bimeron topologies. The skyrmionic SAM textures can be flexibly controlled, such as polarity, vorticity, and helicity. In addition, the two-dimensional projection plane can be arbitrarily oriented within three-dimensional space. By utilizing time-reversal techniques, we obtain the required illumination fields of the 4π-focusing system and subsequently evaluate the tightly focused field using vector Debye integral theory. Our results show that the SAM orientation within the focal field is controlled by the orientation of orthogonal dipole pairs. Using the radiation field of a multi-concentric array of orthogonal dipole pairs, the distribution of SAM orientation in the target plane can be tailored to generate SAM topological structures such as skyrmions and bimerons. Highly localized and tunable SAM engineering holds great potential for applications in optical manipulation, light–matter interactions, optical information processing, transmission, and storage.

In Floquet engineering, we apply a time-periodic modulation to change the effective behavior of a wave system. In this work, we generalize Floquet engineering to more fully exploit spatial degrees of freedom, expanding the scope of effective behaviors we can access. We develop a perturbative procedure to engineer space-time dependent driving forces that effectively transform broad classes of tight-binding systems into one another. We demonstrate several applications, including removing disorder, undoing Anderson localization, and enhancing localization to an extreme in spatially modulated waveguides. This procedure straightforwardly extends to other types of physical systems and different Floquet driving field implementations.

The rapid development of optical technologies, including optical trapping, enhanced imaging, and microscopy, necessitates fundamentally new approaches to higher-dimensional optical beam shaping. We introduce a rigorous theoretical approach for sculpting three-dimensional, topological particle-like objects, such as optical knots or links, including precise control of their individual parts. Universally applicable to knots created using braided zero lines, our method is validated through theoretical analysis and experimental measurements. The proposed approach enables new degrees of freedom in multi-dimensional singularities shaping, including rotations, shifts, and rescaling of their parts for enhanced stability in complex media. These results may find applications in the fields of three-dimensional optical trapping, manipulation, and subwavelength microscopy, as well as probing and imaging through atmospheric or underwater turbulence.

The rotational Doppler effect holds significant potential for remote sensing of rotating objects due to its real-time performance and non-contact advantages. A single-ring beam is used to measure rotation speed. To enhance the signal-to-noise ratio and measure additional parameters, multiple rings are introduced in the context of a rotational Doppler effect. However, the interference between these rings poses a challenge for multitasking detection applications. In this study, cross-polarization superposition was applied to generate an ultra-dense vector perfect vortex beam that exhibited sensitivity to spatial position and object size, and flexibility in designing topological charge combinations for generating frequency combs. A proof-of-principle experiment was conducted to demonstrate its capability in improving the signal-to-noise ratio, and accurately perceiving both the radius of rotation and radial size. An ultra-dense vector perfect vortex beam provides a general strategy for beam construction and the multi-parameter perception of rotating objects, thereby enabling potential applications in the measurement of velocity gradient measurement of fluids.

Absorbing particles have attracted wide interest in multifarious fields due to their strong light absorption characteristics, which can be trapped by optical bottles (OBs), three-dimensional dark regions surrounded by light. Existing OB-based particle manipulation is typically limited to a single functionality, such as the stationary volume or the single manipulated object. This severely limits the versatility and selectivity of micro-manipulation, particularly in the multi-particle system. In this paper, we address these challenges by introducing a dynamic OBs generation method. By modulating optical vortices and multi-parabolic trajectory phases, a series of OBs with targeted positions, numbers, and states is encoded as a battery of holograms, which are imported into the spatial light modulator (SLM). Experimentally, by dynamically reconfiguring the corresponding holograms in the SLM, we validate selectively switching and moving OBs for dynamic particle manipulation. Consequently, a specific fraction of targeted particles can be selectively released, transported 7.2 mm away while the others remain trapped in place, or merged from two 3.5-mm-spaced OBs into a larger single entity. Our results deepen the applications of OB beams and may herald a new avenue for dynamic particle manipulation.

The dynamics of wave packets carrying a spatiotemporal vortex in the spatial fractional system is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator, and the vortex is space-time coupled. Here, we investigate the transmission of spatiotemporal vortices in the spatial fractional wave equation (FWE) and demonstrate the effects of linewidth, vortex topological charge, and linear chirp modulation on the transmission of Bessel-type spatiotemporal vortex pulses (BSTVPs). Under narrowband conditions, we find that the propagation of BSTVP in the FWE can be seen as the coherent superposition of two linearly shifted half-BSTVPs and can reveal orbital angular momentum backflow for the half-BSTVP. Our analysis can be extended to other spatiotemporal vortex pulses.

Optical singularity states, which significantly affect propagation properties of light in free space or optical medium, can be geometrically classified into screw and edge types. These different types of singularity states do not exhibit direct connection, being decoupled from each other in the absence of external perturbations. Here we demonstrate a novel optical process in which a higher-order edge singularity state initially nested in the propagating Gaussian light field gradually involves into a screw singularity with a new-born topological charge determined by order of the edge state. The considered edge state comprises an equal superposition of oppositely charged vortex and antivortex modes. We theoretically and experimentally realize this edge-to-screw conversion process by introducing intrinsic vortex–antivortex interaction. We also present a geometrical representation for mapping this dynamical process, based on the higher-order orbital Poincaré sphere. Within this framework, the edge-to-screw conversion is explained by a mapping of state evolution from the equator to the north or south pole of the Poincaré sphere. Our demonstration provides a novel approach for manipulating singularity state by the intrinsic vortex–antivortex interactions. The presented phenomenon can be also generalized to other wave systems such as matter wave, water wave, and acoustic wave.

There recently has been increasing interest in the research and application of the rotational Doppler effect (RDE), which paves a promising way to detect rotating objects remotely. In order to obtain more information about the rotating object from the rotational Doppler signal, composite vortex beams by coaxial superposition of orbital angular momentum (OAM) modes are often used as the probe beam. However, to the best of our knowledge, the RDE of composite vortex beams with arbitrary OAM spectra has not yet been comprehensively studied. In this paper, the correspondence between the OAM spectrum of a probe beam and the frequency spectrum of a rotational Doppler signal is theoretically analyzed. It is explicitly revealed that the RDE frequency spectrum of scattered light is related to the product of two autocorrelation functions: one from the OAM spectrum of probe beam and the other from the spiral spectrum of rotating object. On the basis of this relation, one can regulate the RDE frequency spectrum on demand via tailoring the OAM spectrum of the probe beam. As a proof of concept we design a special composite vortex beam to eliminate the broadening of the RDE spectrum induced by misalignment. These findings are of practical value in applications such as remote sensing and optical metrology.

The topic of optical precise displacement measurement has garnered significant attention and generated widespread interest recently. The use of optical singularity offers a potential solution for this purpose, although effectively manipulating the singularity in an ideal manner remains challenging. In this work, we propose a theoretical approach to achieve controllable position modulation of the C-point in the focal plane, whose spatial position can be easily modulated by adjusting the relative offset factor β and the offset angle α of an azimuthal polarization beam (APB), while the interval and orientation of the C-points can be flexibly regulated. Notably, the chiral polarization state undergoes a distinct reversal along the link-line connecting the two C-points, thereby providing a promising approach for accurate displacement sensing. To evaluate its sensing characteristics, the varying pattern of the scattered field intensity is monitored when sweeping a gold helix and nanoparticle along the link-line. The results of simulation quality index Q verify that the equilibrium factor of the scattering field possesses an obvious linear relationship with the displacement, signifying a precise sub-nanometric sensitivity. This research introduces new methods for the flexible control of polarization singularities in tightly focused fields, thereby enhancing the utilization of circular polarization properties near C-points for displacement sensing. These findings not only enrich the field of nanometer measurement technology but also pave the way for new avenues of research in this domain.

We present an innovative approach for the simultaneous agile manipulation of high-refractive-index (HRI) and low-refractive-index (LRI) particles. Our method involves introducing a dual-curvilinear optical vortex beam (DC-OVB) generated by superimposing a pair of curved beams: HRI and LRI particles are controlled by the bright curve and the dark channel between the two curves, respectively. The proposed DC-OVB provides customizable motion paths and velocities for both LRI and HRI particles. Each curve of the DC-OVB can support a distinct orbital flow density (OFD), enabling the application of torques to HRI and LRI particles, guiding them to orbit along specified trajectories and prompting them to execute various curvilinear motions simultaneously, including curvilinear movement, revolution, and rotation.

Low-refractive-index particles play significant roles in physics, drug delivery, biomedical science, and other fields. However, they have not attained sufficient utilization in active manipulation due to the repulsive effect of light. In this work, the establishment of customized dark traps is demonstrated to fulfill the demands of versatile manipulation of low-refractive-index particles. The customized dark traps are generated by assembling generalized perfect optical vortices based on the free lens modulation method, by which the beams’ shape, intensity, and position can be elaborately designed with size independent of topological charge. Using the customized dark traps with high quality and high efficiency, rotation along arbitrary trajectories with controllable speed, parallel manipulation, and sorting of low-refractive-index particles by size can be realized. With unprecedented flexibility and quality, the customized dark traps provide tremendous potential in optical trapping, lithography, and biomedicine.

Topological photonics has received extensive attention from researchers because it provides brand new physical principles to manipulate light. Band topology is characterized using the Berry phase defined by Bloch states. Until now, the scheme for experimentally probing the topological phase transition of band topology has always been relatively lacking in topological physics. Moreover, radiation topology can be aroused by the far-field polarization singularities of Bloch states, which is described by the Stokes phase. Although such two types of topologies are both related to Bloch states on the band structures, it is rather surprising that their development is almost independent. Here, in optical analogs of the quantum spin Hall effects (QSHEs) and Su-Schrieffer-Heeger model, we reveal the correlation between the phase transition of band topology and radiation topology and then demonstrate that the radiation topology can be employed to study the band topological transition. We experimentally demonstrate such an intriguing phenomenon in optical analogs of QSHEs. Our findings not only provide an insightful understanding of band topology and radiation topology, but also can serve as a route to manipulate light.

Liquid crystal (LC) photonic devices have attracted intensive attention in recent decades, due to the merits of tunability, cost-effectiveness, and high efficiency. However, the precise and efficient simulation of large-scale three-dimensional electrically stimulated LC photonic devices remains challenging and resource consuming. Here we report a straightforward nonuniform finite difference method (NFDM) for efficiently simulating large-scale LC photonic devices by employing a spatially nonuniform mesh grid. We show that the NFDM can be further accelerated by approximately 504 times by using the improved successive over-relaxation method (by 12 times), the symmetric boundary (by 4 times), the momentum gradient descent algorithm (by 3.5 times), and the multigrid (by 3 times). We experimentally fabricated the large-scale electrically stimulated LC photonic device, and the measured results demonstrate the effectiveness and validity of the proposed NFDM. The NFDM allocates more grids to the core area with steep electric field gradient, thus reducing the distortion of electric field and the truncation error of calculation, rendering it more precise than the finite element method and traditional finite difference method with similar computing resources. This study demonstrates an efficient and highly reliable method to simulate the large-scale electrically stimulated LC photonic device, and paves the way for customizing a large-scale LC photonic device with designable functionalities.

Electric anapoles, arising from the destructive interference of primitive and toroidal electric dipole moments, have recently emerged as a fundamental class of non-scattering sources. On the other hand, super-scattering states represent the opposite regime wherein the scattering cross-section of a subwavelength particle exceeds the single-channel limit, leading to a strong scattering behavior. Here, we demonstrate that the interplay between the topology of light and the subwavelength scatterer can lead to these two opposite responses within an isolated all-dielectric meta-atom. In particular, we present the emergence of a new non-scattering state, referred to as hybrid anapole, which surpasses conventional electric dipole anapoles by achieving a remarkable 23-fold enhancement in the suppression of far-field radiation and almost threefold enhancement in the confinement of electromagnetic energy inside the meta-atom. We also explore the role of particle orientation and its inversion symmetry in the scattering response and predict the possibility of switching between non-scattering and super-scattering states within the same platform. The presented study elucidates the role of light and matter topologies in the scattering response of subwavelength meta-atoms, uncovering two opposite regimes of light-matter interaction and opening new avenues in applications such as nonlinear optics and spectroscopy.

Indefinite metacavities (IMCs) made of hyperbolic metamaterials show great advantages in terms of extremely small mode volume due to large wave vectors endowed by the unique hyperbolic dispersion. However, quality (Q) factors of IMCs are limited by Ohmic loss of metals and radiative loss of leaked waves. Despite the fact that Ohmic loss of metals is inevitable in IMCs, the radiative loss can be further suppressed by leakage engineering. Here we propose a mirror coupled IMC structure which is able to operate at Fabry–Pérot bound states in the continuum (BICs) while the hyperbolic nature of IMCs is retained. At the BIC point, the radiative loss of magnetic dipolar cavity modes in IMCs is completely absent, resulting in a considerably increased Q factor (>90). Deviating from the BIC point, perfect absorption bands (>0.99) along with a strong near-field intensity enhancement (>1.8×104) appear when the condition of critical coupling is almost fulfilled. The proposed BICs are robust to the geometry and material composition of IMCs and anomalous scaling law of resonance is verified during the tuning of optical responses. We also demonstrate that the Purcell effect of the structure can be significantly improved under BIC and quasi-BIC regimes due to the further enhanced Q factor to mode volume ratio. Our results provide a new train of thought to design ultra-small optical nanocavities that may find many applications benefitting from strong light–matter interactions.

Exceptional points, as degenerate points of non-Hermitian parity-time symmetric systems, have many unique physical properties. Due to its flexible control of electromagnetic waves, a metasurface is frequently used in the field of nanophotonics. In this work, we developed a parity-time symmetric metasurface and implemented the 2π topological phase surrounding an exceptional point. Compared with Pancharatnam-Berry phase, the topological phase around an exceptional point can achieve independent regulation of several circular polarization beams. We combined the Pancharatnam-Berry phase with the exceptional topological phase and proposed a composite coding metasurface to achieve reflection decoupling of different circular polarizations. This work provides a design idea for polarimetric coding metasurfaces in the future.

We propose and experimentally realize a class of quasi-one-dimensional topological lattices whose unit cells are constructed by coupled multiple identical resonators, with uniform hopping and inversion symmetry. In the presence of coupling-path-induced effective zero hopping within the unit cells, the systems are characterized by complete multimerization with degenerate -1 energy edge states for open boundary condition. Su–Schrieffer–Heeger subspaces with fully dimerized limits corresponding to pairs of nontrivial flat bands are derived from the Hilbert spaces. In particular, topological bound states in the continuum (BICs) are inherently present in even multimer chains, manifested by embedding the topological bound states into a continuous band assured by bulk-boundary correspondence. Moreover, we experimentally demonstrate the degenerate topological edge states and topological BICs in radio-frequency circuits.

Metasurfaces with spin-selective transmission play an increasingly critical role in realizing optical chiral responses, especially for strong intrinsic chirality, which is limited to complex three-dimensional geometry. In this paper, we propose a planar metasurface capable of generating maximal intrinsic chirality and achieving dual-band spin-selective transmission utilizing dual quasi-bound states in the continuum (quasi-BICs) caused by the structural symmetry breaking. Interestingly, the value of circular dichroism (CD) and the transmittance of two kinds of circular polarization states can be arbitrarily controlled by tuning the asymmetry parameter. Remarkable CD approaching unity with the maximum transmittance up to 0.95 is experimentally achieved in the dual band. Furthermore, assisted by chiral BICs, the application in polarization multiplexed near-field image display is also exhibited. Our work provides a new avenue to flexibly control intrinsic chirality in planar structure and offers an alternative strategy to develop chiral sensing, multiband spin-selective transmission, and high-performance circularly polarized wave detection. The basic principle and design method of our experiments in the microwave regime can be extended to other bands, such as the terahertz and infrared wavelengths.

Overcoming the diffraction limit is crucial for obtaining high-resolution images and observing fine microstructures. With this conventional difficulty still puzzling us and the prosperous development of wave dynamics of light interacting with gravitational fields in recent years, how spatial curvature affects the diffraction limit is an attractive and important question. Here we investigate the issue of the diffraction limit and optical resolution on two-dimensional curved space—surfaces of revolution (SORs) with constant or variable spatial curvature. We show that the diffraction limit decreases and the resolution is improved on SORs with positive Gaussian curvature, opening a new avenue to super-resolution. The diffraction limit is also influenced by the propagation direction, as well as the propagation distance in curved space with variable spatial curvature. These results provide a possible method to control the optical resolution in curved space or equivalent waveguides with varying refractive index distribution and may allow one to detect the presence of the nonuniform strong gravitational effect by probing locally the optical resolution.

We propose and experimentally demonstrate a new technique, to our knowledge, to precisely measure the orbital angular momentum (OAM) spectrum of the fractional helical beam in a single shot. This is realized using a single-path interferometer scheme combined with space division multiplexing and polarization phase-shifting. Such a combination enables the single-shot recording of multiple phase-shifted interferograms, which leads to extracting the phase profile of the incident fractional helical beam. Furthermore, by adopting an orthogonal projection method, this measured phase is utilized to evaluate the corresponding OAM spectrum. To test the efficacy, a set of simulations and experiments for different fractional helical beams is demonstrated. The proposed method shows enormous potential to characterize the OAM spectrum in real time.

Research on parity-time (PT) symmetry and exceptional points in non-Hermitian laser systems has been extensively conducted. However, in practical electrically injected PT-symmetric lasers, the frequency detuning and linewidth enhancement factor of the laser can influence the symmetry breaking of the system in another dimension. We find that the previous exceptional point now transforms into a dynamic phase transition region, where the states are temporally unstable, indicating the occurrence of multimode oscillation. The relative phase and field amplitude ratio in this region also exhibit many novel phenomena indicating its instability. This region can be manipulated by adjusting the coupling strength between adjacent waveguides and the pumping intensity in the loss waveguide. Experimentally, we characterize the near-field, far-field, and spectrum of several structures, and the results validate our theoretical model. This work elucidates the dynamic process and phase transition process of electrically injected PT-symmetric lasers, providing support for the practical application of PT-symmetric lasers.

Parity-time-symmetric (PT-symmetric) metasurfaces exhibit a plethora of fascinating exceptional-point-induced phenomena, including unidirectional negative refraction and electromagnetic impurity-immunity. However, practical realization of these effects is often impeded by the high demand for gain metasurfaces (gain tangent ∼102). Here, we propose a solution to this challenge by constructing a low-gain generalized PT-symmetric system. This is achieved by transforming the high-gain metasurface into a bulky slab and then realizing it utilizing zero-index materials doped with low-gain dopants. Within this generalized PT-symmetric system, the required gain tangent of the dopants is only ∼10-1 for the emergence of a coalesced exceptional point, where the remarkable property of electromagnetic impurity-immunity effect—perfect wave transmission regardless of impurities—appears. Furthermore, we observe a further decrease in demand for gain materials in an asymmetric environment. To validate this approach, a microwave implementation is demonstrated in full-wave simulations. This work provides a feasible strategy for substantially reducing requirements on gain materials in PT-symmetric systems, thereby enabling advanced electromagnetic wave control.

Nondiffracting beams (NDBs) have presented significant utility across various fields for their unique properties of self-healing, anti-diffraction, and high-localized intensity distribution. We present a versatile and flexible method for generating high-order nondiffracting beams predicated on the Fourier transformation of polymorphic beams produced by the free lenses with tunable shapes. Based on the tunability of the digital free lenses, we demonstrate the experimental generation of various long-distance nondiffracting beams, including Bessel beams, polymorphic generalized nondiffracting beams, tilted nondiffracting beams, asymmetric nondiffracting beams, and specially structured beams generated by the superposition of Bessel beams. Our method achieves efficiency of up to about seven times compared with complex beam shaping methods. The generated NDBs exhibit characteristics of extended propagation distance and high-quality intensity profiles consistent with the theoretical predictions. The proposed method is anticipated to find applications in laser processing, optical manipulation, and other fields.

Optical manipulation of objects at the nanometer-to-micrometer scale relies on the precise shaping of a focused laser beam to control the optical forces acting on them. Here, we introduce and experimentally demonstrate surface-shaped laser traps with conformable phase-gradient force field enabling multifunctional optical manipulation of nanoparticles in two dimensions. For instance, we show how this optical force field can be designed to capture and move multiple particles to set them into an autonomous sophisticated optical transport across any flat surface, regardless of the shape of its boundary. Unlike conventional laser traps, the extended optical field of the surface laser trap makes it easier for the particles to interact among themselves and with their environment. It allowed us to optically transport multiple plasmonic nanoparticles (gold nanospheres) while simultaneously enabling their electromagnetic interaction to form spinning optically bound (OB) dimers, which is the smallest case of optical matter system. We have experimentally demonstrated, for the first time, the creation of stable spinning OB dimers with control of their rotational and translational motion across the entire surface. These traveling OB dimers guided by the phase-gradient force work as switchable miniature motor rotors, whose rotation is caused by the combined effects of optical binding forces and optical torque induced by a circularly polarized surface laser trap. The degree of customization of the surface laser traps provides a versatility that can boost the study and control of complex systems of interacting particles, including plasmonic structures as the optical matter ones of high interest in optics and photonics.

Topological insulators are most frequently constructed using lattices with specific degeneracies in their linear spectra, such as Dirac points. For a broad class of lattices, such as honeycomb ones, these points and associated Dirac cones generally appear in non-equivalent pairs. Simultaneous breakup of the time-reversal and inversion symmetry in systems based on such lattices may result in the formation of the unpaired Dirac cones in bulk spectrum, but the existence of topologically protected edge states in such structures remains an open problem. Here a photonic Floquet insulator on a honeycomb lattice with unpaired Dirac cones in its spectrum is introduced that can support unidirectional edge states appearing at the edge between two regions with opposite sublattice detuning. Topological properties of this system are characterized by the nonzero valley Chern number. Remarkably, edge states in this system can circumvent sharp corners without inter-valley scattering even though there is no total forbidden gap in the spectrum. Our results reveal unusual interplay between two different physical mechanisms of creation of topological edge states based on simultaneous breakup of different symmetries of the system.

The interaction between electrons and matter is an effective means of light emission, through mechanisms including Cherenkov radiation and Smith–Purcell radiation (SPR). In this study, we show that the superlight inverse Doppler effects can be realized in reverse Smith–Purcell radiation excited by a free electron beam with a homogeneous substrate. In particular, we find that two types of anomalous SPR exist in the homogenous substrate: special SPR and reverse SPR. Our results reveal that the electron velocity can be tuned to simultaneously excite different combinations of normal SPR, special SPR, and reverse SPR. The proposed manifold light radiation mechanism can offer greater versatility in controlling and shaping SPR.

Fractional vortex beams exhibit a higher degree of modulation dimensions than conventional vortices, thus inheriting superior anti-turbulent transmission properties through the incorporation of additional coherence modulation. However, aliasing the mixed modes induced by coherence degradation makes the quantitative measurement of the topological charge in fractional vortex beams challenging. In this study, a coherence phase spectrum was introduced, and experimental demonstrations to quantitatively determine the fractional topological charge of partially coherent fractional vortex beams were performed. By leveraging the four-dimensional measurement of a partially coherent light field, the source coherence function was inversely reconstructed, and fractional topological charges were determined with high precision by extracting the phase spectrum of the coherence function. Laguerre–Gaussian, elliptical Gaussian, and plane-wave-fraction vortex beams with various degrees of coherence were used to demonstrate measurement precision. The proposed method is applicable to X-rays and electron vortices. It has potential applications in optical encryption, high-capacity optical communication, and quantum entanglement.

The spin Hall effect of a light beam is essentially a product of circular birefringence but is rarely demonstrated. Here, we provide a scheme for initiating off-axis circular birefringence based on the spin-dependent wave vector bifurcation of Bessel beams via a single liquid crystal Pancharatnam–Berry phase element. The tilted Bessel beam shows a detectable photonic spin Hall effect. By introducing the nonlinear propagation trajectories, the spin Hall effect is greatly enhanced. More surprisingly, the two spin states exactly propagate along the scaled trajectories, enabling flexible control of the spin separation. This phenomenon is also applicable to other Bessel-like beams with nonlinear trajectories, which have been already reported.

An optical system for the generation of partially coherent beams with genuine cross-spectral density functions from spatially modulated globally incoherent sources is presented. The spatial intensity modulation of the incoherent source is achieved by quasi-planar metasurfaces based on spatial-frequency modulation of binary Bragg surface-relief diffraction gratings. Two types of beams are demonstrated experimentally: (i) azimuthally periodic, radially quasi-periodic beams and (ii) rotationally symmetric Bessel-correlated beams with annular far-zone radiation patterns.

Zero-energy topological states, which are protected by chiral symmetry against certain perturbations topologically, localize at interfaces between trivial and non-trivial phases in the Su–Schrieffer–Heeger (SSH) chain model. Here, we propose and demonstrate a method to manipulate chiral symmetry itself to improve the localized interfaces and enlarge the mode volume of topological states in the SSH model, thus optimizing the lasing performance of localized interfaces. As multiple defects corresponding to off-diagonal perturbations in an eigenmatrix are introduced, the topological state expands and extends to extra defects at the topological interface without breaking chiral symmetry. We apply the proposed method in electrical pumping semiconductor laser arrays to verify our theoretical prediction and optimize the output characteristics of the devices. The measured results of the proposed multi-defect SSH laser array show that the output power has been increased by 27%, and the series resistance and far-field divergence have been reduced by half compared to the traditional SSH laser array, establishing a high-performance light source for integrated silicon photonics, infrared light detection and ranging, and so on. Our work demonstrates that the proposed method is capable of improving topological localized interfaces and redistributing zero-energy topological states. Furthermore, our method can be applied to other platforms and inspire optimizations of more devices in broader areas.

A precise knowledge of the polarization state of light is crucial in technologies that involve the generation and application of structured light fields. The implementation of efficient methods to determine and characterize polarization states is mandatory; more importantly, these structured light fields must be at any spatial location at a low expense. Here, we introduce a new characterization method that relies on a rather convenient description of electric fields without neglecting their 3D nature. This method is particularly suitable for highly focused fields, which exhibit important polarization contributions along their propagation direction in the neighborhood of the focal region; i.e., the contributions out of the planes transverse to the optical axis, conventionally used to specify the polarization state of these fields. As shown, the method allows the extraction of information about the three field components at relatively low computational and experimental costs. Furthermore, it also allows characterization of the polarization state of a field in a rather simple manner. To check the feasibility and reliability of the method, we determined both analytically and experimentally the local polarization states for a series of benchmark input fields with it, finding excellent agreement between the theory and experiment.

Optical resonators with high quality (Q) factors are paramount for the enhancement of light–matter interactions in engineered photonic structures, but their performance always suffers from the scattering loss caused by fabrication imperfections. Merging bound states in the continuum (BICs) provide us with a nontrivial physical mechanism to overcome this challenge, as they can significantly improve the Q factors of quasi-BICs. However, most of the reported merging BICs are found at Γ point (the center of the Brillouin zone), which intensively limits many potential applications based on angular selectivity. To date, studies on manipulating merging BICs at off-Γ point are always accompanied by the breaking of structural symmetry that inevitably increases process difficulty and structural defects to a certain extent. Here, we propose a scheme to construct merging BICs at almost an arbitrary point in momentum space without breaking symmetry. Enabled by the topological features of BICs, we merge four accidental BICs with one symmetry-protected BIC at the Γ point and merge two accidental BICs with opposite topological charges at the off-Γ point only by changing the periodic constant of a photonic crystal slab. Furthermore, the position of off-Γ merging BICs can be flexibly tuned by the periodic constant and height of the structure simultaneously. Interestingly, it is observed that the movement of BICs occurs in a quasi-flatband with ultra-narrow bandwidth. Therefore, merging BICs in a tiny band provide a mechanism to realize more robust ultrahigh-Q resonances that further improve the optical performance, which is limited by wide-angle illuminations. Finally, as an example of application, effective angle-insensitive second-harmonic generation assisted by different quasi-BICs is numerically demonstrated. Our findings demonstrate momentum-steerable merging BICs in a quasi-flatband, which may expand the application of BICs to the enhancement of frequency-sensitive light–matter interaction with angular selectivity.

In this work, we apply the group representation theory to systematically study polarization singularities in the in-plane components of the electric fields supported by a planar electromagnetic (EM) resonator with generic rotation and reflection symmetries. We reveal the intrinsic connections between the symmetries and the topological features, i.e., the spatial configuration of the in-plane fields and the associated polarization singularities. The connections are substantiated by a simple relation that links the topological charges of the singularities and the symmetries of the resonator. To verify, a microwave planar resonator with the D8 group symmetries is designed and numerically simulated, which demonstrates the theoretical findings well. Our discussions can be applied to generic EM resonators working in a wide EM spectrum, such as circular antenna arrays, microring resonators, and photonic quasi-crystals, and provide a unique symmetry perspective on many effects in singular optics and topological photonics.

We studied the transport properties of a driven-dissipative photonic network, where multiple photonic cavities are coupled through a nonreciprocal bus with unidirectional transmission. For short-range coupling between the cavities, the occurrence of nonreciprocal amplification can be linked to a topological phase transition of the underlying dynamic Hamiltonian. However, for long-range coupling, we show that the correspondence between the nonreciprocal amplification transition and the topological phase transition breaks down as the transition conditions deviate significantly from each other. We found the exact transition condition for nonreciprocal amplification, supported by analytical calculation and numerical simulation. We also investigated the stability, the crossover from short- to long-range coupling, and the bandwidth of the nonreciprocal amplification. Our work has potential applications in signal transmission and amplification, and also paves the way to study other topological and non-Hermitian systems with long-range coupling and nontrivial boundary effects.

Higher-order exceptional points (EPs), which appear as multifold degeneracies in the spectra of non-Hermitian systems, are garnering extensive attention in various multidisciplinary fields. However, constructing higher-order EPs still remains a challenge due to the strict requirement of the system symmetries. Here we demonstrate that higher-order EPs can be judiciously fabricated in parity–time (PT)-symmetric staggered rhombic lattices by introducing not only on-site gain/loss but also non-Hermitian couplings. Zero-energy flatbands persist and symmetry-protected third-order EPs (EP3s) arise in these systems owing to the non-Hermitian chiral/sublattice symmetry, but distinct phase transitions and propagation dynamics occur. Specifically, the EP3 arises at the Brillouin zone (BZ) boundary in the presence of on-site gain/loss. The single-site excitations display an exponential power increase in the PT-broken phase. Meanwhile, a nearly flatband sustains when a small lattice perturbation is applied. For the lattices with non-Hermitian couplings, however, the EP3 appears at the BZ center. Quite remarkably, our analysis unveils a dynamical delocalization-localization transition for the excitation of the dispersive bands and a quartic power increase beyond the EP3. Our scheme provides a new platform toward the investigation of the higher-order EPs and can be further extended to the study of topological phase transitions or nonlinear processes associated with higher-order EPs.

Metasurface has provided unprecedented freedoms in manipulating electromagnetic (EM) waves, exhibiting fascinating functions. Conventionally, these functions are implemented right on metasurfaces, where spatial modulations on EM wave amplitudes or phases are achieved by meta-atoms. This study proposes the concept of virtual metasurface (VM), which is formed by arrays of foci away from the entity metasurface. Unlike conventional metasurfaces, spatial modulations on the amplitudes or phases of EM waves occur in the air, with a focal length distance from the entity metasurface. As a proof of concept, we demonstrated a transmissive VM. The entity metasurface consists of transmissive focusing metasurface tiles (TFMTs) with the same focal length. Two TFMTs were designed with phase difference π to enable the most typical checkerboard configuration. The TFMTs were assembled to form the entity metasurface, whereas their foci formed the VM. Due to the π phase difference among adjacent foci, EM propagation along the normal direction was cancelled, leading to four tilted far-field beams. The concept of VM can be readily extended to higher frequencies from terahertz to optical regimes and may find wide applications in communication, camouflage, and other fields.

Parity–time (PT) symmetric lattices have been widely studied in controlling the flow of waves, and recently, moiré superlattices, connecting the periodic and non-periodic potentials, have been introduced for exploring unconventional physical properties in physics, while the combination of both and nonlinear waves therein remains unclear. Here, we report a theoretical survey of nonlinear wave localizations in PT symmetric moiré optical lattices, with the aim of revealing localized gap modes of different types and their stabilization mechanism. We uncover the formation, properties, and dynamics of fundamental and higher-order gap solitons as well as vortical ones with topological charge, all residing in the finite bandgaps of the underlying linear-Bloch wave spectrum. The stability regions of localized gap modes are inspected in two numerical ways: linear-stability analysis and direct perturbance simulations. Our results provide an insightful understanding of soliton physics in combined versatile platforms of PT symmetric systems and moiré patterns.

Optical geometrical transformation is a novel and powerful tool to switch orbital angular momentum (OAM) states in modern optics. We demonstrate a scheme to operate multiplication and division in OAM by Fermat’s spiral transformation. The characteristics of the output beams in the case of integer and fraction OAM operations are presented in detail. Additionally, the power weight of the output OAM modes and the interference patterns of the output beams are reported to confirm the expected ability of OAM mode conversion by Fermat’s spiral transformation. We further investigate the evolution of OAM beams in operations theoretically and experimentally. This work provides a practical way to perform an optical transformation mapping on OAM beams. It can find application in optical communications with larger OAM mode numbers as well as quantum information in high-dimensional systems.

We report three orders of magnitude optical cooling of the fundamental torsional mode of a 5 mm long, 550 nm diameter optical nanofiber. The rotation of the nanofiber couples to the polarization of guided laser fields. We use a weak laser probe to monitor the rotation and use feedback to modulate the polarization of an auxiliary drive laser providing torque. Our results present a tool for the optomechanical control of large-scale torsional resonators, with metrological applications and potential implications for studying macroscopic objects in quantum states.

Optical skyrmions are quasiparticles with nontrivial topological textures that have significant potential in optical information processing, transmission, and storage. Here, we theoretically and experimentally achieve the conversion of optical skyrmions among Néel, Bloch, intermediate skyrmions, and bimerons by polarization devices, where the fusion and annihilation of optical skyrmions are demonstrated accordingly. By analyzing the polarization pattern in Poincaré beams, we reveal the skyrmion topology dependence on the device, which provides a pathway for the study of skyrmion interactions. A vectorial optical field generator is implemented to realize the conversion and superposition experimentally, and the results are in good agreement with the theoretical predictions. These results enhance our comprehension of optical topological quasiparticles, which could have a significant impact on the transfer, storage, and communication of optical information.

The phenomenon of branched flow has attracted researchers since its inception, with recent observations of the light branching on soap bubbles. However, previous studies have primarily focused on the flat spacetime, overlooking the effect of surface curvature on branched flows. In this paper, we explore the branched flow phenomenon of light on a rough curved surface called constant Gaussian curvature surfaces (CGCSs). Compared with flat space, a CGCS demonstrates that the first branching point advances due to the focusing effect of the positive curvature of the surface. Furthermore, unlike on flat space, optical branches on curved surfaces do not consistently become chaotic during its transmission in a random potential field. On the contrary, the “entropy” decreases at specific positions, which reveals a sink flow phenomenon following the generation of branched flows. This result highlights the time inversion characteristics of CGCSs. Lastly, we demonstrated that the anomalous entropy reduction is related to the transverse and longitudinal coherence transformations of light. We suppose these efforts would fuel further investigation of the thermodynamic evolution and spatiotemporal inversion of random caustics, as well as their future application in the information transmission of random potentials in curved spacetime.

In this paper, we present an approach called the free lens modulation (FLM) method to generate high-perfection 3D generalized perfect optical vortices (GPOVs) with topological charges of 1–80. In addition, 2D and 3D GPOVs were produced by altering the parameters of the freely shaped lenses. To verify the quality of the GPOVs produced with the FLM method, we conducted optical trapping experiments and realized linear control of the rotation rate of the trapped particle. Due to the great advantages of high perfection and high power usage in generating arbitrarily shaped GPOVs, the FLM method is expected to be applied in optical manipulation, optical communications, and other fields.

Structured optical fields embedded with polarization singularities (PSs) have attracted extensive attention due to their capability to retain topological invariance during propagation. Many advances in PS research have been made over the past 20 years in the areas of mathematical description, generation and detection technologies, propagation dynamics, and applications. However, one of the most crucial and difficult tasks continues to be manipulating PSs with multiple degrees of freedom, especially in three-dimensional (3D) tailored optical fields. We propose and demonstrate the longitudinal PS lines obtained by superimposing Bessel-like modes with orthogonal polarization states on composite vector optical fields (VOFs). The embedded PSs in the fields can be manipulated to propagate robustly along arbitrary trajectories, or to annihilate, revive, and transform each other at on-demand positions in 3D space, allowing complex PS’ topological morphology and intensity patterns to be flexibly customized. Our findings could spur further research into singular optics and help with applications such as micromanipulation, microstructure fabrication, and optical encryption.

Photonic topological insulators protected by the lattice spatial symmetry (e.g., inversion and rotation symmetry) mainly support single type edge state, interpreted by either valley or pseudo-spin. Here, we demonstrate theoretically, numerically, and experimentally that a type of judiciously designed two-dimensional Kekulé photonic crystal with time reversal symmetry can possess topological valley and pseudo-spin edge states in different frequency bands. Topologically robust transportation of both the valley and pseudo-spin edge states was confirmed by measuring the transmission of straight and z-shaped interface supported edge mode and comparing with bulk modes in the microwave frequency regime. In addition, we show that due to the distinct topological origins, valley and pseudo-spin edge states can be distinguished by examining their end-scattering into the free space. Our system provides an alternative way in manipulating electromagnetic waves with additional degree-of-freedom, which has potential applications for robust and high-capacity waveguiding and multi-mode dividing.

We develop and apply an optimization method to design unidirectional invisibility cloaks. Our method is based on minimizing the forward scattering amplitude of the cloaked object which, by the optical theorem, is equivalent to the total cross section. The use of the optical theorem circumvents the need to evaluate and integrate the scattering amplitude over an angle at each iteration, and thus provides a simpler, more computationally efficient objective function to optimize structures. We implement the approach using gradient descent optimization and present several gradient-permittivity unidirectional cloaks that reduce scattering by metallic targets of different sizes and shapes.

Second-order topological insulators (SOTIs) have recently attracted much attention due to their capability to support lower-dimensional topological states, namely, the corner states. Here, we demonstrate that properly designed supercell metasurfaces can support photonic corner states, meanwhile further serving as an ideal platform for the implementations of topological polaritons and dynamically reconfigurable corner states by assembling two-dimensional materials. Such metasurfaces consist of an array of finite-sized SOTIs mimicking the two-dimensional Su–Schrieffer–Heeger model. We reveal that the topological transition happens in unit cells without the bandgap, and nondegenerate multipolar corner states emerge in the supercell metasurface due to the inter- and intrasupercell coupling effects. Especially since these corner states are above the light line of the metasurface, we realize the collective stimulation of the two dipolar corner states and their superposition state via far-field excitation. By stacking monolayer hexagonal boron nitride film onto the metasurface, we further achieve the topological phonon polaritons through the strong coupling between the corner state and the phonon, which is confirmed by the Rabi splitting as well as anticrossing behavior emerging in the transmission spectra. Furthermore, we reveal the robustness of the corner state and strong coupling by introducing defects into the metasurface. Finally, tunable corner state and strong coupling with on-demand control are realized by assembling monolayer graphene onto the metasurface. Our theoretical study proposes a unique hybrid-material platform for topological polaritonics and reconfigurable topological photonics, which can promote large-area topological applications in practice.

Metasurface-empowered bound state in the continuum (BIC) provides a unique route for fascinating functional devices with infinitely high quality factors. This method is particularly attractive to the terahertz community because it may essentially solve the deficiencies in terahertz filters, sensors, lasers, and nonlinear sources. However, most BIC metasurfaces are limited to specified incident angles that seriously dim their application prospects. Here, we propose that a dual-period dielectric metagrating can support multiple families of BICs that originate from guided mode resonances in the dielectric grating and exhibit infinite quality factors at arbitrarily tilted incidence. This robustness was analyzed based on the Bloch theory and verified at tilted incident angles. We also demonstrate that inducing geometric asymmetry is an efficient way to manipulate the leakage and coupling of these BICs, which can mimic the electromagnetically induced transparency (EIT) effect in our dual-period metagrating. In this demonstration, a slow-light effect with a measured group delay of 117 ps was achieved. The incidence-insensitive BICs proposed here may greatly extend the application scenarios of the BIC effect. The high Q factor and outstanding slow-light effect in the metagrating show exciting prospects in realizing high-performance filters, sensors, and modulators for prompting terahertz applications.

Zero modes are symmetry protected ones whose energy eigenvalues have zero real parts. In Hermitian arrays, they arise as a consequence of the sublattice symmetry, implying that they are dark modes. In non-Hermitian systems that naturally emerge in gain/loss optical cavities, particle-hole symmetry prevails instead; the resulting zero modes are no longer dark but feature π/2 phase jumps between adjacent cavities. Here, we report on the direct observation of zero modes in a non-Hermitian three coupled photonic crystal nanocavities array containing quantum wells. Unlike the Hermitian counterparts, the observation of non-Hermitian zero modes upon single pump spot illumination requires vanishing sublattice detuning, and they can be identified through far-field imaging and spectral filtering of the photoluminescence at selected pump locations. We explain the zero-mode coalescence as a parity-time phase transition for small coupling. These zero modes are robust against coupling disorder and can be used for laser mode engineering and photonic computing.

Singularities in the spectra of open systems, known as exceptional points (EPs), have been shown to exhibit nontrivial topological properties and enhanced sensitivities. Here, we propose a novel approach to realize the EPs in a plasmon-exciton hybrid system and explore their applications in enhanced nanoscale sensing technology. We consider a plasmon-exciton system composed of a gold nanorod and a monolayer WSe2. By controlling the geometric parameters of the nano-hybrid system, we obtain simultaneous coalescence of the resonance frequencies and loss rates of the hybrid system, which is a unique feature of EPs. Numerical simulations show its application in enhanced nanoscale sensing for environmental refractive indices. Our work opens the way to a new class of sensors based on EP-enhanced sensing, with intrinsic nanoscale sensitivity due to the sub-diffraction-limit size of the plasmon-exciton nano-hybrid system.

Since the discovery of topological insulators, topological phases have generated considerable attention across the physics community. The superlattices in particular offer a rich system with several degrees of freedom to explore a variety of topological characteristics and control the localization of states. Albeit their importance, characterizing topological invariants in superlattices consisting of a multi-band structure is challenging beyond the basic case of two-bands as in the Su–Schreifer–Heeger model. Here, we experimentally demonstrate the direct measurement of the topological character of chiral superlattices with broken inversion symmetry. Using a CMOS-compatible nanophotonic chip, we probe the state evolving in the system along the propagation direction using novel nanoscattering structures. We employ a two-waveguide bulk excitation scheme to the superlattice, enabling the identification of topological zero-energy modes through measuring the beam displacement. Our measurements reveal quantized beam displacement corresponding to 0.088 and -0.245, in the cases of trivial and nontrivial photonic superlattices, respectively, showing good agreement with the theoretical values of 0 and -0.25. Our results provide direct identification of the quantized topological numbers in superlattices using a single-shot approach, paving the way for direct measurements of topological invariants in complex photonic structures using tailored excitations with Wannier functions.

Topological rainbow trapping, which can separate and trap different frequencies of topological states into different positions, plays a key role in topological photonic devices. However, few schemes have been proposed to realize topological rainbow trapping effects in lossy photonic crystal systems, which has restricted their practical applications, since loss is ubiquitous in nanophotonic devices. Here, we propose a method to realize a topological rainbow based on non-Hermitian twisted piecing photonic crystals. Different frequencies of topological photonic states are separated and trapped in different positions without overlap in the lossy photonic crystals. Moreover, the frequencies of interface states can be modulated by loss, and a topological rainbow can also be achieved in both TE and TM modes. This work brings an effective method to realize robust nanophotonic multiwavelength devices in non-Hermitian systems.

Three-dimensional programmable transport of micro/nano-particles can be straightforwardly achieved by using optical forces arising from intensity and phase gradients of a structured laser beam. Repulsor and tractor beams based on such forces and shaped in the form of a curved trajectory allow for downstream and upstream (against light propagation) transportation of particles along the beams, respectively. By using both types of beams, bidirectional transport has been demonstrated on the example of a circular helix beam just by tuning its phase gradient. Specifically, the transport of a single particle along a loop of the helix has been reported. However, the design and generation of helix-shaped beams is a complex problem that has not been completely addressed, which makes their practical application challenging. Moreover, there is no evidence of simultaneous transport of multiple particles along the helix trajectory, which is a crucial requisite in practice. Here, we address these challenges by introducing a theoretical background for designing helix beams of any axial extension, shape, and phase gradient that takes into account the experimental limitations of the optical system required for their generation. We have found that only certain phase gradients prescribed along the helix beam are possible. Based on these findings, we have experimentally demonstrated, for the first time, helix-shaped repulsor and tractor beams enabling programmable bidirectional optical transport of particles en masse. This is direct evidence of the essential functional robustness of helix beams arising from their self-reconstructing character. These achievements provide new insight into the behavior of helix-shaped beams, and the proven technique makes their implementation easier for optical transport of particles as well as for other light–matter interaction applications.

We address space–frequency domain coherence properties of broadband light-emitting diodes (white LEDs) and fields radiated by them. Inverse-source techniques are employed to determine the spectral degree of spatial coherence of an effective planar source representing a real LED, and coherent elementary fields associated with it. By fitting with experimental measurements, we formulate simple analytical coherence models that can be used as a basis for theoretical and experimental studies of the coherence of polychromatic stationary light in free space and in various optical systems. In particular, we find that radiation from white LEDs follows closely Wolf’s scaling law for spectral invariance [Phys. Rev. Lett.56, 1370 (1986)PRLTAO0031-900710.1103/PhysRevLett.56.1370] in the blue and the phosphor-generated parts of the spectrum separately, but not across the entire white-light spectrum.

The optical coupled resonant system consisting of an integrated resonator with gain and a resonator with loss provides an excellent platform to create exceptional points (EPs) in non-Hermitian systems. Most previous studies have focused on the striking intensity feature of EPs, but its phase response is seldom investigated. In this work, we present a thorough study on the phase response of an EP system. Intriguingly, the phase response exhibits distinct behavior depending on the ordering of the ring resonators: when the input light in a bus waveguide is coupled directly or indirectly to the ring with a gain, the phase response is featured by nonmonotonic transition and 2π monotonic transition, respectively. We also prove that the newly identified phase features are theoretically guaranteed. These phase responses produce unique group delays that have never been found in other coupled resonant systems. The results deepen our understanding on EPs in non-Hermitian systems and are potentially useful for practical applications exploiting phase features.

In the study of exceptional point (EP)-based sensors, the concrete form of the output spectrum is often dismissed, and it is assumed that there is a corresponding relation between the peaks/valleys in the transmission spectrum and the real parts of the eigenvalues of the system. We point out that this assumption does not always hold. An effect, which is mathematically similar to electromagnetically induced transparency (EIT), may result in a ‘pseudo spectrum splitting’ that does not correspond to the splitting between the eigenvalues. The effect shall be taken care of when designing an EP-based sensor since it may cause measurement error and misunderstanding such as recognization of the spectrum splitting as the eigenvalue splitting at the exceptional point. We also propose to intentionally utilize this ‘pseudo splitting’ to design a sensor, which does not work at an EP, that has an EP-like spectrum splitting.

With its unique and exclusive linear and nonlinear optical characteristics, epsilon-near-zero (ENZ) photonics has drawn a tremendous amount of attention in the recent decade in the fields of nanophotonics, nonlinear optics, plasmonics, light-matter interactions, material science, applied optical science, etc. The extraordinary optical properties, relatively high tuning flexibility, and CMOS compatibility of ENZ materials make them popular and competitive candidates for nanophotonic devices and on-chip integration in all-optical and electro-optical platforms. With exclusive features and high performance, ENZ photonics can play a big role in optical communications and optical data processing. In this review, we give a focused discussion on recent advances of the theoretical and experimental studies on ENZ photonics, especially in the regime of nonlinear ENZ nanophotonics and its applications. First, we overview the basics of the ENZ concepts, mechanisms, and nonlinear ENZ nanophotonics. Then the new advancements in theoretical and experimental optical physics are reviewed. For nanophotonic applications, the recent decades saw rapid developments in various kinds of different ENZ-based devices and systems, which are discussed and analyzed in detail. Finally, we give our perspectives on where future endeavors can be made.

Single molecular localization microscopy (SMLM) is a useful tool in biological observation with sub-10-nm resolution. However, SMLM is incapable of discerning two molecules within the diffraction-limited region unless with the help of a stochastic on–off switching scheme which yet entails time-consuming processes. Here, we produce a novel kind of focal spot pattern, called sub-diffraction dark spot (SDS), to localize molecules within the sub-diffraction region of interest. In our proposed technique nominated as sub-diffracted dark spot localization microscopy (SDLM), multiple molecules within the diffraction-limited region could be distinguished without the requirement of stochastic fluorescent switches. We have numerically investigated some related impacts of SDLM, such as detection circle diameter, collected photon number, background noise, and SDS size. Simulative localization framework has been implemented on randomly distributed and specifically structured samples. In either two- or three-dimensional case, SDLM is evidenced to have ∼2 nm localization accuracy.

In this paper, an ultrathin and ultrabroadband metamaterial absorber based on 3D water microchannels is proposed. The experimental results show an absorption rate over 90% and a relative bandwidth up to 165% in the frequency band between 9.6 and 98.9 GHz. This polarization-independent absorber can work at a wide angle of incidence and exhibits good thermal stability. Benefiting from ultrabroadband absorption, thin thickness, low cost, and environmentally friendly materials, the proposed metamaterial absorber can be used in the fields of electromagnetic wave stealth and electromagnetic radiation protection. Related device design and research methods can be extended to the applied research in the terahertz and optical bands.

We report an experimental observation of a record-breaking ultrahigh rotation frequency about 6 GHz in an optically levitated nanoparticle system. We optically trap a nanoparticle in the gravity direction with a high numerical aperture (NA) objective lens, which shows significant advantages in compensating the influences of the scattering force and the photophoretic force on the trap, especially at intermediate pressure (about 100 Pa). This allows us to trap a nanoparticle from atmospheric to low pressure (10-3 Pa) without using feedback cooling. We measure a highest rotation frequency about 4.3 GHz of the trapped nanoparticle without feedback cooling and a 6 GHz rotation with feedback cooling, which is the fastest mechanical rotation ever reported to date. Our work provides useful guides for efficiently observing hyperfast rotation in the optical levitation system and may find various applications such as in ultra-sensitive torque detection, probing vacuum friction, and testing unconventional decoherence theories.

Epsilon-near-zero and epsilon near-pole materials enable reflective systems supporting a class of symmetry-protected and accidental embedded eigenstates (EEs) characterized by a diverging phase resonance. Here we show that pairs of topologically protected scattering singularities necessarily emerge from EEs when a non-Hermitian parameter is introduced, lifting the degeneracy between oppositely charged singularities. The underlying topological charges are characterized by an integer winding number and appear as phase vortices of the complex reflection coefficient. By creating and annihilating them, we show that these singularities obey charge conservation, and provide versatile control of amplitude, phase, and polarization in reflection, with potential applications for polarization control and sensing.

The exploration of quantum inspired symmetries in optical systems has spawned promising physics and provided fertile ground for developing devices exhibiting exotic functionalities. Founded on the anti-parity–time (APT) symmetry that is enabled by both spatial and temporal interplay between gain and loss, we demonstrate theoretically and numerically bi-color lasing in a single micro-ring resonator with spatiotemporal modulation along its azimuthal direction. In contrast to conventional multi-mode lasers that have mixed-frequency output, our laser exhibits stable, demultiplexed, tunable bi-color emission at different output ports. Our APT-symmetry-based laser may point out a new route for realizing compact on-chip coherent multi-color light sources.

Bound states in the continuum (BICs) and Fano resonances in planar photonic lattices, including metasurfaces and photonic-crystal slabs, have been studied extensively in recent years. Typically, the BICs and Fano resonances are associated with the second stop bands open at the second-order Γ point. This paper addresses the fundamental properties of the fourth stop band accompanied by BICs at the third-order Γ point in one-dimensional leaky-mode photonic lattices. At the fourth stop band, one band edge mode suffers radiation loss, thereby generating a Fano resonance, while the other band edge mode becomes a nonleaky BIC. The fourth stop band is controlled primarily by the Bragg processes associated with the first, second, and fourth Fourier harmonic components of the periodic dielectric constant modulation. The interplay between these three major processes closes the fourth band gap and induces a band flip whereby the leaky and BIC edges transit across the fourth band gap. At the fourth stop band, an accidental BIC is formed owing to the destructive interplay between the first and second Fourier harmonics. When the fourth band gap closes with strongly enhanced radiative Q factors, Dirac cone dispersions can appear at the third-order Γ point.

The control of spin electromagnetic (EM) waves is of great significance in optical communications. Although geometric metasurfaces have shown unprecedented capability to manipulate the wavefronts of spin EM waves, it is still challenging to independently manipulate each spin state and intensity distribution, which inevitably degrades metasurface-based devices for further applications. Here we propose and experimentally demonstrate an approach to designing spin-decoupled metalenses based on pure geometric phase, i.e., geometric metasurfaces with predesigned phase modulation possessing functionalities of both convex lenses and concave lenses. Under the illumination of left-/right-handed circularly polarized (LCP or RCP) terahertz (THz) waves, these metalenses can generate transversely/longitudinally distributed RCP/LCP multiple focal points. Since the helicity-dependent multiple focal points are locked to the polarization state of incident THz waves, the relative intensity between two orthogonal components can be controlled with different weights of LCP and RCP THz waves, leading to the intensity-tunable functionality. This robust approach for simultaneously manipulating orthogonal spin states and energy distributions of spin EM waves will open a new avenue for designing multifunctional devices and integrated communication systems.

Optical angular momentum (OAM)-based structured light beams provide an additional degree of freedom for practical applications ranging from optical communication to laser-based material processing. Many techniques exist for generating such beams within laser sources and these primarily rely upon the use of specially designed optical components that limit laser power scaling and ready tunability of the topological charge and polarization of the output OAM beams. Here we show that some of these limitations can be overcome by employing a computer controlled reflective phase-only spatial light modulator to adaptively tailor the input (and subsequent output) beam wavefront and polarization in a few-mode fiber amplifier. In this way modal-coupling-induced beam distortion within the fiber amplifier can be mitigated and we are able to generate at will any desired supported spatial mode guided in the fiber, including conventional linearly polarized (LP) modes, scalar OAM modes, and cylindrical vector modes, at average powers >10 W and with a peak power of >11 kW. Our results pave the way to the realization of practical high-power structured laser sources with tunable chirality and polarization.

Deep-subwavelength all-dielectric composite materials are believed to tightly obey the Maxwell Garnett effective medium theory. Here, we demonstrate that the Maxwell Garnett theory could break down due to evanescent fields in deep-subwavelength dielectric structures. By using two- and three-dimensional dielectric composite materials with inhomogeneities at a scale of λ/100, we show that local evanescent fields generally occur near the dielectric inhomogeneities. When tiny absorptive constituents are placed there, the absorption and transmission of the whole composite will show strong dependence on the positions of the absorptive constituents. The Maxwell Garnett theory fails to predict such position-dependent characteristics because it averages out the evanescent fields. By taking the distribution of the evanescent fields into consideration, we have made a correction to the Maxwell Garnett theory so that the position-dependent characteristics become predictable. We reveal not only the breakdown of the Maxwell Garnett theory, but also a unique phenomenon of “invisible” loss induced by the prohibition of electric fields at deep-subwavelength scales. We believe our work promises a route to control the macroscopic properties of composite materials without changing their composition, which is beyond the traditional Maxwell Garnett theory.

A concise, efficient, and practical direct-view scheme is presented to generate arbitrary cylindrical vector (CV) beams, including CV beams, vortex beams, and cylindrical vector vortex (CVV) beams, by a vortex half-wave plate (VHP). Six kinds of first-order and other high-order CV beams, such as azimuthally polarized (AP) beams, antivortex radial polarization mode beams, and three-order AP beams, are formed by simply rotating a half-wave plate. The Stokes parameters and double-slit interference of multitype CV beams are investigated in detail. The polarization parameters, including degree of polarization, polarization azimuth, and ellipticity, are obtained, which demonstrates the efficient generation of CV beams. In addition, the double-slit interference experiment is introduced in the setup, and fringe misplacement and tilt appear for CVV beams, in which the misplacement number M is 2P+1 for P≤2 and 2P-1 for P≥3, where P is the polarization order number, and the fringe tilt offset is positively related to the topological charge number l of CVV beams. In addition, new types of VHPs can be formed by cascading two or more VHPs when the types of available VHPs are limited, assisting in more flexible generation of multitype CV beams. It is experimentally demonstrated that arbitrary CV beams with high quality are effectively achieved by the proposed setup, and the double-slit interference method can be utilized to determine and analyze CV beams rapidly and concisely by practical performance, which shows the potential to be implemented as a commercial device.

The physical origin of the fractal topological band-gap structure in the one-dimensional Thue–Morse system has been revealed, which is characterized by the evolutions of two types of topological singularities with zero-scattering properties and the paths of phase vortex points, which are the mirrored paths of the first-type singularities. The field distribution of the upper and lower gap-edge states will interchange when the traditional gaps are closed and reopened. The topologically protected edge-states are found at both traditional gaps and fractal gaps. Our work broadens the topological properties of quasicrystals or aperiodic systems and provides potential applications in new optoelectronic devices.

Photonic topological edge states in one-dimensional dimer chains have long been thought to be robust to structural perturbations by mapping the topological Su–Schrieffer–Heeger model of a solid-state system. However, the edge states at the two ends of a finite topological dimer chain will interact as a result of near-field coupling. This leads to deviation from topological protection by the chiral symmetry from the exact zero energy, weakening the robustness of the topological edge state. With the aid of non-Hermitian physics, the splitting frequencies of edge states can be degenerated again, with topological protection recovered by altering the gain or loss strength of the structure. This point of coalescence is known as the exceptional point (EP). The intriguing physical properties of EPs in topological structures give rise to many fascinating and counterintuitive phenomena. In this work, based on a finite non-Hermitian dimer chain composed of ultra-subwavelength resonators, we propose theoretically and verify experimentally that the sensitivity of topological edge states is greatly affected when the system passes through the EP. Using the EP of a non-Hermitian dimer chain, we realize a new sensor that is sensitive to perturbation of on-site frequency at the end of the structure and yet topologically protected from internal perturbation of site-to-site couplings. Our demonstration of a non-Hermitian topological structure with an EP paves the way for the development of novel sensors that are not sensitive to internal manufacturing errors but are highly sensitive to changes in the external environment.

One of the most prominent features of quantum entanglement is its invariability under local unitary transformations, which implies that the degree of entanglement or nonseparability remains constant during free-space propagation, true for both quantum and classically entangled modes. Here we demonstrate an exception to this rule using a carefully engineered vectorial light field, and we study its nonseparability dynamics upon free-space propagation. We show that the local nonseparability between the spatial and polarization degrees of freedom dramatically decays to zero while preserving the purity of the state and hence the global nonseparability. We show this by numerical simulations and corroborate it experimentally. Our results evince novel properties of classically entangled modes and point to the need for new measures of nonseparability for such vectorial fields, while paving the way for novel applications for customized structured light.

Recent advances in the development of a nanocavity based on a metal–insulator–metal (MIM) structure have provided a great opportunity to enhance the performance of photonic devices. However, the underlying physics behind the emission enhancement obtained from such cavities is under debate. Here, in this work, we designed and investigated MIM nanocavities to reveal the mechanisms for the observed 260-fold photoluminescence enhancement from LDS 798 fluorescent dye. This study provides a pathway to engineer the emission properties of an emitter not only through the enhancement of the Purcell factor but mainly through enhancement of the excitation rate. Our numerical simulations support the experimentally acquired results. We believe an MIM cavity and dye-based hybrid system design based on the revealed enhancement process and structural simplicity, will provide more efficient, lithography free, and low-cost advanced nanoscale devices.

Anapole metamaterials have attracted growing attention in recent years due to their unique nonradiating and nontrivial properties. Although anapole modes have been demonstrated in metamaterials with three-dimensional structures, the design and realization of planar anapole metamaterials in a wide frequency range is still a big challenge. Here we propose and experimentally demonstrate a planar anapole metamaterial consisting of dumbbell-shaped apertures on a stainless-steel sheet at terahertz frequencies. The planar metamaterial can generate a resonant transparency in the terahertz spectrum due to the excitation of the anapole mode. Particularly, the frequency of anapole-induced resonant transparency can be tuned easily in the range of 0.15–0.93 THz by simply varying one geometric parameter of the dumbbell apertures. We anticipate that the resonant transparency in planar anapole metamaterials can be potentially used in filters, sensors, or other photonic devices.

Controlling the polarization state of electromagnetic waves is an important topic in microwaves due to the enormous application potential in radar technology and mobile communications. Here, we propose a programmable metasurface based on single-pole double-throw switches to realize multifunctional polarization conversions. A structure of the double-sided metallic pattern is adopted in the metasurface, in which a novel double-pole double-throw hub is achieved to guide the energy direction. Such a mechanism successfully induces multiple transmission channels into the metasurface structure for functional design. By controlling the states of the switches with a field programmable gate array, the x- and y-polarizations of the incident waves can be efficiently modulated into linear co- and cross-polarizations of transmitted waves, suggesting a higher degree of freedom on wave manipulations. The proposed metasurface can be developed as a near-field information encoder to transmit binary coding sequence according to the energy distribution. Character transmissions are realized by programming binary ASCII codes on the transmitted fields. Nine supercells on the metasurface can encode 9-bit binary information in one frame of near-field imaging, which can be switched in real time with high speed. We envision that this work will develop digital coding applications to control the polarization information.

Non-mode-selective (NMS) multiplexers (muxes) are highly desirable for coherent power combining to produce a high-power beam with a shaped profile (wavefront synthesis) from discrete, phase-locked emitters. We propose a design for a multi-plane light conversion (MPLC)-based NMS mux, which requires only a few phase masks for coherently combining hundreds of discrete input beams into an output beam consisting of hundreds of Hermite–Gaussian (HG) modes. The combination of HG modes as a base can further construct a beam with arbitrary wavefront. The low number of phase masks is attributed to the identical zero-crossing structure of the Hadamard-coded input arrays and of the output HG modes, enabling the practicality of such devices. An NMS mux supporting 256 HG modes is designed using only seven phase masks, and achieves an insertion loss of -1.6 dB, mode-dependent loss of 4.7 dB, and average total mode crosstalk of -4.4 dB. Additionally, this design, featuring equal power for all input beams, enables phase-only control in coherent power combining, resulting in significant simplifications and fast convergence compared with phase-and-amplitude control.

As an analog model of general relativity, optics on some two-dimensional (2D) curved surfaces has received increasing attention in the past decade. Here, in light of the Huygens–Fresnel principle, we propose a theoretical frame to study light propagation along arbitrary geodesics on any 2D curved surfaces. This theory not only enables us to solve the enigma of “infinite intensity” that existed previously at artificial singularities on surfaces of revolution but also makes it possible to study light propagation on arbitrary 2D curved surfaces. Based on this theory, we investigate the effects of light propagation on a typical surface of revolution, Flamm’s paraboloid, as an example, from which one can understand the behavior of light in the curved geometry of Schwarzschild black holes. Our theory provides a convenient and powerful tool for investigations of radiation in curved space.

Unconventional Weyl points with topological charges higher than 1 can transform into various complex unconventional Weyl exceptional contours under non-Hermitian perturbations. However, theoretical studies of these exceptional contours have been limited to tight-binding models. Here, we propose to realize unconventional Weyl exceptional contours in photonic continua—non-Hermitian anisotropic chiral plasma, based on ab initio calculation by Maxwell’s equations. By perturbing in-plane permittivity, an unconventional Weyl point can transform into a quadratic Weyl exceptional ring, a type I Weyl exceptional chain with one chain point, a type II Weyl exceptional chain with two chain points, or other forms. Realistic metamaterials with effective constitutive parameters are proposed to implement these unconventional Weyl exceptional contours. Our work paves a way toward exploration of exotic physics of unconventional Weyl exceptional contours in non-Hermitian topological photonic continua.

Pulse shaping has become a powerful tool in generating complicated ultrafast optical waveforms to meet specific application needs. Traditionally, pulse shaping focuses on the temporal waveform synthesis. Recent interests in structuring light in the spatiotemporal domain rely on Fourier analysis. A space-to-time mapping technique allows us to directly imprint complex spatiotemporal modulation through taking advantage of the relationship between frequency and time of chirped pulses. The concept is experimentally verified through the generation of spatiotemporal optical vortex (STOV) and STOV lattice. The power of this method is further demonstrated by STOV polarity reversal, vortex collision, and vortex annihilation. Such a direct mapping technique opens tremendous potential opportunities for sculpturing complex spatiotemporal waveforms.

Optical manipulation of metallic microparticles remains a significant challenge because of the strong scattering forces arising from the high extinction coefficient of the particles. This paper reports a new mechanism for stable confinement of metallic microparticles using a tightly focused linearly polarized Gaussian beam. Theoretical and experimental results demonstrate that metallic microparticles can be captured off the optical axis in such a beam. Meanwhile, the three-dimensionally confined particles are observed spinning transversely as a response to the asymmetric force field. The off-axis levitation and transverse spinning of metallic microparticles may provide a new way for effective manipulation of metallic microparticles.

Optical logical operations demonstrate the key role of optical digital computing, which can perform general-purpose calculations and possess fast processing speed, low crosstalk, and high throughput. The logic states usually refer to linear momentums that are distinguished by intensity distributions, which blur the discrimination boundary and limit its sustainable applications. Here, we introduce orbital angular momentum (OAM) mode logical operations performed by optical diffractive neural networks (ODNNs). Using the OAM mode as a logic state not only can improve the parallel processing ability but also enhance the logic distinction and robustness of logical gates owing to the mode infinity and orthogonality. ODNN combining scalar diffraction theory and deep learning technology is designed to independently manipulate the mode and spatial position of multiple OAM modes, which allows for complex multilight modulation functions to respond to logic inputs. We show that few-layer ODNNs successfully implement the logical operations of AND, OR, NOT, NAND, and NOR in simulations. The logic units of XNOR and XOR are obtained by cascading the basic logical gates of AND, OR, and NOT, which can further constitute logical half-adder gates. Our demonstrations may provide a new avenue for optical logical operations and are expected to promote the practical application of optical digital computing.

Research interest in resonance and topology for systems at near-zero frequency, whose wavelength could be 2 orders larger than the scale of resonators is very rare, since the trivial effective-medium theory is generally thought to be correct in this regime. Also, the complex frequency regime is generally thought to be irrelevant to the topological properties of Hermitian systems. In this work, we find the general conditions to realize near-zero frequency resonance for a resonator and theoretically propose two kinds of realizations of such resonators, which are confirmed by numerical methods. The photonic crystals with such a resonator as the unit cell present rich topological characteristics at the near-zero frequency regime. The topological singularity that corresponds to the resonant frequency of the unit cell can be pushed to zero frequency at the bottom of the first band by tuning a certain parameter to a critical value. Surprisingly, we find that, when the parameter is tuned over the critical value, the singularity has disappeared in the first band and is pushed into the imaginary frequency regime, but now the topology of the first band and gap is still nontrivial, which is demonstrated by the existence of the topological edge state in the first gap, the negative sign of imaginary part of the surface impedance, and the symmetry property of Wannier functions. So, we are forced to accept that the singularity in the imaginary frequency regime can influence the topology in the real frequency regime. So, for the first time, to the best of our knowledge, we find that the singularity in the pure imaginary regime can still cause the observable topological effects on the real frequency regime, even for the Hermitian systems. Now, zero frequency acts as a novel exceptional point for Hermitian systems and the topology of the first band and first gap could be quite different from other bands and gaps, since they are intrinsically connected with zero frequency. Other new phenomena are also observed when the singularity is at the near-zero frequency regimes (real or imaginary), e.g., the cubic relationship between reflection coefficient and the frequency, the robust wide-bandwidth high transmission at very low frequency, etc. Besides the theoretical importance, some basic applications, such as the robust deep subwavelength wide bandwidth high-transmission layered structures, the subwavelength wide bandwidth absorbers, and the cavity from the topological subwavelength edge state are proposed, which can inspire new designs in many areas of optics, microwaves, and acoustics. This work opens a new window for rich topological physics and revolutionary device designs at the near and beyond zero-frequency regimes.

Increasing interest has been drawn to optical manipulation of metal (plasmonic) nanoparticles due to their unique response on electromagnetic radiation, prompting numerous applications in nanofabrication, photonics, sensing, etc. The familiar point-like laser tweezers rely on the exclusive use of optical confinement forces that allow stable trapping of a single metal nanoparticle in 3D. Simultaneous all-optical (contactless) confinement and motion control of single and multiple metal nanoparticles is one of the major challenges to be overcome. This article reports and provides guidance on mastering a sophisticated manipulation technique harnessing confinement and propulsion forces, enabling simultaneous all-optical confinement and motion control of nanoparticles along 3D trajectories. As an example, for the first time to our knowledge, programmable transport of gold and silver nanospheres with a radius of 50 and 30 nm, respectively, along 3D trajectories tailored on demand, is experimentally demonstrated. It has been achieved by an independent design of both types of optical forces in a single-beam laser trap in the form of a reconfigurable 3D curve. The controlled motion of multiple nanoparticles, far away from chamber walls, allows studying induced electrodynamic interactions between them, such as plasmonic coupling, observed in the presented experiments. The independent control of optical confinement and propulsion forces provides enhanced flexibility to manipulate matter with light, paving the way to new applications involving the formation, sorting, delivery, and assembling of nanostructures.

Exceptional points are spectral singularities in open quantum and wave systems that exhibit a strong spectral response to perturbations. This feature can be exploited for a new generation of sensors. This paper explains the basic mechanism and comprehensively reviews the recent developments. In particular, it highlights the influence of classical noise and fundamental limitations due to quantum noise.

The evolutions of polarization and orbital angular momentum (OAM) states of light in helically twisted birefringent photonic crystal fibers (TB-PCFs) are analyzed. It is shown that a circular polarization (CP) component (S3 of a Stokes parameter) is periodically excited when usual linearly polarized (LP) modes of PCF are launched. The excitation originates from a geometric phase in TB-PCFs. The S3 excitation is larger for larger linear birefringence for a fixed twisting rate. If the linear birefringence is large enough, a CP filtering behavior can be seen in addition to the S3 excitation. From the analytical consideration of the sign of the geometric phase, the TB-PCF with periodical inversion of twisting is proposed to generate arbitrary polarization state on the Poincaré sphere. Next, an OAM state generation in multimode TB-PCFs is shown for higher-order LP mode input. By observing a far-field interference pattern from TB-PCF mixed with LP01 mode, a vortex associated with the OAM state can be seen. Similar to the single-mode case, by using periodical twisting inversion, efficient OAM generation is possible. These results indicate that by simply launching fiber’s LP mode into TB-PCF, arbitrary polarization and OAM states can be generated, leading to a novel mechanism for the manipulation of the spatial state of light.

We propose a linear mapping relationship between the polarization of the fundamental mode and the cylindrical vector (CV) modes on the first-order Poincaré sphere (FOPS) in fiber. The new method is based on the four-dimensional complex Jones matrices in terms of the linearly polarized mode bases. With our theoretical model, an all-fiber approach to generate arbitrary CV beams on the FOPS is proposed theoretically and verified experimentally. In the experiment, through the combination of a mode converter and a two-segment cascaded few-mode fiber with fixed stresses, it is possible to generate all CV modes on the FOPS by only adjusting the polarization of the fundamental mode. The Stokes parameters of the output light are measured to verify our scheme, which shows good agreement with the theoretical prediction. The method may provide a convenient way to generate CV beams and evolve the polarization states in any path on the FOPS, which is expected to have potential applications in encoding information and quantum computation.

Photonic spin Hall effect (SHE) provides new opportunities for achieving spin-based photonics applications. However, flexibly manipulating the spin-dependent splitting (SDS) of photonic SHE and imposing extra phase modulation on the two spin components are always a challenge. Here, a controllable SHE mechanism based on phase function construction is reported. It is concluded that the phases with specific functional structures performing a coordinate translation are equivalent to integrating a gradient phase to the original phases. Hence, the original phase can be used for independent phase modulation, and the gradient phase originating from the coordinate translation is capable of manipulating the SDS. A metasurface with Pancharatnam–Berry phase that can impose conjugate phases to the two spin components of light is fabricated to verify this mechanism. By shifting the light position, the SDS is continuously manipulated in the visible region, which is successfully used for detecting the polarization ellipticity. The extra phase modulation is also performed with the original phase and thus enables measuring singular beams. It is anticipated that the controllable SHE manipulation method may open new avenues in the fields of spin photonics, optical sensing, optical communications, etc.

Training an artificial neural network with backpropagation algorithms to perform advanced machine learning tasks requires an extensive computational process. This paper proposes to implement the backpropagation algorithm optically for in situ training of both linear and nonlinear diffractive optical neural networks, which enables the acceleration of training speed and improvement in energy efficiency on core computing modules. We demonstrate that the gradient of a loss function with respect to the weights of diffractive layers can be accurately calculated by measuring the forward and backward propagated optical fields based on light reciprocity and phase conjunction principles. The diffractive modulation weights are updated by programming a high-speed spatial light modulator to minimize the error between prediction and target output and perform inference tasks at the speed of light. We numerically validate the effectiveness of our approach on simulated networks for various applications. The proposed in situ optical learning architecture achieves accuracy comparable to in silico training with an electronic computer on the tasks of object classification and matrix-vector multiplication, which further allows the diffractive optical neural network to adapt to system imperfections. Also, the self-adaptive property of our approach facilitates the novel application of the network for all-optical imaging through scattering media. The proposed approach paves the way for robust implementation of large-scale diffractive neural networks to perform distinctive tasks all-optically.

Laser cooling of mechanical degrees of freedom is one of the most significant achievements in the field of optomechanics. Here, we report, for the first time to the best of our knowledge, efficient passive optomechanical cooling of the motion of a freestanding waveguide coupled to a whispering-gallery-mode (WGM) resonator. The waveguide is an 8 mm long glass-fiber nanospike, which has a fundamental flexural resonance at Ω/2π=2.5 kHz and a Q-factor of 1.2×105. Upon launching ～250 μW laser power at an optical frequency close to the WGM resonant frequency, we observed cooling of the nanospike resonance from room temperature down to 1.8 K. Simultaneous cooling of the first higher-order mechanical mode is also observed. The strong suppression of the overall Brownian motion of the nanospike, observed as an 11.6 dB reduction in its mean square displacement, indicates strong optomechanical stabilization of linear coupling between the nanospike and the cavity mode. The cooling is caused predominantly by a combination of photothermal effects and optical forces between nanospike and WGM resonator. The results are of direct relevance in the many applications of WGM resonators, including atom physics, optomechanics, and sensing.

A multipoint interferometer (MI), uniformly distributed point-like pinholes in a circle, was proposed to measure the orbital angular momentum (OAM) of vortex beams [Phys. Rev. Lett.101, 100801 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.100801], which can be used for measuring OAM of light from astronomical sources. This is a simple and robust method; however, it is noted that this method is only available for low topological charge because the diffracted intensity patterns for vortex beams with higher OAM will repeat periodically. Here, we propose an improved multipoint interferometer (IMI) for measuring the OAM of an optical vortex with high topological charge. The structure of our IMI is almost the same as the MI, but the size of each pinhole is larger than a point in the MI. Such a small change enables each pinhole to get more phase information from the incident beams; accordingly, the IMI can distinguish any vortex beams with different OAM. We demonstrate its viability both theoretically and experimentally.

We propose a conceptual design of optical power limiters with abrupt limiting action and enhanced power-handling capabilities that is based on exceptional point degeneracies (EPDs). The photonic circuit consists of two coupled cavities with differential Q factors. One of the cavities includes a Kerr-like nonlinear material. The underlying mechanism that triggers an abrupt transmittance suppression relies on the interplay between a nonlinear instability and an abrupt destruction of EPDs due to a resonance detuning occurring when the incident power exceeds a critical value. Our proposal opens up possibilities for the use of EPDs in optical power switching, Q switching, routing, and so on.

Perfect optical vortices (POVs) provide a solution to address the challenge induced by strong dependence of classical optical vortices on their carried topological charges. However, traditional POVs are all shaped into bright rings with a single main lobe along the radial direction. Here we propose a method for enhanced control on the ring profile (the radial intensity profile of circular rings) of POVs based on modulated circular sine/cosine radial functions, which is realized by a circular Dammann grating embedded with a spiral phase. Specifically, a type of “absolute” dark POVs surrounded by two bright lobe rings in each side is presented, which provides a perfect annular potential well along those dark impulse rings for trapping low-index particles, cells, or quantum gases. In addition, several POVs with different ring profiles, including conventional POVs with bright rings, the dark POVs mentioned above, and also POVs with tunable ring profiles, are demonstrated. This work opens up new possibilities to controllably tune the ring profile of perfect vortices, and this type of generalized POVs will enrich the content of singular optics and expand the application scope of perfect vortices in a range of areas including optical manipulation, both quantum and classical optical communications, enhanced optical imaging, and also novel structured pumping lasers.

Chirped random-phase gratings are designed to produce experimentally a super-bunched focusing effect with a high bunching peak value of g(2)(0)=15.38±0.05 and a high visibility of 92.5%, greatly surpassing the theoretical bunching peak of 2 of thermal light. Both slit-width-chirped and period-chirped random-phase gratings are studied theoretically and experimentally. The full width at half-maximum of the super-bunched curve decreases significantly with an increase in the slit number, focusing the photon pairs within a decreasing spot size. This super-bunched focusing effect can be useful for improving the resolution and the visibility of the correlation image simultaneously.

Optical activity (OA) is the rotation of the polarization orientation of the linearly polarized light as it travels through certain materials that are of mirror asymmetry, including gases or solutions of chiral molecules such as sugars and proteins, as well as metamaterials. The necessary condition for achieving OA is the birefringence of two circular polarizations in material. Here, we propose a new kind of self-accelerated OA in free space, based on the intrinsic Gouy phase induced mode birefringence of two kinds of quasi-non-diffracting beams. We provide a detailed insight into this kind of self-accelerated OA by analyzing angular parameters, including angular direction, velocity, acceleration, and even the polarization transformation trajectory. As the Gouy phase exists for any wave, this kind of self-accelerated OA can be implemented in other waves beyond optics, from acoustic and elastic waves to matter waves.

An equivalence is made between the exceptional points proposed by the field of non-Hermitian quantum mechanics and the dead band observed in laser gyroscopes. The sensitivity enhancement near this exceptional point is plagued by increased uncertainty due to broadening of the beat-note bandwidth. Also, near the dead band the gyroscope response is caused by Rabi intensity oscillations and not solely by a phase modulation. Finally, a distinction is made between conservative and non-conservative coupling.

An all-optically reconfigurable generation of optical vortices would be highly beneficial to the implementation of next-generation optical communication and advanced information processing. The previously demonstrated approaches based on the parametric nonlinear optical processes, however, have exhibited limited conversion efficiency due to the group velocity mismatch and nonlinear phase shifts, and require the cumbersome preparation of either the optical element or initial seed beam having a non-zero topological charge. Here, we propose and analyze a novel scheme for highly efficient all-optical generation and control of optical vortices based on the dynamic acoustic vortex grating created by forward stimulated intermodal Brillouin scattering in a subwavelength-hole photonic waveguide. The dual-frequency pump beams in two different hybrid optical modes drive an acoustic vortex mode, which transforms a signal in the fundamental optical mode into an optical vortex mode. This scheme not only eliminates the need for the initial preparation of an angular-momentum-carrying medium or an optical vortex seed but also guarantees high modal purity and nearly 100% conversion efficiency assisted by the energy-momentum conservation. We also investigate the feasibility and practicability of the subwavelength-hole waveguides by examining the intermodal conversion efficiency and robustness of guidance of the optical vortices, taking into account the impact of the Kerr-type nonlinear effects on the intermodal Brillouin interactions based on our rigorous full-vectorial analytical theory.

Controlled obtaining of orbital angular momentum (OAM) modes of light at high power over arbitrary orders has important implications for future classical and quantum systems. Appreciable optical amplification has recently been observed for low-order or specific-order OAM modes. However, large amplification of high-order OAM modes still remains challenging. Here we report on flat-gain amplification of arbitrary OAM modes via Brillouin interactions and demonstrate that the OAM modes with various orders can be efficiently and relatively uniformly amplified by imaging the wave source of OAM mode propagation in a nonlinear medium. Meanwhile, the propagation properties of beams carrying OAM with arbitrary modes are high-fidelity maintained. This work provides a practicable way to flatten the mode gain and represents a crucial necessity to realize OAM mode filters with controllable mode gain bandwidth.

We have theoretically designed and experimentally observed free-space propagation of topological singular lines of cylindrical vector optical fields with non-integer topological charges. The polarization singular lines are due to the orientation uncertainty of the polarization states, caused by non-integer topological charges. The results reveal that during propagation, evolution of the polarization singular lines results in the special intensity pattern, distribution of polarization states, and chains of polarization singularities. We have also proposed a method to generate triple straight and spiral singular lines, which may contribute to the research of complex optical fields.

A coherence vortex (CV) carrying topological-charge information in its correlation dimension is a new option for optical manipulation and communication. CV generation by directly modulating the correlation function enables a way to control the light field in this dimension. However, few experimental realizations on this issue have been reported because of the difficulty in phase modulation when the light arrays are of low coherence. In this paper, we propose a method for generating a CV by utilizing partially coherent light arrays. A proper design of random arrays at the input plane leads to a complex CV field at the output plane after free-space propagation. This generation mechanism works well for beamlets of low coherence.

A large number of different types of second-order non-Hermitian degeneracies called exceptional points (EPs) were found in various physical systems depending on the mechanism of coupling between eigenstates. We show that these EPs can be hybridized to form higher-order EPs, which preserve the original properties of the initial EPs before hybridization. For a demonstration, we hybridize chiral and supermode second-order EPs, where the former and the latter are the results of intra-disk and inter-disk mode coupling in an optical system comprised of two Mie-scale microdisks and one Rayleigh-scale scatterer. The high sensitivity of the resulting third-order EP against external perturbations in our feasible system is emphasized.

Based on the dispersive interaction between a high quality factor microcavity and nano-objects, whispering-gallery-mode microcavities have been widely used in highly sensitive sensing. Here, we propose a novel method to enhance the sensitivity of the optical frequency shift and reduce the impact of the laser frequency noise on the detection resolution through Brillouin cavity optomechanics in a parity-time symmetric system. The optical spring effect is sensitive to the perturbation of optical modes around the exceptional point. By monitoring the shift of the mechanical frequency, the detection sensitivity for the optical frequency shift is enhanced by 2 orders of magnitude compared with conventional approaches. We find the optical spring effect is robust to the laser frequency noise around the exceptional point, which can reduce the detection limitation caused by the laser frequency instability. Thus, our method can improve the sensing ability for nano-object sensing and other techniques based on the frequency shift of the optical mode.

Tiny but universal beam shifts occur when a polarized light beam is reflected upon a planar interface. Although the beam shifts of Gaussian beams have been measured by the weak measurement technique, the weak measurement for orbital angular momentum (OAM)-induced spatial shifts of vortex beams is still missing. Here, by elaborately choosing the preselection and postselection states, the tiny OAM-induced Goos–H nchen and Imbert–Fedorov shifts are amplified at an air–prism interface. The maximum shifts along directions both parallel and perpendicular to the incident plane are theoretically predicted and experimentally verified with optimal preselection and postselection states. These maximum shifts can be used to determine the OAM of vortex beams.

Starting from well-known absolute instruments that provide perfect imaging, we analyze a class of rotationally symmetric compact closed manifolds, namely, geodesic lenses. We demonstrate with a numerical method that light rays confined on geodesic lenses form closed trajectories, and that for optical waves, the spectrum of a geodesic lens is (at least approximately) degenerate and equidistant. Moreover, we fabricate two geodesic lenses in micrometer and millimeter scales and observe curved light rays along the geodesics. Our experimental setup may offer a new platform to investigate light propagation on curved surfaces.

We apply the notion of discrete supersymmetry based on matrix factorization to quantum systems consisting of coupled bosonic oscillators to construct isospectral bosonic quantum networks. By using the algebra that arises due to the indistinguishability of bosonic particles, we write down the Schr dinger equations for these oscillators in the different boson-number sectors. By doing so, we obtain, for every partner quantum network, a system of coupled differential equations that can be emulated by classical light propagation in optical waveguide arrays. This mathematical scheme allows us to build quasi-two-dimensional optical arrays that are either isospectral or share only a subset of their spectrum after deliberately omitting some chosen eigenstates from the spectrum. As an example, we use this technique (which we call bosonic discrete supersymmetry or BD-SUSY) to design two optical, silica-based waveguide arrays consisting of six and three elements, respectively, with overlapping eigenspectrum.

Polarization oscillating beams, namely, polarization standing waves, commonly formed by a pair of coherent counterpropagating light waves with orthogonal polarizations, oscillate their states of polarization periodically within a wavelength interval, offering conceptual and practical interests in light-matter interactions such as the nonreciprocal magnetoelectric effect, and impressive applications in optical imaging, sensing, and chirality detection. Here, we propose a new class of polarization oscillating beams that longitudinally vary states of polarization with spatial intervals within centimeters via the superposition of two copropagating optical frozen waves with preshaped longitudinal intensity profiles and transverse phase structures. The flexibility and manipulability are demonstrated by creating several polarization oscillating beams with different polarization structures. This work paves a new way to manipulate other waves and may be useful for applications of optical standing waves in optical manipulation, light guiding of atoms, polarization-sensitive sensing, etc.

In this paper, we design a one-dimensional (1D) parity-time-symmetric periodic ring optical waveguide network (PTSPROWN) and investigate its extraordinary optical characteristics. It is found that quite different from traditional vacuum/dielectric optical waveguide networks, 1D PTSPROWN cannot produce a photonic ordinary propagation mode, but can generate simultaneously two kinds of photonic nonpropagation modes: attenuation propagation mode and gain propagation mode. It creates neither passband nor stopband and possesses no photonic band structure. This makes 1D PTSPROWN possess richer spontaneous PT-symmetric breaking points and causes interesting extremum spontaneous PT-symmetric breaking points to appear, where electromagnetic waves can create ultrastrong extraordinary transmission, reflection, and localization, and the maximum can arrive at 6.6556×1012 and is more than 7 orders of magnitude larger than the results reported previously. 1D PTSPROWN may possess potential in designing high-efficiency optical energy saver devices, optical amplifiers, optical switches with ultrahigh monochromaticity, and so on.

We present a highly efficient method of generating and shaping ellipse perfect vector beams (EPVBs) with a prescribed ellipse intensity profile and continuously variant linear polarization state. The scheme is based on the coaxial superposition of two orthogonally polarized ellipse laser beams of controllable phase vortex serving as the base vector components. The phase-only computer-generated hologram is specifically designed by means of a modified iteration algorithm involving a complex amplitude constraint, which is able to generate an EPVB with high diffraction efficiency in the vector optical field generator. We experimentally demonstrate that the efficiency of generating the EPVB has a notable improvement from 1.83% in the conventional complex amplitude modulation based technique to 11.1% in our method. We also discuss and demonstrate the simultaneous shaping of multiple EPVBs with independent tunable ellipticity and polarization vortex in both transversal (2D) and axial (3D) focusing structures, proving potentials in a variety of polarization-mediated applications such as trapping and transportation of particles in more complex geometric circumstances.

The redistribution of the energy flow of tightly focused ellipticity-variant vector optical fields is presented. We theoretically design and experimentally generate this kind of ellipticity-variant vector optical field, and further explore the redistribution of the energy flow in the focal plane by designing different phase masks including fanlike phase masks and vortex phase masks on them. The flexibly controlled transverse energy flow rings of the tightly focused ellipticity-variant vector optical fields with and without phase masks can be used to transport multiple absorptive particles along certain paths, which may be widely applied in optical trapping and manipulation.

We measure the electromagnetic degree of temporal coherence and the associated coherence time for quasi-monochromatic unpolarized light beams emitted by an LED, a filtered halogen lamp, and a multimode He–Ne laser. The method is based on observing at the output of a Michelson interferometer the visibilities (contrasts) of the intensity and polarization-state modulations expressed in terms of the Stokes parameters. The results are in good agreement with those deduced directly from the source spectra. The measurements are repeated after passing the beams through a linear polarizer so as to elucidate the role of polarization in electromagnetic coherence. While the polarizer varies the equal-time degree of coherence consistently with the theoretical predictions and alters the inner structure of the coherence matrix, the coherence time remains almost unchanged when the light varies from unpolarized to polarized. The results are important in the areas of applications dealing with physical optics and electromagnetic interference.

In this paper, we examine the tiny polarization rotation effect in total internal reflection due to the spin–orbit interaction of light. We find that the tiny polarization rotation rate will induce a geometric phase gradient, which can be regarded as the physical origin of photonic spin Hall effect. We demonstrate that the spin-dependent splitting in position space is related to the polarization rotation in momentum space, while the spin-dependent splitting in momentum space is attributed to the polarization rotation in position space. Furthermore, we introduce a quantum weak measurement to determine the tiny polarization rotation rate. The rotation rate in momentum space is obtained with 118 nm, which manifests itself as a spatial shift, and the rotation rate in position space is achieved with 38 μrad/λ, which manifests itself as an angular shift. The investigation of the polarization rotation characteristics will provide insights into the photonic spin Hall effect and will enable us to better understand the spin–orbit interaction of light.