Deep-subwavelength, dilute, weakly nonlinear dielectric composites are widely assumed to obey the nonlinear Maxwell-Garnett effective medium theory (NMGT). Here, we demonstrate that evanescent fields can cause NMGT breakdown at deep-subwavelength scales. We show that strong evanescent fields near linear dielectric components, even at λ0/100 scale, create local optical hotspots and zero-field regions. When nonlinear components are positioned within these regions, the composite's nonlinear response becomes highly sensitive to component placement, a behavior that conventional NMGT fails to capture due to its averaging approximation. We overcome this limitation by developing a semi-analytic corrected NMGT that incorporates evanescent-field effects in dilute, weakly nonlinear composites. By harnessing these evanescent fields, we further demonstrate a nonlinear quenching effect and design a metamaterial with extreme nonlinear anisotropy. Our findings unveil the mechanisms underlying NMGT breakdown at deep-subwavelength scales and enable new strategies for nonlinear optical engineering.

To realize achromatic metalenses, existing approaches typically rely on extended depth of focus, inverse design, and compensation-phase-based methods. However, these strategies are constrained by strict trade-offs among the achievable compensation phase range, lens size, and operating bandwidth. As a result, chromatic aberration caused by phase mismatch remains difficult to eliminate, preventing light from being fully focused onto the desired image plane. To overcome these trade-offs, this work introduces a unique hybrid strategy that combines the compensation-phase-based method with extended depth of focus. This integration mitigates key challenges in conventional approaches, namely the limited physical aperture size and restricted phase compensation range. The proposed strategy is numerically validated through finite difference time domain (FDTD) simulations of designed achromatic metalens for 600 nm to 700 nm incident wavelengths. The numerical results have verified that the axial chromatic aberration of designed metalens is reduced compared with chromatic metalens. Thus, the approach holds potential applications in advanced imaging systems, such as on-chip microscopy, holography, and augmented reality and virtual reality displays.

Dyadic Green's function is an important tool of computational photonics, giving deeper insights into light-matter interaction. We present an operator approach to the derivation of the dyadic Green's function of a generic anisotropic planarly-layered medium for both electric and magnetic fields. The resulting Green's function is expressed through the evolution operators (a kind of transfer matrices) of the comprising layers and the surface impedance tensors, the singular term being naturally separated from other terms. The operator approach to the Green's function simplifies both the conceptual understanding of the problem and the subsequent practical applications, some of which are demonstrated here. The proposed approach can be easily generalized to the case of spherical and cylindrical layers. The obtained results can be applied in nanophotonics engineering problems.

Exceptional points (EPs) are the most intriguing features of non-Hermitian systems associated with symmetry- and topology-driven applications. In this paper, we study the influence of tunable anisotropy on the topological properties of EPs in PT-symmetric layered structures. In particular, the eigenvalues exchange and eigenmodes exchange are predicted at the points of equal light transmission of different polarizations. We also unveil that the EPs tailored by the anisotropy parameters are associated with the π phase jump of reflection coefficients. Indirect evidence for the topological nature of EPs shown here is important for deeper insights into behaviors of anisotropic non-Hermitian systems and can be further used for the development of tunable non-Hermitian sensors and other applications.

Layered niobium oxide dihalides NbOX2 (X = I, Cl), as a new family of van der Waals (vdW) ferroelectrics, have attracted extensive attention, but achieving nonvolatile modulation of their optical and electrical properties remains challenging, thereby limiting their integration into next-generation nanoelectronics and optoelectronics. Here, we report the controlled fabrication of highly crystalline NbOI2-xClx vdW alloys with composition-driven tunable optical and electrical properties via a chemical vapor transport method. Comprehensive experimental characterization combined with first-principles calculation shows that the crystal lattices, phonon modes, and band structures of NbOI2-xClx can be well tailored, which are distributed between NbOI2 and NbOCl2. Both the amplitude and polarization of the second harmonic generation optical signal in NbOI2-xClx exhibit pronounced compositional dependence, offering optical evidence for tunable in-plane ferroelectric characteristics. Moreover, field-effect transistors based on NbOI2-xClx display robust n-type semiconducting behavior, with threshold voltage and carrier mobility precisely modulated through adjustment of I/Cl molar ratio. Furthermore, 2D NbOI2-xClx photodetectors across all compositions exhibit exceptional gate-tunable current on/off ratio and strong polarization-sensitive photo-response. This study thus provides a new vdW ferroelectric material platform with tunable optical and electrical properties, paving the path for its implementation in modern nanophotonics and nanoelectronics.

Optical manipulation is a tool for full controlling positions of microparticles by means of the optical forces exerting from light field configurations. Here we study how to manage the direction of the force using light polarization, but not the intensity gradient. Using a couple of plane waves as a gradientless optical beam, we numerically investigate the longitudinal optical forces exerted on a dielectric spherical particle and systematically study dependence on the polarization angle, incident angle, particle refractive index and polarizations of partial plane waves. We observe a continuous transition from pushing to pulling when tailoring the polarization state, but the value of the force can be also switched using the abrupt change of the polarization of one of the plane waves. We also reveal an exceptional point of the open system of two plane waves and find out that the pulling force can be achieved in the oscillating phase, while exponential phase is not adapted for pulling. This study offers a useful reference for further design of optical manipulation and particle trapping systems.

Weyl semimetals are prospective topological materials, in which conduction and valence bands touch each other in a discrete number of points. This opens up prominent electronic properties of Weyl semimetals and noticeably influences light-matter interaction. In this work, we study the light scattering by a spherical particle with a radially oriented gyrotropy axis inspired by the Weyl semimetal response. Using the operator scattering theory, we represent the transfer matrix of the gyrotropic spherical layer as a product of matrix exponentials, which allows us to calculate the wavelength-dependent scattering efficiency and analyze the multipole structure of the observed resonances. We demonstrate the change of the scattering pattern upon polarization ellipse deformation for considered Weyl semimetal scatterers and reveal the scattering peculiarities of multilayer Weyl semimetal particles with alternating orientation of the gyrotropy axis. In this research, we pave the way for designing polarization-sensitive nanophotonic devices.

The net angular momentum of light remains conserved during propagation. This conservation leads to a spin transport which becomes evident when light encounters a refractive index gradient, i.e., when it is reflected, refracted, or scattered. The phenomenon is so-called as the spin-orbit interaction (SOI) of light has paved the way to manipulate the light-matter interaction at the nanoscale and has remained the core of many recent studies. Particularly, the photonic spin Hall effect (PSHE) which is the microscopic spin splitting into circular polarization has given rise to novel applications, for example, precision metrology. The PSHE is well explored at planar interfaces, however much less attention is given to it when the optical potential gradient is of higher dimensionality, i.e., for nanoparticles. In this review, the theoretical description of the PSHE as well as the SOI in the scattering of light from nanoparticles are covered. Recent advances and trends in the PSHE in nanoparticles are reviewed. The review is concluded with suggestions for some novel directions in the field of PSHE of nanoparticles.

Reservoir computing (RC) is a powerful computational framework that addresses the need for efficient, low-power, and high-speed processing of time-dependent data. While RC has demonstrated strong signal processing and pattern recognition capabilities, its practical deployment in physical hardware is hindered by a critical challenge: the lack of efficient, scalable parameter optimization methods for real-world implementations. Traditionally, RC optimization has relied on software-based modeling, which limits the adaptability and efficiency of hardware-based systems, particularly in high-speed and energy-efficient computing applications. Herein, an in situ optimization approach was employed to demonstrate an optoelectronic delay-based RC system with digital delayed feedback, enabling direct, real-time tuning of system parameters without reliance on external computational resources. By simultaneously optimizing five parameters, normalized mean squared error (NMSE) values of 0.028, 0.561, and 0.271 are achieved in three benchmark tasks: waveform classification, time series prediction, and speech recognition, outperforming simulation-based optimization with NMSEs 0.054, 0.543, and 0.329, respectively, in two of the three tasks. This method enhances the feasibility of physical reservoir computing by bridging the gap between theoretical models and practical hardware implementation.

The photonic spin Hall effect, arising from the spin-orbit interaction of light, has attracted rapt scientific interest owing to its applicability. Due to the limited strength of the spin-orbit interaction, the resulting photonic spin Hall shift (PSHS) is very small. In addition, the low scattering intensity hinders the applicability of the PSHS in higher-dimensional systems. Here, we explore the effect of the chirality of the particle on the far-field PSHS and the scattered intensity. We demonstrate that the chiral particle strongly supports quasi-dual symmetry when the handedness of the incident wave and the sphere match, in contrast to unmatched handedness. Under dual transformation, the spin-orbit interaction is amplified, resulting in enhanced PSHS with a characteristic redshift. Meanwhile, the far-field scattering intensity is optimized without changing the geometry of the particle. The strong spin-orbit interaction in the near-field arises due to the optical singularities in the far-vicinity, which leads to a large effective transverse force. Our results not only provide a route to tune the PSHS and scattering efficiency but might have the potential to characterize the degree of handedness of the nanoparticle.

A new concept of a nonlinear nanoantenna with multiple functions is suggested. We give theoretical research on the temporal dynamics for this asymmetric system which consistis of a pair of graphene-wrapped dielectric nanoparticles with tunable Fermi energies. It is demonstrated that asymmetry can lead to an enlarged stationary multistable regime and enrich the temporal dynamical behaviors compared to the symmetry counterpart. Such a nanoantenna can provide a chance to switch among coexisting nonlinear states under the illumination of a sequence of external pulses, which simultaneously leads to not only the manipulation of the angular scanning sector and scattering pattern of nanoantenna but also the controllable multistate optical switching or coding element. This kind of asymmetric dimer system may represent a possible step toward the development of tunable applications in nonlinear nanophotonics and biophotonics.

Probing and manipulating the intriguing nonlinear optical responses in new two‐dimensional (2D) van der Waals ferroelectrics are of great significance to the development of 2D material‐based nonlinear optical devices. Herein, the simultaneous detection of second‐harmonic generation (SHG) and third‐harmonic generation (THG) optical responses in a recently discovered 2D in‐plane ferroelectric material, NbOI 2 is reported, as well as the giant modulation of SHG and THG in NbOI 2 by integrating with atomically thin MoS 2 . Both experimental and theoretical results show that NbOI 2 , ranging from few‐layer to thick‐layer dimensions, exhibits robust SHG and THG responses with pronounced dependence on excitation polarization and wavelength. This behavior is attributed to the anisotropic band structure and excitonic resonance effects in NbOI 2 . By interfacing a few‐layer NbOI 2 with a monolayer MoS 2 , the amplitude and polarization of both SHG and THG signals are effectively modulated, which can be further tailored by excitation wavelength and twist angle. The nonlinear optical control in MoS 2 /NbOI 2 heterostructures is correlated with polar symmetry coupling, which is well modeled via nonlinear electromagnetic theory. This study thus provides a new material platform based on van der Waals ferroelectric heterostructures for dynamic control of nonlinear light intensity and polarization, paving the path for developing advanced nonlinear photonic nanodevices.

Probing and manipulating the intriguing nonlinear optical responses in new two-dimensional (2D) van der Waals ferroelectrics are of great significance to the development of 2D material-based nonlinear optical devices. Herein, the simultaneous detection of second-harmonic generation (SHG) and third-harmonic generation (THG) optical responses in a recently discovered 2D in-plane ferroelectric material, NbOI2 is reported, as well as the giant modulation of SHG and THG in NbOI2 by integrating with atomically thin MoS2. Both experimental and theoretical results show that NbOI2, ranging from few-layer to thick-layer dimensions, exhibits robust SHG and THG responses with pronounced dependence on excitation polarization and wavelength. This behavior is attributed to the anisotropic band structure and excitonic resonance effects in NbOI2. By interfacing a few-layer NbOI2 with a monolayer MoS2, the amplitude and polarization of both SHG and THG signals are effectively modulated, which can be further tailored by excitation wavelength and twist angle. The nonlinear optical control in MoS2/NbOI2 heterostructures is correlated with polar symmetry coupling, which is well modeled via nonlinear electromagnetic theory. This study thus provides a new material platform based on van der Waals ferroelectric heterostructures for dynamic control of nonlinear light intensity and polarization, paving the path for developing advanced nonlinear photonic nanodevices.

Weyl semimetals are prospective materials to tailor light-matter interaction due to their gyrotropic properties caused by a couple of chiral Weyl points. Here, we study electromagnetic scattering characteristics from infinitely long multilayer cylindrical particles containing Weyl semimetal layers. We develop a modification of operator scattering theory that uses evolution operators to describe a set of layers. We reveal asymmetry in differential scattering cross sections stemming from the axion term of Weyl semimetal permittivity tensor, trace the radiation pattern change for multilayer particles, analyze the interference of lower multipoles with perspective of generalizing the Kerker effect, and carry out multipolar decomposition of the scattered radiation. Both the scattering theory and the numerical results can be useful for device engineering in nanophotonics.

In this paper, we propose a concept of resolution enhancement for sub-terahertz (THz) images by employing the coupling between a dielectric sphere and a time-domain THz spectrometer. The terajet effect is used as a simple approach to overcome the diffraction limit. Correlation between the resolutions in the x- and y-directions and the frequency of the incident THz beam is analyzed both analytically and experimentally.

The shift of an image of a dielectric sphere asymmetrically irradiated by a terahertz Gaussian beam in terahertz imaging systems has been demonstrated experimentally. Numerical calculations using the operator scattering theory have shown the bending of the localization region of the electromagnetic field near the shadow surface of the dielectric sphere when it is shifted with respect to the waist center of the Gaussian beam, leading to the formation of the so-called “photonic hook” with the properties depending on the polarization and frequency of the incident radiation. The possibility of reaching a spatial resolution of 0.38λ in the studied range has been shown experimentally. The obtained results can be used to increase the resolution of commercial scanning terahertz systems.

Parity-time (PT) symmetry provides an outstanding improvement of photonic devices’ performance due to the remarkable physics behind it. Resonance energy transfer (RET) as an important characteristic mediating the molecules that can be tailored in the PT-symmetric environment, too. We study how planar bilayer PT-symmetric systems affect the process of resonance energy transfer occurring in the vicinity thereof. First, we investigate the reflectance and transmittance spectra of such systems by calculating reflection and transmission coefficients as well as total radiation amplification as functions of medium parameters. We obtain that reflectance and total amplification are greatest near the exceptional points of the PT-symmetric system. Then, we perform numerical calculations of the RET rate and investigate its dependence on the complex permittivity of the PT-symmetric medium, dipole orientation, frequency of radiation and layer thickness. Optically thick PT-symmetric systems may operate at lower gain at the expense of the appearance of chaotic-like behaviors. These appear owing to the dense oscillations in the reflectance and transmittance spectra and vividly manifest themselves as stochastic-like positions of the exceptional points for PT-symmetric bilayers. The RET rate, being a result of the field interference, can be significantly amplified and suppressed near exceptional points exhibiting a Fano-like lineshape.

This chapter overviews the physics of non-Hermitian degeneracies at the so-called exceptional points. We give an introduction to theoretical aspects of non-Hermitian physics and fundamentals of exceptional points, supporting our conclusions with specific examples from optics and photonics. In particular, we consider exceptional points on the ground of both passive components and active media containing loss and gain. In the latter case, the optical PT symmetry, an especially fruitful notion, is feasible. Exceptional points in PT-symmetric systems can be also defined as a border between symmetric and symmetry-broken phases. The chapter embraces discussion of topological properties of exceptional points observed under static and dynamic encircling, and the basics of enhanced sensing near exceptional points able to detect single molecules. Finally, we show that the exceptional points are useful for studying the strong light-matter coupling in polariton physics.

Exceptional points are the most intriguing features of non-Hermitian photonics, providing clues for enhanced sensitivity, asymmetric light reflection, laser-absorber effect, topological switching, and other applications. The materials used in non-Hermitian optical structures are usually supposed to be isotropic. In this paper, we study the archetypal anisotropic non-Hermitian system consisting of the PT-symmetric bilayer (with balanced loss and gain) supplemented with the anisotropic defect (interlayer). Starting from the analysis of isotropic case, we show that anisotropy results in doubling the number of exceptional points and nontrivial splitting of the PT-symmetry-broken regions. We demonstrate that to shift the exceptional points, it is not enough to change the orientation of anisotropic medium optical axis in the transverse plane, but two anisotropic layers with differently oriented axes are needed. In the latter case, an experimentally feasible way is proposed to tune the system to an exceptional point by simply controlling the relative optical axes orientation. Moreover, we show that the exceptional points in anisotropic structures generally lose their association with unity transmission. Our results will be helpful for better understanding exceptional points and other features of non-Hermitian systems and for plenty of applications inspired by the rich physics behind the scene.

Asymmetric optical transmission (AOT) has been an enduring hot topic of interest in various fields, including optical communication, information processing, and so on. Particularly, the development of reciprocal micro-nanostructures achieving AOT further facilitates and accelerates the miniaturization and integration of traditional optical components. However, most of these optical components merely consider a single AOT band and transmission in a specified direction, limiting the development of their versatile functions. In this paper, we theoretically propose an all-dielectric metamaterial consisting of a nanograting and a defective multilayer photonic crystal, exhibiting multi-band and bidirectional multiplexing AOT. More specifically, the proposed metamaterial demonstrates both narrowband and wideband AOT for incidence from the nanograting to the photonic crystal, and a completely different narrowband AOT for the opposite incidence, namely, from the photonic crystal to the nanograting. These distinctive AOT spectral features are achieved by matching the diffraction effect of the nanograting with the special energy band of the defective multilayer photonic crystal. Remarkably, the device exhibits a transmittance difference of up to 0.974 and a contrast ratio of up to 0.997 (transmittance ratio of up to 673), with a transmission bandwidth of 62.7 nm for incident light with a wavelength of 624 nm illuminating from the nanograting to the defective multilayer photonic crystal. Furthermore, the bandwidth and number of transmission bands can be flexibly tuned by changing the polarization angle of the incident light, showcasing its excellent polarization multiplexing characteristics. The designed metamaterial provides an effective strategy for the realization of versatile AOT devices and is conducive to expanding the application scenarios of AOT devices.