Tellegen response is a nonreciprocal effect that couples electric and magnetic responses of the medium and enables unique optical properties. Here, we develop a semi-analytical model of a Mie-resonant Tellegen meta-atom made of magneto-optical material and explicitly compute its magnetoelectric polarizability. We demonstrate that it could substantially exceed the geometric mean of electric and magnetic polarizabilities, giving rise to a strong and controllable effective Tellegen response in metamaterials.

Effective axion fields emerge in condensed matter and photonic systems with broken parity and time-reversal symmetries resulting in nonreciprocal optical phenomena. Here, we predict a distinct type of electromagnetic response which has the same symmetry properties as an axion one, manifests itself only at the boundaries of the material and features the same coupling to incident plane waves. However, the response to the external sources introduced inside is profoundly different, allowing one to distinguish the predicted dual axion field experimentally. We prove that the behavior of such materials is captured by electrodynamics with magnetic charge, put forward a specific metamaterial realizing this physics and suggest possible experiments to observe it. We anticipate that this response is general and occurs in a variety of photonic and condensed matter structures.

Artificial media provide unique playground to test fundamental theories allowing one to probe the laws of electromagnetism in the presence of hypothetical axions. While some materials are known to realize this physics, here we propose the nonlocal extension of axion electrodynamics. Compared to the usual axion case, the suggested metamaterial features similar optical properties including Kerr and Faraday rotation. However, the external sources in this structure do not induce dyon charges eliminating well-celebrated Witten effect. We put forward the design of such nonreciprocal non-local metamaterial and discuss its potential applications.

We study feasible physical mechanisms for tuning the electromagnetic topological states in one-dimensional arrays of coupled dielectric resonators. We demonstrate two approaches for varying the topological properties: (i) mechanical, based on the mutual orientation of meta-atoms with a broken mirror symmetry, and (ii) thermal, based on temperature variation.

We consider the design of metamaterials whose behavior embodies the equations of axion electrodynamics. We derive an effective medium description of an assembly of magneto-optical layers with out-of-plane magnetization analytically and show how to achieve effective axion response with tunable parameters. We display some key predictions and validate them numerically.

Rapid development of topological concepts in photonics unveils exotic phenomena such as unidirectional propagation of electromagnetic waves resilient to backscattering at sharp bends and disorder-immune localization of light at stable frequencies. Recently introduced higher-order topological insulators (HOTIs) bring in additional degrees of control over light confinement and steering. However, designs of photonic HOTIs reported so far are solely exploiting lattice geometries which are hard to reconfigure thus limiting tunability. This article reports a conceptually new mechanism to engineer topological edge and corner states including higher-order topological phases which exploits both electric and magnetic responses of the meta-atoms. Hybridization between these responses gives rise to the difference in the effective coupling which is controlled by the meta-atoms mutual orientations. This feature allows to tailor photonic band topology exclusively via particle alignment and flexibly reconfigure the topological phase. Focusing on the kagome array of split-ring resonators, the topological edge and corner states are experimentally demonstrated in the microwave domain. To highlight the generality of this proposal, the formation of higher-order topological phase is also predicted numerically in a C-6-symmetric lattice of split-ring resonators. These findings provide a new promising route to induce and control higher-order topological phases and states.

Topological states offer an increased versatility in disorder-robust localization of electromagnetic waves at the edges and corners of photonic structures. In most of the cases, such properties are achieved due to the appropriate lattice symmetry. Here, by contrast, we explore an alternative design strategy where the topological states in a simple square lattice are tailored due to the orientation of non-centrosymmetric split-ring resonators comprising the meta-structure. We numerically predict the emergence of the nontrivial topological properties and confirm our prediction by fabricating the structure and observing the localized edge and corner states experimentally.

Topological photonics promotes an efficient approach to resilient light manipulation by exploiting spatiotemporal symmetries of the system and dual symmetry of the electromagnetic field. Various prospective device applications pose the need to flexibly control robust field localization associated with topological modes. Here we design a topological array of resonant dielectric meta-atoms with bianisotropic response induced by a spatial symmetry reduction. Mutual orientation of the designed meta-atoms encodes a staggered bianisotropy pattern capable of trapping topological states in a one-dimensional array containing a small number of particles. We show that the topological interface state can be tailored by the rotation of coaxial bianisotropic particles arranged in an equidistant lattice. Our experimental implementation based on ceramic horseshoe-shaped disks demonstrates remarkable reconfigurability of electromagnetic topological states.

We demonstrate experimentally the emergence of higher-order topological states induced by bianisotropy in a photonic metasurface formed by split-ring resonators (SRR) arranged into a kagome lattice.

Topological phases exhibit a plethora of striking phenomena, including disorder-robust localization and the propagation of waves of various nature. While this physics is actively explored in bosonic and fermionic cases, the topological phases of anyons --- particles with fractional quantum statistics --- are largely uncharted. Here, we unveil the topological transition mediated by the particles' quantum statistics that arises for two-anyon and three-anyon excitations in a one-dimensional array described by the extended Hubbard model. As we demonstrate, the interplay of two-particle interactions and tunneling processes enables topological edge states of anyon pairs whose existence and localization at one or another edge of the one-dimensional system is governed by the quantum statistics of particles. Since a direct realization of the proposed system is challenging, we develop a rigorous method to emulate the eigenmodes and eigenenergies of anyon pairs with resonant electrical circuits.

Electromagnetic topological states uncover a broad assortment of promising tools for light manipulation allowing for extraordinary robustness of wave propagation and localization to disorder and perturbations. Basically, tailoring of topological states relies on the external fields introduction or lattice symmetry adjustment, which both restrict their performance and tunability. Here, we propose a novel strategy to implement electromagnetic topological states exploiting on-site degree of freedom of a single scatterer - bianisotropy, which is manifested in a spatial-inversion-symmetry broken meta-atom. In this case, the effective coupling between two meta-atoms is controlled by their mutual orientation and, therefore, can be easily tuned. We demonstrate topological phase transitions in 1D arrays of bianisotropic particles (split-ring resonators) in full-wave numerical simulations. The proposed approach opens an alternative route of photonic topological states engineering which potentially can be generalized to higher dimensions and higher-order topological states on plasmonic as well as all-dielectric platform.

Photonic topological structures supporting spin-momentum locked topological states underpin a plethora of prospects and applications for disorder-robust routing of light. One of the cornerstone ideas to realize such states is to exploit uniform bianisotropic response in periodic structures with appropriate lattice symmetries, which together enable the topological bandgaps. Here, it is demonstrated that staggered bianisotropic response gives rise to the topological states even in a simple lattice geometry whose counterpart with uniform bianisotropy is topologically trivial. The reason behind this intriguing behavior is in the difference of the effective coupling between the resonant elements with the same and with the opposite signs of bianisotropy. Based on this insight, a one-dimensional equidistant array is designed, which consists of high-index all-dielectric particles with alternating signs of bianisotropic response. The array possesses chiral symmetry and hosts topologically protected edge states pinned to the frequencies of hybrid magneto-electric modes. These results pave a way towards flexible engineering of topologically robust light localization and propagation by encoding spatially varying bianisotropy patterns in photonic structures.

Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are typically controlled by the external parameters. In contrast, in this Letter, we predict the topological transition in the two-particle interacting system driven by the particles' quantum statistics. As a toy model, we investigate an extended one-dimensional Hubbard model with two anyonic excitations obeying fractional quantum statistics in-between bosons and fermions. As we demonstrate, the interplay of two-particle interactions and tunneling processes enables topological edge states of anyon pairs whose existence and localization at one or another edge of the one-dimensional system is governed by the quantum statistics of particles. Since a direct realization of the proposed system is challenging, we develop a rigorous method to emulate the eigenmodes and eigenenergies of anyon pairs with resonant electric circuits.

Rapid development of topological concepts in photonics unveils exotic phenomena such as unidirectional propagation of electromagnetic waves resilient to backscattering at sharp bends and disorder-immune localization of light at stable frequencies. Recently introduced higher-order topological insulators (HOTIs) bring in additional degrees of control over light confinement and steering. However, designs of photonic HOTIs reported so far are solely exploiting lattice geometries which are hard to reconfigure thus limiting tunability. Here, we elaborate a conceptually new mechanism to engineer higher-order topological phases which relies on the dual nature of electromagnetic field and exploits both electric and magnetic responses of the meta-atoms. Hybridization between these responses gives rise to the difference in the effective coupling which is controlled by the meta-atoms mutual orientations. This feature facilitates us to tailor photonic band topology exclusively via particle alignment and to flexibly reconfigure the topological phase. Focusing on the kagome array of split-ring resonators, we experimentally demonstrate topological edge and corner states in the microwave domain. Our findings provide a new promising route to induce and control higher-order topological phases and states.

Mie-resonant high-index dielectric particles are at the core of modern all-dielectric photonics. In many situations, their response to the external fields is well-captured by the dipole model which neglects the excitation of higher-order multipoles. In that case, it is commonly assumed that the dipole moments induced by the external fields are given by the product of particle polarizability tensor and the field in the particle center. Here, we demonstrate that the dipole response of non-spherical subwavelength dielectric particles is significantly more complex since the dipole moments are defined not only by the field in the particle center but also by the second-order spatial derivatives of the field. As we prove, such nonlocal response is especially pronounced in the vicinity of anapole minimum in the scattering cross-section. We examine the excitation of high-index dielectric disk in microwave domain and silicon nanodisk in near infrared applying group-theoretical analysis and retrieving the nonlocal corrections to the dipole moments. Extending the discrete dipole model to include nonlocality of the dipole response, we demonstrate an improved agreement with full-wave numerical simulations. These results provide important insights into meta-optics of Mie-resonant non-spherical particles as well as metamaterials and metadevices based on them.

Magneto-electric coupling known also as bianisotropy plays a fundamental role in time-reversal-invariant photonic topological metamaterials being responsible for opening of a topological bandgap. To further uncover the fundamental link between bianisotropy and photonic topological states, we investigate scattering of light from the individual bianisotropic disk and reveal polarization dependence of scattering which provides a photonic analogue of spin Hall effect originating from the coupling between electric and magnetic responses of the disk. Based on the field patterns from the individual meta-atom, we further design a linear array of such bianisotropic disks. Employing coupled-dipole model, we demonstrate that local modification of the disk bianisotropy translates into the modification of coupling constants in the effective photonic Hamiltonian thus opening an avenue to engineer electromagnetic topological states via the staggered bianisotropy pattern. To confirm our findings, we realize a representative example of such one-dimensional array experimentally and detect the interface states at the domain wall.

Abstract We propose a strategy to realize one-dimensional electromagnetic topologically protected states by modifying on-site properties of particles keeping linear equidistant geometry of the array. Based on the discrete dipole approximation, we demonstrate the existence of non-trivial topology of photonic bands and mapping to the Su-Schrieffer-Heeger model. We investigate the properties of an isolated ceramic disk to optimize its electromagnetic response, namely, the splitting of electric and magnetic dipole resonances due to bianisotropy. Using full-wave simulations we demonstrate the presence of the topological interface state in the microwave spectral range.

Resonant dielectric particles constitute the basis of modern all-dielectric photonics. Many remarkable electromagnetic phenomena are associated with the interplay of electric and magnetic dipole modes of a particle. Usually, the induced dipole moments are assumed to be proportional to an external field. However, it is not obvious a priori that the dipole moments of nonspherical particles should depend only on the fields in the particle center, but not their spatial derivatives. Here, we reveal the nonlocal dipole response of nonspherical particles and interpret the nonlocal corrections to the dipole moments based on symmetry analysis, thus providing new insights into the resonant response of dielectric scatterers.