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Excitons are fundamental excitations that govern the optical properties of semiconductors. Interacting excitons can lead to various emergent phases of matter and large nonlinear optical responses. In most semiconductors, excitons interact via exchange interaction or phase space filling. Correlated materials that host excitons coupled to other degrees of freedom offer hitherto unexplored pathways for controlling these interactions. Here, we demonstrate magnon-mediated excitonic interactions in CrSBr, an antiferromagnetic semiconductor. This interaction manifests as the dependence of exciton energy on exciton density via a magnonic adjustment of the spin canting angle. Our study demonstrates the emergence of quasiparticle-mediated interactions in correlated quantum materials, leading to large nonlinear optical responses and potential device concepts such as magnon-mediated quantum transducers.

The Dirac equation is a paradigmatic model that describes a range of intriguing properties of relativistic spin-1/2 particles, from the existence of antiparticles to Klein tunneling. However, the Dirac-like equations have found application far beyond its original scope, and has been used to comprehend the properties of graphene and topological phases of matter. In the field of photonics, the opportunity to emulate Dirac physics has also enabled topological photonic insulators. In this paper, we demonstrate that judiciously engineered synthetic potentials in photonic Dirac systems can offer physical properties beyond both the elementary and quasi-particles, and topological realms. Specifically, we introduce a new class of optical Dirac waveguides, whose guided electromagnetic modes are endowed with pseudo-spin degree of freedom. Pseudo-spin coupled with the ability to engineer synthetic gauge potentials acting on it, enables control over the guided modes which is unattainable in conventional optical waveguides. In particular, we use a silicon nanophotonic metasurface that supports pseudo-spin degree of freedom as a testing platform to predict and experimentally confirm a spin-full nature of the Dirac waveguides. We also demonstrate that, for suitable trapping potentials, the guided modes exhibit spin-dependent field distributions, which gives rise to their distinct transport and radiative properties. Thereby, the Dirac waveguides manifest spin-dependent radiative lifetimes - the non-Hermitian spin-Hall effect - and open new avenues for spin-multiplexing, controlling characteristics of guided optical modes, and tuning light-matter interactions with photonic pseudo-spins.

We propose a non-Hermitian topological system protected by the generalized rotational symmetry which invokes rotation in space and Hermitian conjugation. The system, described by the tight-binding model with nonreciprocal hopping, is found to host two pairs of in-gap edge modes in the gapped topological phase and is characterized by the non-Hermitian (NH) Chern number $C_{NH}=2$. The quantization of the non-Hermitian Chern number is shown to be protected by the generalized rotational symmetry $\^H^{+}=\^U\^H\^U^{+}$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants and hosting multiple in-gap edge states, which can be used for topologically resilient multiplexing.

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.

The rise of quantum science and technologies motivates photonics research to seek new platforms with strong light-matter interactions to facilitate quantum behaviors at moderate light intensities. One promising platform to reach such strong light-matter interacting regimes is offered by polaritonic metasurfaces, which represent ultrathin artificial media structured on nano-scale and designed to support polaritons - half-light half-matter quasiparticles. Topological polaritons, or 'topolaritons', offer an ideal platform in this context, with unique properties stemming from topological phases of light strongly coupled with matter. Here we explore polaritonic metasurfaces based on 2D transition metal dichalcogenides (TMDs) supporting in-plane polarized exciton resonances as a promising platform for topological polaritonics. We enable a spin-Hall topolaritonic phase by strongly coupling valley polarized in-plane excitons in a TMD monolayer with a suitably engineered all-dielectric topological photonic metasurface. We first show that the strong coupling between topological photonic bands supported by the metasurface and excitonic bands in MoSe2 yields an effective phase winding and transition to a topolaritonic spin-Hall state. We then experimentally realize this phenomenon and confirm the presence of one-way spin-polarized edge topolaritons. Combined with the valley polarization in a MoSe2 monolayer, the proposed system enables a new approach to engage the photonic angular momentum and valley degree of freedom in TMDs, offering a promising platform for photonic/solid-state interfaces for valleytronics and spintronics.

Nonreciprocity and nonreciprocal optical devices play a vital role in modern photonic technologies by enforcing one-way propagation of light. Most nonreciprocal devices today are made from a special class of low-loss ferrites that exhibit a magneto-optical response in the presence of an external static magnetic field. While breaking transmission symmetry, ferrites fail to satisfy the need for miniaturization of photonic circuitry due to weak character of nonreciprocal responses at optical wavelengths and are not easy to integrate into on-chip photonic systems. These challenges led to the emergence of magnetic-free approaches relying on breaking time reversal symmetry, e.g. with nonlinear effects modulating optical system in time. Here, we demonstrate an all-optical approach to nonreciprocity based on nonlinear valley-selective response in transition metal dichalcogenides (TMDs). This approach overcomes the limitations of magnetic materials and it does not require an external magnetic field. We provide experimental evidence of photoinduced nonreciprocity in a monolayer WS2 pumped by circularly polarized light. Nonreciprocity stems from valley-selective exciton-exciton interactions, giving rise to nonlinear circular dichroism controlled by circularly polarized pump fields. Our experimental results reveal a significant effect even at room temperature, despite considerable intervalley-scattering, showing potential for practical applications in magnetic-free nonreciprocal platforms. As an example, we propose a device scheme to realize an optical isolator based on a pass-through silicon nitride (SiN) ring resonator integrating the optically biased TMD monolayer.

The properties of topological systems are inherently tied to their dimensionality. Higher-dimensional physical systems exhibit topological properties not shared by their lower dimensional counterparts and, in general, offer richer physics. One example is a d-dimensional quantized multipole topological insulator, which supports multipoles of order up to 2^d and a hierarchy of gapped boundary modes with topological 0-D corner modes at the top. While multipole topological insulators have been successfully realized in electromagnetic and mechanical 2D systems with quadrupole polarization, and a 3D octupole topological insulator was recently demonstrated in acoustics, going beyond the three physical dimensions of space is an intriguing and challenging task. In this work, we apply dimensional reduction to map a 4D higher-order topological insulator (HOTI) onto an equivalent aperiodic 1D array sharing the same spectrum, and emulate in this system the properties of a hexadecapole topological insulator. We observe the 1D counterpart of zero-energy states localized at 4D HOTI corners - the hallmark of multipole topological phase. Interestingly, the dimensional reduction guarantees that one of the 4D corner states remains localized to the edge of the 1D array, while all other localize in the bulk and retain their zero-energy eigenvalues. This discovery opens new directions in multi-dimensional topological physics arising in lower-dimensional aperiodic systems, and it unveils highly unusual resonances protected by topological properties inherited from higher dimensions.

Topological photonic systems represent a new class of optical materials supporting boundary modes with unique properties, not found in conventional photonics. While the early research on topological photonics has focused on edge and surface modes in 2D and 3D systems, respectively, recently higher-order topological insulators (HOTIs) supporting lower-dimensional boundary states have been introduced. In this work we design and experimentally realize a photonic kagome metasurface exhibiting a Wannier-type higher-order topological phase. We demonstrate and visualize the emergence of a topological transition and opening of a Dirac cone by directly exciting the bulk modes of the HOTI metasurface via solid-state immersion spectroscopy. The open nature of the metasurface is then utilized to directly image topological boundary states. We show that, while the domain walls host 1D edge states, their bending induces 0D higher-order topological modes confined to the corners. The demonstrated metasurface hosting topological boundary modes of different dimensionality paves the way to a new generation of universal and resilient optical devices which can controllably scatter, trap and guide optical fields in a robust way.

Recently extended from the modern theory of electric polarization, quantized multipole topological insulators (QMTIs) describe higher-order multipole moments, lying in nested Wilson loops, which are inherently quantized by lattice symmetries. Overlooked in the past, QMTIs reveal new types of gapped boundaries, which themselves represent lower-dimensional topological phases and host topologically protected zero-dimensional (0D) corner states. Inspired by these pioneering theoretical predictions, tremendous efforts have been devoted to the experimental observation of topological quantized quadrupole phase in a variety of two dimensional (2D) metamaterials. However, due to stringent requirements of anti-commuting reflection symmetries in crystals, it has been challenging to achieve higher-order quantized multipole moments, such as octupole moments, in a realistic three-dimensional (3D) structure. Here, we overcome these challenges, and experimentally realize the acoustic analogue of a quantized octupole topological insulator (QOTIs) using negatively coupled resonators. We confirm by first-principle studies that our design possesses a quantized octupole topological phase, and experimentally demonstrate spectroscopic evidence of a topological hierarchy of states in our metamaterial, observing 3rd order corner states, 2nd order hinge states and 1st order surface states. Furthermore, we reveal topological phase transitions from higher- to lower-order multipole moments in altered designs of acoustic TIs. Our work offers a new pathway to explore higher-order topological states (HOTSs) in 3D classical platforms.

The discovery of topological phases has recently led to a paradigm shift in condensed matter physics, and facilitated breakthroughs in engineered photonics and acoustic metamaterials. Topological insulators (TIs) enable the generation of electronic, photonic, and acoustic modes exhibiting wave propagation that is resilient to disorder, irrespective of manufacturing precision or unpredictable defects induced by the operational environment, known as topological protection. While originally limited to a dimensionality of the protected states that is one dimension lower than the host TI material, the recent discovery of higher-order topological insulators (HOTIs) provides the potential to overcome this dimensionality limitations by offering topological protection over an extended range of dimensionalities. Here we demonstrate 2D photonic HOTI (PHOTI) with topological states two dimensions lower than the one of the host system. We consider a photonic metacrystal of distorted Kagome lattice geometry that exhibits topological bulk polarization, leading to the emergence of 1D topological edge states and of higher order 0D states confined to the corners of the structure. Interestingly, in addition to corner states due to the nearest neighbour interactions and protected by generalized chiral symmetry 1, we discover and take advantage of a new class of topological corner states sustained by long-range interactions, available in wave-based systems, such as in photonics. Our findings demonstrate that photonic HOTIs possess richer physics compared to their condensed matter counterparts, offering opportunities for engineering novel designer electromagnetic states with unique topological robustness.

In the past years classical wave-systems have constituted an excellent platform for emulating complex quantum phenomena. This approach has been especially fruitful in demonstrating topological phenomena in photonics and acoustics: from chiral edge states of Chern insulators and helical edge states of topological insulators to higher-dimensional topological states of quasiperiodic systems and systems with synthetic dimensions. Recently, a new class of topological states localized in more than one dimension of a D-dimensional system, referred to as higher-order topological (HOT) states, has been reported, offering an even more versatile platform to confine and control classical radiation and mechanical motion. However, because experimental research of HOT states has so far been limited to two-dimensional (2D) systems, third and higher-order states have evaded experimental observation. Studying higher-dimensional classical systems therefore opens an opportunity to emulate higher-order topological insulators and explore HOT states beyond second order. In this letter, we design and experimentally study a 3D acoustic metamaterial supporting third-order (0D) topological corner states, along with second-order (1D) edge states within the same topological bandgap, thus establishing a full hierarchy of HOT states in three dimensions, co-existing robustly within the same topological bandgap. The metamaterial is implemented over a versatile additive manufacturing platform, which enables rapid prototyping of metaatoms and metamolecules, which can be snapped together to form 3D metamaterials with complex geometries. The assembled 3D topological metamaterial represents the acoustic analogue of a pyrochlore lattice made of interconnected molecules, and is shown to exhibit topological bulk polarization, leading to the emergence of topological HOT states localized in all three or in two dimensions.

Electric and magnetic resonances of dielectric particles have recently uncovered a range of exciting applications in steering of light at the nanoscale. Breaking of particle inversion symmetry further modifies its electromagnetic response giving rise to bianisotropy known also as magneto-electric coupling. Recent studies suggest the crucial role of magneto-electric coupling in realization of photonic topological metamaterials. To further unmask this fundamental link, we design and test experimentally one-dimensional array composed of dielectric particles with overlapping electric and magnetic resonances and broken mirror symmetry. Flipping over half of the meta-atoms in the array, we observe the emergence of interface states providing photonic realization of the celebrated Jackiw-Rebbi model. We trace the origin of these states to the fact that local modification of particle bianisotropic response affects its effective coupling with the neighboring meta-atoms which provides a promising avenue to engineer topological states of light.

Recent advances in condensed matter physics have shown that the valley degree of freedom of electrons in 2D materials with hexagonal symmetry, such as graphene, h-BN, and TMDs, can be efficiently exploited, leading to the emergent field of valleytronics, which offers unique opportunities for efficient data transfer, computing and storage. The ability to couple the valley degree of freedom of electrons with light can further expand the ways one manipulate this degree of freedom, thus envisioning a new class of solid-state-photonic interfaces and devices. Besides this expansion of control of valley by light-waves, coupling of photons with valley-polarized electrons can dramatically expand the landscape of available optical responses, which may bring new means of controlling light in photonic devices. In this work we design such hybrid solid-state photonic metasurface integrating 2D TMD and photonic all-dielectric metasurface. While TMD is naturally endowed with the property of valley to optical-polarization coupling, the photonic metasurface is designed to produce chiral field which selectively couples to the valley degree of freedom of solid-state TMD component. We experimentally demonstrate that such coupling leads to controlled valley polarization due to the coupling of 2D materials with the chiral photonic metasurface. The measured emission from valley excitons in this hybrid system yields the preferential emission of specific helicity.

Topological systems are inherently robust to disorder and continuous perturbations, resulting in dissipation-free edge transport of electrons in quantum solids, or reflectionless guiding of photons and phonons in classical wave systems characterized by Chern or spin-Chern topological invariants. These established examples of topological physics, however, do not exhaust all possible topological phases, and recently a new class of topological metamaterials characterized by bulk polarization has been introduced. In addition to edge conduction, these systems have been shown to host higher-order topological modes. Here, we introduce and measure topological bulk polarization in 3D printed two-dimensional acoustic meta-structures, and observe topological transitions as the design parameters are tuned. We also demonstrate that our topological meta-structure hosts both 1D edge and higher-order 0D corner states with unique acoustic properties. The edge states have spin polarization that reverses for opposite propagation direction, thus supporting directional excitation. Corner states are pinned to the meta-structure corners, and rapidly decay both along the edges and into the bulk. Interestingly, these 0D states can spectrally overlap with the continuum of bulk states, but are not compatible with radiation, thus enabling embedded topological eigenstates within the continuum of bulk modes. Their confinement and inherent topological robustness is experimentally confirmed by deliberately introducing disorder. Our findings open new directions in acoustics for advanced sound propagation and manipulation.

Topological phases in quantum and classical systems have been of significant recent interest due to their fascinating physical properties. While a range of different mechanisms to induce topological order have been introduced, a quest for the most viable solution for practical systems is still open. Floquet topological insulator represent one of possible venues to engineer topological phases, yet they have been so far largely restricted to temporal modulation of Hermitian potentials. On the other hand, in many physical systems, including acoustic and optical systems, modulating loss or gain can be more straightforwardly achieved. Two of such examples are graphene, which enables strong modulation of its conductivity due to saturable absorption, and quantum wells where population inversion can be achieved in an ultrafast manner. On the other hand, non-Hermitian Floquet potentials have not been shown to yield novel topological phases to date. It is therefore of great interest to explore time-modulated non-Hermitian potentials in periodic lattices, and the emergence of topological phases associated with them. Here we demonstrate that non-Hermitian Hamiltonians can indeed result in topological phases supporting nonreciprocal edge states propagating without dissipation, as well as new regimes of dissipative and amplifying topological edge transport.

Pseudo-spin and valley degrees of freedom (DOFs) engineered in photonic analogues of topological insulators (TI) provide potential approaches to optical encoding and robust signal transport. Here we observe a ballistic edge state whose spin-valley indices are locked to the direction of propagation along the interface between a valley photonic crystal and a metacrystal emulating the quantum spin Hall effect. We demonstrate the inhibition of inter-valley scattering at a Y-junction formed at the interfaces between photonic TIs carrying different spin-valley Chern numbers. These results open up the possibility of using the valley DOF to control the flow of optical signals in 2D structures.

We demonstrate that the non-Hermitian parity-time (PT) symmetric interfaces formed between amplifying and lossy crystals support dissipationless edge states. These PT edge states exhibit gapless spectra in the complex band structure interconnecting complex-valued bulk bands as long as exceptional points (EPs) of edge states exist. As a result, regimes exist where the edge states can spectrally overlap with the bulk continuum without hybridization, and leakage into the bulk states is suppressed due to the PT symmetry. Two exemplary PT symmetric systems, based on valley and quantum hall topological phases, are investigated, and the connection with the corresponding Hermitian systems is established. We find that the edge states smoothly transit to the valley edge states found in Hermitian systems if the magnitude of gain/loss vanishes. The topological nature of the PT edge states can be established within the non-Hermitian Haldane model, where the topological invariance is found to be unaffected by gain or loss. Nonreciprocal PT edge states are discovered at the interfaces between PT-Haldane phases, indicating the interplay between the gain/loss and the magnetic flux. The proposed systems are experimentally feasible to realize in photonics. This has been verified by our rigorous full-wave simulations of edge states in PT-symmetric silicon-based photonic graphene.

Advances of condensed matter physics in exploiting the spin degree of freedom of electrons led to the emergence of the field of spintronics, which envisions new and more efficient approaches to data transfer, computing, and storage [1-3]. These ideas have been inspiring analogous approaches in photonics, where the manipulation of an artificially engineered pseudo-spin degrees of freedom is enabled by synthetic gauge fields acting on light [4,5,6]. The ability to control these additional degrees of freedom can significantly expand the landscape of available optical responses, which may revolutionize optical computing and the basic means of controlling light in photonic devices across the entire electromagnetic spectrum. Here we demonstrate a new class of photonic systems, described by effective Hamiltonians in which competing synthetic gauge fields engineered in pseudo-spin, chirality/sublattice and valley subspaces result in band gap opening at one of the valleys, while the other valley exhibits Dirac-like conical dispersion. It is shown that such effective response has dramatic implications on photon transport, among which: (i) spin-polarized and valley-polarized one-way Klein tunneling and (ii) topological edge states that coexist within the Dirac continuum for opposite valley and spin polarizations. These phenomena offer new ways to control light in photonics, in particular for on-chip optical isolation, filtering and wave-division multiplexing by selective action on their pseudo-spin and valley degrees of freedom.

A new class of phenomena stemming from topological states of quantum matter has recently found a variety of analogies in classical systems. Spin-locking and one-way propagation have been shown to drastically alter our view on scattering of electromagnetic waves, thus offering an unprecedented robustness to defects and disorder. Despite these successes, bringing these new ideas to practical grounds meets a number of serious limitations. In photonics, when it is crucial to implement topological photonic devices on a chip, two major challenges are associated with electromagnetic dissipation into heat and out-of-plane radiation into free space. Both these mechanisms may destroy the topological state and seriously affect the device performance. Here we experimentally demonstrate that the topological order for light can be implemented in all-dielectric on-chip prototype metasurfaces, which mitigate the effect of Ohmic losses by using exclusively dielectric materials, and reveal that coupling of the system to the radiative continuum does not affect the topological properties. Spin-Hall effect of light for spin-polarized topological edge states is revealed through near-field spectroscopy measurements.

Topological phase transitions in condensed matter systems have shown extremely rich physics, unveiling such exotic states of matter as topological insulators, superconductors and superfluids. Photonic topological systems open a whole new realm of research exhibiting a number of important distinctions from their condensed matter counterparts. Photonic modes can couple to the continuum of free space modes which makes it feasible to control and manipulate scattering properties of the photonic structure via topology. At the same time, the direct connection of scattering and topological properties of the photonic states allows their probing by spectroscopic means via Fano resonances. Here we demonstrate that the radiative coupling of modes supported by an all-dielectric metasurface can be controlled and tuned under topological phase transitions due to band inversion, correspondingly inducing a distinct switching of the quality factors of the resonances associated with the bands. In addition, we develop a technique to retrieve the topological properties of all-dielectric metasurfaces from the measured far-field scattering characteristics. The collected angle-resolved transmission and reflection spectra allow extracting the momentum-dependent frequencies and lifetimes of the photonic modes. This enables retrieval of the effective photonic Hamiltonian, including the effects of a synthetic gauge field, and topological invariants~-- pseudo-spin Chern numbers. Our results thus open a new avenue to design a new class of metasurfaces with unique scattering characteristics controlled via topological effects. This work also demonstrates how topological states of open systems can be explored via far-field measurements.

The discovery of two-dimensional topological photonic systems has transformed our views on electromagnetic propagation and scattering of classical waves, and a quest for similar states in three dimensions, known to exist in condensed matter systems, has been put forward. Here we demonstrate that symmetry protected three-dimensional topological states can be engineered in an all-dielectric platform with the electromagnetic duality between electric and magnetic fields ensured by the structure design. Magneto-electric coupling playing the role of a synthetic gauge field leads to a topological transition to an insulating regime with a complete three-dimensional photonic bandgap. An emergence of surface states with conical Dirac dispersion and spin-locking is unimpeded. Robust propagation of surface states along two-dimensional domain walls defined by the reversal of magneto-electric coupling is confirmed numerically by first principle studies. It is shown that the proposed system represents a table-top platform for emulating relativistic physics of massive Dirac fermions and the surface states revealed can be interpreted as Jackiw-Rebbi states confined to the interface between two domains with opposite particle masses.

The propagation of surface plasmon polaritons in thin films of topological insulators is studied. The materials considered are second generation three dimensional topological insulators Bi$_2$Se$_3$, Bi$_2$Te$_3$, and Sb$_2$Te$_3$. Dispersion relations and propagation lengths are estimated numerically, taking into account the variation of bulk dielectric functions of topological insulators as well as substrate using the Drude-Lorentz model. Key factors affecting propagation length are identified and ways to modify the dispersion relations are suggested. The explanation of the apparent discrepancy between the experimental data for Bi$_2$Se$_3$ and theory is proposed.

We analyze third-harmonic generation from high-index dielectric nanoparticles and discuss the basic features and multipolar nature of the parametrically generated electromagnetic fields near the Mie-type optical resonances. By combining both analytical and numerical methods, we study the nonlinear scattering from simple nanoparticle geometries such as spheres and disks in the vicinity of the magnetic dipole resonance. We reveal the approaches for manipulating and directing the resonantly enhanced nonlinear emission with subwavelength all-dielectric structures that can be of a particular interest for novel designs of nonlinear optical antennas and engineering the magnetic optical nonlinear response at nanoscale.

The canonical Su-Schrieffer-Heeger (SSH) model is one of the basic geometries that have spurred significant interest in topologically nontrivial bandgap modes with robust properties. Here, we show that the inclusion of suitable third-order Kerr nonlinearities in SSH arrays opens rich new physics in topological insulators, including the possibility of supporting self-induced topological transitions based on the applied intensity. We highlight the emergence of a new class of topological solutions in nonlinear SSH arrays, localized at the array edges. As opposed to their linear counterparts, these nonlinear states decay to a plateau with non-zero amplitude inside the array, highlighting the local nature of topologically nontrivial bandgaps in nonlinear systems. We derive the conditions under which these unusual responses can be achieved, and their dynamics as a function of applied intensity. Our work paves the way to new directions in the physics of topologically non-trivial edge states with robust propagation properties based on nonlinear interactions in suitably designed periodic arrays.

The unique conduction properties of condensed matter systems with topological order have recently inspired a quest for similar effects in classical wave phenomena. Acoustic topological insulators, in particular, hold the promise to revolutionize our ability to control sound, allowing for large isolation in the bulk and broadband one-way transport on their edges, with topological immunity against structural defects and disorder. So far these fascinating properties have been obtained relying on moving media, which inherently introduce noise and absorption losses, hindering the practical applicability of topological acoustics. Here, we overcome these limitations by modulating in time the acoustic properties of a lattice of resonators, introducing the concept of acoustic Floquet topological insulators. Acoustic modulation at ultrasonic frequencies can reach values as high as a few percents, enabling broadband effects with an on-site, moderate modulation strategy that surprisingly does not require phase uniformity across the lattice. Using first-principle numerical experiments, we show that acoustic waves provide a fertile ground to apply the anomalous physics of Floquet topological insulators, and demonstrate their relevance for a wide range of acoustic applications, including broadband acoustic isolation and topologically protected, nonreciprocal acoustic emitters.

We introduce the concept of nonlinear graphene metasurfaces employing the controllable interaction between a graphene layer and a planar metamaterial. Such hybrid metasurfaces support two types of subradiant resonant modes, asymmetric modes of structured metamaterial elements ("metamolecules") and graphene plasmons exhibiting strong mutual coupling and avoided dispersion crossing. High tunability of graphene plasmons facilitates strong interaction between the subradiant modes, modifying the spectral position and lifetime of the associated Fano resonances. We demonstrate that strong resonant interaction, combined with the subwavelength localization of plasmons, leads to the enhanced nonlinear response and high efficiency of the second-harmonic generation.

We demonstrate that graphene placed on top of structured substrates offers a novel approach for trapping and guiding surface plasmons. A monolayer graphene with a spatially varying curvature exhibits an effective trapping potential for graphene plasmons near curved areas such as bumps, humps and wells. We derive the governing equation for describing such localized channel plasmons guided by curved graphene and validate our theory by the first-principle numerical simulations. The proposed confinement mechanism enables plasmon guiding by the regions of maximal curvature, and it offers a versatile platform for manipulating light in planar landscapes. In addition, isolated deformations of graphene such as bumps are shown to support localized surface modes and resonances suggesting a new way to engineer plasmonic metasurfaces.

Existence of robust edge modes at interfaces of topologically dissimilar systems is one of the most fascinating manifestations of a novel nontrivial state of matter, topological insulators. Such electronic states were originally predicted and discovered in condensed matter physics, but they find their counterparts in other fields of physics, including the physics of classical waves and electromagnetics. Here, we present the first experimental realization of a topological insulator for electromagnetic waves based on engineered bianisotropic metamaterials. By employing the near-field scanning technique, we demonstrate experimentally the topologically robust propagation of electromagnetic waves around sharp corners without back reflection.

Topological states of quantum matter exhibit unique disorder-immune surface states protected by underlying nontrivial topological invariants of the bulk. Such immunity from backscattering makes topological surface or edge states ideal carriers for both classical and quantum information. So far, topological matters have been explored only in the realms of electronics and photonics, with limited range of bulk properties and largely immutable materials. These constraints thus impose severe performance trade-offs in experimentally realizable topologically ordered states. In contrast, phononic metamaterials not only provide access to a much wider range of material properties, but also allow temporal modulation in the non-adiabatic regime. Here, from the first-principles we demonstrate numerically the first phononic topological metamaterial in an elastic-wave analogue of the quantum spin Hall effect. A dual-scale phononic crystal slab is used to support two effective spins of phonon over a broad bandwidth, and strong spin-orbit coupling is realized by breaking spatial mirror symmetry. By preserving the spin polarization with an external load or spatial symmetry, phononic edge states are shown to be robust against scattering from discrete defects as well as disorders in the continuum. Our system opens up the possibility of realizing topological materials for phonons in both static and time-dependent regimes.

Control of the electromagnetic waves in nano-scale structured materials is central to the development of next generation photonic circuits and devices. In this context, hyperbolic metamaterials, where elliptical isofrequency surfaces are morphed into surfaces with exotic hyperbolic topologies when the structure parameters are tuned, have shown unprecedented control over light propagation and interaction. Here we show that such topological transitions can be even more unusual when the hyperbolic metamaterial is endowed with nonreciprocity. Judicious design of metamaterials with reduced spatial symmetries, together with the removal of time-reversal symmetry through magnetization, is shown to result in nonreciprocal dispersion and one-way topological phase transitions in hyperbolic metamaterials.

Classical emulation of a ubiquitous quantum mechanical phenomenon of double-continuum Fano (DCF) interference using metasurfaces is experimentally realized by engineering the near-field interaction between two bright and one dark plasmonic modes. The competition between the bright modes, with one of them effectively suppressing the Fano interference for the orthogonal light polarization, is discovered and explained by the analytic theory of the plasmonic DCF interference, which is further applied to predicting the circularly dichroic optical field concentration by plasmonic metasurfaces.

Plasmonic metasurfaces represent a promising platform for enhancing light-matter interaction. Active control of the optical response of metasurfaces is desirable for applications such as beam-steering, modulators and switches, biochemical sensors, and compact optoelectronic devices. Here we use a plasmonic metasurface with two Fano resonances to enhance the interaction of infrared light with electrically controllable single layer graphene. It is experimentally shown that the narrow spectral width of these resonances, combined with strong light/graphene coupling, enables reflectivity modulation by nearly an order of magnitude leading to a modulation depth as large as 90%. . Numerical simulations demonstrate the possibility of strong active modulation of the phase of the reflected light while keeping the reflectivity nearly constant, thereby paving the way to tunable infrared lensing and beam steering

We demonstrate that the violation of the time-reversal (TR) symmetry in the presence of a gyromagnetic substrate can produce an analog of electromagnetically induced transparency in metallic meta-molecules. The simplest implementation of such gyromagnetically induced transparency (GIT) in a meta-surface comprised of an array of resonant antenna pairs placed on a gyromagnetic substrate and illuminated by a normally incident electromagnetic wave is analyzed. TR symmetry breaking introduced by the magnetic field makes meta-molecules bi-anisotropic and causes spectrally-sharp Fano interference between the otherwise uncoupled electric and magnetic dipolar resonances of the meta-molecules. The applied magnetic field results in a sharp transmission peak through the otherwise reflective meta-surface. We show that, for oblique wave incidence, one-way GIT can be achieved by the combination of spatial dispersion and TR symmetry breaking. These theoretically predicted phenomena pave the way to non-reciprocal switches and isolators that can be dynamically controlled by electric currents.

Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal invariant topological insulators. Because of limitations imposed by nature, topologically non-trivial electronic order seems to be uncommon except in small-band-gap semiconductors with strong spin-orbit interactions. In this Article we show that artificial electromagnetic structures, known as metamaterials, provide an attractive platform for designing photonic analogues of topological insulators. We demonstrate that a judicious choice of the metamaterial parameters can create photonic phases that support a pair of helical edge states, and that these edge states enable one-way photonic transport that is robust against disorder.

Three different periodic optical metasurfaces exhibiting Fano resonances are studied in mid-IR frequency range in the presence of a substrate. We develop a rigorous semi-analytical technique and calculate how the presence of a substrate affects optical properties of these structures. An analytical minimal model based on the truncated exact technique is introduced and is shown to provide a simple description of the observed behavior. We demonstrate that the presence of a substrate substantially alters the collective response of the structures suppressing Wood's anomalies and spatial dispersion of the resonances. Different types of Fano resonances are found to be affected differently by the optical contrast between the substrate and the superstrate. The dependence of the spectral position of the resonances on the substrate/superstrate permittivities is studied and the validity of the widely used effective medium approaches is re-examined.

Highly confined "spoof" surface plasmon-like (SSP) modes are theoretically predicted to exist in a perforated metal film coated with a thin dielectric layer. Strong modes confinement results from the additional waveguiding by the layer. Spectral characteristics, field distribution, and lifetime of these SSPs are tunable by the holes' size and shape. SSPs exist both above and below the light line, offering two classes of applications: "perfect" far-field absorption and to efficient emission into guided modes. It is experimentally shown that these plasmon-like modes can turn thin, weakly-absorbing semiconductor films into perfect absorbers.

We report the observation of a Fano resonance between continuum Mie scattering and a narrow Bragg band in synthetic opal photonic crystals. The resonance leads to a transmission spectrum exhibiting a Bragg dip with an asymmetric profile, which can be tunably reversed to a Bragg rise. The Fano asymmetry parameter is linked with the dielectric contrast between the permittivity of the filler and the specific value determined by the opal matrix. The existence of the Fano resonance is directly related to disorder due to non-uniformity of a-SiO2 opal spheres. Proposed theoretical "quasi-3D" model produces results in excellent agreement with the experimental data.