Nonlocal topological insulators: Deterministic aperiodic arrays supporting localized topological states protected by nonlocal symmetries.

The properties of topological systems are inherently tied to their dimensionality. Indeed, higher-dimensional periodic systems exhibit topological phases not shared by their lower-dimensional counterparts. On the other hand, aperiodic arrays in lower-dimensional systems (e.g., the Harper model) have been successfully employed to emulate higher-dimensional physics. This raises a general question on the possibility of extended topological classification in lower dimensions, and whether the topological invariants of higher-dimensional periodic systems may assume a different meaning in their lower-dimensional aperiodic counterparts. Here, we demonstrate that, indeed, for a topological system in higher dimensions one can construct a one-dimensional (1D) deterministic aperiodic counterpart which retains its spectrum and topological characteristics. We consider a four-dimensional (4D) quantized hexadecapole higher-order topological insulator (HOTI) which supports topological corner modes. We apply the Lanczos transformation and map it onto an equivalent deterministic aperiodic 1D array (DAA) emulating 4D HOTI in 1D. We observe topological zero-energy zero-dimensional (0D) states of the DAA-the direct counterparts of corner states in 4D HOTI and the hallmark of the multipole topological phase, which is meaningless in lower dimensions. To explain this paradox, we show that higher-dimension invariant, the multipole polarization, retains its quantization in the DAA, yet changes its meaning by becoming a nonlocal correlator in the 1D system. By introducing nonlocal topological phases of DAAs, our discovery opens a direction in topological physics. It also unveils opportunities to engineer topological states in aperiodic systems and paves the path to application of resonances associates with such states protected by nonlocal symmetries.

Observation of higher-order topological acoustic states protected by generalized chiral symmetry.

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 topological invariants. Recently, a new class of topological materials characterized by bulk polarization has been introduced, and was shown to host higher-order topological corner states. Here, we demonstrate theoretically and experimentally that 3D-printed two-dimensional acoustic meta-structures can possess nontrivial bulk topological polarization and host one-dimensional edge and Wannier-type second-order zero-dimensional corner states with unique acoustic properties. We observe second-order topological states protected by a generalized chiral symmetry of the meta-structure, which are localized at the corners and are pinned to 'zero energy'. Interestingly, unlike the 'zero energy' states protected by conventional chiral symmetry, the generalized chiral symmetry of our three-atom sublattice enables their spectral overlap with the continuum of bulk states without leakage. Our findings offer possibilities for advanced control of the propagation and manipulation of sound, including within the radiative continuum.

Photonic spin Hall effect mediated by bianisotropy.

Coupling of electric and magnetic responses of a scatterer, known as bianisotropy, enables rich physics and unique optical phenomena, including asymmetric absorption or reflection, one-way transparency, and photonic topological phases. Here we demonstrate yet another feature stemming from bianisotropic response, namely, polarization-dependent scattering of light by bianisotropic dielectric meta-atom with broken mirror symmetry, which yields a photonic analogue of spin Hall effect. Based on a simple dipole model, we explain the origin of the effect confirming our conclusions by experimental observation of photonic spin Hall effect both for a single meta-atom and for an array of them.

Probing the Band Structure of Topological Silicon Photonic Lattices in the Visible Spectrum.

We study two-dimensional hexagonal photonic lattices of silicon Mie resonators with a topological optical band structure in the visible spectral range. We use 30 keV electrons focused to nanoscale spots to map the local optical density of states in topological photonic lattices with deeply subwavelength resolution. By slightly shrinking or expanding the unit cell, we form hexagonal superstructures and observe the opening of a band gap and a splitting of the double-degenerate Dirac cones, which correspond to topologically trivial and nontrivial phases. Optical transmission spectroscopy shows evidence of topological edge states at the domain walls between topological and trivial lattices.

Giant enhancement of Faraday rotation due to electromagnetically induced transparency in all-dielectric magneto-optical metasurfaces.

In this Letter we introduce a new class of Fano-resonant all-dielectric metasurfaces for enhanced, high figure of merit magneto-optical response. The metasurfaces are formed by an array of magneto-optical bismuth-substituted yttrium iron garnet nano-disks embedded into a low-index matrix. The strong field enhancement in the magneto-optical disks, which results in over an order of magnitude enhancement of Faraday rotation, is achieved by engineering two (electric and magnetic) resonances. It is shown that while enhancement of rotation also takes place for spectrally detuned resonances, the resonant excitation inevitably results in stronger reflection and low figure of merit of the device. We demonstrate that this can be circumvented by overlapping electric and magnetic resonances of the nanodisks, yielding a sharp electromagnetically induced transparency peak in the transmission spectrum, which is accompanied by gigantic Faraday rotation. Our results show that one can simultaneously obtain a large Faraday rotation enhancement along with almost 100% transmittance in an all-dielectric metasurface as thin as 300 nm. A simple analytical model based on coupled-mode theory is introduced to explain the effects observed in first-principle finite element method simulations.

Robust reconfigurable electromagnetic pathways within a photonic topological insulator.

The discovery of topological photonic states has revolutionized our understanding of electromagnetic propagation and scattering. Endowed with topological robustness, photonic edge modes are not reflected from structural imperfections and disordered regions. Here we demonstrate robust propagation along reconfigurable pathways defined by synthetic gauge fields within a topological photonic metacrystal. The flow of microwave radiation in helical edge modes following arbitrary contours of the synthetic gauge field between bianisotropic metacrystal domains is unimpeded. This is demonstrated in measurements of the spectrum of transmission and time delay along the topological domain walls. These results provide a framework for freely steering electromagnetic radiation within photonic structures.

Guiding electromagnetic waves around sharp corners: topologically protected photonic transport in metawaveguides.

The wave nature of radiation prevents its reflections-free propagation around sharp corners. We demonstrate that a simple photonic structure based on a periodic array of metallic cylinders attached to one of the two confining metal plates can emulate spin-orbit interaction through bianisotropy. Such a metawaveguide behaves as a photonic topological insulator with complete topological band gap. An interface between two such structures with opposite signs of the bianisotropy supports topologically protected surface waves, which can be guided without reflections along sharp bends of the interface.

Photonic topological insulators.

Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal-invariant topological insulators. A remarkable and useful property of these materials is that they support unidirectional spin-polarized propagation at their surfaces. Unfortunately topological insulators are rare among solid-state materials. Using suitably designed electromagnetic media (metamaterials) we theoretically demonstrate a photonic analogue of a topological insulator. We show that metacrystals-superlattices of metamaterials with judiciously designed properties-provide a platform for designing topologically non-trivial photonic states, similar to those that have been identified for condensed-matter topological insulators. The interfaces of the metacrystals support helical edge states that exhibit spin-polarized one-way propagation of photons, robust against disorder. Our results demonstrate the possibility of attaining one-way photon transport without application of external magnetic fields or breaking of time-reversal symmetry. Such spin-polarized one-way transport enables exotic spin-cloaked photon sources that do not obscure each other.

Gyromagnetically induced transparency of metasurfaces.

We demonstrate that the presence of a (gyro) magnetic substrate can produce an analog of electromagnetically induced transparency in Fano-resonant metamolecules. The simplest implementation of such gyromagnetically induced transparency (GIT) in a metasurface, comprised of an array of resonant antenna pairs placed on a gyromagnetic substrate and illuminated by a normally incident electromagnetic wave, is analyzed. Time reversal and spatial inversion symmetry breaking introduced by the dc magnetization makes metamolecules bianisotropic. This causes Fano interference between the otherwise uncoupled symmetric and antisymmetric resonances of the metamolecules giving rise to a sharp transmission peak through the otherwise reflective metasurface. We show that, for an oblique wave incidence, one-way GIT can be achieved by the combination of spatial dispersion and gyromagnetic effect. These theoretically predicted phenomena pave the way to nonreciprocal switches and isolators that can be dynamically controlled by electric currents.

Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared.

Graphene is widely known for its anomalously strong broadband optical absorptivity of 2.3% that enables seeing its single-atom layer with the naked eye. However, in the mid-infrared part of the spectrum graphene represents a quintessential lossless zero-volume plasmonic material. We experimentally demonstrate that, when integrated with Fano-resonant plasmonic metasurfaces, single-layer graphene (SLG) can be used to tune their mid-infrared optical response. SLG's plasmonic response is shown to induce large blue shifts of the metasurface's resonance without reducing its spectral sharpness. This effect is explained by a generalized perturbation theory of SLG-metamaterial interaction that accounts for two unique properties of the SLG that set it apart from all other plasmonic materials: its anisotropic response and zero volume. These results pave the way to using gated SLG as a platform for dynamical spectral tuning of infrared metamaterials and metasurfaces.

Pseudo-spin switches and Aharonov-Bohm effect for topological boundary modes.

Topological boundary modes in electronic and classical-wave systems exhibit fascinating properties. In photonics, topological nature of boundary modes can make them robust and endows them with an additional internal structure-pseudo-spins. Here, we introduce heterogeneous boundary modes, which are based on mixing two of the most widely used topological photonics platforms-the pseudo-spin-Hall-like and valley-Hall photonic topological insulators. We predict and confirm experimentally that transformation between the two, realized by altering the lattice geometry, enables a continuum of boundary states carrying both pseudo-spin and valley degrees of freedom (DoFs). When applied adiabatically, this leads to conversion between pseudo-spin and valley polarization. We show that such evolution gives rise to a geometrical phase associated with the synthetic gauge fields, which is confirmed via an Aharonov-Bohm type experiment on a silicon chip. Our results unveil a versatile approach to manipulating properties of topological photonic states and envision topological photonics as a powerful platform for devices based on synthetic DoFs.

Polaritonic states trapped by topological defects.

The miniaturization of photonic technologies calls for a deliberate integration of diverse materials to enable novel functionalities in chip-scale devices. Topological photonic systems are a promising platform to couple structured light with solid-state matter excitations and establish robust forms of 1D polaritonic transport. Here, we demonstrate a mechanism to efficiently trap mid-IR structured phonon-polaritons in topological defects of a metasurface integrated with hexagonal boron nitride (hBN). These defects, created by stitching displaced domains of a Kekulé-patterned metasurface, sustain localized polaritonic modes that originate from coupling of electromagnetic fields with hBN lattice vibrations. These 0D higher-order topological modes, comprising phononic and photonic components with chiral polarization, are imaged in real- and Fourier-space. The results reveal a singular radiation leakage profile and selective excitation through spin-polarized edge waves at heterogeneous topological interfaces. This offers impactful opportunities to control light-matter waves in their dimensional hierarchy, paving the way for topological polariton shaping, ultrathin structured light sources, and thermal management at the nanoscale.

Contrast between surface plasmon polariton-mediated extraordinary optical transmission behavior in epitaxial and polycrystalline Ag films in the mid- and far-infrared regimes.

In this Letter we report a comparative study, in the infrared regime, of surface plasmon polariton (SPP) propagation in epitaxially grown Ag films and in polycrystalline Ag films, all grown on Si substrates. Plasmonic resonance features are analyzed using extraordinary optical transmission (EOT) measurements, and SPP band structures for the two dielectric/metal interfaces are investigated for both types of film. At the Si/Ag interface, EOT spectra show almost identical features for epitaxial and polycrystalline Ag films and are characterized by sharp Fano resonances. On the contrary, at the air/Ag interface, dramatic differences are observed: while the epitaxial film continues to exhibit sharp Fano resonances, the polycrystalline film shows only broad spectral features and much lower transmission intensities. In corroboration with theoretical simulations, we find that surface roughness plays a critical role in SPP propagation for this wavelength range.

Improved electrical conductivity of graphene films integrated with metal nanowires.

Polycrystalline graphene grown by chemical vapor deposition (CVD) on metals and transferred onto arbitrary substrates has line defects and disruptions such as wrinkles, ripples, and folding that adversely affect graphene transport properties through the scattering of the charge carriers. It is found that graphene assembled with metal nanowires (NWs) dramatically decreases the resistance of graphene films. Graphene/NW films with a sheet resistance comparable to that of the intrinsic resistance of graphene have been obtained and tested as a transparent electrode replacing indium tin oxide films in electrochromic (EC) devices. The successful integration of such graphene/NW films into EC devices demonstrates their potential for a wide range of optoelectronic device applications.

Perovskite Microlaser Integration with Metasurface Supporting Topological Waveguiding.

Halide perovskite nano- and microlasers have become a very convenient tool for many applications from sensing to reconfigurable optical chips. Indeed, they exhibit outstanding emission robustness to crystalline defects due to so-called "defect tolerance" allowing for their simple chemical synthesis and further integration with various photonic designs. Here we demonstrate that such robust microlasers can be combined with another class of resilient photonic components, namely, with topological metasurfaces supporting topological guided boundary modes. We show that this approach allows to outcouple and deliver the generated coherent light over tens of microns despite the presence of defects of different nature in the structure: sharp corners in the waveguide, random location of the microlaser, and defects in the microlaser caused by mechanical pressure applied during its transfer to the metasurface. As a result, the developed platform provides a strategy to attain robust integrated lasing-waveguiding designs resilient to a broad range of structural imperfections, both for electrons in a laser and for pseudo-spin-polarized photons in a waveguide.

Adiabatic topological photonic interfaces.

Topological phases of matter have been attracting significant attention across diverse fields, from inherently quantum systems to classical photonic and acoustic metamaterials. In photonics, topological phases offer resilience and bring novel opportunities to control light with pseudo-spins. However, topological photonic systems can suffer from limitations, such as breakdown of topological properties due to their symmetry-protected origin and radiative leakage. Here we introduce adiabatic topological photonic interfaces, which help to overcome these issues. We predict and experimentally confirm that topological metasurfaces with slowly varying synthetic gauge fields significantly improve the guiding features of spin-Hall and valley-Hall topological structures commonly used in the design of topological photonic devices. Adiabatic variation in the domain wall profiles leads to the delocalization of topological boundary modes, making them less sensitive to details of the lattice, perceiving the structure as an effectively homogeneous Dirac metasurface. As a result, the modes showcase improved bandgap crossing, longer radiative lifetimes and propagation distances.

Spin-dependent properties of optical modes guided by adiabatic trapping potentials in photonic Dirac metasurfaces.

The Dirac-like dispersion in photonic systems makes it possible to mimic the dispersion of relativistic spin-1/2 particles, which led to the development of the concept of photonic topological insulators. Despite recent demonstrations of various topological photonic phases, the full potential offered by Dirac photonic systems, specifically their ability to emulate the spin degree of freedom-referred to as pseudo-spin-beyond topological boundary modes has remained underexplored. Here we demonstrate that photonic Dirac metasurfaces with smooth one-dimensional trapping gauge potentials serve as effective waveguides with modes carrying pseudo-spin. We show that spatially varying gauge potentials act unevenly on the two pseudo-spins due to their different field distributions, which enables control of guided modes by their spin, a property that is unattainable with conventional optical waveguides. Silicon nanophotonic metasurfaces are used to experimentally confirm the properties of these guided modes and reveal their distinct spin-dependent radiative character; modes of opposite pseudo-spin exhibit disparate radiative lifetimes and couple differently to incident light. The spin-dependent field distributions and radiative lifetimes of their guided modes indicate that photonic Dirac metasurfaces could be used for spin-multiplexing, controlling the characteristics of optical guided modes, and tuning light-matter interactions with photonic pseudo-spins.

Photonic Dirac cavities with spatially varying mass term.

In recent years, photonics has proven itself as an excellent platform for emulation of relativistic phenomena. Here, we show an example of relativistic-like trapping in photonic system that realizes Dirac-like dispersion with spatially inhomogeneous mass term. The modes trapped by such cavities, their energy levels, and corresponding orbitals are then characterized through optical imaging in real and momentum space. The fabricated cavities host a hierarchy of photonic modes with distinct radiation profiles directly analogous to various atomic orbitals endowed with unique characteristics, such as pseudo-particle-hall symmetry and spin degeneracy, and they carry topological charge which gives rise to radiative profiles with angular momentum. We demonstrate that these modes can be directionally excited by pseudo-spin-polarized boundary states. In addition to the fundamental interest in the structure of these pseudo-relativistic orbitals, the proposed system offers a route for designing new types of nanophotonic devices, spin-full resonators and topological light sources compatible with integrated photonics platforms.

Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers.

Engineered optical metamaterials present a unique platform for biosensing applications owing to their ability to confine light to nanoscale regions and to their spectral selectivity. Infrared plasmonic metamaterials are especially attractive because their resonant response can be accurately tuned to that of the vibrational modes of the target biomolecules. Here we introduce an infrared plasmonic surface based on a Fano-resonant asymmetric metamaterial exhibiting sharp resonances caused by the interference between subradiant and superradiant plasmonic resonances. Owing to the metamaterial's asymmetry, the frequency of the subradiant resonance can be precisely determined and matched to the molecule's vibrational fingerprints. A multipixel array of Fano-resonant asymmetric metamaterials is used as a platform for multispectral biosensing of nanometre-scale monolayers of recognition proteins and their surface orientation, as well as for detecting chemical binding of target antibodies to recognition proteins.