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.

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.

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.

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.

Synthetic Pseudo-Spin-Hall effect in acoustic metamaterials.

While vector fields naturally offer additional degrees of freedom for emulating spin, acoustic pressure field is scalar in nature, and it requires engineering of synthetic degrees of freedom by material design. Here we experimentally demonstrate the control of sound waves by using two types of engineered acoustic systems, where synthetic pseudo-spin emerges either as a consequence of the evanescent nature of the field or due to lattice symmetry. First, we show that evanescent sound waves in perforated films possess transverse angular momentum locked to their propagation direction which enables their directional excitation. Second, we demonstrate that lattice symmetries of an acoustic kagome lattice also enable a synthetic transverse pseudo-spin locked to the linear momentum, enabling control of the propagation of modes both in the bulk and along the edges. Our results open a new degree of control of radiation and propagation of acoustic waves thus offering new design approaches for acoustic devices.

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.

Experimental observation of topological Z2 exciton-polaritons in transition metal dichalcogenide monolayers.

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. Topological polaritons (TPs) offer an ideal platform in this context, with unique properties stemming from resilient topological states of light strongly coupled with matter. Here we explore polaritonic metasurfaces based on 2D transition metal dichalcogenides (TMDs) as a promising platform for topological polaritonics. We show that the strong coupling between topological photonic modes of the metasurface and excitons in TMDs yields a topological polaritonic Z2 phase. We experimentally confirm the emergence of one-way spin-polarized edge TPs in metasurfaces integrating MoSe2 and WSe2. Combined with the valley polarization in TMD monolayers, the proposed system enables an approach to engage the photonic angular momentum and valley and spin of excitons, offering a promising platform for photonic/solid-state interfaces for valleytronics and spintronics.

All-optical nonreciprocity due to valley polarization pumping in transition metal dichalcogenides.

Nonreciprocity and nonreciprocal optical devices play a vital role in modern photonic technologies by enforcing one-way propagation of light. Here, we demonstrate an all-optical approach to nonreciprocity based on 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 (CP) light. Nonreciprocity stems from valley-selective exciton population, giving rise to nonlinear circular dichroism controlled by CP pump fields. Our experimental results reveal a significant effect even at room temperature, despite considerable intervalley-scattering, showing promising potential for practical applications in magnetic-free nonreciprocal platforms. As an example, here 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.

Near-Field Characterization of Higher-Order Topological Photonic States at Optical Frequencies.

Higher-order topological insulators (HOTIs) represent a new type of topological system, supporting boundary states localized over boundaries, two or more dimensions lower than the dimensionality of the system itself. Interestingly, photonic HOTIs can possess a richer physics than their original condensed matter counterpart, supporting conventional HOTI states based on tight-binding coupling, and a new type of topological HOTI states enabled by long-range interactions. Here, a new mechanism to establish all-dielectric infrared HOTI metasurfaces exhibiting both types of HOTI states is proposed, supported by a topological transition accompanied by the emergence of topological Wannier-type polarization. Two kinds of near-field experimental studies are performed: i) the solid immersion spectroscopy and ii) near-field imaging using scattering scanning near-field optical microscopy to directly observe the topological transition and the emergence of HOTI states of two types. It is shown that the near-field profiles indicate the displacement of the Wannier center across the topological transition leading to the topological dipole polarization and emergence of the topological boundary states. The proposed all-dielectric HOTI metasurface offers a new approach to confine the optical field in micro- and nano-scale topological cavities and thus paves the way to achieve a novel nanophotonic technology.

Demonstration of a quantized acoustic octupole topological insulator.

Recently introduced quantized multipole topological insulators (QMTIs) reveal new types of gapped boundary states, which themselves represent lower-dimensional topological phases and host symmetry protected zero-dimensional corner states. Inspired by these predictions, tremendous efforts have been devoted to the experimental observation of quantized quadrupole topological phase. However, due to stringent requirements of anti-commuting reflection symmetries, it is challenging to achieve higher-order quantized multipole moments, such as octupole moments, in a three-dimensional structure. Here, we overcome this challenge, and experimentally realize the acoustic analogue of a quantized octupole topological insulator 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 hierarchy of boundary modes, observing 3rd order topological corner states. Furthermore, we reveal topological phase transitions from higher- to lower-order multipole moments. Our work offers a pathway to explore higher-order topological states in 3D classical platforms.

Demonstration of a third-order hierarchy of topological states in a three-dimensional acoustic metamaterial.

Classical wave systems have constituted an excellent platform for emulating complex quantum phenomena, such as demonstrating topological phenomena in photonics and acoustics. 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. Here, we design and experimentally study a 3D topological acoustic metamaterial supporting third-order (0D) topological corner states along with second-order (1D) edge states and first-order (2D) surface states within the same topological bandgap, thus establishing a full hierarchy of nontrivial bulk polarization-induced states in three dimensions. The assembled 3D topological metamaterial represents the acoustic analog of a pyrochlore lattice made of interconnected molecules, and is shown to exhibit topological bulk polarization, leading to the emergence of boundary states.

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.

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.

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.

Pseudo-spin-valley coupled edge states in a photonic topological insulator.

Pseudo-spin and valley degrees of freedom engineered in photonic analogues of topological insulators 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 topological insulators carrying different spin-valley Chern numbers. These results open up the possibility of using the valley degree of freedom to control the flow of optical signals in 2D structures.

Spin- and valley-polarized one-way Klein tunneling in photonic topological insulators.

Recent advances in condensed matter physics have shown that the spin degree of freedom of electrons can be efficiently exploited in the emergent field of spintronics, offering unique opportunities for efficient data transfer, computing, and storage (1-3). These concepts have been inspiring analogous approaches in photonics, where the manipulation of an artificially engineered pseudospin degree of freedom can be enabled by synthetic gauge fields acting on light (4-6). The ability to control these degrees of freedom significantly expands 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. We demonstrate a new class of photonic systems, described by effective Hamiltonians in which competing synthetic gauge fields, engineered in pseudospin, chirality/sublattice, and valley subspaces, result in bandgap opening at one of the valleys, whereas the other valley exhibits Dirac-like conical dispersion. We show that this effective response has marked implications on photon transport, among which are as follows: (i) a robust pseudospin- and valley-polarized one-way Klein tunneling and (ii) topological edge states that coexist within the Dirac continuum for opposite valley and pseudospin 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 pseudospin and valley degrees of freedom.