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Synthetic optical materials have been recently employed as a powerful platform for the emulation of topological phenomena in wave physics. Topological phases offer exciting opportunities, not only for fundamental physics demonstrations, but also for practical technologies. Yet, their impact has so far been primarily limited to their claimed enhanced robustness. Here, we clarify the role of robustness in topological photonic systems, and we discuss how topological photonics may offer a wider range of important opportunities in science and for practical technologies, discussing emergent and exciting research directions.

The unique conduction properties of condensed matter systems with topological order have recently inspired a quest for the 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 along their edges, with topological immunity against structural defects and disorder. So far, these fascinating properties have been obtained relying on moving media, which may introduce noise and absorption losses, hindering the practical potential 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. 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. One-way sound propagation has been recently proposed in the context of topological acoustics, but is challenged by introducing uniform media motion. Here, Fleury et al. present a practical scheme to achieve topological propagation by modulating in time the acoustic properties of a lattice of resonators, resembling Floquet topological insulators in condensed matter.

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.

Surface waves in topological states of quantum matter exhibit unique protection from backscattering induced by disorders, making them ideal carriers for both classical and quantum information. Topological matters for electrons and photons are largely limited by the range of bulk properties, and the associated performance trade-offs. In contrast, phononic metamaterials provide access to a much wider range of material properties. Here we demonstrate numerically a 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 for phonons 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, demonstrating topological protection for phonons in both static and time-dependent regimes. Metamaterials are engineered media with properties that mimic those of natural materials, but offer a much wider range of possibilities. Here, the authors numerically demonstrate an elastic-wave analogue of the quantum spin Hall effect in a phononic topological metamaterial.

Topological insulators do not allow conduction in the bulk, yet they support edge modes that travel along the boundary only in one direction, determined by the carried electron spin, with inherent robustness to defects and disorder. Topological insulators have inspired analogues in photonics and optics, in which one-way edge propagation in topologically protected two-dimensional materials is achieved breaking time-reversal symmetry with a magnetic bias. Here, we introduce the concept of topological order in classical acoustics, realizing robust topological protection and one-way edge propagation of sound in a suitably designed resonator lattice biased with angular momentum, forming the acoustic analogue of a magnetically biased graphene layer. Extending the concept of an acoustic nonreciprocal circulator based on angular-momentum bias, time-reversal symmetry is broken here using moderate rotational motion of air within each element of the lattice, which takes the role of the electron spin in determining the direction of modal edge propagation. Topological order for sound remains largely unexplored. Here, Khanikaev et al . introduce the concept of topological order in classical acoustics, realizing robust topological protection and one-way edge propagation of sound in a suitably designed resonator lattice, thus expanding the ability to tailor acoustic waves.

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 3 rd 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. Although multipole topological insulators have been theoretically described and experimentally observed in 2D, third-order topological insulators in 3D have not been observed yet. Here, the authors realize for the first time a quantized octupole 3D topological state in an acoustic metamaterial.

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. Valleys in the photonic band structure provide an additional degree of freedom to engineer topological photonic structures and devices. Here, Kang et al. demonstrate that inter-valley scattering is inhibited at a Y-junction between three sections with different valley topology.

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. Plasmonic nanostructures are known to be an attractive platform for highly sensitive molecular sensors, although they often lack specificity. A plasmonic device with a sharp optical resonance tuned to biomolecules selectively captured on the surface of the device now offers a versatile yet highly specific platform for molecular sensing.

Topological phase transitions in condensed matter systems give rise to exotic states of matter such as topological insulators, superconductors, and superfluids. Photonic topological systems open a whole new realm of research and technological opportunities, exhibiting a number of important distinctions from their condensed matter counterparts. Photonic modes can leak into free space, which makes it possible to probe topological photonic phases by spectroscopic means via Fano resonances. Based on this idea, we develop a technique to retrieve the topological properties of all-dielectric metasurfaces from the measured far-field scattering characteristics. Collected angle-resolved spectra provide the momentum-dependent frequencies and lifetimes of the photonic modes that enable the retrieval of the effective Hamiltonian and extraction of the topological invariant. Our results demonstrate how the topological states of open non-Hermitian systems can be explored via far-field measurements, thus paving a way to the design of metasurfaces with unique scattering characteristics controlled via topological effects. Topological modes in photonics systems are not completely confined to the structure but can leak into free space. Here, Gorlach et al. exploit these leaky modes to probe the topological properties of a dielectric metasurface from far-field scattering measurements.

We demonstrate that an acoustic Kagome lattice formed by an array of interconnected resonant cavities exhibits a new class of topological states protected by C3 symmetry, and it is characterised by a topological invariant in the form of a winding number in Pauli vector space. This acoustic topological metamaterial can be considered as the two-dimensional analogue of the Su-Schrieffer-Heeger model, exhibiting a topological transition when a detuning is introduced between the inter-cell and intra-cell hopping amplitudes. The topological transition caused by such detuning is accompanied by the opening of a complete topological band gap, which may host edge states. The edge states emerge on either truncated ends of the lattice terminated by a cladding layer or at the domain walls between topologically nontrivial and trivial domains. First-principles simulations based on full-wave finite element method are used to design the lattice and confirm our analytical predictions.