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Topological order for sound remains largely unexplored. Here, Khanikaevet 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.

Quantum emitters respond to weak near-field coupling with topological photonic waveguides, revealing polarization and spectral reshaping.

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.

Nonlinear circuit arrays can exhibit self-induced topological transitions as a function of input intensity and topological immunity against defects and disorder.

Non-trivial topological phases can allow for one-way spin-polarized transport along the interfaces of topological insulators but they are relatively uncommon in the condensed state of matter. By arranging judiciously designed metamaterials into two-dimensional superlattices, a photonic topological insulator has now been demonstrated theoretically, enabling unidirectional spin-polarized photon propagation without the application of external magnetic fields or breaking of time-reversal symmetry.

Topological traps and guides for polaritons expand the potential for light-matter wave manipulation in ultrathin materials, facilitating photonic on-chip integration. Here the authors demonstrate a chiral-defect cavity in a planar metasurface that efficiently trap mid-IR phonon-polaritons in topological defects.

A nonlinear optical response to a new form of light, dubbed chiral topological light owing to its local chirality and global topological characteristics, is enabling unprecedented enantiosensitivity and robustness of chiro-optical spectroscopies as a result of structured light–matter interactions at deep subwavelength scales.

Using pump-power-dependent exciton absorption spectroscopy, the authors reveal magnon-mediated exciton–exciton interactions and a consequent nonlinear optical response in CrSBr, an antiferromagnetic semiconductor.

Smooth topological photonic interfaces lead to less localized boundary modes which improves their guiding characteristics in both spin- and valley Hall metasurfaces. The modes become insensitive to the lattice details, showcasing improved bandgap crossing and longer propagation distances.

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.

Controlling emission and propagation of acoustic waves offers new design opportunities for acoustic devices. Here the authors demonstrate such controls thanks to the emergence of a synthetic pseudo-spin in two-dimensional acoustic metamaterial.

One- and zero-dimensional optical states are revealed in photonic higher-order topological insulators.

Kerr optical nonlinearities are known to be well suited for achieving optical isolation, but the fact that the degree of non-reciprocity is signal-level dependent brings new opportunities as well as limitations.

In the quest for on-chip optical isolation, scientists demonstrate non-reciprocal optical response based on a 'synthetic' magnetic field in an all-silicon platform. This may open directions to optical routing, on-chip lasers and integrated nanophotonic signal processing.

Topological concepts have been demonstrated in microwave photonic systems but laser-written waveguides show the way to topological physics for light at optical frequencies.

The theoretical study of a 3D photonic topological metacrystal based on an all-dielectric metamaterial platform shows robust propagation of surface states along 2D domain walls, making it a promising solution for photonics applications. The proposed metacrystal design might also open the way for the observation of elusive fundamental physical phenomena.

A three-dimensional spectroscopic sensor is demonstrated that uses a polarization-resolved scattering technique to determine the location and orientation of small particles. It exploits strong Fano resonance between a pair of particles, one barely visible and another that is relatively bright, to obtain nanoscale orientation information.

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.

In this work light and matter have been coupled in a strong interaction between exciton resonances and topological photonic bands. The authors herein demonstrate a Z2 spin-Hall topological polaritonic phase enabling new coupling schemes in valleytronics and spintronics.

Photonic Dirac metasurfaces with smooth trapping potentials guide optical modes endowed with pseudo-spin. Such potentials give rise to different radiative properties of modes of opposite pseudo-spin.

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.

Nonreciprocity is viewed as a useful feature for many future optical devices. Here, the authors observe all-optically-induced nonreciprocal dichroism in monolayer WS2, which is explained by valley-selective response.

A temporal modulation protocol enriches topological Floquet physics by enabling the realization of bimorphic Floquet systems where Chern and anomalous Floquet phases coexist in a single platform of laser-written waveguides.

The physics of a second-order topological insulator, such as two-dimensional polarization, one-dimensional edge states and zero-dimensional corner states, are demonstrated experimentally in an acoustic breathing kagome lattice.

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.

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.

Topologically protected states at the interface of magnetic domain walls in a parallel plate waveguide with adjustable rods, are shown to be directed along different paths, as the waveguide geometry changes.

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.

Departing from common approaches to designing Floquet topological insulators, here the authors present a photonic realization of Floquet topological insulators revealing topological phases that simultaneously support Chern and anomalous topological states.

Synthetic gauge fields that enable controllable confinement and guiding via bound states in the continuum are demonstrated, offering new ways to confine and manipulate localization of radiation in space and opportunities to new applications of artificial gauge fields in photonics.

By introducing a further modal dimension to transform a two-dimensional photonic waveguide array, a photonic topological insulator with protected topological surface states in three dimensions, enabled by a screw dislocation, is demonstrated.

Understanding localization and delocalization phenomena is important for studying wave propagation in many types of disordered photonic systems. Here, a theoretical study of one-dimensional photonic crystal structures reveals the importance of Fano interference in wave transport in the presence of disorder.

Thanks to its topological properties, a CMOS-compatible photonic crystal shows reflectionless transmission of light at telecommunication wavelengths even along a path with sharp turns.

Hofstadter’s butterfly is a fractal pattern which pictorially represents the behavior of electrons under an applied magnetic field in a 2D lattice as a pair of butterfly wings. Here, the authors recreate this pattern by measuring the acoustic density of states in a fine-tuned one-dimensional acoustic array.

The nonlinear properties of photonic topological insulators remain largely unexplored, as band topology is linked to linear systems. But nonlinear topological corner states and solitons can form in a second-order topological insulator, as shown by experiments.

Topological photonic structures offer unique features such as reflection-free and non-reciprocal devices. This Review highlights the experimental progress in the relatively new field of photonic topology.