The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It is thus noteworthy that an entirely novel class of electromagnetic waves, known as "topological edge states," has recently been demonstrated. These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder. Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids. The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers.

Recently discovered1,2 valley photonic crystals (VPCs) mimic many of the unusual properties of two-dimensional (2D) gapped valleytronic materials [3][4][5][6][7][8][9] . Of the utmost interest to optical communications is their ability to support topologically protected chiral edge (kink) states [3][4][5][6][7][8][9] at the internal domain wall between two VPCs with opposite valley-Chern indices. Here we experimentally demonstrate valley-polarized kink states with polarization multiplexing in VPCs, designed from a spin-compatible four-band model. When the valley pseudospin is conserved, we show that the kink states exhibit nearly perfect out-coupling e ciency into directional beams, through the intersection between the internal domain wall and the external edge separating the VPCs from ambient space. The out-coupling behaviour remains topologically protected even when we break the spin-like polarization degree of freedom (DOF), by introducing an e ective spin-orbit coupling in one of the VPC domains. This also constitutes the first realization of spin-valley locking for topological valley transport.

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the ‘topological protection' in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can break the topological protection, but do not exist in electronic topological insulators. This is also an experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants.

Confining photons in a finite volume is in high demand in modern photonic devices. This motivated decades ago the invention of photonic crystals, featured with a photonic bandgap forbidding light propagation in all directions 1-3 . Recently, inspired by the discoveries of topological insulators (TIs) 4,5 , the confinement of photons with topological protection has been demonstrated in two-dimensional (2D) photonic structures known as photonic TIs 6-8 , with promising applications in topological lasers 9,10 and robust optical delay lines 11 . However, a fully three-dimensional (3D) topological photonic bandgap has never before been achieved. Here, we experimentally demonstrate a 3D photonic TI with an extremely wide (> 25% bandwidth) 3D topological bandgap. The sample consists of split-ring resonators (SRRs) with strong magneto-electric coupling and behaves as a "weak TI", or a stack of 2D quantum spin Hall insulators. Using direct field measurements, we map out both the gapped bulk bandstructure and the Dirac-like dispersion of the photonic surface states, and demonstrate robust photonic propagation along a non-planar surface. Our work extends the family of 3D TIs from fermions to bosons and paves the way for applications in topological photonic cavities, circuits, and lasers in 3D geometries.

Recent theories have proposed a concept of valley photonic crystals as an analog of gapped valleytronic materials such as MoS 2 and bilayer graphene. Here, we further extend the applicability of valley photonic crystals to surface electromagnetic waves and experimentally demonstrate a valley surface-wave photonic crystal on a single metal surface as a photonic duplicate of MoS 2 . Both bulk transport and edge transport are directly mapped with a near-field microwave imaging system. The photonic valley pseudospins are demonstrated, together with the photonic valley Hall effect that splits the opposite photonic valley pseudospins into two opposite directions. The valley edge transport in MoS 2 or other transition-metal dichalcogenide monolayers, which is different from bilayer graphene but still stays unrealized in condensed-matter systems, is demonstrated on this MoS 2 -like photonic platform. Our study not only offers a tabletop platform to study the valleytronic physics, but also opens a venue for on-chip integrated photonic device applications using valley-polarized information.