The study for exotic topological effects of sound has attracted uprising interests in fundamental physics and practical applications. Based on the concept of valley pseudospin, we demonstrate the topological valley transport of plate-mode waves in a homogenous thin plate with periodic stubbed surface, where a deterministic two-fold Dirac degeneracy is form by two plate modes. We show that the topological property can be controlled by the height of stubs deposited on the plate. By adjusting the relative heights of adjacent stubs, the valley vortex chirality and band inversion are induced, giving rise to a phononic analog of valley Hall phase transition. We further numerically demonstrate the valley states of plate-mode waves with robust topological protection. Our results provide a new route to design unconventional elastic topological insulators and will significantly broaden its practical application in the engineering field.

The topological sound transport, as an interesting phenomenon discovered in sonic crystals, has drawn tremendous interest in recent years. Here, in resonant acoustic systems, we demonstrate the existence of band inversion by slightly changing the lengths of tube resonators, which unveils the acoustic valley Hall phase transition characterized by the inverted valley Chern number. However, when the valley topological insulator is largely distorted, we can obtain flat-band-like edge states in the bandgaps with topological protection still existing. Those edge states can propagate along zigzag delay-lines with the backscatterings suppressed to a large amount. Our work provides a prototype of topological-insulator-based acoustic devices with the frequency-selecting functionality.

Artificial topological insulators in classical systems are thriving, especially the meta-atom-based threedimensional (3D) topological lattices. Here we propose a paradigm based on engineering coupling networks in a generalized spatial Floquet lattice, which gives rise to low-loss and broadband 3D topological systems. A mapping between time and space dimensions is utilized to construct the Floquet system with chirality-assisted coupling patterns periodically modulated in spatial dimensions. The cyclotron orbiting motion of sound in the bulk and reversely orbiting motion on the surface are demonstrated, which provides a direct acoustic analogue of the electronic transport in Chern insulators. Weyl points and Fermi arc-like surface states unveil the topological transport of edge states. Splicing together two Floquet lattices with opposite chirality, we realize low-loss topological negative refraction on the surface, where the mirror reflection at the interface is prohibited. Our findings provide diverse ways to construct 3D devices with topological functionalities in acoustics and beyond.

Topological manipulation of sound has recently been a hot spot in acoustics due to the fascinating property of defect immune transport. To the best of our knowledge, the studies on one-dimensional (1D) topological acoustic systems hitherto mainly focus on the case of the Su-Schrieffer-Heeger model. Here, we show that topologically protected bound states may also exist in 1D periodically modulated acoustic waveguide systems, viz., 1D Floquet topological insulators. The results show that tuning the coupling strength in a waveguide lattice could trigger topological phase transition, which gives rise to topologically protected interface states as we put together two waveguide lattices featured with different topological phases or winding numbers. However, for the combined lattice, input at the waveguides other than the interfacial ones will excite bulk states. We have further verified the robustness of interface bound states against the variation of coupling strengths between the two distinct waveguide lattices. This work extends the scope of topological acoustics and may promote potential applications for acoustic devices with topological functionalities.

In quantum mechanics, a norm-squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the fuzzy structure of microcosmos. Recently, hybrid neural structures raised intense attention, resulting in various intelligent systems with far-reaching influence. Here, we propose a probability-density-based deep learning paradigm for the fuzzy design of functional metastructures. In contrast to other inverse design methods, our probability-density-based neural network can efficiently evaluate and accurately capture all plausible metastructures in a high-dimensional parameter space. Local maxima in probability density distribution correspond to the most likely candidates to meet the desired performances. We verify this universally adaptive approach in but not limited to acoustics by designing multiple metastructures for each targeted transmission spectrum, with experiments unequivocally demonstrating the effectiveness and generalization of the inverse design.