Third-order square-root topological insulators on decorated diamond sonic crystals.

The square-root operation can generate novel topological phases, whose nontrivial topological properties are inherited from the parent Hamiltonian. Here we report the acoustic realization of third-order square-root topological insulators by adding additional resonators between the site resonators of original diamond lattice. Due to the square-root operation, multiple acoustic localized modes appear in doubled bulk gaps. The bulk polarizations of the tight-binding models are employed to reveal the topological feature of the higher-order topological states. By tuning the coupling strength, we find the emergence of third-order topological corner states in doubled bulk gaps on tetrahedron-like and rhombohedron-like sonic crystals, respectively. The shape dependence of square-root corner states provides an extra degree of freedom for flexible manipulation on the sound localization. Furthermore, the robustness of the corner states in three-dimensional (3D) square-root topological insulator is well elucidated by introducing random disorders into the irrelevant bulk region of the proposed 3D lattices. This work extends square-root higher-order topological states into 3D system, and may find possible applications in selective acoustic sensors.

Square-root-like higher-order topological states in three-dimensional sonic crystals.

The square-root descendants of higher-order topological insulators were proposed recently, whose topological property is inherited from the squared Hamiltonian. Here we present a three-dimensional (3D) square-root-like sonic crystal by stacking the 2D square-root lattice in the normal (z) direction. With the nontrivial intralayer couplings, the opened degeneracy at theK-Hdirection induces the emergence of multiple acoustic localized modes, i.e., the extended 2D surface states and 1D hinge states, which originate from the square-root nature of the system. The square-root-like higher order topological states can be tunable and designed by optionally removing the cavities at the boundaries. We further propose a third-order topological corner state in the 3D sonic crystal by introducing the staggered interlayer couplings on each square-root layer, which leads to a nontrivial bulk polarization in thezdirection. Our work sheds light on the high-dimensional square-root topological materials, and have the potentials in designing advanced functional devices with sound trapping and acoustic sensing.

Probability-Density-Based Deep Learning Paradigm for the Fuzzy Design of Functional Metastructures.

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.

Super-resolution acoustic image montage via a biaxial metamaterial lens.

Ever since the Victorian era, montage, the process of pictorial composition made by juxtaposing or superimposing photographs, has been a very popular post-editing imaging technique. Despite showing a strong power in demonstrating complex wave field effects, this technique has neither been fully explored in acoustic imaging nor been realized in real-time systems with the capability beyond diffraction limits. On the other hand, the recent prospect of metamaterials has shown their great potentials in super-resolution acoustic imaging. However, the miracle jigsaw of more advanced functional modulation of acoustic wave fields at deep subwavelength scale still remains elusive. Here we report the experimental implementation of super-resolution acoustic image montage through a judiciously designed biaxial metamaterial lens. Based on the non-diffraction birefringence in the biaxial metamaterials, we realized various montage functionalities such as duplication, composition, and decomposition of sound images with distinctive deep subwavelength features. Our work represents an important step in developing versatile functional acoustic metamaterial devices for imaging purposes, as it provides on-demand editing of sound field patterns beyond diffraction limits.

Mirror-symmetry induced topological valley transport along programmable boundaries in a hexagonal sonic crystal.

Valley states, labeling the frequency extrema in momentum space, carry a new degree of freedom (valley pseudospin) for topological transport of sound in sonic crystals. Recently, the field of valley acoustics has become a hotspot due to its potentials in developing various topological-insulator-based devices. In most previous works, topological valley transport is implemented at the interfaces of two connected artificial crystals. With respect to the interface, the mirror symmetry of crystal structures supports either even-mode or odd-mode valley states. In this work, we propose a physical insight of transforming one hexagonal crystal into a virtual lattice by utilizing the mirror operation of rigid or soft boundaries, which greatly reduces the dimension of the acoustic structure and provides a possible way to implement the programmable routing of topological propagation. We investigate two cases that the rigid and soft boundaries are introduced either at the edge or inside a single hexagonal crystal. Our results clearly demonstrate the high-transmission valley transport along the folded boundaries, where reflection or scattering is prohibited at the sharp bending or corners due to topological protection. Three functional devices are exemplified, which are single-crystal-based topological delay-line filter, delay-line switcher and beam splitter. Our work reveals the inherent relation between the field symmetries of valley states and structural symmetries of sonic crystals. Programmable routing of topological sound transport through boundary engineering provides a platform for developing integrated and versatile topological-insulator-based devices.

Topologically protected edge transport of sound in coupled cavities of a modified honeycomb lattice.

In this work, we investigate comprehensively the unidirectional transport of sound in coupled cavities of a modified honeycomb lattice. The results clearly show that a pair of topological states carrying opposite pseudospins can be constructed at the edge of truncated lattices of non-trivial band gaps, which is different from previous schemes where topological states with opposite pseudospins were constructed at the interface of modified honeycomb lattices of trivial and non-trivial band gaps. Our work paves the way to exploring unidirectional edge transport of sound with topological protection in closed systems that are beneficial in large-scale device integration and low-loss operation.