in 2D system. To date, HOTIs have been theoretically predicted and experimentally realized in elastics, [34,35] microwaves, [36] electric circuits, [37] photonics, [38][39][40] and acoustic systems. [41][42][43][44][45][46] In order to make HOTIs more attractive for real-world applications as in sound wave control, several hurdles must be overcome. For example, most of the reported results focus solely on a single frequency band, whose limitations ought to be overcome in order to provide a broadband response for topologically robust acoustics. Also, the above reported acoustic implementations have, for the most part, been implemented inside waveguides or were designed in an acoustically rigid enclosure, which hinders their capabilities from external insonification. Lastly, in terms of compactness, it is desired to utilize building blocks of the HOTI on a subwavelength scale in order to confine sound in tight areas beyond the diffraction limit.In this work, we design topologically protected acoustic corner states at deep subwavelength scales by constructing a perforated crystal, also known as holey metamaterials. The advantage in using holey metamaterials resides in their high levels of integration and miniaturization at scales much smaller than the sound wavelength. Without being pierced by holes, those metamaterials would not be able to sustain surface-confined wave propagation. With perforations on the other hand, externally incident radiation is able to bind to the structure in the form of "spoof" surface acoustic waves (SAWs), thus enabling sound energy confinement way beyond the classical diffraction limit. [47,48] In addition to breaking the diffraction limit for spoof SAWs, we demonstrate that a topological phase transition, which is derived from an extended 2D Zak phase, can be tuned by simply shrinking or expanding the distance among a group of holes within the unit cell. Beyond measuring corner states within multiple nontrivial bandgaps, the first-order resonance in particular displays the strongest topological sound energy confinement down to a feature size of λ/50. Lastly, we experimentally verify their resilience against defects and design a HOTI device for topological subwavelength imaging, which may be relevant for sound energy focusing and detection. Figure 1a illustrates the schematic of deep-subwavelength acoustic SOTI under consideration, which is realized by a perforated rigid material whose holes are arranged in a square lattice. The perforation depth and the radii of holes are H = 12 cm and r = 0.5 cm, respectively. The lattice constant is a = 4.8 cm.The center-to-center distance between the adjacent holes in the unit cell is defined as R, which is chosen to be R/a = 0.5 for the Higher-order topological insulators (HOTIs) belong to a new class of materials with unusual topological phases. They have garnered considerable attention due to their capabilities in confining energy at the hinges and corners, which is entirely protected by the topology, and have thus become attractive structures for...

We present the mechanism for the asymmetric absorption of acoustic waves in a two-port transparent waveguide system by shunting detuned Helmholtz resonators (HRs) pairs in cascade. Theoretical analysis, numerical simulations, and experimental measurements verify that sound energy is almost totally absorbed (96.1%) at ∼373 Hz when sound waves are incident from one side while it is largely reflected back from the opposite side by judiciously designed HRs to provide manipulated surface impedance matching/mismatching to that of air at the opposite sides of the waveguide. Thus, asymmetric acoustic absorber is achieved at a low frequency. We have further demonstrated the flexibility of this methodology to get non-reciprocal absorption and reflectance in multiband and broadband. Our design advances the concept of asymmetric acoustic manipulation in passive two-port systems and may enable sound-absorbing devices for more versatile applications.

The emerging absorptive metasurface relies on arrays of structured meta-atoms with various geometries for customized sound localization, which can significantly enhance the energy dissipation. However, most of the existing absorbers are for given frequencies at an optimal incident angle. This limitation on the working frequency and incident angle remains a challenging obstacle for their practical applications, in addition to the perfect absorptance demand. Guided by the causality principle, a physical model is established in which the absorptive properties of such systems can be fully controlled by two simple parameters (i.e., leakage factor and loss factor) which are dictated by the geometrical properties of the underlying structures. We demonstrate a subwavelength metasurface absorber which shows near-perfect absorptance (at 95%) in a broad frequency regime from 228 Hz to 319 Hz (wavelength λ from 12.6 to 9.0 times thickness) and even allows 93% reduction with a large incident angle of 60°. We prove that this broadband near-perfect absorption behavior stems from the tunable damping conditions, which can be achieved by coupling an ordinary ultrathin surface sponge coating with an artificial underdamped multiband absorptive system. From the view of the causality principle, the subwavelength near-perfect absorptions originate from the finite working bandwidth. As the research premise, we also demonstrate a λ/21.7-thick, 16.7%-filling ratio ultrasparse absorber with unity absorptance by modulating the displacements between uniformly sized coiled space resonators. The paradigm may pave the way for versatile devices in noise remediation engineering.