Deep‐Subwavelength Holey Acoustic Second‐Order Topological Insulators

Abstract

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...

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