Fig. 7: Topological acoustics-based directional sound propagation.

a-c Compact topological waveguide for enhanced acoustic directional radiation: a Upper panel: schematic illustration of the Su-Schrieffer-Heeger (SSH) chain, its corresponding band structure, and the nonradiable topological interface state. Lower panel: schematic illustration of double SSH chain, its corresponding band structure, and the radiable topological interface state. b State distributions of the waveguides with and without distinct topological phases. c Pressure field distributions of the two radiable interface modes from leaky-wave waveguides with 16 cells. Adapted with permission from ref. ⁸⁶., Copyright © 2022, AIP Publishing. d-g Directional acoustic antennas based on valley-Hall topological insulators: d Dispersion relation of the ribbon-shaped 2D structure. e Superdirectional sound radiation by out-coupling of valley-polarized edge states from the topological acoustic antenna. f Simulated and measured far-field pattern with normalized energy emerging from the negative-type interface at 8.66 kHz. g Experimentally detected spectral relation between acoustical energy and the directional angle within the entire topological band gap. Adapted with permission from ref. ⁸⁷., Copyright © 2018, John Wiley and Sons. h-k Topological surface states in a gyroid acoustic crystal: h Geometry of gyroid acoustic crystals. i Bulk dispersion along the high symmetry lines of the 3D Brillouin zone. j Dispersion of surface states in the surface Brillouin zone. The equifrequency contour at 16.5 kHz acts as a demonstration of open surface arcs. k Experimental measured acoustic field distribution at 18.4 kHz. Adapted with permission from ref. ⁸⁸., Copyright © 2022, Yuning Guo et al.