Fig. 9: Directional sound propagation with other types of acoustic artificial structures.

a-c Directional emission through acoustic anisotropic metamaterials: a Schematic illustration of the anisotropic metamaterial, featuring a unit composed of a straight channel and four symmetrical side branch cavities. Simulated distributions of the pressure fields in (b) x-direction and (c) y-direction of the metamaterial array at 3540 Hz with an incident plane wave. Adapted with permission from ref. ¹³⁰., Copyright © 2022, Elsevier. d, e Interfacial wave between acoustic media with Willis coupling: d Detailed view of the designed 2D slab waveguide with C-shaped Helmholtz resonators. The red dotted line indicates the interface of two different acoustic Willis materials, and θ represents the orientation angle of the Helmholtz resonator. e Simulated and experimental acoustic fields of the slab waveguide with two Willis materials oriented at angles of (left panel) −135° and 45°, and (right panel) 45° and −135°, respectively. Adapted with permission from ref. ¹³¹., Copyright © 2022, Elsevier. f-h Bioinspired directional emission via hybrid metamaterials: f Physics-based porpoise model. g Acoustic beam formations of the model with air component V at 30 kHz. h Acoustic beam formation of physics-based porpoise model with I, II, III, IV, and V at 30 kHz. Adapted with permission from ref. ¹³²., Copyright © 2019, Erqian Dong et al. i-k Directional acoustic emission in a Penrose quasi-crystal structure: i Geometry of a Penrose quasicrystal realized with 86 rods. j Distribution of the acoustic pressure outside the circular Penrose quasi-crystal with 86 rods at 459.5 kHz. k Experimental mapping of the directivity pattern of the water-immersed quasi-crystal with the non-directional source positioned at the center. Adapted with permission from ref. ¹³³., Copyright © 2019, Elsevier.