Figure 1
From: Dynamic generation and modulation of acoustic bottle-beams by metasurfaces

Illustration of an arbitrary convex trajectory x = f(z) (red line), the tangent line (blue lines) and the AM (brown line). \({\rm{\Phi }}(x)=\varphi (x)+\varphi ^{\prime} (x,\phi )\) is the spatial phase profile in the x-axis, where ϕ(x) is the phase shift caused by the AM and \(\varphi ^{\prime} (x,\phi )\) is the phase shift caused by the incident angle φ. x0,z0 is a point on the trajectory and θ is the angle between the z-axis and the tangent line through the point x0,z0. (b) Schematic of a three-layered acoustic space-coiling subunit with a variable t. (c) Relative phase shift (the dashed line for the left-hand scale) and transmissivity (solid line for the right-hand scale) of the three-layered acoustic space-coiling subunit as a function of t.