Figure 8: Design methodology of acoustic bottle beams.
From: Generation of acoustic self-bending and bottle beams by phase engineering

(a) Illustration of the method. (b–e) Numerical simulation results. As shown in a, from the one-to-one mapping between the rays (thin black lines) and the boundary of the bottle beam (red curve) at the critical plane (z=0, except the singular point), we first construct the wavefront (blue curve) and then the pure phase map (b) at the critical plane (vertical dashed line). With a backward propagating process, we can obtain the amplitude (c) and phase modulation (d) required for the production of the designed bottle beam at z=−z0, the intensity cross-section of which is shown in e, where the white dashed curves depict the predesigned bottle shape. Scale bar, 0.1 m. a.u., arbitrary unit.