Phase-coded approach for controllable generation of acoustical vortices

Abstract

Based on the acoustic radiation of point source, a phase-coded approach is proposed as a general technology to generate controllable acoustical vortices. For N sources, acoustical vortices can be generated with the phase difference of 2πm/N for the source topological charge m. It is proved that more circular pressure distributions of acoustical vortices with higher pressure peak amplitude can be generated for more sources. The number and spiral direction of phase twists are demonstrated to be determined by m and the maximum topological charge of acoustical vortices is |L|=Fix[(N−1)/2], where Fix(x) rounds the element x toward zero. To produce acoustical vortices with a maximum topological charge L, the minimum source number of Nmin=max(2|L|+1,4) should be employed with the phase difference of 2πL/Nmin and the phase difference resolution is also demonstrated to be π. The phase-coded approach has been verified by a 6-source experiment. The measured distributions of pressure and phase as well as the topological charge of acoustical vortices agree well with theoretical results, which suggest the feasibility of the phase-coded approach for controllable generation of acoustical vortices.

Electromagnetic vortex topologies from sparse circular phased arrays

“…For higher values of N, we obtain an array of doughnuts for N = 6 and we obtain a single-doughnut structure for N = 12. Also, for lower N secondary vortices appear (with the same topological charge as the central vortex), but these secondary vortices are eliminated by increasing the element number N. Such behavior can be attributed to higher-order Bessel states in equation (6), as also revealed in figure 2.…”

“…In previous studies, the authors of [6] performed a numerical study of the problem for acoustical waves and concluded that to produce vortices with a maximum topological charge l, the minimum source number of and phase singularities were demonstrated both experimentally and theoretically [7][8][9][10][11][12] for as low as N = 3, but no analytic summation over N for arbitrary phase parameters l were performed, and therefore contributions from sub-leading vortices were not analyzed. Presence of sub-leading vortices, contributing to equations ( 6) and (8) expansion, is important since they may become a source of background in optical or acoustic communications.…”

“…In this study, we address a question of what vortex topologies are possible given a limited number of elements (or wave sources). Previously, the problem was studied in acoustics using numerical simulations [6]. In optics, formation of vortices from a limited number of plane waves, spherical waves or individual laser beams with controlled relative phases was extensively studied both theoretically and experimentally [7][8][9][10][11][12].…”

“…It is the main analytic result of this paper. To the best of our knowledge, in previous analyses of vortex formation from limited sources [6][7][8][9][10][11][12] analytic summation over the sources was not performed and Fourier-Bessel representation as in equation ( 6) was not used. It can be verified by direct substitution that the above expression equation ( 6) is invariant under transformations l → l ± N, similar to well-known Born-Kármán cyclic boundary conditions for a chain of N atoms in crystals.…”

Generation of acoustic helical wavefronts using metasurfaces

“…Hefner et al proposed then an alternative technique, based on a circular array of phase-shifted transducers [22]. This method has been adopted since then in most of the studies to create acoustical vortices, requiring many transducers which are individually controlled [23]. Gspan et al used optoacoustics for the generation of ultrasonic screw dislocations [24].…”