Phase-coded approach for controllable generation of acoustical vortices

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 $2\pi m/N$ 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 $\left|L\right|=\text{Fix}[(N-1)/2]$ , where $\text{Fix}(x)$ rounds the element $x$ toward zero. To produce acoustical vortices with a maximum topological charge $L$ , the minimum source number of $N_{\min }=\max (2\left|L\right|+1,4)$ should be employed with the phase difference of $2\pi L/N_{\min }$ and the phase difference resolution is also demonstrated to be $\pi$ . 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.