Theoretical and experimental study of the topological charge of linear and nonlinear acoustical vortices

Abstract

An acoustical or optical vortex is a beam whose phase is winding along a line of phase singularity. The intensity associated to such a beam, also called screw dislocation, has a doughnught shape. The number of 2π jumps of the phase around the singularity line is called the topological charge. Using the concept of pseudo‐momentum, a general relation linking the pseudo‐energy, the angular pseudo‐momentum and the topological charge of an acoustical vortex is derived. In an inviscid and isotropic medium, this relation can be interpreted as a conservation law of the topological charge for linear vortices, while it implies a linear increase of the topological charge with the order of harmonics for nonlinear vortices. These behaviors of the topological charge have been experimentally confirmed for linear and nonlinear acoustical vortices. Experimental results obtained by a new and versatile experimental set‐up will be presented.