Pseudo Angular Momentum and Topological Charge Conservation for Nonlinear Acoustical Vortices

We study acoustical vortices (AVs) and their connection with optical vortices (OVs). We show that AVs and OVs have the same properties if the concept of pseudomomentum is used. Radiation stress and conservation of topological charge are obtained with the pseudomomentum rule. In a weak nonlinear regime, the conservation of pseudo angular momentum imposes a linear increase of the topological charge with the harmonic order. This last result is experimentally verified.

Figure 1

Average intensity (top figures) and instantaneous phase (bottom figures) measurements of AVs of charges 1 (left) and 2 (right) at weak amplitude.

Figure 2

Instantaneous phase measurements of harmonics 2, 4, and 6 of the vortex of charge 1 (top figures) and of harmonics 1, 2, and 3 of the vortex of charge 2 (bottom figures) at finite amplitude.