Numerical investigation of the properties of nonlinear acoustical vortices through weakly heterogeneous media

Acoustical vortices (AV) are the acoustical equivalent of optical vortices (OV) that are a key feature in the discipline of singular optics. For linear waves, OV and AV possess the same properties. But as nonlinearities are different in optics and acoustics, the nonlinear behavior of these structures has to be different. In this paper, a numerical investigation of the three-dimensional (3D) nonlinear propagation of acoustical vortices through homogeneous or heterogeneous media is reported. First, an original numerical method is described and compared to existing ones. Then, it is used to study the dynamics of AV in a nonlinear regime. The nonlinear properties of acoustical vortices in a homogeneous medium are investigated. It is shown that shock waves can be produced during propagation, leading to an interesting spatiotemporal wave field with an azimuthal shock. The dynamics of the topological charge, intrinsic property of AV or OV, is studied in the nonlinear regime through different focusing lenses. Inversion of the topological charge is observed if the AV propagates through a 1D focusing medium (cylindrical lens), while the charge remains constant if the medium is 2D (spherical lens). These last results already observed in linear optics are generalized here to the nonlinear behavior through the investigation of harmonics which show the same behavior as the fundamental with respect to inversion.