Vortex X-wave propagation through von Kármán oceanic turbulence with anisotropy.

Vortex X-waves with coupling effects of orbital angular momentum (OAM) and spatiotemporal invariance are introduced into the research of underwater wireless optical communication systems (UWOCSs). We establish the OAM probability density of vortex X-waves and channel capacity of UWOCS using Rytov approximation and correlation function. Furthermore, an in-depth analysis of OAM detection probability and channel capacity is performed on vortex X-waves carrying OAM in von Kármán oceanic turbulence with anisotropy. The results show that an increase in OAM quantum number results in a "hollow X" shape in the received plane, where the energy of vortex X-waves is injected into the lobes, reducing the received probability of the vortex X-waves transmitted to the receiving end. As the Bessel cone angle increases, the energy gradually concentrates toward the energy distribution center, and the vortex X-waves become more localized. Our research may trigger the development of UWOCS for bulk data transfer based on OAM encoding.