Interaction of astigmatic hyperbolic sinusoidal Gaussian beams in strongly nonlocal nonlinear media

In this paper, we obtain analytical expressions for the co-propagation of two and four interacting astigmatic hyperbolic sinusoidal Gaussian beams in strongly nonlocal nonlinear media by using nonlocal nonlinear Schrodinger equation. Through numerical simulations, we characterize their interaction properties and dif-ferences between the interaction of two beams and four beams, primarily focusing on the transverse intensity distribution of beam clusters and the evolution of intensity along the axis. We find that in strongly nonlocal nonlinear media, the evolution of multiple interacting astigmatic hyperbolic sinusoidal Gaussian beams periodic. Regardless of whether the beams are in-phase or out-of-phase, the interaction among multiple beams is always attractive. The difference lies in the fact that in the case of complete in-phase beams, there are two small intensity peaks at the center of the interaction region, whereas this is not the case for other scenarios. Furthermore, among the four beams, the evolution of the in-phase interaction between vertically adjacent beams is exactly opposite to the out-of-phase interaction between horizontally adjacent beams. This research provides valuable insights for interaction of multiple beams and optical wireless communication.