Propagation of self-accelerating Hermite complex-variable-function Gaussian wave packets in highly nonlocal nonlinear media

The evolution dynamic properties of self-accelerating Hermite complex-variable-function Gaussian (SHCG) wave packets in highly nonlocal nonlinear media are investigated. Analytical results from a (3+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(3+1)$$\end{document}-dimensional Snyder–Mitchell model show that various SHCG wave packets carrying multi-order vortices rotate smoothly. Increasing the distribution factor will cause the intensity layout to cluster more closely around the center, while the vortices will be farther away. The SHCG wave packets can reverse the positions of their temporal side lobes. The role of the power ratio in determining the rotation period and the angular velocity is also discussed. Furthermore, numerical results of the nonlocal nonlinear Schrödinger equation are simulated to illustrate the effects of different nonlocalities and initial perturbations. The SHCG wave packets show interesting features during propagation, which can provide new ideas for the regulation of the multi-dimensional optical field.