Spatiotemporal airyprime Ince-Gaussian wave packets in strongly nonlocal nonlinear media

Abstract This article extended the evolution theory of self-accelerating wave packets in strongly nonlocal nonlinear media (SNNM), by focusing on the evolution of spatiotemporal Airyprime Ince-Gaussian (ApIG) wave packets in SNNM. Based on the (1+3)-dimensional nonlocal nonlinear Schrödinger equation, expression of the targeted wave packets propagating in SNNM was simplified to the Snyder-Mitchell equation. Analytical solutions covering spatiotemporal evolution and phase distribution of the targeted wave packets in SNNM were obtained by the method of separation of variables. Besides, Poynting vector of the wave packets in SNNM was also analyzed. Results demonstrated that the main propagation characteristics such as the wave packets shape, stability, and propagation path were primarily influenced by the ratio of input power to critical transmission power, ellipticity, attenuation factor, and noise perturbation. Notably, this paper constructs for the first time a spatiotemporal wave packet model combining Airyprime function and Ince- Gaussian function, revealing the wave packet shape under different elliptic parameter (Laguerre→Hermit), which enables symmetry manipulation. This study would provide a theoretical foundation and methodology for designing structured light field in SNNM, and offer reference value for nonlinear optical communications.