Stability of (2+1)D solitons in the generally nonlocal regime

Abstract

Since the description of accessible solitons by Snyder and Mitchel, the exploration of nonlocality in nonlinear media as a way to stabilize multidimensional solitons has received increasing attention. However, while the regimes of weak and strong nonlocality have been explored substantially, the case of general nonlocality remains scarcely investigated. This work seeks to explore this area, by testing the stability of (2+1)D beam profiles obtained through a perturbative approach, focusing on the generally nonlocal case of response functions of the Gaussian and exponential-decay types. The resulting semi-analytical expressions are perturbed LG modes, and their stability is tested under propagation using a split-step Fourier method. The simulations show that the beam profiles are very close to the exact soliton solutions within the generally nonlocal regime, which is an indication of the adequacy of the perturbative method to find soliton states. Both non OAM-carrying and OAM-carrying beams are explored. This work seeks to set a precedent for more detailed exploration of general nonlocality, which could provide advantages over simulation of other regimes, such as less computational costs.