Nonlinear self-accelerating beam in atomic ensembles: Mathematical models and numerical calculations

The eigenmodes based on paraxial accelerating beams in nonlinear atomic vapors with Kerr and cubic-quintic nonlinearities are demonstrated from mathematical models and numerical simulations. Upon adjusting the generation and propagation conditions, these nonlinear accelerating beams exhibit different evolution properties. We show numerically that the adopted beams can propagate robustly in the medium regardless of its absorption properties. The shape and peak intensity of the main lobes of these beams, based on the fact that they are the eigenmodes of the nonlinear Schrödinger equation in atomic media, are preserved for a significantly long propagation distance. If such beams are not the modes of the system, they are subject to the under-healing or over-healing effect, which damages the shape of the self-accelerating beams. In a numerical investigation, we also discuss the interactions between truncated accelerating beams, which readily generate non-accelerating solitons and soliton pairs.