Collision-induced amplitude dynamics of fast 2D solitons in saturable nonlinear media with weak nonlinear loss

Abstract

We study the amplitude dynamics of two-dimensional (2D) solitons in a fast collision described by the coupled nonlinear Schrödinger equations with a saturable nonlinearity and weak nonlinear loss. We extend the perturbative technique for calculating the collision-induced dynamics of two one-dimensional (1D) solitons to derive the theoretical expression for the collision-induced amplitude dynamics in a fast collision of two 2D solitons. Our perturbative approach is based on two major steps. The first step is the standard adiabatic perturbation for the calculations on the energy balance of perturbed solitons and the second step, which is the crucial one, is for the analysis of the collision-induced change in the envelope of the perturbed 2D soliton. Furthermore, we also present the dependence of the collision-induced amplitude shift on the angle of the two 2D colliding-solitons. In addition, we show that the current perturbative technique can be simply applied to study the collision-induced amplitude shift in a fast collision of two perturbed 1D solitons. Our analytic calculations are confirmed by numerical simulations with the corresponding coupled nonlinear Schrödinger equations in the presence of the cubic loss and in the presence of the quintic loss.

arXiv comment25 pages, 6 figures

References in corpus (13)

• Solitons in nonlinear lattices
• Multidimensional solitons in a low-dimensional periodic potential
• Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides
• Soliton dynamics in the multiphoton plasma regime
• Criteria for the experimental observation of multi-dimensional optical solitons in saturable media
• Stabilization of two-dimensional solitons in cubic-saturable nonlinear lattices
• Colliding solitons for the nonlinear Schrodinger equation
• Radiation dynamics in fast soliton collisions in the presence of cubic loss
• Transmission stability and Raman-induced amplitude dynamics in multichannel soliton-based optical waveguide systems
• Soliton-like behavior in fast two-pulse collisions in weakly perturbed linear physical systems
• Frequency shifting for solitons based on transformations on the Fourier domain and applications
• Many-body interaction in fast soliton collisions
• Dynamics and stabilization of bright soliton stripes in the hyperbolic-dispersion nonlinear Schrödinger equation

Cited by in corpus (3)

• Analysis of a Crank-Nicolson finite difference scheme for (2+1)D perturbed nonlinear Schrödinger equations with saturable nonlinearity
• Fast two-beam collisions in a linear optical medium with weak cubic loss in spatial dimension higher than 1
• Strong effects of fast collisions between pulsed optical beams in a linear medium with weak cubic loss