Collision between fractional solitons in fibre lasers

Abstract

In this study, a framework of fractional nonlinear Schrödinger equations (FNLSEs) is modelled that utilizes the effective fractional group-velocity dispersion (FGVD), which was recently provided to the experiment, to model the co-propagation of optical waves carried by distinct wavelengths in fibre-laser cavities. The FGVD terms are denoted in the FNLSE system through Riesz derivatives, each accompanied by its corresponding Levy Index (LI). The FNLSEs, which comprise self-phase modulation (SPM) nonlinearity, are coupled by cross-phase modulation (XPM) terms and separated by a group-velocity mismatch (rapidity). We examine collisions and bound states of solitons in the XPM-coupled system utilizing systematic simulations, altering the LI and GV mismatch. Collisions between solitons can result in rebound, conversion of single-component solitons into two-component ones, merger into a breather, and elastic effects. Additionally, families consisting of stable two-component soliton-bound states are generated, exhibiting an intermediate rate of acceleration between the two components.

-