Multi-Stages Iterative Process for Conservative Economic Finite-Difference Schemes Realization for the Problem of Nonlinear Laser Pulse Interaction with a Medium

We consider a problem of laser pulse interaction with a nonlinear medium which is accompanied by different nonlinear phenomena. Among them, we highlight the laser pulse self-action, optical bistability realization, formation of laser-induced complicated spatio-temporal structures. For computer modeling of these strongly nonlinear effects, using robust conservative numerical methods is required. Well-known, there are two widely applied approaches for the construction of numerical method: the conservative finite-difference schemes and additive finite-difference schemes (the split-step methods or decomposition methods). The first ones are non-economic, as a rule, while the second type of the methods is economic ones, however they possess well-known disadvantages. In our study, we joint advantages of both approaches by developing an original multi-stage iterative process for the conservative finite-difference scheme realization. Using computer simulation results, we demonstrate the feasibility of the proposed approach for investigating certain nonlinear optical phenomena.

Collision-induced amplitude dynamics of pulses in linear waveguides with the generic nonlinear loss

We study the effects of the generic weak nonlinear loss on fast two-pulse interactions in linear waveguides. The colliding pulses are described by a system of coupled Schrödinger equations with a purely nonlinear coupling in the presence of the weak (2m + 1)-order of nonlinear loss, for any m ≥ 1. We derive the analytic expression for the collision-induced amplitude shift in a fast two-pulse interaction. The analytic calculations are based on a generalization of the perturbation technique for calculating the effects of weak perturbations on fast collisions between solitons of the nonlinear Schrödinger equation. The theoretical predictions are confirmed by the numerical simulations with the full propagation model of coupled Schrödinger equations.