Explicit high-order symplectic integrators of coupled Schrodinger equations for pump-probe systems

TL;DR

This paper develops a high-order explicit symplectic integrator for coupled Schrödinger equations modeling two-beam nonlinear optical interactions, validated against particle-in-cell simulations.

Contribution

It introduces a novel high-order explicit symplectic algorithm for solving coupled Schrödinger equations in nonlinear optics, ensuring accurate and efficient simulations.

Findings

The Hamiltonian structure of the coupled Schrödinger equations was confirmed.

The developed BEAM code's results agree well with particle-in-cell simulations.

The method can be extended to other nonlinear optical interactions.

Abstract

Two-beam coupling within the field of nonlinear optics, which transfers energy from one light beam to the other under certain conditions, has received considerable attention in inertial confinement fusion (ICF) and plasma optics. To evaluate the coupling dynamics precisely, we modeled this process with full-wave coupled Schrodinger equations (CSEs) and a nonlinear refractive index. We found that the CSEs constituted a Hamiltonian system and proposed an arbitrary higher-order explicit symplectic algorithm to solve the CSEs numerically. The numerical results given by the developed BEAM code showed a good agreement with those from particle-in-cell simulations, which demonstrated the validity of the model and algorithm. The model and numerical algorithm presented in this work can be extended to more nonlinear optical interactions described by coupled-wave equations.