Interactions of two co-propagating laser beams in underdense plasmas using a generalized Peaceman–Rachford ADI form

A generalized Peaceman–Rachford ADI form based on the regularized finite difference scheme is employed to study the nonlinear interactions of two co-propagating laser beams in underdense plasmas. A numerical scheme using the form is constructed for the solution of two coupled 2D time-dependent nonlinear Schrödinger equations for quasineutral plasmas in paraxial approximation.In the constructed scheme, the coupled equations are reduced to systems of nonlinear tridiagonal equations that are solved using the matrix factorization and a direct explicit iteration method. In the stability analysis, a time-varying control parameter is introduced for a conditionally stable solution at varying conditions.The scheme has a good agreement with a previous simulations at similar conditions, and in comparison with other algorithms, the scheme presents a better conservation characteristic for the photons power. Finally, the simulations results confirmed that the scheme is suitable to simulate the interactions of two co-propagating laser beams in underdense plasma and it can successively simulate the associated phenomena at different parameters and conditions.