Simulation of Laser Beam Propagation With a Paraxial Model in a Tilted Frame

TL;DR

This paper analyzes a tilted paraxial Schrödinger model for laser beam propagation, deriving analytical solutions for constant coefficients, proposing a numerical method based on these solutions, and extending the model to time-dependent scenarios relevant for laser plasma interactions.

Contribution

It introduces an analytical solution for a tilted paraxial Schrödinger equation with constant coefficients and develops a numerical method leveraging this solution, extending to time-dependent models.

Findings

Analytical formula for the solution in simple cases.

Numerical method based on analytical expression.

Extension to time-dependent laser plasma interaction models.

Abstract

We study the Schr\"odinger equation which comes from the paraxial approximation of the Helmholtz equation in the case where the direction of propagation is tilted with respect to the boundary of the domain. In a first part, a mathematical analysis is made which leads to an analytical formula of the solution in the simple case where the refraction index and the absorption coefficients are constant. Afterwards, we propose a numerical method for solving the initial problem which uses the previous analytical expression. Numerical results are presented. We also sketch an extension to a time dependant model which is relevant for laser plasma interaction.