Simulation of Laser Beam Propagation With a Paraxial Model in a Tilted Frame
Provides a mathematical and numerical framework for simulating laser beam propagation in tilted geometries, relevant to laser-plasma interaction studies.
The authors derive an analytical solution for the paraxial Schrödinger equation with tilted propagation direction under constant coefficients, and propose a numerical method based on it. Numerical results are presented, with an extension to time-dependent laser-plasma interaction.
We study the Schrödinger 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.