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

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

2008-10-07

arxiv.org/abs/0810.1097v1

Mathematics

Numerical Analysis

Scientific paper

10.1016/j.jcp.2008.10.009

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.

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