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Simulation of laser beam propagation with a paraxial model in a tilted frame. (English) Zbl 1156.78321
Summary: 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 dependent model which is relevant for laser-plasma interaction.

MSC:
78A60 Lasers, masers, optical bistability, nonlinear optics
82D10 Statistical mechanical studies of plasmas
78M25 Numerical methods in optics (MSC2010)
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