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

Marie Doumic (1) , Frédéric Duboc (2) , François Golse (3) , Rémi Sentis (2)

1 BANG - Nonlinear Analysis for Biology and Geophysical flows
2 DAM/DIF - DAM Île-de-France
3 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Mots clés: transparent; absorbing boundary conditions; Laser plasma interaction; advection Schrödinger equation; Fast Fourier Transform; finite volume scheme

Domaines: Analyse numérique [math.NA]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Marie Doumic, Frédéric Duboc, François Golse, Rémi Sentis. Simulation of Laser Beam Propagation With a Paraxial Model in a Tilted Frame. Journal of Computational Physics, 2009, 228 (3), pp.861--880. ⟨10.1016/j.jcp.2008.10.009⟩. ⟨hal-00327179⟩