Boundary Value Problem for an Oblique Paraxial Model of Light Propagation

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. This model has been proposed in [12]. Our primary interest here is in the boundary conditions successively in a half-plane, then in a quadrant of $\bbfR^2$. The half-plane problem has been used in [11] to build a numerical method, which has been introduced in the HERA plateform of CEA.

Keywords

Laser plasma interaction, paraxial approximation of Helmholtz equation, W.K.B. approximation, transparent and absorbing boundary condition, Schrödinger equation

2010 Mathematics Subject Classification

35E05, 35J05, 35L05, 78A40

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Published 1 January 2009