  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.
