Simulation of beam propagation in off-axis optical systems

We present different numerical tools useful for simulating laser beam propagation in an off-axis optical system and for computing power losses in order to give specifications to the system. We first recall the basis of Fourier-transform beam-propagation, and then we calculate the phase factor corresponding to an off-axis reflection on an optical surface (spherical or parabolic mirrors). We then develop an extension of the Fourier-transform beam propagation method to compute the propagation through a plane parallel plate, frequently used to compensate for astigmatism. We give numerical examples, involving a two mirrors off-axis beam expander.