Abstract

The beam propagation method, also known as the split-step or marching algorithm, is well known for its application to the simulation of wave propagation in inhomogeneous or cubically nonlinear (Kerr) media. In essence it treats the propagation medium as a sequence of thin phase filters (self-induced in the nonlinear case) separated by thin regions of homogeneous space.¹ Reflections due to gradients of the refractive index in the nominal propagation direction are ignored. One recent variant of the technique,² used for optical waveguide investigations, takes into account multiple discrete reflections by a global iteration scheme. Our proposed method deals with continuous reflections in a marching algorithm fashion, analogous to the way the actual field gradually builds up in the medium. We will present 1-D and 2-D verifiable simulations of (a) backward Bragg reflection interaction with a continuously [n(z)] variable refractive index and (b) reflection off an oblique interface treated as an inhomogeneous [n(x, z)] medium.

© 1989 Optical Society of America