Bi-directional beam propagation method for problems with multiple dielectric interfaces

Conventional beam propagation methods (BPM) only deal with the forward propagating optical field, and, thus, they are useful only if the structure has a sufficiently slowly-varying index along the propagation direction such that the accumulated reflections are negligible. However, many practical guided-wave optical devices involve junctions of different waveguides, laser facets, grating structures, anti-reflection or high-reflection coatings, etc. In all these structures there exists a refractive index discontinuity or variation along the direction of propagation of the optical field, hence consideration of coupling the forward and backward waves must be included for accurate modeling. We present an iterative approach to dealing with problems involving multiple dielectric interfaces, which has significantly reduced memory requirements