Fast three-dimensional split-step algorithm for vectorial wave propagation in integrated optics

An efficient split-step modification of the finite-difference vector beam propagation methods (BPM) based on transverse magnetic fields is presented. Two substeps are introduced by separately treating and alternating the transverse directions, resulting in a tridiagonal system matrix. The novel scheme reduces calculation effort considerably by maintaining accuracy. To demonstrate this, a circular test structure is chosen of which the exact modal field solution is known. In addition, performance of the algorithm is illustrated by launching a linear polarized Gaussian field into a buried rectangular waveguide where the generation of a stationary field distribution is observed during the propagation process.>