Very-wide-angle beam propagation methods for integrated optical circuits

In this paper, outlines of the derivation of two recently developed finite difference beam propagation methods based on the higher-order Fade approxim ations are given to simulate the optical field propagation of tilted and tu rning waveguides. In order to investigate the accuracy and limitation for a propagation angle of these approaches, numerical results are presented for two benchmark tests. The present algorithms will offer, to our knowledge, the new beam propagation methods in optics.