Propagation of beams through optical waveguiding structures: comparison of the beam-propagation method and the collocation method

Abstract

We compare the beam-propagation method (BPM) and the collocation method for the total field propagation through optical waveguiding structures. In order to facilitate comparison, we first develop an intermediate method, using the collocation principle with the orthonormal basis of sinusoidal functions (finite plane waves, as in the BPM). Our results show that the collocation method is more accurate than the BPM as a propagation method, while the Hermite-Gauss basis functions are much better suited than the sinusoidal functions for waveguiding problems. We also show that another advantage of the collocation method over the BPM is that variable transformations can be used to improve the accuracy of propagation.