Abstract

The beam propagation method has proven to be an extremely important tool in the simulation of guided-wave optics since its inception. Although initially limited to the study of paraxial beams, methods have been recently reported^1-4 that include approximate treatments of wide-angle propagation. However, all the methods presently available suffer from serious drawbacks. Those based upon eigenfunction expansions require recalculation of the eigenfunctions whenever there is a change in waveguide structure. Another method based upon an expansion of the field in terms of a set of so-called Lanczos vectors² has been found to exhibit convergence problems⁵. Several authors^1,4,6 have employed various Pade approximations of the Helmholtz operator. In one case⁶ this approach leads to difference equations that are only first order accurate in the propagation step size. Otherwise, the lower order Pade approaches¹ are numerically attractive, but their range of validity is still somewhat limited.

© 1993 Optical Society of America