Numerical studies of split-operator finite-difference alternating-direction implicit propagation techniques based on generalized Padé approximants

Abstract

We study numerically high-order propagation methods that incorporate representations of the exponential of two noncommuting operators as alternating products of Padé approximants of the individual operators. We demonstrate that these generalized Padé approximants are easily assembled through simple recursions and verify the central fact that their order need be far less than that of the overall method. We then analyze light propagation through an integrated-optic microlens using a sixth-order generalized Padé technique and compare its rate of convergence to that of standard propagation algorithms.