Abstract
We have previously constructed a series of high-order Fresnel propagation methods based on the split-step fast Fourier transform procedure by expressing an exponential of two non-commuting operators as an alternating product of exponentials of the individual operators. Here we demonstrate that these decompositions are equally valid for the split-operator finite difference and finite element methods if the exponential operators are replaced by (1,1) Pade approximants. Such "generalized Pade approximants" can be easily generated through simple recursion formulas and implemented in a straightforward fashion. We illustrate our technique with a sixth-order calculation of light propagation through an integrated optic microlens.
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