## Abstract

A new wide-angle (WA) beam propagation method (BPM) is developed whereby the exact scalar Helmholtz propagator is replaced by any one of a sequence of higher-order $(m,n)$ Padé approximant operators. Unlike the previous well-known WA-BPM proposed by
Hadley [Opt. Lett. **17**, 1426 (1992)]
, the resulting formulations allow one a direct solution of the second-order scalar wave equation without having to make slowly varying envelope approximations so that the WA formulations are completely general. The accuracy and improvement of this approximate calculation of the propagator is demonstrated in comparison with the exact result and existing approximate approaches. The method is employed to simulate two-dimensional (2D) and three-dimensional (3D) optical waveguides and compared with the results obtained by the existing approach.

© 2009 Optical Society of America

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