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Wide-angle beam propagation using Padé approximant operators

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Abstract

A new beam-propagation method is presented whereby the exact scalar Helmholtz propagation operator is replaced by any one of a sequence of higher-order (n, n) Padé approximant operators. The resulting differential equation may then be discretized to obtain (in two dimensions) a matrix equation of bandwidth 2n + 1 that is solvable by using Standard implicit solution techniques. The final algorithm allows (for n = 2) accurate propagation at angles of greater than 55 deg from the propagation axis as well as propagation through materials with widely differing indices of refraction.

© 1992 Optical Society of America

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