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Discrete Transparent Boundary Conditions for Fresnel’s Equation

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Abstract

This paper describes how to derive general discrete transparent boundary conditions for the paraxial wave equation (z-discretized with a one step method). Our approach is a general one comparable to methods using the discretization of known Green’s functions for homogeneous semi-infinite spaces to describe the influence of the boundary domain. However, our approach does not need a Green’s function and therefore it is applicable in situations where such a function is not known. The characteristic function we need is recursively generated in each propagation step in a fast and numerically stable manner. For the purpose of demonstration we describe the technique using the implicit Euler discretization. Fresnel’s equation in two dimensions is given by

© 1994 Optical Society of America

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