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Rigorous near- to far-field transformation for vectorial diffraction calculations and its numerical implementation

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Abstract

A rigorous method for transforming an electromagnetic near-field distribution to the far field is presented. We start by deriving a set of self-consistent integral equations that can be used to represent the electromagnetic field rigorously everywhere in homogeneous space apart from the closed interior of a volume encompassing all charges and sinks. The representation is derived by imposing a condition analogous to Sommerfeld’s radiation condition. We then examine the accuracy of our numerical implementation of the formula, also on a parallel computer cluster, by comparing the results with a case when the analytical solution is also available. Finally, an application example is shown for a nonanalytical case.

© 2006 Optical Society of America

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