We introduce a local signal decomposition method for the analysis of
three-dimensional (3D) diffraction fields involving curved surfaces. We
decompose a given field on a two-dimensional curved surface into a sum of
properly shifted and modulated Gaussian-shaped elementary signals. Then we write
the 3D diffraction field as a sum of Gaussian beams, each of which corresponds
to a modulated Gaussian window function on the curved surface. The Gaussian
beams are propagated according to a derived approximate expression that is based
on the Rayleigh–Sommerfeld
diffraction model. We assume that the given curved surface is smooth enough that
the Gaussian window functions on it
can be treated as written on planar patches. For the surfaces that satisfy this
assumption, the simulation results show that the proposed method produces quite
accurate 3D field solutions.
© 2012 Optical Society of America
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