We present a powerful multiple-scattering approach to wave diffraction by media whose permittivity contains overlapping periodic modulations, such as those found in thick holograms or in other applications involving superposed volume gratings. For this purpose we consider sequential wave scattering in a planar model having two periodic variations that are inclined at an arbitrary angle Δϕ with respect to each other. We thus show that all the diffracted fields can be described by flow diagrams that provide physical insight into the wave-scattering process. We then examine the particularly relevant case of small angular separations Δϕ and find that the individual diffracted orders can be evaluated by applying simple flow-graph considerations to the mathematical formulation. This procedure readily provides accurate numerical results, together with an estimate of the errors incurred if simplifying approximations are introduced. Furthermore, we show that the two-grating model can be readily extended to situations having any number of superposed periodicities.
© 1990 Optical Society of AmericaPDF Article