A coupled-wave analysis is given for Bragg-angle diffraction of light within a thick holographic emulsion containing two incoherently superimposed phase gratings with a common Bragg angle. Algebraic formulas are given for the amplitude of the coupled diffracted waves. Applications to holographic multi-beam splitters and beam combiners are given and experimental verification is discussed.
Steven K. Case, "Coupled-wave theory for multiply exposed thick holographic gratings," J. Opt. Soc. Am. 65, 724-729 (1975)