Coupled-mode analysis of volume holograms in discretized domain

The Born approximation with paraxial assumption has often been utilized for a volume hologram analysis, which is a simple and useful method but has limits in the consideration of incident-wave depletion and multiple diffractions of both longitudinal and angular directions. In recent years, the random-phase code multiplexing has received considerable attention because it gives a sharp selectivity compared to other methods, such as angular multiplexing, wavelength multiplexing, etc. In this case, the image of the reference beam is randomly patterned that its spatial frequency bandwidth is widely spread. As the grain size of the random pattern decreases, its spatial frequency of the reference beam becomes more spread. As a result, the paraxial approximation may be insufficient with this case. In addition, the effect of multiple diffractions between different angular spectra can also be magnified because the structures of multiplexed volume holograms are more complicated than others. Here we analyze the volume holographic gratings based on the coupled-mode theory in discrete Fourier domain without assuming the paraxial approximation, in which the continuous spatial spectra of lights are discretized by discrete Fourier transform and the couplings among them are simultaneously considered into account. We propose two methodologies for the coupled-mode analysis of volume hologram: one is by discretization approach and the other by a first-order approximation. These approaches can be extended to any kind of volume hologram analysis, such as for the Fourier or Fresnel plane hologram that includes lenses or not. The selectivity and crosstalk of random-phase-multiplexed volume holograms are discussed by the two methods.