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Optical data storage that exploit thick holograms have been investigated extensively in the area of neural networks and optical signal processing[1]. To overcome the low capacity of the thin holograms, a volume holographic interconnection scheme using volume holograms has been proposed[2]. Volume holographic interconnections exploit the third spatial dimension of the volume hologram to superpose a large number of gratings that are used to implement data storage. The angular selectivity arising from volume holograms has been recognized early on by Van Heerden to increase the storage capacity dramatically[3]. Light diffraction from volume sinusoidal gratings has been studied by many authors[4-8]. However, the number of gratings they cionsidered was not more than two. On the other hand, the number of gratings in the volume holographic interconnects is hundreds or billions. In this case, we need a simple and systematic method of handling many gratings to assess the crosstalks. Crosstalk effects due to adjacent gratings among a large number of superposed gratings was shown to limit the maximal data storage capacity of a volume hologram[2]. This result was based on a simple coupled-mode theory[9]. Recently, more detailed analysis using iteration method of integral equation of Maxwell's wave equation was carried out to study the crosstalk effects[1O]. However, this analysis has the following limitations. First, the analysis was limited to the case of transverse optical polarazations. Furthermore, the wave vectors of the incident light and volume index gratings were assumed to be in the same plane. These two assumptions eliminated the possibility of polarization mixing and graddivE term in the Maxwell's wave equation was automatically disappeared. In real situation, incident light waves propagate in many different directions. Volume index gratings also have different wave vectors and they are not in the same plane. Therefore, polarization mixing of the light waves should be considered to obtain correct results on crosstalk effects. Second, the analysis did not account for backward diffraction from volume index gratings. In this paper, we use a rigorous method of perturbative integral expansion to study the crosstalk effects due to superposed gratings. The method by Tu et. al. was based on calculating perturbative integrals in wave vector space. However, in our method, the integral is calculated directly in the space domain. Our method can be applied to arbitrary interaction geometries of optical waves and volume index gratings. It also accounts for backward as well as forward diffractions simultaneously.
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