Design of holographic optical beam splitters based on thin grating sequential diffraction technique

Bragg diffractions by superimposed transmission phase gratings are important schemes for the realization of optical beam splitters for optical fanout interconnection, neural network implementation, data storage, and parallel optical processing and computing. The theory of optical beam diffractions by superimposed transmission phase gratings have been developed by several authors [1-13]. However, the existing techniques are limited to 2-D diffraction geometry, suffering from numerical problems when the superimposed grating number increases, and/or restricted to small-angle diffractions. For 3-D diffractions by superimposed transmission phase gratings, required for holographic beam splitting applications, there is no simple theoretical model to treat such problem. Complete modal analysis [6,7] already yields complicated results for single-grating diffraction, because the grating vector can have an arbitrary orientation with respect to the plane of incidence. As a consequence the s- and p-polarized field components become coupled inside the grating region and can no longer be treated separately by conventional coupled-wave theory [14]. The coupled 3-D diffraction is much more complicated than the single-grating case. It is, so far, hard for a design engineer to determine suitable grating index combinations prior to device implementation. As a result, superimposed gratings are often recorded through trial and error in hoping on getting a desired energy distributions for splitted beams.