Angular directivity of diffracted wave in Bragg-mismatched readout of volume holographic gratings

We investigated theoretically and experimentally angular directivity of a diffracted beam in volume holographic gratings. We measured the angular direction of the diffracted beam as a function of Bragg-angle deviation of the read beam and showed that the experimental result agrees well with the Ewald sphere vector model (ESVM). We also showed that the Kogelnik’s coupled-wave theory (CWT) is correct in predicting the diffraction efficiency, but is incomplete in its description of the direction of the diffracted wave. We show that the ESVM and the CWT theories taken together produce a self-consistent mathematical model of wave propagation inside the gratings that is confirmed with experimental results. The proper model for the direction of the output beam as presented here is important in developing theoretical models of image propagation through thick gratings for holographic imaging and correlation applications.