Generalization of the boundary diffraction method for volume gratings

The boundary diffraction method (BDM) is an approximate method that permits the derivation of analytic solutions for the output beams, both forward and backward propagating, that arise from the fundamental nature of holographic gratings. The method is based on the assumption that the volume scatter inside the grating can be supplemented by boundary diffraction coefficients. The boundary diffraction method is used for analysis of thick transmission geometry gratings in a unified way that deals with both the slanted and the unslanted cases. During the analysis, evidence emerges for the superiority of the first-order two-wave beta-value method over the Kogelnik k-vector closure method. The BDM is then further generalized to the case of a volume transmission grating, index matched to its surroundings, and replayed normally on-Bragg, i.e., satisfying the Bragg condition for normal incidence. The analytic equations derived are compared with results calculated with the rigorous coupled-wave method.