Three-dimensional (vector) rigorous coupled-wave analysis of anisotropic grating diffraction

Abstract

The rigorous coupled-wave analysis of diffraction by grating(s) formed in general anisotropic media is reviewed and extended. The method is first applied to a single slanted phase and/or amplitude grating with general three-dimensional incidence of a plane wave. The regions external to the grating can be isotropic, uniaxial, or biaxial anisotropic. The cases of gratings in isotropic media and of the grating vector lying in the plane of incidence (scalar analysis) are obtained as limiting cases of this general analysis. Coupling between the two orthogonal polarizations vanishes in these limiting cases. The Bragg conditions for various combinations of ordinary (for isotropic and uniaxial) and extraordinary (for uniaxial) polarized waves are quantified. The analysis is then extended to multiple cascaded gratings and to volume-superposed gratings. Sample calculations are presented for single anisotropic gratings (a lithium niobate photorefractive hologram in air and an interdigitated-electrode-induced grating in an electro-optic crystal), for multiple cascaded gratings (a lithium niobate hologram with grating strength varying with thickness), and for superposed gratings (multiplexed hologram storage). Applications for this analysis include optical storage, switching, modulation, deflection, optical interconnects, beam splitting, beam combining, and data processing.