Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings

Abstract

The diffraction by one or an arbitrary number of cascaded anisotropic planar gratings with slanted fringes is analyzed by using rigorous three-dimensional vector coupled-wave theory. Arbitrary angle of incidence and polarization are treated. The existence of uniaxial external regions and the treatment of both phase and amplitude anisotropic slanted gratings are included in the analysis. The anisotropy and the three-dimensionality of the problem cause coupling between orthogonally polarized waves. The Bragg conditions for various combinations of ordinary (O) and extraordinary (E) polarized waves are quantified. Sample calculations are presented for single anisotropic gratings (a lithium niobate hologram in air and an interdigitated-electrode-induced electro-optic grating in an optical waveguide), for two cascaded anisotropic gratings (a pair of interdigitated-electrode-induced gratings satisfying the OOO forward Bragg condition, the EEE forward Bragg condition, and the OOO backward Bragg condition), and for multiple cascaded gratings (a lithium niobate hologram with depth modulation). The same analysis applies in the limiting cases of isotropic materials, a grating vector lying in the plane of incidence, etc. Applications for this analysis include optical storage, switching, modulation, deflection, and data processing.