Rigorous coupled-wave analysis and applications of grating diffraction

A review of the rigorous coupled-wave analysis (RCWA) as applied to the diffraction of electromagnetic waves by gratings is presented. The analysis is valid for any polarization, angle of incidence, and for conical diffraction. Cascaded and/or multiplexed gratings as well as material anisotropy and loss can be incorporated under the same formalism. Volume and surface-relief gratings can be analyzed. Convergence analysis is presented for rectangular-groove surface-relief dielectric and metallic gratings. The role of multilevel surface-relief and holographic gratings in the substrate-mode photonic interconnect configuration is investigated. Results obtained using the RCWA are presented for 1-, 2-, 4-, 8-, and 16-level surface-relief gratings and are compared with the predictions of the simple scalar model. Two practical configurations are analyzed: (a) a silicon substrate at a freespace wavelength of 1.3 microns and (b) a glass substrate at a freespace wavelength of 0.84 microns. Equivalent holographic gratings are also designed and compared. Small period rectangular groove gratings can also be modeled using approximately equivalent uniaxial homogeneous layers (effective media). The ordinary and extraordinary refractive indices of these layers depend on the grating filling factor, the refractive indices of the substrate and superstrate, and the ratio of the freespace wavelength to grating period. It is shown how these models result from the eigenvalue equation of the boundary-value rectangular-groove grating problem. Comparisons of the homogeneous effective medium approximations with the rigorous coupled-wave analysis are presented. Antireflection designs (single-layer or multilayer) using the effective medium models are presented and compared.