Improved coupled wave analysis of two-dimensional planar multiple gratings

An improved coupled wave approach is presented for the analysis of diffraction behavior of a two-dimensional spatially periodic or almost periodic dielectric layer illuminated by TE polarized plane waves. This method applies to any simultaneous composition of arbitrarily modulated planar transmission gratings with any permittivity in neighboring regions. Two major improvements have been made. In the first part, the eigenvalues and eigenvectors of coupled wave system of equations are first-order corrected to reduce the inherent errors generated by neglecting second-order derivatives. In the second part, a scattering matrix method is used to model the effect of boundaries. Using this method, the applicability range of coupled wave approach is extended to higher modulation depths and thicker grating layers. The main advantages of the proposed method compared with rigorous coupled wave analysis are ease of simulation, ease of extension to multiple grating structures, and increased speed. Results are presented for single and multiple grating structures, and comparisons with results obtained using rigorous coupled wave analysis are made to verify the accuracy of the proposed method.