Extension of Reflectance and Transmission Coefficient Matrix to C-method for study of periodic multilayer system

The C-method is one of the most efficient and versatile method designed for diffraction gratings. The boundary conditions of the grating can be greatly simplified when the coordinate systems coincide with the surfaces of the grating. Reflectance and Transmission Coefficient Matrix (RTCM) with clearly physical concept is a powerful propagation algorithm proposed for steady and fast calculation of multilayer gratings. In this paper, the C-method is extended to treat the multilayer diffraction grating with the identical or nonidentical surface shapes. Numerical examples including diffraction efficiencies of both dielectric and metallic grating are presented. In addition, the excellent convergence for various adjacent-heights and diffracted orders of our propagation algorithm for TE and TM polarizations is also included.