ABSTRACT
This chapter utilizes the denomination of "rigorous coupled-wave theory" (RCW) despite its inconveniences. The RCW method uses the same Fourier basis as the differential method, it suffered for a long time from the slow convergence of the Fourier series of the field when analyzing metallic gratings lighted with TM polarized waves. The chapter illustrates the RCW theory on the case of a lamellar grating illuminated in the cross-section plane, so that the diffraction problem decouples into the two TE and TM fundamental cases of polarization. The RCW method has been widely used and is very efficient when applied in TE polarization case. It is also very efficient on thick phase gratings with continuous variations of refractive index, provided it is combined with the S-matrix propagation algorithm, for both TE and TM polarization. The chapter presents a comparative study of three different methods, based on the differential theory: classical differential method, RCW method and modal method.
