Improved rigorous coupled-wave analysis for polar magnetic gratings

The rigorous coupled-wave analysis method with Airy-like Internal-Reflection Series for the polar gyrotropic grating is improved with the Fourier factorization rule. In the process of derivation, Maxwell's equation is reformulated in order to avoid type 3 product and, either Laurent's rule or the inverse rule is used for the product of two Fourier series with discontinuities. The number of Fourier coefficients or the size of the coefficient matrix required for the proper convergence is reduced by more than 50% compared to our previous works for the calculation of the diffracted Kerr rotation from the polar magnetic gratings.