Differential theory for diffraction gratings: a new formulation for TM polarization with rapid convergence

A new formulation of the differential method in TM polarization, based on c orrect representation of truncated Fourier series of products of discontinu ous functions, is proposed. Although the derived equations are more complic ated than in the classical formulation, the convergence rate with respect t o the truncation parameter (with the number of diffraction orders taken int o account) is much faster for arbitrary grating profiles, approaching the c onvergence rate in TE polarization. Numerical examples are presented for di electric and metallic sinusoidal gratings with a 100% modulation ratio. (C) 2000 Optical Society of America.