Improved convergence in the analysis of thin metallic gratings with thickness profiles

A combination of the Fourier series expansion method and the multilayered step method is applied to analysis of the scattering problem by a thin metallic grating with a thickness profile. The extremely large permittivity profiles of metallic gratings may affect accuracy of calculations adversely. The convergence of the Fourier expansion method is improved using the spatial harmonics of flux densities instead of electromagnetic fields normal to the surface of a metallic grating. In using the multilayered step method, the scheme used to partition the grating region and the distribution function of dielectric constant within each layer are examined.