Mathematical simulation of impedance diffraction gratings

In this paper the eigenwaves of a periodic impedance diffraction grating (DG), and the reflection and transmittance on a finite DG are under investigation. The approximate boundary conditions (ABC) were used for simulations. The refined expression for impedance dielectric strips is obtained. Singular part of the approximate integral equations (IE) is extracted and analytically transformed. As a result an IE of second type with a smooth kernel has been derived and solved with the collocation method and the Galerkin method.