New analytical expressions for the coupling matrix elements related to scattering from a planar single-strip grating

This paper presents an alternative approach for finding the coupling matrix elements in the multimode equivalent network that describes plane-wave scattering from a planar periodic single-strip grating at a dielectric interface. The relevant integral equation valid for TM-obstacle and TE-aperture formulations is a singular integral equation with the cotangent kernel. A simple method is used to give a new closed-form solution of this equation. After another integration which is performed analytically simple formulas for the coupling matrix elements are obtained.