New closed-form expression for coupling matrix elements related to scattering from planar periodic single-strip grating

A new closed-form expression for 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 is presented. After solving a Fredholm integral equation of the first kind whose kernel has a logarithmic singularity, the coupling matrix elements are obtained in the form of certain ordinary integrals involving the Legendre polynomials, which can be evaluated analytically