Closed-form expression for the coupling matrix elements related to TM- scattering from a symmetric double strip grating

This paper treats the problem of TM plane-wave scattering from a planar periodic symmetric double-strip grating placed at a dielectric interface. The formulation is based on a multimode equivalent network representation and the relevant integral equation defined on two separate symmetrically spaced intervals is rigorously solved by reducing to two simpler equations with known solutions. From this a new simple closed form expression is obtained for the coupling matrix elements. Some computations based on this new expression are carried out and the results are compared to those obtained by the Reimann-Hilbert method and also to some previously obtained single-strip results in the limiting case.