Multimode network description of a planar periodic metal-strip grating at a dielectric interface. III. Rigorous solution

For pt.II see (ibid., vol.37, no.3, p.542-52, 1989). In pt.I the solution to the scattering problem posed by a plane-wave incident at an angle on a plane, periodic, metal-strip grating at a dielectric interface was formulated in terms of novel multimode equivalent network representations. The analytical phrasing followed in pt.I led to two Fredholm integral equations of the first kind with singular kernels. Here, the authors derive a rigorous analytical solution for one of the two integral equations derived in pt.I (see ibid., vol.37, no.3, p.534-41, 1989). Closed-form, rigorous, analytical expressions for the elements involved in the equivalent network representations derived are obtained. Numerical results obtained by using these rigorous equivalent network representations are presented for TE-mode and TM-mode incidence for the case in which the same dielectric is present on both sides of the grating as well as for the case in which the two dielectric media are different.<>