Green's Function Construction II

Abstract

A waveguide and wedge were used to illustrate the usage of the generalized separation of variables (GSV) for Green's function construction. In this chapter, these techniques are used to obtain Green's functions for several problems: a grounded dielectric slab, a dielectric half space and a bare‐and dielectric‐coated cylinder. A metal strip grating on a grounded dielectric slab is used to illustrate the use of the slab Green's function, to demonstrate the application of Floquet's theorem and to obtain the complex propagation constant for this structure. The Green's function for any open boundary problem is in terms of a complex plane line integral having its endpoints at infinity and branch points in the integrand. These are the so‐called Sommerfeld integrals. The analytical treatment involves a Riemann surface. The chapter presents the saddle point method, which is a useful approximate asymptotic technique for evaluating Sommerfeld‐type integrals.