A Novel Asymptotic Solution to the Sommerfeld Radiation Problem: Analytic field expressions and the emergence of the Surface Waves

The well-known "Sommerfeld radiation problem" of a small -Hertzian- vertical dipole above flat lossy ground is reconsidered. The problem is examined in the spectral domain, through which it is proved to yield relatively simple integral expressions for the received Electromagnetic (EM) field. Then, using the Saddle Point method, novel analytical expressions for the scattered EM field are obtained, including sliding observation angles. As a result, a closed form solution for the subject matter is provided. Also, the necessary conditions for the emergence of the so-called Surface Wave are discussed as well. A complete mathematical formulation is presented, with detailed derivations where necessary.Comment: 14 pages, 3 figures, Submitted for publication to "Progress in Electromagnetics Research" (PIER) at 21/09/201

ONE-DIMENSIONAL INVERSE SCATTERING: EXACT METHODS AND APPLICATIONS

In this report new methods are developed to solve coupled integral equations of the Gel\u27fand-Levitan-Marchenko type. First, an iterative numerical method which uses leapfrogging in time and space is developed to solve the inverse scattering problem associated with the Zakharov-Shabat coupled mode equations. Second, both an analytical and a numerical method are developed for solving the corresponding two-potential inverse scattering problem and they are applied in order to synthesize lossy nonuniform transmission lines. The analytical method is based on the construction of appropriate differential operators transforming the integral equations to linear differential equations which can be easily solved, while the numerical method consists in a generalization of the iterative numerical method mentioned above. Furthermore, a numerical technique of successive kernel approximations is developed in order to solve coupled Gel\u27fand-Levitan-Marchenko integral equations which appear in a formulation of the inverse scattering problem associated with energy-dependent Schrodinger potentials and lossy inhomogeneous dielectrics. Subsequently, a numerical implementation of these problems is performed. The solutions resulting from the methods developed here are compared with those based on independent methods of they are reduced to known results in some special cases. Finally, possible applications of this work in other areas such as integrated optics and soliton theory are indicated