Electromagnetic wave scattering from an arbitrarily shaped bi-isotropic body of revolution

Abstract

An efficient method for analyzing the scattering of electromagnetic waves from a bi-isotropic body is developed in this dissertation. Although the techniques developed in [31] is applicable for analyzing wave scattering from an arbitrarily shaped bi-isotropic body, it can hardly be used in an optimization process nor computer-aided product design because the computational time required for one iteration is very long and the memory required is exorbitantly huge. It is noted that significant time could be saved if an exact solution is not required. In fact, finding an exact solution is only possible for a few simple configurations. In many practical cases, excellent results can be obtained by approximating the original scatterers by some simple configurations. In the present study, attention is focused on the study of a body of revolution. With this approximation, the computational time will be substantially shortened and the memory required drastically reduced. Most important of all, many useful information will be obtained and significant insight be extracted from this study. In fact, a body of revolution finds many practical applications such as missiles, pipeline and chimney. As chirality is one of the key characteristics in a bi-isotropic material, the techniques developed for studying a chiral body of revolution [30] is chosen as a starting point for developing our method. The novelty conceived in this study is the adoption of the field-splitting techniques developed by [24] for the study of bi-isotropic BORs. The techniques are then extended to cover bi-isotropic materials. Without loss of generality, this bi-isotropic body is illuminated by a plane wave. Based on the classical EM theory, a set of surface integral equations for analyzing the scattered field exterior to the bi-isotropic body is derived in terms of the equivalent surface currents on the body. On the other hand, the fields penetrated into the bi-isotropic medium are more complicated. Following the field-splitting concept, the electric and magnetic fields E and H in bi-isotropic medium are split into two parts: the “plus” part + E , + H and the “minus” part − E , − H . Similarly, the sources in a bi-isotropic medium are also split into “ + J , + M ” and “ − J , − M .” Each part sees the bi-isotropic medium as an equivalent medium with modified medium parameters ε + , μ + and ε − , μ − , and they are independent of each other. Thus, both “plus” and “minus” fields can be expressed in terms of “plus” and “minus” currents, respectively. With these manipulations, the issue of concern is determination of the unknown currents, namely, + J , + M , − J , and − M . These unknowns can be obtained by enforcing the boundary condition on the surface of a bi-isotropic body; that is, the tangential electric and magnetic fields exterior to the bi-isotropic body as determined by solving the field equations in the free space must be equal to those just beneath the surface as evaluated in the bi-isotropic medium. Similar to the traditional analysis, an analytical solution in a closed form can only be derived for a simple structure. For an arbitrarily shaped BOR, the usual practice is to determine the scattering fields by a numerical method, such as the method of moment. Taking advantage of rotational symmetry, the equivalent currents are expanded in terms of Fourier modes, which allow us to solve the integral equations one mode at a time. As a result, the integral equations are transformed into a matrix equation. By solving this matrix equation, the equivalent surface currents can be evaluated. Once the equivalent surface electric and magnetic currents are determined, most scattering characteristics can be readily calculated, such as radar cross section (RCS) and the fields in the Fraunhofer region. In this dissertation, the bi-static RCS of a bi-isotropic sphere and a bi-isotropic cylinder are studied in Chapter 4. The results are compared with the exact solutions or data available in literature. Future development of the present methodology and possible extensions will be discussed in Chapter 5.