Time domain integral equations for scattering and radiation by three-dimensional homogeneous bi-isotropic objects with arbitrary shape

Abstract

Bi-isotropic and bi-anisotropic media have received considerable attention from many researchers, because these materials have been recognized as two of the miracle substances for fueling multi-disciplinary developments in the new century. For example, exotic material has been used to load an antenna for enhancing channel capacity, suppressing interferences, improving sensitivity, and reducing its size. Electromagnetic modeling of these exotic substances is much sophisticated, especially for the case of three-dimensional arbitrary shape. Hence, this dissertation concentrates on devising a time-domain integral equation solver for radiation and scattering problems associated with complex media. Simply put, the contributions of this work are summarized into two parts: (i) to generalize the surface integral equations in the time domain for investigating the wave scattering by homogeneous bi-isotropic objects, (ii) to extend the coupled surface integral equations in the time domain for predicting the radiation by bi-isotropic body loaded dipole antenna. In the first chapter, a brief introduction of the bi-isotropic media is given. At first, the main characteristics of bi-isotropic media are presented together with the constitutive relations. Then the research procedure about chirality property evolved from optical frequency into microwave frequency is explained. Next the constitutive equations about the two subclasses of bi-isotropic material, chiral media and Tellegen media are described. Also, the 3-dimensional tensor parameters of the bi-anisotropic media are introduced. Finally, the objective of the study is proposed. Chapter two is the review of the marching-on in time (MOT) and marching-on in degree (MOD) methods for solving the time domain integral equations (TDIE). The TDIE solver outperforms finite difference time domain (FDTD) method in some aspects, and the reason is outlined in the introduction section. In the second section, the formulation of the integral equations incorporated with the MOT method for scattering by homogeneous dielectric body is given at first, and then the numerical implementation is described using the method of moment (MoM). Compared to MOT, the MOD method is more stable and can eliminate the late-time instabilities. The formulation and the numerical procedure of the MOD method are reported in the last section. Subsequently, the extension of the surface integral equation from homogeneous dielectric objects to bi-isotropic bodies is presented in chapter 3. It is rather difficult to make a straightforward extension because the Green’s functions are very complicated to handle numerically. In the second section, the field decomposition scheme is used to replace the bi-isotropic medium with two respective isotropic ones, namely the plus" and "minus" mediums. The procedure to obtain the parameters of the two equivalent isotropic media is described. Using the surface equivalence principle, a set of the coupled integral equations using the renowned Poggio-Miller-Chang- -Harrington-Wu-Tsai (PMCHWT) formulations are eventually derived. Following the integral equations series is the numerical implementation for the scattering of general bi-isotropic bodies. The surface integral equations are solved using the MoM involving separate spatial and temporal testing procedures. The famous Rao-Wilton-Gllison (RWG) functions are selected as the temporal basis and testing function, and the weighted Laguerre functions are chosen as the temporal basis and testing functions. To validate the accuracy of the proposed TDIE method, the scattering of bi-isotropic objects is analyzed, and the transient currents, far scattered fields, and bistatic radar cross-sections are presented. At the same time, the parametric study on the convergence test is conducted, and the influence of the parameters on the accuracy of results has been summarized. In the fifth chapter, the surface integral equation in the time domain is further extended for the dipole antenna in the vicinity of a bi-isotropic body. A very narrow perfectly electric conducting (PEC) strip is placed near the bi-isotropic object as the loaded antenna. By enforcing the boundary condition separately on the strip dipole and the surface of the bi-isotropic materials, a series of coupled integral equations are obtained and solved numerically using MoM. The numerical results show that the method provides accurate prediction of the radiation compared with the previous solutions. Finally, the conclusion of this thesis is given in chapter 6, and the further extensions of the proposed MOD based TDIE method are discussed.