Electromagnetic scattering by arbitrarily shaped inhomogeneous biisotropic and bianisotropic bodies

Abstract

Rapid development in electromagnetism provokes an increasing need for accurate and e¢ cient characterization of electromagnetic wave propagation and scattering in complex media. Among these complex media, the bi-isotropic or bi-anisotropic medium has been emerged as one of the most challenging topics owing to the spe- cial form of their constitutive relationships. Electromagnetic modeling of these ex- otic substances is of considerable sophistication, in particular for the case of three- dimensional arbitrary shape. This thesis is dedicated to devising a class of e¢ cient algorithms based on the integral equation method for solving such complex me- dia. For the bi-isotropic material, a generalized surface integral equation method is developed for solving the wave scattering problem. For the more complicated bi-anisotropic case, a new formulation based on the volume integral equation is con- structed to solve the uni ed model, in which inhomogeneous bi-isotropic material is treated as its subset. In short, the contribution of this work is three folded: (i) to generalize the surface integral equations for studying wave scattering by homo- geneous bi-isotropic bodies, (ii) to develop an e¢ cient volume integral equations for determining wave scattering by inhomogeneous bi-anisotropic bodies, (iii) to extend the coupled surface integral equation method for predicting scattering by compos- ite bi-isotropic and perfectly electric conducting (PEC) bodies with a much larger electrical size. The straightforward extension of the surface integral equation to homogeneous bi-isotropic bodies is di¢ cult since the Green’s functions involved are rather compli- cated to be handled numerically. In the second chapter, a eld decomposition scheme is introduced to separate one bi-isotropic medium into two respective isotropic ones, namely the “minus”and “plus”medium. As a result, the solution to the bi-isotropic media is simpli ed into that of the isotropic media. With the aid of the surface equiv- alence principle, a set of surface integral equations are eventually derived and solved using the method of moments (MoM). For modeling the arbitrarily shaped surfaces, the well-known Rao-Wilton-Gllison (RWG) function is selected as the basis and testing function de ned over each triangular element. The e¤ects of the bi-isotropic material parameters on the scattering characteristics of a bi-isotropic body, such as bistatic radar cross-section (RCS), are investigated. In the third chapter, the surface integral equation is further extended for the mixed bi-isotropic and conducting bodies of electrically large size by considering the important application of bi-isotropic materials as coatings in controlling scattering characteristics of the enclosed conducting bodies. By enforcing the boundary con- dition between the bi-isotropic and conducting cores, a series of coupled integral equations are obtainable and solvable numerically. To reduce computational cost, the fast multipole method has been incorporated into the integral formulations. The numerical results show that the method provides accurate prediction of scattering as compared with the exact solution. For an inhomogeneous bi-isotropic or bi-anisotropic body, the surface integral equation method cannot be employed for modeling because it requires the material of the body under analysis to be homogeneous in space. Although the conventional volume integral equation method, free of this limitation, is a possible suitable candi- date for the inhomogeneous cases, it still su¤ers from other embarrassment in nding the relevant dyadic Green’s functions. In chapter four, the issue is circumvented by devising a pair of “bi-anisotropic”equivalent sources for the volume integral equa- tions. Consequently, not only do the resulting integral equations in terms of these new equivalent sources have an identical and simple form with that of free space, but the Green’s function involved does. The complexity of the solution can be then reduced greatly. Furthermore, the use of edge-based solenoidal function, instead of the face-based basis function, also decreases the computational cost in the MoM solution of the obtained volume integral equations. A detailed numerical treatment, particularly for handling the singularities contained in the integral representations, is presented. Indeed, a new scheme, based on the mathematical identities, is devel- oped to precisely calculate not only the self-terms but also the o¤-terms having the nearly singularities. All the theoretical formulations are carefully validated with illustrative exam- ples. The numerical results for typical structures are well compared with the exact solutions or the data available in the literatures. Although the emphasis of the methods in this thesis is mainly placed on the scattering analysis, its extension to radiation analysis regarding the bi-isotropic and bi-anisotropic media will only need minor modi cations to the exciting sources. Finally, an important point should be stressed that the method developed in the fourth chapter is very versatile and can be directly applied for almost all the complex media such as moving media, plasmas, chiral metamaterials and omega media. Therefore, it is hoped that the methods developed in this thesis could become an useful analysis tool for exploring potential applications of the complex materials in microwave engineering.