Efficient simulation of EM response of dielectric objects in multilayered media

Fast and accurate simulation of dielectric objects in a multilayered medium has many applications such as microwave/millimeter-wave integrated circuits and geophysical exploration. In this thesis the method of moments (MoM) combined with the mixed potential integral equation (MPIE) and Michalski's Formulation-C Green's functions is applied to the simulation of dielectric objects in multilayered media. The spatial-domain Green's functions are calculated through the discrete complex image method (DCIM). Both the volume integral formulation and the surface integral formulation are implemented and the numerical results are compared with each other. Two types of structures are considered. The first one is dielectric resonator (DR) without a feeding structure, for which the complex resonant frequency and modal field distribution are calculated. The second one is DR with a feeding structure, for which S-parameters are calculated.; There are mainly two innovations in this thesis. The first innovation is the solution of resonance problems in arbitrarily shaped dielectric objects by using surface integral equations and Method of Moments. Although surface integral equations have been extensively used for solving the scattering problem of dielectric objects, they have not been applied to the resonance problem successfully before due to some difficulties. In this thesis the Method of Moments with RWG basis functions is applied to the electric field integral equation (EFIE) for solving the resonance problem of dielectric objects. The resonant frequency is obtained by searching for the minimum of the reciprocal of the condition number of the impedance matrix in the complex frequency plane, and the modal field distribution is obtained through singular value decomposition (SVD). The determinant of the impedance matrix is not used since it is difficult to find its roots. For the exterior EFIE, the original basis functions are used as testing functions; for the interior EFIE, the basis functions rotated by 90 degrees are used as testing functions. To obtain an accurate modal field solution, the impedance matrix needs to be reduced by half before SVD is applied to it.; The second innovation of this thesis is the use of combined entire-domain and sub-domain basis functions in the Method of Moments. Traditionally only sub-domain or entire-domain basis functions are used. The advantage of sub-domain basis functions is their versatility, but use of them results in a large number of unknowns. Use of entire-domain basis functions results in fewer unknowns, but the entire-domain basis functions of higher order require longer time in numerical integration, which is not efficient. In many practical cases, approximate analytical solutions can be found for the dielectric or perfectly electrically conductive (PEC) objects, where the approximate analytical solution can be used as entire-domain basis functions. Combined with sub-domain basis functions, both efficiency and versatility can be achieved.