A Novel Dispersive FDTD Modeling For Complex Media

Abstract

The finite-difference time-domain (FDTD) method is popular for the transient analysis of various electromagnetic (EM) problems due to its robustness and easy programming. To investigate transient EM interactions with dispersive media, a proper FDTD dispersive modeling is necessary because EM fields are analyzed in the time-domain. Therefore, the primary focus of this dissertation is the development of full-wave dispersive FDTD modeling for the transient analysis of EM and is the transient analysis of EM for complex media. I proposes a novel dispersive FDTD modeling based on complex rational function (CRF) suitable for the electromagnetic analysis of complex media. This dispersive modeling has higher degrees of freedom (DOF) than the conventional dispersive modeling such as Debye, Drude, and Lorentz modeling and thus it is highly suitable for the EM transient analysis of dielectrics with complicated permittivity. Cole-Cole, Davidson-Cole, and Harvriliak-Negami models can be used for a more complex dispersive media. However, its FDTD implementation is difficult because of the fractional order differentiators in the model. The dispersion relation of complex media is characterized by the 2-pole complex rational function (2-pole CRF) that leads to an accurate FDTD algorithm in the frequency of interest. The coefficients of the 2-pole CRF dispersion model are extracted by applying the complex-curve fitting technique, without initial guess. In order to fit a more accurate the 2-pole CRF model to measurement data, I uses a particle swarm optimization (PSO) technique. I also discusses an efficient memory storage strategy using a state-space approach. To fully apply the 2-pole CRF-FDTD for general complex media, the numerical accuracy and the numerical stability are investigated in detail. Numerical examples are used to validate the 2-pole CRF-FDTD and numerical stability issues are discussed in detail. I discusses a high-order CRF dispersion model to consider a more complicated complex media in a wideband frequency range. In this work, the 4-pole complex rational function (4-pole CRF) dispersion is considered. I also discusses the computational accuracy and the computational efficiency of an arbitrary N-pole CRF-FDTD. As mentioned above for the 2-pole CRF dispersion model, the similar procedure is applied to the 4-pole CRF dispersion model.