Finite Difference Time Domain (FDTD) method is a widely used full-wave numerical technique for solving electromagnetic problems in a wide range of applications. It has significant advantages over other numerical techniques, namely that it is easy to understand, simple to implement, and is well suited for solving general type of problems involving complex structures and arbitrarily inhomogeneous materials that require wideband solutions. In recent years, the development in parallel computation has led to a parallelized version of the FDTD solver, which has become one of the most desirable tools for treating extremely large and complex problems in a time-efficient manner.
In this dissertation we focus our attention primarily on two aspects, namely the implementation of a parallelized 3-D FDTD algorithm and its application to the modeling of metamaterials. First, we begin by proposing an efficient, parallel implementation of the Periodic Boundary Condition (PBC) in FDTD, which is based on the split-field method. The parallel scheme is based on a one-cell overlapping approach that is employed in the conventional FDTD method, which is extended in this work to include the PBC to model problems with periodic geometries. Next, a new, stable implementation of the Convolutional Perfectly Matched Layer (CPML) is implemented in the PBC/FDTD algorithm to truncate the computational domain with open boundaries.
Second, we propose a scheme to excite a desired incident field distribution in the computational domain to solve scattering problems that involve infinite structures. This scheme is based on modifying the conventional Total-Field/Scattered-Field (TF/SF) technique, which, in its original form, applies only to finite structures. The performance of the proposed scheme is studied by launching two different incident field distributions, namely a Gaussian beam and a plane wave.
Third, we carry out an extensive study of the electromagnetic (EM) response of a Double-Negative (DNG) slab, comprising of a combination of split-rings and wires, by using the parallel FDTD technique. Initially, we perform a preliminary analysis of the scattering characteristics of an infinite DNG slab, by using the proposed PBC/FDTD technique, to retrieve the effective material parameters via the modified inversion approach, which is described in this work. Some problem areas that may be encountered when using effective material parameters in real-world applications are identified, and the importance of carrying out rigorous simulations, which model the original structure, comprising of inclusions in a background medium accurately, is recognized. Finally, the EM response of a finite, artificial-DNG slab, illuminated either by a Gaussian beam or a small dipole is studied by using the parallel FDTD solver.