| In this research, a new technique for modeling periodic structures in the finite-difference time-domain (FDTD) method is developed, and the technique is applied to the study of structural color in insects.;First, the FDTD method is presented. The method is developed by starting with Maxwell's equations in time-domain, differential-equation form. The derivatives are replaced by central differences, and a marching-in-time algorithm is found. Various recent supplements to the FDTD method, such as a nearly-perfect plane-wave injector and convolutional perfectly matched layer absorbing boundary conditions, are used. For modeling electrically large structures, significant computer resources are required; a method for implementing the FDTD method on a parallel, distributed-memory computer cluster is given.;To model a periodic structure, a single periodic cell is terminated by periodic boundary conditions (PBCs). A new technique for incorporating PBCs into the FDTD method is presented. The simplest version of the technique is limited to two-dimensional, singly-periodic geometries, or to three-dimensional, doubly-periodic geometries when the direction of propagation for the incident plane wave is in a principle plane of the cell. The computational cost for the method is found to depend on the direction of propagation. The accuracy of the method is demonstrated by comparing to independent results calculated with a frequency-domain, mode-matching method.;The periodic FDTD method is then extended to the more general case of doubly-periodic problems in which the propagation vector of the incident plane wave is not in a principle plane. This extension requires additional steps and imposes new limitations that are not present for the simpler case. The computational cost and limitations of the method are presented. The accuracy is demonstrated by modeling the scattering from dielectric slabs and comparing to the exact solution, and by modeling a pair of complementary structures and demonstrating that the results are consistent with Babinet's principle.;Certain species of butterflies exhibit structural color, which is caused by quasi-periodic structures on the scales covering the wings. Numerical experiments are performed to develop a technique for modeling quasi-periodic structures using the periodic FDTD method. The observed structural color of butterflies is then calculated from the electromagnetic data using colorimetric theory.;Three types of butterflies are considered. The first type are from the Morpho genus. These are typically a brilliant, almost metallic, blue color. The second type is the Troides magellanus, which exhibits an interplay of structural and pigmentary color, but the structural color is only visible near grazing incidence. These two types exhibit iridescence on the dorsal side of the wings. The final type is the Ancyluris meliboeus, which exhibits iridescence on the ventral side. For all cases, the effects of changing the dimensions of various structural elements are considered. This type of analysis is only possible using a detailed computational model.;Finally, some earlier work on the design of TEM horn antennas is presented. This subject was considered as a possible thesis topic. The TEM horn is a simple and popular antenna, but only limited design information is available in the literature. A parametric study was performed, and the results are given. A complete derivation of the characteristic impedance of the basic antenna is also presented. |
