This thesis presents an analysis of the behavior of an equiangular spiral antenna using a mixture of numerical and measurement techniques. The antenna is studied as an isolated element and as a part of a spiral-based ground-penetrating radar (GPR) detection system. The numerical modeling was based on the parallelized finite-difference time-domain method and the model was validated by comparison with a prototype antenna and detection system. The intention is to isolate the effect of varying different geometrical parameters that define the spiral element or the spiral GPR system. With some notion of each parameter's effect, systems that use the spiral antenna can be designed more easily. The analysis of the spiral antenna in isolation provides a set of design graphs for the antenna. A set of design graphs are constructed that allow one to better understand the effect of the chosen dielectric substrate on the characteristic impedance of the antennas. A second set of design graphs give very specific data about the lower cut-off frequency possible for the antennas given a requirement on its minimum boresight gain, axial ratio, or voltage standing-wave ratio when matched with an appropriate transmission line. The analysis of the spiral antenna in the context of a detection system provides information on the effect of the ground on the GPR system and to what extent the circular polarization properties of the spiral antenna play a role in GPR. It is shown that a spiral antenna used in a monostatic radar configuration will reject a symmetric scatterer well into the near-field. The importance of a resistive loading to the spiral arms is demonstrated for this rejection to be optimal. In addition, it is shown that increasing the dielectric constant of the ground narrows the pattern and polarization properties, making the antenna more directive towards boresight when the spiral antennas radiate into a flat ground. In addition to this work, a method for reducing the truncation error when calculating the planewave spectrum of an antenna is described.

An efficient numerical analysis method for wavelength-scale and sub-wavelength-scale photonic structures is developed. It is applied to metal-clad nano-lasers and photonic crystal-based DBRs to calculate intrinsic losses (from open boundaries), and to photonic crystal-based waveguides to calculate intrinsic and extrinsic losses (due to fabrication errors). Our results show that a metal-clad surface plasmon-based laser in a cylindrical configuration requires more gain to lase than is available from a semiconductor gain region. However, the lowest order TE and HE guided modes exhibit less loss than the other modes, and hold the most promise for lasing. For photonic crystal-based structures, our matrix-free implementation of the planewave expansion method for calculating layer modes combined with mode-matching between layers using a few lower order modes is shown to be a computationally efficient and reliable method. This method is then used to introduce robust design concepts for designing photonic crystal-based structures in the presence of fabrication uncertainties. Accounting for fabrication uncertainties is shown to be particularly important in the regions of the device where the light exhibits very low group velocity (`slow light'). Finally, the modal discrimination properties of photonic crystal-based DBRs (Distributed Bragg Reflectors) are compared with the properties of conventional oxide-DBR combinations to analyze the contribution of out-of-plane diffraction losses to modal discrimination.