|Ph.D Thesis||Department of Electrical Engineering|
|Supervisor:||Prof. Leviatan Yehuda|
|Full Thesis text|
Photonic crystals are periodic structures that exhibit a special spectral property that is referred to as a photonic bandgap. A photonic bandgap is a frequency range for which no electromagnetic wave can propagate inside the structure. The existence of a bandgap can provide complete control of light propagation in those materials and offers many potential technological applications.
With the fast-growing interest in the development of devices that are based on photonic-crystals, the demand for computational methods that allow fast and accurate analysis of these periodic structures has also increased. In this work we introduce a solution method that is based on the source-model technique for the problem of electromagnetic wave scattering by a two-dimensional photonic crystal slab illuminated by a plane wave. We begin with a solution in the frequency domain, where the proposed solution method takes advantage of the periodicity of the slab by solving the problem within a unit cell. The method is then extended to treat a photonic-crystal slab with perturbations. Results for the perfectly periodic photonic crystal slab provide a valuable insight into the relationship between the dimensions of a finite periodic structure and its frequency bandgap characteristics. Results for the perturbed photonic crystal slab provide physical insight into waveguiding and defect coupling mechanisms typical of finite-thickness photonic crystal slabs.
The last part of this study considers the development of a time-domain computational method that is based on the source-model technique and allows the analysis of periodic structures such as the aforementioned photonic crystal slab. Since the use of the source-model technique in the time-domain is relatively new, a few unexplored aspects of this method, such as stability and causality, had to be studied before utilization. The results of this study together with means to improve stability and causality will be briefly discussed. Finally, applying the suggested time-domain source-model technique, we study the temporal behavior of a short pulse impinging on a photonic crystal slab.