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A 2-D photonic crystal cavity device is investigated in this thesis. A simplified flexible local approximation method (FLAME) is used to analyze the electromagnetic characteristics of the cavity. / FLAME is a computational technique that is well suited to problems involving a large number of repeated structures. It has been used before to analyze photonic crystal cavities. In this thesis, an improved FLAME is developed, leading to a standard eigenproblem, which allows the use of sparse-matrix solution methods. Consequently, much larger problems can be solved. In addition, a graded perfectly matched layer (PML) is applied to absorb more effectively the out-going waves. / The new method is applied to cavities based on NxN arrays of rods, from N=3 to 9. Good accuracy is achieved compared with the finite-element method (FEM), with an error of less than 0.001% in the resonant frequency for a density of 42.6 nodes per wavelength (when N=5), which shows better consistency than the previous FLAME. Further, the new method converges more quickly than the FEM with linear elements, as the node density is increased, though it is less accurate than the FEM with quadratic elements.

Doctor of Philosophy (PhD) / In this thesis we consider several novel photonic crystal structures that derive their properties from optical resonances and mode coupling effects. We present first a theoretical analysis of a new class of photonic crystal device based on the combination of mode coupling and Fabry-Perot resonance effects. These structures exhibit characteristics that make them promising candidates as compact, integrated photonic components. The second aspect we consider is highly-efficient coupling into uniform photonic crystals. The results of this study identify inherent advantages of rod-type photonic crystals over the more common hole-type structures for in-band applications. The third contribution of this thesis is the demonstration of an efficient and powerful theoretical approach to studying photonic crystal devices. Throughout this work, we combine general numerical methods with simple physical models to develop physical insight into the behaviour of photonic crystal structures. We show that this can lead to novel device geometries with highly attractive properties.

Thesis (Ph.D.)--Technische Universiteit Delft, 2007. / Vita. Includes bibliographical references.

Techn. Univ., Diss.--Delft, 2007.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1975. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.