Localization Properties And Applications Of Photonic Crystal Coupled Cavities

Photonic crystal (PC), in which optical parameters (such as the linear and/or nonlinear electric permittivity and/or magnetic permeability) change periodically in space, is one of the most fruitful optical fields in the last two decades. Due to the merits of photonic band gap and strong localization, PCs exhibit promising future in optical integrated circuits (OIC) and all optical communication systems. In this dissertation, using both theoretical analysis and numerical simulation methods, we investigate the localization properties and potential applications of photonic crystal coupled cavity (CC) structures in one- and two-dimensions. The CC structures include linear and Kerr nonlinear cavities, and the functionalities realized include broad band and multimode optical bistable switchings, broad band optical limiting and optical waveguiding.Our studies show that there are two different types of states for the CC structures: The first one is continuous eigenmode state. In this state, the eigenfrequencies form a continuous band, and the field localization intensities in all the cavities are approximately the same. This state can be described properly by the well known tight binding (TB) theory. The other is discrete eigenmode state. In this state, the eigenfrequencies are completely separated (discrete), and the localizations in various cavities are completely different, and TB theory is invalid in this case. Therefore, we developed a coupled mode theory (CMT) to describe the discrete mode states, and the eigenfrequencies, quality factors and the electric eigenfields of the states are derived. Although the two states can be converted to each other by tuning the confinements to the two ends, the two states show very different properties in both the linear and nonlinear devices.When the coupled cavity structure operates in the continuous mode state, broad band optical bistable switching and limiting in the whole band of the CC structures are realized by introducing Kerr medium into one (or more) of the cavities. Due to the Kerr effects excited by the incident light, the coupling strength between the cavities are tuned, then high and low transmissions are realized dynamically. Therefore, all optical limiting and bistable switching are achieved successfully.