Study On The Dispersion And Effect Of The Edge State Of Two - Dimensional Photonic Crystal

Graphene, a single layer of graphite, has attracted much attention owing to its perfect2D structure and unusual electronic properties. With the presence of a boundary graphene has edge states resulting in interesting transport properties of charge and spin. On the other hand, edge states may also be present in photonic systems such as photonic crystals (PCs) and plasmonic lattices with interesting optical properties. This thesis focuses on the investigations of edge states on the boundaries of honeycomb photonic crystals (HC-PCs), which is the photonic analog of graphene. Edge states is a kind of surface states which are localized near the edges and are evanescent both inside and outside the PCs. We show dispersion of edge states in HC-PCs can be tuned conveniently by modifying the parameters of the edge cylinders. Owning to sub-wavelength confinement and tunability of dispersion, slow light on the edge of HC-PCs is investigated.This thesis tries to discuss the following three questions. Firstly, what are photonic edge states? Secondly, why is HC-PC? What is unique on edge states of HC-PCs? Finally, what are potential applications of edge states? The thesis is arranged as follows.A brief introduction to PCs and two kinds of important surface wave of photonic nanostructures is given in chapter one, including surface states in PCs and surface plasmon-polaritons bounded at metal-dielectric interfaces. Simulation methods used in this thesis are introduced briefly in the chapter two.In chapter three, we start from introduction to graphene and answer the second foregoing question. Then we mainly discuss the properties of edge states on the boundary of HC-PC. We design edge sate waveguides and analyze their performance. Waveguide bends with high bending efficiency are obtained.In chapters four and five, we investigate the potential applications of edge states on slow light. Chirped edge state waveguides are designed to realize rainbow trapping effect of light, a phenomena means that light with different frequencies slow down and stop at different locations finally. Sinusoidal dispersion of edge states suppresses the high-order dispersion effectively. Slow light with zero dispersion on the edge of HC-PCs is realized.