Formation And Coupling Of Surface Modes In Two-Dimensional Photonic Graphene

Graphene is becoming a promising material for future electronic devices as for its peculiar electron transport behaviors.Moreover,the surface / edge modes in the topological insulators attract a lot of research attentions in recent years.As predicted in 2007,the quantum Hall Effect in grapheme aroused the interest to study the surface mode of grapheme or grapheme-like structures.However,due to technical difficulties,the fabrication of grapheme sheets with different type of edge is challenging.At the meantime,the study of topological behavior of photonic crystals brings some new development to this area.Due to the similar band diagram to grapheme,especially the existence of Dirac cone dispersions,various interesting electron transport behaviors predicted or observed in grapheme have optical analogies in photonic crystals,including Zitterbewegung effect,back-scattering immune surface modes et al.Due to fabrication easiness,photonic crystal could be a perfect platform for classical simulations of quantum systems.The dissertation is organized as follows:In the chapter one,we research the background and progress of photonic crystals,surface modes of photonic crystals,calculation of band structure in photonic crystal,graphene and photonic crystals with a dirac con.In the chapter two,we study the surface modes formation and coupling at zigzag edge in photonic graphene(honeycomb lattice photonic crystals).We analysis the existence of surface mode at zigzag edge by tight banding.And we also study the coupling of surface mode in photonic grapheme.In the chapter three,we study the surface mode at bearded edge in photonic graphene.We analysis the existence of surface mode at bearded edge by tight banding.Based on the simulation results,we designed a microwave experiment to observe the bearded edge mode.As the technical difficulties in the fabrication of grapheme sheet with bearded edge,we study photonic grapheme with bearded edge instead.