Deterministic Interface States In Photonic Crystals With Graphene-like Structures

Due to its peculiar band diagram,graphene has many novel and interesting properties and is widely used in many fields.Similar in structure,graphene allotropes or graphene-like structures can provide further configurability to band diagrams and properties.As for the same symmetry and similar photonic band diagrams,photonic crystals with graphene-like structures have aroused many research interests.As an optical analog to an electronic crystal,photonic crystal is constructed by periodically arranging dielectric materials and can be used to manipulate electromagnetic waves.In this thesis,we focus on the realization of deterministic interface states,interface states that are determined by bulk photonic band properties and various topology-related states are achieved by symmetry designs.The main work of this article is as follows:(1)We extend the Zak phase theory in one-dimensional photonic crystals to two-dimensional photonic crystals and three different principles for achieving deterministic interface states are introduced.We design graphene-like complex photonic crystals,with multiple cylinders in one site of honeycomb lattice.By arranging these cylinders,different symmetries(including C3v?C3?C2vand C2)of the graphene-like photonic crystal can be maintained and unidirectional interface channels were constructed by arranging two graphene-like photonic crystals with different symmetries.(2)We have theoretically and experimentally studied the topological properties of a photonic crystal with complex graphene-like structure accommodating both the quantum spin Hall effect and the valley spin Hall effect.By introducing both lattice deformation and sub-lattice breaking at the same time,gapped topological interface states appear in this new type of graphene-like photonic crystal.Topological corner states and their coupling are observed experimentally when the two effects coexist.We also reanalyze the system using the concept of high-order topological insulators.By allowing a coupling interface between two high-order topological insulators,topological corner states irrespective of the unit cell symmetry can be found.Finally,we summarize our research work,and discuss the future directions.Using all-dielectric photonic crystals,we can extend the current design to optical frequencies by scaling down.Protected by topology,our design may effectively reduce the impact of precision in manufacturing,improve the performance of the device,and play key roles in optical communication,photon integration and optical computing et.al.