Topological Properties And Transport In Two Dimensional Photonic Crystal

Photonic crystals(PCs),periodic arrangement of dielectric materials,have been intensively studied in the past decades.PCs provide a useful platform to control the flow of electromagnetic waves.In analogy to topological insulators in condensed matter physics,introducing pseudospin degrees of freedom in the electromagnetic systems has attracted extensive research attention recently.In our works,based on various two-dimensional(2D)PC structures,we successfully manipulate their band diagrams and optical analogies to topological insulators are achieved.Their topological properities are characterized and their intriguing tranaport properities are demonstrated in both simulations and microwave experiments.1.The investigation of Zak phase and deterministic interface in 2D PCsZak phases were found to determine the bulk band if 1D PCs,indicating that deterministic interface states exist at the interface between two PCs with different bulk topology.We extend the theory of Zak phases in 1D PCs to 2D systems.In chapter 2,we propose three different methods to create deterministic interface states in 2D PCs.By manipulating geometric parameters of PCs,we can tune their bulk band properities to creat a common band gap with inverted band properities,indicating a topological phase transition.Interface states are guaranteed on these PC boundaries.These results are foundations of studies of unidirectional electromagnetic channels in chapter 3-5.Microwave experiments of these deterministic interface states were carried out where we found good consistence with our theory and simulations.An optical waveguide with multiple deterministic interface states is also proposed to boost future optical communication bandwidth.2.The investigation of photonic quantum spin Hall effectIn chapter 3,we realize a photonic analogy to quantum spin Hall effect using 2D dielectric PCs and unidirectional electromagnetic propagations with respect to time reversal symmetry are achieved experimentally.A pseudospin degree of freedom is introduced in photonic system,which arise from the deformation of honeycomb-lattice PC.It serves as the photonic analogy to electronic Kramers pairs.We characterize the unidirectional microwave propagation of a specific pseudospin along the interface between topological and trivial PCs.We utilize the properities of robust transport of topological PCs to construct 2D topological PC cavities.Discrete whispering gallery modes can propagate unidirectional along the topological cavity circumferemce.Interestingly,different to traditional cavities,these whispering gallery modes are insensitive to shapes of cavities.We also propose an optical directional coupler based on the topological PC cavity.As only pure dielectrics are used to design topological PCs,our scheme can be extended to visible light to inspire future applications in optics.3.The investigation of photonic valley spin Hall effectIn chapter 4,we discuss the photonic valley spin Hall(QVH)effect.Firstly,in analogy to AB/BA stacking bilayer graphene,we construct 2D valley PCs by breaking the inversion symmetry of honeycomb lattice.Inequivalent valleys in the momentum space can be manipulated by engineering diameters of cylinders in unit cells.Bulk valley polarizations are visualized in simulations.We also realize unidirectional propagations of valley interface states on a domain wall by two PCs with different valley Chern numbers.As the bulk valley polarizations and valley interface states share the same optical votex indices,we successfully couple valley interface states with bulk valley polarizations.Valley filters and valley couplers can be thus designed.We extend our studies of valley PC to triangular lattice.By simply rotating Y-shape cylinders to construct valley PC,valley degeneracy is lifted and we experimentally characterize its bulk valley polarizations.Unidirectional propagation is also visualized by selectively excitations using a homemade chiral source.4.The investigation of topological corner states in photonic crystalsTopological interface states exist in both phtonic system with quantum spin Hall effect and valley spin Hall effect,which correspond to lattice deformation and sublattice staggering respectively.In chapter 5,we study the difference between these two systems and discover a new novel mechanism to realize topological corner modes in PCs.(?)and and AB-BA domain walls are constructed to realize gapless topological kink states in perivious two chapters.We find that the coexistence of these two mechanisms can induce gapped topological kink states.Significantly,the intersection of these two types of domain walls gives rise to a topological corner state localized at the crossing point.Through the manipulation of domain walls,we also study the coupling between topological corner states by manipulating domain walls.Conclusions of our works in this thesis are presented finally along with a brief discussion about future works.In most of our works presented,we foucs on using low loss dielectrics to realize interface states of PCs in microwave experiments.By sacling down the size of PC structures,our scheme can be extended to infrared even visible light wavelength.Based on topological physics,we design optical components and hope they may inspire many future applications of optical decvies.