Study Of Some Topological Phenomena In Optical Systems

In recent years,geometric topology related area of physics have attracted much attention,especially for optics,topological photonics has become a research hotspot at current stage.As the most common optical system,photonic crystals(Ph Cs)play the crucial role in the aspect of simulating fundamental physics in electronic system.However,due to the basic distinctions between photon and electron,the study in topological photonics cannot follow the way in the electronic system.So far in the terms of realizing the topological phenomena in optical system,there at least have two problems: one is to realize spin degree,and the other is to realize spin-orbital coupling and to explore novel topological states.In this thesis,we mainly focus on these problems.The main results are as follows:1.Realizing photonic quantum spin hall effect in all-dielectic core-shell Ph Cs.According to the tight-binding method in Ph Cs,various accidental degeneracies between different bands in the two-dimensional(2D)all-dielectric core-shell Ph Cs are realized,via tuning the structural parameters.Among them,two kinds of double degenerate states with opposite parity at ? point,which protected by C6 symmetry stem from triangular lattice,formed four-fold degenerate double Dirac point under certain structural parameters.We further gapped the Dirac point by parameter tuning and define the photonic topological insulator and normal photonic insulator according to the parity order of the bands at ? point.Also,topological phase diagrams based on structural/material parameters are presented.Furthermore,according to the numerical simulations,the helical edge states in the energy spectrum are gapped due to the symmetry break in the boundary,which is in sharp contrast with that in electronic system,whereas the crossing point is protected by Kramers theorem.2.Three dimensional photonic Dirac point and Weyl point by ultilizing C6 point group symmetryThe 2D core-shell Ph Cs are generalized to the three-dimensional(3D)Ph Cs by designing a hexagonal lattice Ph C with hollow cylinders connected by six mircopillars.According to the symmetry analysis and k·p Hamiltonian derivation,we demonstrated that a pair of Z2 topological Dirac point are appeared in the high symmetry line ?A and corresponding to the transition point of the 2D optical system.This kind of Z2 topology Dirac points protected by C6 symmetry are exist in a wide parameter space.When the inversion symmetry(IS)break induced,the Z2 topology Dirac points are gapped into two pairs of Weyl dipoles with certain optical angular momentum.We remarked that the angular momentum wave-vector locking within IS break system is at the heart of various novel properties in topological Ph C which can be detected by optical transmission/reflection measurement.3.Various topological nodes/lines induced by nonsymmorphic symmetry in three dimensional Ph Cs.The non-symmorphic symmetry represented by screw symmetry in Ph Cs,can produce double degeneracy for all Bloch states on certain Brillounin zone planes,and thus offer an effective method to realized topological Ph Cs.Both type-II Dirac point and Weyl point and the deterministic line node in non-symmorphic Ph C are found.By symmetry analysis and k · p Hamiltonian derivation,the conical dispersion in kx-kz plane and exotic optical dispersion in kx-ky plane,as well as the optical properties in the system with type-I and typeII Dirac point are also unveiled.We further remark that such non-symmorphic Ph C possessed with Z2 topology Dirac point can also be utilized as open cavity,due to the topological surface states localized on the surface,which pave the way to topological light-matter interaction in the future.