Formation Mechanism And Application Research Of Topological Edge States And Corner States Based On Photonic Crystals

Electron topological states,as a new state of matter,have been quickly introduced into the field of optics due to their novel topological properties.Photonic crystal,an artificial microstructure,has the characteristic that the energy band structure can be designed artificially.Based on principles of electron topological states,various symmetries are introduced into photonic crystals.Photonic topological states have been realized quickly,and topological states of photonic crystals are deeply studied,which provide many new mechanisms for light field manipulation,such as one-way transmission with backscatter suppression,direction-selective transmission of pseudospin wave vector locking,and high-dimensional light field regulation.Based on topological energy band theory and topological polarization theory,this paper mainly studies the formation mechanism,regulation methods and application prospects of topological one-dimensional boundary states and zero-dimensional corner states by constructing various topological photonic crystals and high-order topological photonic crystals.The specific research contents are as follows:(1)The formation mechanism of photonic crystals one-dimensional topological edge states is studied.Using the lattice symmetry of photonic crystals to construct photonic pseudo-spin states and pseudo-time-reversal symmetry,a photonic crystal system that satisfies the C6 lattice symmetry is constructed based on elliptical dielectric columns.By stretching and compressing the honeycomb lattice,topological phase transitions and band inversions are achieved,and backscatter-suppressed unidirectional light transport is realized at the boundaries of different topological photonic crystal regions.In addition,a C6 photonic crystal primitive cell is constructed based on a split-ring dielectric column,and topological phase transition and band inversion are realized by changing the inner and outer radii of the split-ring dielectric column,and topological edge states with immunity to structural defects are realized in the common photonic bandgap.On this basis,a photonic crystal,with the C3 lattice symmetry,is proposed,which realizes multiple topological phase transitions by flexibly adjusting the distance between two groups of dielectric cylinders and the center of primitive cell,and the topological boundary state are observed in the photonic bandgap.(2)The formation mechanism and local feature of photonic crystals topological corner state are researched.A square lattice photonic crystal cell composed of four silicon elliptical dielectric cylinders is proposed,and topological phase transition and band inversion are realized by stretching and compressing the dielectric cylinders.For "#" shape combined topological photonic crystal system,three groups of zero-dimensional angular states are observed simultaneously in the discrete spectrum of the eigenmode.Further,the optical local characteristics of the three groups of corner states are analyzed,the formation mechanism of the three groups of topologicla corner states are researched.In addition,a square lattice photonic crystal cell composed of a dielectric column in the center of the background is proposed.The topological phase transition is realized by exchanging the materials of the background and the dielectric cylinder,and two box-type combined topological photonic crystal systems are constructed based on topological polarization theory,and the topological corner states are successfully realized,the formation mechanism and control method of the corner state are studied and analyzed.(3)The applied research on photonic crystals topological boundary states is carried out.Based on elliptical dielectric cylinder photonic crystal,a coupling system of topological waveguide and resonator are constructed.By analyzing the different transmission characteristics of traveling mode and standing mode in the coupled system,topological optical band pass filter and topological optical add/drop multiplexer are proposed.In the split-ring dielectric cylinder photonic crystal,the material of the split-ring dielectric cylinders on the topological interface is changed from Si to Al2O3,and a line defect structure that does not mix pseudo-upper and pseudo-lower spin states is introduced to achieve unidirectional transmission.The topological line defect waveguide is robust to structural defects such as sharp bends,cavities and disorder.This waveguide has stronger optical localization and can effectively reduce the broadening of light perpendicular to the transmission direction,which can improve the application prospect of one-dimensional topological boundary as an information carrier.On this basis,a topological beam splitter is designed,which can realize the optical beam splitting function in a large frequency range.In addition,two box-type combination structures and a "#" shape combination structure are constructed by using the topological trivial and nontrivial photonic crystals of square lattice.The method to adjust the frequency range and local electric field of the topological corner states is analyzed.Based on the coupling effect between topological edge state and topological corner state in the "#" shape combination structure,a topological narrowband filter is designed.