Research On The Topological Edge State Characteristics Of Photonic Crystals

Since the 1960 s,with the rapid development of semiconductor technology,people have mastered the means to control electronic transmission.By controlling the doping,the electronic bandgap of the semiconductor can be adjusted,and the electron flow characteristics can be easily manipulated.The discovery of semiconductors brought about a technological revolution and had a profound impact on the progress of human civilization.Based on the correspondence between electron and photon,people always seek to realize the corresponding control means in optical system.In recent years,topological photon state has become a hotspot of research.Since the electromagnetic parameters of photonic crystals are periodically distributed in space,similar to the energy band structure of electronic crystals,the energy band topological phase of photonic crystals can also be characterized by quantized topological invariants.When two photonic crystal structures with different topological properties are connected,a topologically protected boundary state will appear at the interface between them.Topological boundary states are robust to some local defects and disturbances,and can easily bypass these defects for transmission,and almost no reflection occurs,thus achieving the regulation of electromagnetic wave propagation characteristics.Based on the robust one-way transmission boundary state,the photon topological insulator provides a novel idea for the regulation and transport of electromagnetic waves.Analogically to the quantum hall effect in electron systems,a simple two-dimensional dielectric photonic crystal is designed to realize spin dependent topological boundary states.The photonic crystals are triangular arrays of silicon columns with an equilateral triangular cross-section arranged in the air.After rotating the silicon column,the energy band inversion of state and state is realized in the center of brillouin region.By using the symmetries of the two pairs of double degenerate states,this paper constructs the pseudo time inversion symmetry operator and the wild wild spin state,and obtains the effective Hamiltonian and spin number near the brillouin region based on the perturbation theory,thus proving that the energy band inversion of states and states is essentially a topological phase transition process.The numerical results reveal that the boundary state can be transmitted unidirectionally on the interface of photonic crystal with non-mediocrity topology and mediocrity topology,and the boundary state is immune to defects such as bending and cavitation.The photonic crystals constructed in this paper are only composed of dielectric materials and have simple structure.It is not necessary to change the filling rate of the silicon column when realizing topological phase transition,but only need to rotate an Angle.Therefore,this kind of structure is more convenient in the application of photon quantum spin hall effect boundary state.