Study On Reflected Imbert-Fedorov Displacement Effect Of Topological Insulator With Finite Thickness

Topological insulators have unique physical properties and have been a hot topic of research in recent years.Topological insulators are insulated internally like ordinary insulators,but their surfaces are conductive and protected by temporal inversion symmetry.This is determined by the nontrivial topological band properties of topological insulators.When a magnetic field is applied to a topological insulator or a magnetic material is covered,the temporal inversion symmetry is broken and the surface state band gap is induced.At this time,topological magnetoelectric coupling effect will exist,that is,the electromagnetic properties of topological insulators will change,magnetization will be induced by electric field,and polarization will be induced by magnetic field.Topological magnetoelectric coupling effect has important research significance in many fields.In the case of surface parallel magnetization,both Kerr polarization deflection and Faraday deflection are enhanced obviously.Imbert-Fedorov(IF)shift is the shift of the reflected beam in the direction perpendicular to the plane of incidence.In recent years,it has been found that the IF shift is essentially the same as the photon spin Hall effect.Energy flow method is a common method to calculate IF shift.In this paper,the reflection IF shift effect of TE wave and TM wave incident is studied respectively for topological insulators with finite thickness model(single layer structure)with infinite surface bandgap approximation and finite surface bandgap.Specific work arrangements are as follows:Firstly,the IF shift and photon spin Hall effect are reviewed.These physical phenomena are introduced,and then topological insulators are reviewed to study the topological magnetoelectric coupling effect and modify the constitutive relationship of topological insulators.Then the energy flow method is modified so that it can be applied to the calculation of single layer topological insulators.Through the boundary conditions of topological insulator and ordinary medium,Maxwell’s equations and constitutive equations,the reflection coefficient matrix and transmission coefficient matrix are solved in the case of single interface.The reflection coefficient matrix and transmission coefficient matrix of single-layer structure can be obtained by combining the multiple reflection characteristics in single-layer structure.The energy flow of the upper and lower media outside the single-layer structure can be directly calculated by using the coefficient matrix,and then the energy flow inside the single-layer structure can be solved by using the undetermined coefficient method.The IF shift can be obtained by substituting the modified formula.According to the reflection and transmission coefficient matrix,the IF shift of single-layer topological insulator is analyzed by different factors,such as polarization state of incident wave,magnetization state of topological insulator,incident Angle,layer thickness and topological magnetoelectric polarization.The simulation results show that the polarization state of incident wave is different,the IF shift varies with the incident Angle,and the amplitude is also different.You get extreme values around Brewster’s Angle.The direction of IF shift can be affected by changing the magnetization direction of the topological insulator regardless of the incidence of TE wave or TM wave.With different incidence angles,topological magneto-electric polarizability changes will have different effects on IF shift.In addition,with the increase of layer thickness,more oscillations will occur in IF shift.Finally,the IF shift characteristics of the single layer reflection of a topological insulator with finite surface bandgap are studied.The effects of incident wave polarization state,incident Angle,surface band gap size,magnetization state and layer thickness on IF shift are analyzed.The simulation results show that the mutation of IF shift will occur with the change of incidence Angle.With the increase of finite band gap,the value of IF shift will decrease gradually.And the different magnetization states directly affect the positive and negative directions of IF shift.Changing the direction of magnetization on the upper and lower surfaces at the same time gives the opposite IF shift.