Study On The Propagation And Scattering Of Laguerre Gaussian Beams In Topological Insulators Layered Media And Spherical Particles

Topological insulator is a new quantum state with special energy band structure,they have a full energy gap in the bulk and the surface presents the incompetent gap of the energy band structure,which are protected by time reversal symmetry.It can resist disorder effect and local disturbance.Its low thermal conductivity enables it to transmit energy and information without loss.Its good optical transmittance,nonlinear optical characteristics and electrical conductivity make it have a good application prospect in the design and production of electronic equipment and optical equipment.In this thesis,the transmission and scattering characteristics of the Laguerre Gaussian beam incident on topological insulator are studied,the main contents include:1.Based on the plane angular spectrum expansion method and transmission matrix theory,we research the reflection and transmission characteristics of the linear polarization Laguerre Gaussian beam incident on the interface of topology insulator and the periodic layered film containing topological insulator with the constitutive relationship of topological insulator maxwell equations and boundary conditions,and give the reflection matrix,transmission matrix and transmission matrix expression connecting the reflection and transmission fields.Numerical analysis and discussion the intensity distribution of Laguerre Gaussian beam of the reflection and transmission fields in different topological magneto-electric polarizability of topological insulator and different periods of the topological insulator film in detail.2.Based on the generalized Mie theory,the incident and scattering electromagnetic fields are expanded by the spherical vector wave function,and the expansion coefficients of the scattering field and the inner field of the sphere are obtained by using the method of separating variables and the boundary conditions.Under Rayleigh approximation,numerical analysis the far-field scattering characteristics of Laguerre Gaussian beam by a topological insulator spherical particle.The influence of the waist radius of Laguerre Gaussian beam,the size of the spherical particle and the topological magneto-electric polarizability of the topological insulator on the intensity of the internal scattering intensity,the scattering efficiency factor and the backward scattering efficiency factor are discussed.The results show that the topological magneto-electric polarizability of the topological insulator and the number of periods of the thin film have great influence on the intensity distribution,and the light field of Laguerre Gaussian beam can be manipulated by changing the topological magneto-electric polarizability or the number of periods,the proposed theoretical method can be applied to the study of the transmission characteristics of Laguerre Gaussian beam from other new layered materials.Under Rayleigh scattering,the scattering efficiency factor of spherical particles with the same size increase with the increase of topological magneto-electric polarizability,and the backward scattering efficiency factor have a minimum value under different permeability,and the minimum value change with the change of topological magneto-electric polarizability;Changing the waist radius of Laguerre Gaussian beam and the size of the spherical particle can adjust the scattering efficiency factor or the scattering intensity.These conclusions not only have certain significance for studying the application of Laguerre Gaussian beam in the wireless laser communication field,but also provide new ideas for exploring the optical characteristics of topological insulator materials.