Optical Topological Transition And Hyperbolic Frequency Characteristics Of Layered Structure Of Ferrite And Magneto-optical Materials

Hyperbolic metamaterial is a kind of artificial medium with sub-wavelength structure,which has abnormal optical properties and is widely used in far field sub-wavelength imaging,nano lithography and emission engineering.The hyperbolic metamaterial is an anisotropic medium,which is characterized by the hyperbolic dispersion relation,rather than the ellipsoid of traditional materials.Just as the topological shape of Fermi surface defines the properties of free electrons in metals and semiconductors,the geometry of the medium frequency surface in the phase space of electromagnetic wave propagation also determines the optical properties of these materials.In addition,compared with the Lifshitz transition in condensed matter physics,the change of the topological structure of the constant frequency surface has a great influence on the emission,propagation and scattering of electromagnetic waves.In recent years,the research focus of metamaterials has shifted to active and tunable metamaterials,as well as simplifying the structure while retaining many abnormal characteristics and functions.In this thesis,the special material with external magnetic field is used to replace the traditional isotropic material layer to construct hyperbolic metamaterials.By adjusting the intensity of external magnetic field,the optical properties of hyperbolic material,such as the topological structure transition of frequency surface and hyperbolic frequency band,are studied.The specific research is as follows:Firstly,different from the previous isotropic materials,this study uses anisotropic layers to construct hyperbolic metamaterials.Under the external magnetic field,ferrite and magneto-optical materials show magnetic anisotropy and electrical anisotropy respectively,and the optical properties and material parameters of ferrite and magneto-optical materials are studied.Then,the principle,advantages and disadvantages of two common methods to solve the dispersion equation are introduced.In the theory of equivalent medium,the composite structure is regarded as a uniform material,and its equivalent parameters are calculated.Then,the dispersion equation is obtained by substituting it into Maxwell's equation.Considering the layered characteristics of the composite structure,the transmission matrix method is used to connect the wave amplitudes of two interfaces separated by one cycle,and then the dispersion equation is derived by combining the Bloch theorem.In this paper,based on the transmission matrix and Bloch theorem,the dispersion equation of the two-layer periodic structure constructed by anisotropic layer is derived,which is prepared for the simulation analysis of the dispersion characteristics later.The hyperbolic characteristics of single ferrite material are studied,and the topologicalstructure of constant frequency surface is analyzed.It is found that the external magnetic field can adjust the frequency bandwidth,which is of great significance to hyperbolic materials.Then,considering the double-layer periodic structure of isotropic ferrite and dielectric and the double-layer periodic structure of anisotropic ferrite,the dispersion equation is obtained by two methods,and the characteristics of optical topology transition and hyperbolic frequency band are analyzed.Because of the surface plasmon polaritons,the composite structure can produce a new topology.The topological structure is a mixture of ellipsoid and hyperboloid.The dispersion equations of magneto-optical material and magneto-optical material dielectric composite structure are derived,and the topological transition diagram of constant frequency surface is drawn according to the dispersion equation,and the law of the frequency band width changing with the applied magnetic field is summarized.In the electric hyperbolic metamaterials constructed by magneto-optical material,new topological structure can also be generated and the hyperbolic bandwidth can be adjusted.Compared with the magnetic hyperbolic metamaterials constructed by ferrite,it has its own uniqueness.In conclusion,the electric and magnetic hyperbolic metamaterials constructed by special material layers are summarized and their material characteristics are analyzed to lay a foundation for the subsequent application of anisotropic materials in the hyperbolic field.