Theoretical Research On Electromagnetic Properties Of Antiferromagneitc Photonic Crystals

Magnetic materials are prospective constituents for photonic crystals, since the magnetic materials make magnetic photonic crystals possessing many novel properties. The resonant frequencies of antiferromagnetic material lie in far infrared frequency region, i.e. terahertz frequency region, which is valuable for the develpment of communication. In this dissertation, we investigate the band structures and optical properties of one-dimensional and two-dimensional antiferromagnetic photonic crystals by applying both the theoretical and numerical simulation methods, and explore a therotical method with fast numerical convergent speed for calculating the band structures of two-dimensional antiferromagnetic photonic crystals. The negative refraction phonomen and second harmonic generation of antiferromagnetic/ionic- crystal mulitilayer are also studied.Band structures and transmission spectra of a one-dimensional antiferromagnetic photonic crystal waveguide are calculated by using the transfer matrix method. This waveguide is composed of one-dimensional antiferromagnetic photonic crystal embedded into slab metal waveguide. Besides photonc band gaps, another kind of frequency band gaps appears around the antiferromagnetic resonant frequency inside the waveguide, depending on the thickness of the waveguide and the antiferromagnetic resonant property. The width of this kind of gaps can reach to about 15 times that of the antiferromagnetic bulk by properly tuning the direction of the antiferromagntic anisotropic axis and the thickness of the waveguide. Under certain condition, some electromagnetic wave modes can pass through the antiferromagnetic photonic crystal waveguide in the frequency gap region of the antiferromagnetic bulk. Therefore, by changing the properties of the antiferromagnetic material and the thickness of the waveguide, the waveguide can realize different features from the antiferromagnetic bulk so that we can control the transport behaiver of electromagnetic waves inside the waveguide.A multilayer structure consisting of alternating antiferromagnetic and ionic-crystal layers is proposed, where the transverse optical phonon frequency of ionic-crystal material is slightly lower than the resonant frequency of the antiferromagnetic material. In certain frequency region, the short-period multilayer structure exhibits left-handedness-like and negative refraction phenomenon The effective permittivity and permeability of the multilayer in an external magnetic field are obtained by the effective-medium theory. The angle between the wave vector and energy flow of an electromagnetic wave inside the multilayered effective medium and the refractive angle are computed, respectively. Meanwhile, an analytical condition of the presence of both left-handedness-like and negative refraction phenomenon in the effective medium is found. However, the negative refraction phenomenon vanishes when the thickness of antiferromagnetic layers is thiner than that of ionic-crystal layers. These analytical conclusions are proved by numerical simulation results based on FeF2/TlBr mulitilayered effective medium.Second harmonic generation from an antiferromagnetic/ionic-crystal multilayer is investigated in an external magnetic field, where the generated harmonic waves rusult from the magnetically nonlinear response in the antiferromagnetic material. The effective second-order susceptibility of the multilayered structure is calculated by using the nonlinear effective-medium theorem, and the output power density of second harmonic wave from antiferromagnetic/ionic-crystal multilayered effective medium is computed and studied. It is shown that the system can exhibit negative refractive index for the pumping wave and positive refractive index for the second harmonic wave, so the second harmonic generation is greatly amplified in the vicinity of each antiferromagnetic resonat frequency. For the multilayered effective medium FeF2/TlBr, the output power density of second harmonic wave is about 8 times that of the FeF2 bulk.The Green's function method in the electronic energy band theory is introduced into the study of band structures of magnetic photonic crystals. The band structure of a two-dimensional antiferromagnetic photonic crystal in an external magnetic field is investigated by using the Green's function method. The photonic crystal is constructed by a square array of antiferromagnetic cylinders embedded inside a dielectric background, where the permeability of the antiferromagnetic cylinders is a tensor. Numerical simulations for MnF2/air two-dimensional antiferromagnetic photonic crystal show that this method allows fast convergent speed in both the antiferromagnetic resonant and non-resonant frequency regions. In the non-resonant frequency region, the photonic crystal is similar to an ordinary dielectric photonic crystal in the band structure. However, in the resonant frequency region, two magnetic band gaps emerge in the band structure of the two-dimensional antiferromagnetic photonic crystal. Their frequency positions and widths can be tunable with an external magnetic field, and we have also discussed the dependence of the two magnetic gap widths on the antiferromagnetic cylinder radius. The transmission spectrum of the two-dimensional antiferromagnetic photonic crystal is also calculated by the scattering theory, and the results of the numerical simulations are agreed with those of the corresponding band structures.