Study On The Characteristics Of Anisotropic Photonic Crystals

Anisotropic photonic crystal (PC) is a kind of novel PC consisting of anisotropic materials, and has special bandgap characteristics because its constitutive materials exhibit different refractive index contrasts under different polarized waves. Based on plane wave expansion (PWE) method, band structures and bandgaps for various types of anisotropic PCs are calculated and analyzed in this thesis.Firstly, the absolute bandgaps (APGs) of anisotropic dielectric PC consisting of hexgonal Te rods with simple lattices are studied and compared with the cases that the section of Te rods is circular, square or oval. Based on defect theory, resonance defect modes for the point defect and effective localized modes for the linear defect are also calculated. Results show that anisotropy helps to get the APGs and strong rotational symmetry of Te rods could lead to larger APGs. Besides, the APGs of two-dimensional (2D) plasma photonic crystal (PPC) consisting of circular Te rods are studied in detail, and the band structures of 2D anisotropic magnetized PPC and three-dimensional PPCs are also calculated. We found that filling factor, plasma frequency and external magnetic field which respectively behave as structural parameter, plasma parameter and external factor could modulate the bandgaps within a large range.Secondly, for the 2D PCs containing hyperbolic metamaterials (HMMs) which is anisotropic dispersive, formulas for calculating the bands based on the PWE method are derived. In two cases of HMM rods as scatters and HMM as background material, the band structures of TE waves and TM waves are analyzed. For the HMMs, changing the dielectric constants and filling ratios of the constitutive materials could affect their macroscopic properties in different frequnecy range, and thus could modulate the band structures and bandgaps, which shows greater flexibility than the case of the PPCs.Finally, an introduction to the practical application of anisotropic PCs, a kind of liquid crystal (LC) filled photonic crystal bandgap fiber is designed, and the general form of the eigenvalue equation for the PCs containing LC is derived. The results show that manipulating the director vector of the LC could make the guide modes appear or disappear, which points out the switching characteristic of this fiber.