Diffraction properties of a two-dimensional photonic crystal is presented. Diffraction experiments are carried out using a
ring beam and the relevant experimental designs are shown. Drastic ring deformations are observed after diffractions, for
different kind of ring beams. The diffraction properties are analyzed using the equ-frequency surface and the photonic
band structure of a photonic crystal. The paper also describes the fundamental difference between the diffraction
properties of photonic crystals with weak and finite modulation in their dielectric property.
Large and controllable polarization splitting effects are demonstrated based on liquid crystal infiltrated two-dimensional photonic crystals with silicon as a background material. Due to the strong birefringence of the liquid crystal, the dispersion curves of the two polarizations are distinctly different, resulting in large splitting between the two polarizations. Extremely large splitting, as large as 90 degree, can be obtained. Moreover, the splitting can be substantially tuned upon re-orienting the optic axis of liquid crystal. The influence of incident angle and the birefringence of the LC to the polarization splitting are also analyzed.
The band gap characteristics of one-dimensional and two-dimensional photonic crystals made of uniaxial anisotropic materials were analyzed with a focus on the band gap characteristics as a function of optical axis orientation in the aniostropic material. For one-dimensional case, with optical axis normal to periodicity axis, the two polarization of on axis light will experience different refractive indexes and thus the degeneracy in photonic band will disappear. Theoretically we show that in some nonlinear materials, with presence of certain symmetry, the band lines correspond to two polarizations will degenerate under a high electric field. It is also shown that the gap position and size varies as the position of the optical axis varies and the range is limited by the birefringence of the anisotropic material. In two dimensional photonic crystal, we showed that, changing the position of optical axis in the propagation plane is simply change of symmetry in photonic band structure. If the position of the optical axis is varied in the transversal direction, we can open or close the band gap. The characteristic of anisotropic material, the direction dependant refractive index can be used to improve the band structure of conventional isotropic photonic crystal.