The Propagation Characteristics Of Electromagnetic Field In Two-dimensional Photonic Crystals Is Studied

Traditionally, the investigations on photonic crystal focused mainly on its band gap characteristics. Recently, the propagation characteristics of electromagnetic fields outside of the band gap in photonic crystals become a new hot issue, which has important significances for controlling the propagation of light. In this thesis, the propagation characteristics of electromagnetic field outside of the band gap in the photonic crystal are studied, which lies in the several aspects as follows:1. To analyze the propagation of Gaussian beam from the isotropic homogeneous medium to photonic crystal, we make use of time-domain pulse propagation method, and replace the temporal frequency of a finite-size Gaussian beam with the spatial frequency. By which we show that the diffraction properties of photonic crystal are closely related to the curvature of the iso-frequency contour at corresponding point.2. Self-collimation phenomenon of a two-dimensional square lattice photonic crystal is studied via numerical analysis. One-to-two beam splitter is realized by means of interpolating defect in the photonic crystal. The relation of optical divide ratio versus the refractive index of the defect is discussed.3. We realize Self-collimation propagation of TE and TM modes simultaneously. Based on which, a polarization beam splitter is designed by arranging a line defect for the band gap of TM mode in the photonic crystal, where TE and TM modes can be separated with high efficiency and large angle over a wide range of frequency. Polarization extinction ratios of transmitted and reflected light are14.82dB and17.45dB.4. With the aid of simulation, we show that the negative refraction phenomenon with any incident angle can be realized in the square lattice photonic crystal. The influence on the frequency spectrum zone of negative refraction by the relevant parameters of a2D photonic crystal is studied. Our results show that the Gaussian beam can rapidly focuses inside the photonic crystal, and the photonic crystal have the capability of sub-wavelength imaging.5. Using the abrupt change of the shape of iso-frequency contour, in. the same incident angle, we realize the conversion between the positive and negative refraction with the frequency increases, and achieve superprism effect with angular dispersion of0.5193(°)/nm.6. Using the contraction state of the iso-frequency contour caused by the band cross-fold, the conversion between the positive and negative refraction is achieved, such phenomenon can be regarded as a special superprism effect, it has a high angular dispersion10.64(°)/nm.