A Study On Photonic Crystal And Left-Handed Medium

In the present thesis,I mainly report my research results in two areas,photonic crystal and negative material. The present thesis covers a wide range of topics,including computational methods,basic theory of photonic crystal,and new physical phenomena.My work in the above mentioned two areas is list as:1. On computational methods in photonic crystalFinite difference time domain method (FDTD) and plane wave expansion method (PWE) are widely used in calculation the dispersion relation of the photonic crystals. I carried my research on both the two computation methods and fruitful results were obtained. For the FDTD method,I solved the instability problem of the method in the non-orthogonal coordinate system. For the PWE method,I introduce the linear transform in to calculate analytically the Fourier coefficients of complicated photonic crystals. Detailed discussions can be found in the chapter 2 and 3.2. On the degeneracy properties in the dispersion relation of photonic crystalIt is an intractable problem to explain the dispersion relation and degeneracy properties in it for photonic crystals. I find it is useful to create photonic crystals with big complete forbidden bands by changing the translational symmetry of the photonic crystal. Having developed two theorems in the present thesis on the degeneracy properties of the photonic crystal in the super cell,I can give how the degeneracy will change in the band structure of the photonic crystal corresponds to the change of the translational symmetry of the photonic crystal. Detailed discussion can be found in chapter 4.3. On unusual phenomena in the one dimensional alternate structure of left-handed material and right-handed materialI found three unusual phenomena for the one dimensional periodic structure consisting both left-handed material and right-handed material. They are spurious complex frequency,discrete mode,and photon tunneling mode. I also carried some research on the Bragg grating composed by alternate left-handed material andright-handed material. In the reflective spectrum of the Bragg grating,there exists Bragg top zone (with reflectance almost 100%). However,I found that there exists some narrow transmission bands located in the Bragg zone under some conditions. Physical explanations are given in the present thesis. Detailed discussions can be found in chapter 5 and 6.