Theoretical Study Of Tunable Photonic Crystal, The Polarization-independent Photonic Crystals And Photonic Crystal Quantum Well Structure

In this thesis, from the view of application, we study the properties of the tunable photonic crystals, polarization-independent photonic crystals and the photonic quantum-well structures containing negative-index materials. The thesis consists of five chapters.In the first chapter, we firstly introduce the general properties of photonic crystals and the development of the research of photonic crystals in these years. Then we introduce the concrete property of another research highlight—metamaterials.In the second chapter, two important numerical methods of calculating photonic band structures and transmissions are presented: the plane-wave expansion method and the transfer-matrix method. We investigate in detail the plane-wave based transfer-matrix method.In the third chapter, we firstly introduce several kinds of tunable photonic crystals, then we propose a new kind of tunable photonic crystals, the band structures of which can be tuned by means of an external magnetic field due to the magneto-optical effect. This is shown by calculating the photonic band structure of a GaAs-based two-dimensional photonic crystal with a square or triangular lattice of cylindrical air holes. We also compare it with other kinds of tunable photonic crystals. We further propose the concept of extrinsic photonic crystals, showing the significance of this new kind of photonic crystals in theory and application. We present a model of extrinsic photonic crystals based on the upper tunable photonic crystals and introduce its concrete properties.In the fourth chapter, the polarization-independent photonic crystals are introduced. We firstly show the merit of this kind of photonic crystals and the method to realize it by others. Then we introduce our method to realize the polarization-independent photonic crystals, including the theoretical presentation and simulation results. We also show how to get this kind of polarization-independent photonic crystals with the metamaterials.In the fifth chapter, we introduce a photonic quantum-well structure containing negative-index materials. First we show the limitation of the conventional photonicquantum-well structures. With the unique property of the zero- n gap ofone-dimensional photonic crystals containing negative-index materials, we propose a new type of photonic quantum-well structures. This type of photonic quantum-well structures can be used as a polarization-independent multiple channeled filter that is nearly independent on incident angles, and invariant with scaling and disorder.