Classical Wave Propagation Characteristics In Periodic And Quasi-periodic System

Photonic crystals are formed by periodically-distributed dielectric media embedded in a background medium with a different permittivity. Optical waves are scattered by the periodic scatters and Bloch waves are formed subsequently according to the Bloch-Floquet theorem. In photonic crystals, similar to electronic system, there existed band structures and localized states as well. Since the introduction of the concept of photonic crystals, a lot of attention has been paid due to the capacities of controlling and molding lights, and the enormous potential applications in the fields of optoelectronics and integrated optics. At first, photonic band gap and the derived physical characteristics from band gap were the major concerns, and photonic localization was focused as well. However, recently, as the developments of theoretical methods and experimental conditions, some breakthroughs have been obtained. It' s found that photonic defect modes benefit guiding light quite well, which can be used to conquer the difficulties of guiding light through bended waveguide when using traditional fiber waveguide. Negative refraction appears under the long-wavelength limit in meta-materials, and similar negative refraction phenomena were found in dielectric photonic crystals as well. Negative refraction can be used to fabricate perfect lens beyond diffraction limit. Quasiperiodic state is an intermediate state between periodic and disordered states, and recently photonic quasicrystals were found to show many physical characteristics different from periodic systems. These new advances broaden both intension and extension of photonic crystals, and also promote the research in the relative fields, such as acoustic system and system of surface waves of water.Based on the recently promotion in photonic crystal research, in this thesis, we studied the existed problem in photonic crystal waveguides and the transportation characteristics of light in photonic crystal slabs. We studied new-type photonic crystal structures and negative refractions of these structures. Our work in the thesis includes the following parts:[1] Theoretical research on leaky modes of photonic crystal slabsPhotonic crystal slabs are types of "quasi-3D" photonic crystals, which can be used to fabricate cavities with high-Q value by introducing point defects to restrict spontaneous emission, and used to guide light via line defects caused by the coupling of a series of neighbored point defects. The advantage of photonic crystal waveguide over common fiber waveguide is that light can be guided through bended photonic crystal waveguide at any incident angle without radiation losses. However, great loss will be involved when guiding light through bended waveguide fabricated by optical fiber. The mechanisms of radiation losses can be classified into two types: (1) intrinsic losses, caused by leaky modes; (2) non-intrinsic losses, and the former are the primary concern in this thesis. In Chapter 3, we used scattering-matrix method to calculate the optical properties of leaky modes of photonic crystal slabs fabricated by dispersive and non-dispersive media, and then we used Variable-angle Reflectance method to obtain their band structure. We found that, compared with ideal 2D photonic crystals, (1) blue-shift appears in bands of leaky modes; (2)a new band appears, and the mechanism of this new band is still unknown. We also studied the polarization conversion in this structure, which is caused by the lack of translations symmetry in the z-direction. We found that in the directions containing mirror-symmetry, the efficiency of polarization conversion equals zero, and we explained this vanishing is caused by the symmetry restriction on polarizations.[2] Theoretical research on negative refraction of two-dimensional photonic crystal slabs.When an incident wave is incident from a normal medium to a left-handed one, the refracted wave will be in a "wrong" way compared with normal refraction. Under the long-wavelength limit, an effective negative permittivity can be provided by periodically-aligned metallic wires and an effective negative permeability can be provided by split-ring resonators (SRR) structure. These kinds of structures are called left-handed composite materials. A perfect lens can be fabricated by LHM. Negative refraction and focusing are realized in dielectric photonic crystals theoretically and experimentally as well. In Chapter 4, we used FDTD to calculate the optical properties of 2D triangular lattice with elliptical-profile rods. We found that in this structure, negative refraction and negative focusing can be realized. We calculate the FWHM of the image, and found that FWHM=0.39λ, which is smaller than diffraction limit 0.5λ. In the second case, we used multiple-scattering method to calculate the optical properties of 2D square photonic crystal with hollow-profile rods. We found that in the normalized frequency region f = 1.17 -1.19, negative refraction exists.[3] Theoretical research on negative refraction of two-dimensional photonic quasi-crystal slabs and phase vector field.Quasicrystals contain 5, 8, 12 and 20 rotation symmetries, but they lack of long-range translation symmetry. Quasicrystals are intermediate states between periodic and disordered systems, and the counterparts of some phenomena appear in periodic and disordered systems can be found in quasicrystals. In 2005, Feng et. al. found that in a 12-rotation-symmetry photonic quasicrystal, negative refraction and focusing appear for the normalized frequency region 11.78GHz -11.9GHz. In Chapter 5, we used multiple-scattering method to calculate the acoustic properties of a 12-rotation-symmetry acoustic quasicrystal. We found that in the normalized frequency region f = 0.54-0.66 , there is a band gap and a micro-band with the normalized frequency region f = 0.588-0.63 . By numerical simulation, we found that in the normalized frequency region f = 0.664 -0.68 , negative refraction exists. We also used Phase Diagram Technique to examine the phase-vectors field of quasi-periodic state, and found that a quasi-periodic state is an intermediate state between extended and localized states.