Theoretical Studies On Light Propagation Properties In Low-dimensional Photonic Band Gaps With Special Structure

Since the year Yablonovitch and John first demonstrated the characteristic of photonic bandgap structure, a great deal of development has been achieved on photonic crystals. When nonlinear medium is induced, the properties of photonic crystals device are changed with the incident light intensity, which directly cause the alternation of effective refractive index. Many structures consisted of nonlinear photonic crystals have been integrated in optical circuits utilized their specialties such as:optical limiting, optical switching, optical diodes and bistability. Photonic Crystal Fiber is one of important applications of Photonic Crystals. Great interest has recently been concentrated on the new science of photonic crystal fibers - silica optical fibers with a cladding, which is consisting of a regular air-holes lattice running along the fiber axis. Depending on its unique feature, the arrangement of the air-holes, the guiding of light can be provided by being modified either by total-internal-reflection (TIR) or photonic bang gap (PBG) confinement effect.The theoretical studies focus on the optical transmission characteristics in one-dimensional photonic crystal with quantum dot and parameter-dependent dispersion of a novel tunable photonic crystal fiber in the paper.First, based on the third-order susceptibilities and light induced refractive index, the transmission properties of one-dimensional photonic crystal with inserting defect layers into quantum dots has investigated. The transmission spectra of one- dimensional photonic crystal are calculated by using a theoretical model based on the transfer matrix method, in which many perfect transmission peaks are numerically obtained. It will be shown that the transmission spectra of this multilayer structure can be employed for filter with narrow band gap.Then depending on the properties of photonic band gap materials, a novel photonic crystal fiber (PCF), formed by lithium niobate and liquid crystal, has been studied numerically. Dispersion relationships and transmission spectra of the PCF are calculated by methods of the full-vector modal and the finite difference time domain (FDTD), respectively. The parameter-dependent dispersion and transmission of the PCF have been found. It is shown that the design of the novel photonic crystal fiber could be supported by the theoretical analysis in fourth chapter.Finally, we calculated the dispersion of two typical PCF structure, and discussed the relationship of the waveguide dispersion and the pitch A and magnitude M (M=a/A). The results showed that the zero dispersion point moves to longer wavelength. We investigated the modulability of PCF base on the optical and thermal characteristics of LC. It is shown that field-induce effect changes the zero dispersion point more remarkably than thermal-induce effect by influencing the refractive index of LC. Depending on the property of modulability, it will play a significant role in designing of the zero dispersion fiber and dispersion compensating fiber.