The Photonic Bandgap, Optical Bistability And Phase-conjugation Wave In One Dimensional Photonic Crystals

In 1987 Yablonovitch and John, respectively and independently, proposed the notion of photonic crystals, which is an analogy to the conventional crystals and its principal properties are photonic band-gap and photonic localization. The photonic crystal is a kind of microstructured optical materials, its microstructure dimension is in the same order with the wavelength of relevant electromagnetic radiation, and its optical properties can be realized by adjusting the spatial periodicity of the medium refractive index. The properties of photonic crystals can be applied to controlling the light flow in photonic crystals, fabricating extremely miniature optical devices, such as frequency filters, optical waveguides, nonlinear optical switches and low threshold lasers etc. Now photonic crystals fabricated in laboratory have been extended from the microwave band to the optical frequency band, that means photonic crystals will be the foundation of novel photonic devices, therefore study on the composition and optical transmission properties of photonic crystals is of importance to fundamental physics and material science.1D photonic crystals may consist of positive refractive-index materials (or Right -Handed Materials, RHM) with different refractive indices, or positive and negative refractive index materials (the latter is called Left-Handed Materials, LHM), or dielectric and metallic materials. Combining methods of numerical calculation and theoretical analysis, the properties of RHM-RHM and RHM-LHM 1D photonic crystals, respectively, and (nonlinear) Bragg cavity have been investigated, such as photonic band-gap, photonic localization, polarization characteristic, optical bistability and phase-conjugation wave. It is revealed the law of defect mode frequency varying with the defect layer thickness in the RHM-LHM Bragg cavity, different from the law in the RHM-RHM Bragg cavity. The expanded phase diagram, a new tool to determine the position and characteristic of forbidden band of RHM-RHM 1D photonic crystal, is presented. In the vicinity of the central frequency of forbidden band the Dowling transmittance formula and all the transfer matrix elements are, respectively, expanded in the Taylor series and expressed in the first order approximation, thus the analytical expressions are, respectively, obtained for the positions of forbidden band centers and the transmittance in the central domain of forbidden band in the RHM-RHM 1D photonic crystal, the relations of the defect mode frequency and quality factor of the RHM-LHM Bragg cavity to the layer thicknesses of different mediums . The analytical expression is also obtained for the gains factor of phase -conjugation wave arisen from the third order nonlinear medium in the RHM-RHM nonlinear Bragg cavity. The influence of various factors on the switch threshold of bistability and their function mechanism are analyzed, the ways to lower the bistable threshold are also proposed. All numerical calculations and theoretical analyses are in accordance.