The Nonlinear Transmission Property For One-dimensional Photonic Crystals Containing Composite Defects

Photonic crystal is a new type of man-made photonic materials, of which the constituents'refractive indexes are arranged periodically in space. The size for period is comparable to the wavelength of electromagnetic wave propagating through the whole structure. Forbidden band is the basic characteristic of photonic crystal. Like the semi-conductor controlling the movement of electron, photonic crystal can freely control the transmission filtering and propagation of electromagnetic wave for some a frequency or in a certain frequency range through the design of structure,which brings revolutionary innovation ideas for optics communications, especially for the conventional microwave communications.Investigations to new constituents and new physics property are always hot topics for the research of photonic crystals. This dissertation deals nonlinear transmission property for new type of one-dimensional photonic crystals containing composite defects consisting of negative-index material, subwavelength material and Kerr-type nonlinear materials. It's expcted that the research results can further complete the nonlinearity for one-dimensional photonic crystals and provide valuable information for the design of new parts of apparatus. The main works involved are follows as:First, we investigate the transmission property of a one-dimensional photonic band gap structure with two coupled nonlinear defects separated by a linear middle layer and find that such composite structure exhibits a bistability that's strongly dependent of the linear middle layer. When the optics thickness of the linear middle layer fixed, the switching threshold values become smaller and smaller as the refractive index increases. While, the threshold values reduce periodically with the increment of thickness of the linear middle layer when the refractive index is fixed. The threshold values can be greatly reduced just by choosing the proper parameters of the linear middle layer.Second,we construct a composite defect using a linear thin film and a Kerr-type nonlinearity, and investigate the influence of the linear defect layer on the electrical field distribution, the linear defect mode frequency and the threshold intensities of optical bistability when the linear film is of negative-index material and positive-index material, respectively. And find that the variation of the above three parameters with the physics parameters of the linear film is quitely opposite for cases of negative and positive.Third, we develope the nonlinear matrice descriping the Kerr-type nonlinearity and deduce the formula to compute the relationship between the Goos-H?nchen shift and the incident intensity. We investigate the variation of Goos-H?nchen shift with the incident intensity for a one-dimensional photonic crystal containg a Kerr-type defect layer and find the hysteretic response between the Goos-H?nchen shift and the incident intensity. We call this phenomonon as bistable shift. When the incident intensity reduces from a high value over the high threshold value of optical bistability, the Goos-H?nchen shift is enhanced greatly and reaches the highest value near the low threshold value of optical bistability. We discuss the influence of the thickness and the linear refractive index of the Kerr defect layer, the incident frequency and incidence angle on the bistable shift. The peak value of bistable shift reduces as the linear refractive index increases. When the photonic structure and the incidence angle is fixed, bistable shift is decided by how far the linear defect mode frequency deviates away from the incident frequency. As the incident frequency comes close to the linear defect mode frequency, the peak value increases drastically. However, bistable shift disappears when the incident frequency comes very close to or even exceeds the linear defect mode frequency.Fourth, we investigate the modulation of a subwavlength layer on the bistable shift of a one-dimensional photonic crystal containing a nonlinear defect layer. Theoretical results reveals that a subwavelength of negative-index material can change the characteristic obviously. As the absolute value of the magnetic permeability increases, the upper part of the hysteresis moves downwards while the bottom part moves upwards, and the interval between the two parts decreases until they basically overlaps. Afterwards, with further increment of the absolute value of the magnetic permeability, the primary bottom part of the hysteresis exceeds the primary upper part and the interval between the two parts becomes larger and larger. The sequence of the thin film of negative index material and the nonlinear layer has a major impact on this anomalous bistable shift. And the difference becomes more and more obvious as the absolute value of the magnetic permeability. For structure (AB) 3 ADCA( BA)3, the direction of the hysteresis curve suddenly switches from upwards to downwards and the majority of lateral shifts become negative. This anomalous phenomenon results from the interference of each transmitted constituent. With introduction of the subwavelength layer of air, the Goos-H?nchen shift near the band gap is greatly enhanced while the transmittance is almost not affected. Besides,Goos-H?nchen shifts are negative and positive for the two edges of the forbidden band, respectively. On the other hand, the shifts show positive and negative value alternatively on any edge. If we change the sequence of the subwavelength layer and the nonlinear layer, positive shifts on the low frequency edge become negative and negative shifts become positive. While, opposite cases occur on the other frequency edge of the band.