含复合缺陷的一维光子晶体的非线性传输特性的研究
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摘要
光子晶体是一种新型的人工合成光学材料,其组成材料的折射率在空间呈周期性分布。光子晶体的尺度与电磁辐射波长具有相同数量级,其最根本特征是具有光子带隙。能够像半导体控制电子的运动一样,通过对材料结构的优化设计,光子晶体可以自由地控制一定频率范围内或某固定频率的电磁波在空间不同方向上的发射、输运和滤波。这一思想给光通信技术,特别是给传统的微波通信技术带来革命性的创新理念。
合成新型光子晶体、探讨新的物理特性及应用,一直是光子晶体研究的热点。本文将采用亚波长材料、负折射率材料、非线性材料来构造一维光子晶体的复合缺陷,深入研究光在其中的非线性传播特性,期盼研究结果能够进一步完善光子晶体的非线性特性,为新型光学器件的设计提供新思路。本文的主要工作和创新点概括如下:
(1)研究了具有中间线性隔层的耦合非线性缺陷对一维光子晶体双稳态特性的影响。发现这种复合结构的光学双稳态受到中间线性介质层的强烈调制,当中间线性层光学厚度固定时,双稳态阈值随其折射率的减小而减小,当中间线性层的折射率固定时,双稳态阈值随其厚度的增加呈周期性变化。恰当选择中间线性介质层的参数可大大降低双稳态阈值。
(2)用线性薄膜和Kerr材料构造一维光子晶体的复合缺陷,分别研究了线性缺陷膜为双负折射率材料和右手材料两种情况下,线性缺陷膜对一维光子晶体的电场分布、线性缺陷模频率和双稳态阈值的影响,发现当线性缺陷膜为双负材料时,上述三个参量随线性薄膜物理参数变化的趋势与具有相同绝对值参数的正折射率线性薄膜时的情形完全相反。
(3)对计算Kerr介质的非线性特征矩阵进行了推导和演化。推导出斜入射时,透(反)射波束的Goos-H?nchen位移与入射波强度变化的关系式。利用所推导的关系式分析了中间位置含Kerr材料的一维光子晶体透射波束纵向位移随入射波强度的变化关系,首次发现Goos-H?nchen位移随入射光强度的改变呈双稳态变化,提出了双稳态位移的概念。当入射波强度从较大值减小时,Goos-H?nchen位移被大大增强,在低阈值附近达到最大值。详细讨论了Kerr缺陷膜的厚度、线性折射率、入射波频率以及入射角对双稳态位移的影响,发现双稳态位移的峰值随非线性材料线性折射率的成倍增长而减小。当光子晶体结构和入射角确定时,双稳态位移取决于入射波频率偏离线性缺陷模频率的程度。随着入射波频率逐渐接近线性缺陷模频率,位移峰值急剧增大,但当入射波频率非常接近线性缺陷模频率甚至超过线性缺陷模频率时,双稳态位移消失。
(4)研究了亚波长缺陷膜对含Kerr类型非线性缺陷的一维光子晶体缺陷模频率附近透射波束双稳态位移特性的调制作用。研究表明双负折射率亚波长缺陷膜能明显改变双稳态位移特性。随着磁导率绝对值的增加,双稳态阈值增大,位移峰值却减小,回滞曲线上下两部分间的距离先是变得越来越小,直到两部分重合在一起,而后随着磁导率绝对值的增加,原来位于回滞曲线下面的部分移动到了上面,而原来上面的那部分却移动到了下面,并且随着磁导率绝对值的增加两部分间的距离增大。研究还发现,亚波长缺陷膜和Kerr缺陷膜的前后位置次序对双稳态位移的阈值和峰值产生剧烈影响,并且磁导率的绝对值越大,影响越明显。对于(AB) 3 ADCA( BA)3结构,当亚波长缺陷膜磁导率的绝对值较大时,双稳态位移的方向突然从向上翘变为向下翘,并且随着入射光强的变化,位移大部分变为负值。这些特性都是普通右手材料所不具备的,这主要是由于亚波长材料的负折射率和非线性介质内有效折射率随入射波强度的缓慢变化共同作用造成的。亚波长空气薄膜的引入,对光子晶体禁带边缘的反射谱线基本上没影响,但能够大大增强光子晶体禁带边缘的Goos-H?nchen位移。并且,禁带的上边缘和下边缘处一边为正值,另一边为负值,任何一边位移都是正负相间隔。当更换亚波长空气薄膜和非线性薄膜的位置次序时,禁带下边缘的位移由正值变为负值,而负值却变为正值,在禁带的上边缘,情形却恰恰相反。
所取得的理论结果对新型光学器件(特别是光子技术中缺少的光逻辑元件、记忆存储元件和光转换器等)的设计与开发具有一定的指导作用。
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.
合成新型光子晶体、探讨新的物理特性及应用,一直是光子晶体研究的热点。本文将采用亚波长材料、负折射率材料、非线性材料来构造一维光子晶体的复合缺陷,深入研究光在其中的非线性传播特性,期盼研究结果能够进一步完善光子晶体的非线性特性,为新型光学器件的设计提供新思路。本文的主要工作和创新点概括如下:
(1)研究了具有中间线性隔层的耦合非线性缺陷对一维光子晶体双稳态特性的影响。发现这种复合结构的光学双稳态受到中间线性介质层的强烈调制,当中间线性层光学厚度固定时,双稳态阈值随其折射率的减小而减小,当中间线性层的折射率固定时,双稳态阈值随其厚度的增加呈周期性变化。恰当选择中间线性介质层的参数可大大降低双稳态阈值。
(2)用线性薄膜和Kerr材料构造一维光子晶体的复合缺陷,分别研究了线性缺陷膜为双负折射率材料和右手材料两种情况下,线性缺陷膜对一维光子晶体的电场分布、线性缺陷模频率和双稳态阈值的影响,发现当线性缺陷膜为双负材料时,上述三个参量随线性薄膜物理参数变化的趋势与具有相同绝对值参数的正折射率线性薄膜时的情形完全相反。
(3)对计算Kerr介质的非线性特征矩阵进行了推导和演化。推导出斜入射时,透(反)射波束的Goos-H?nchen位移与入射波强度变化的关系式。利用所推导的关系式分析了中间位置含Kerr材料的一维光子晶体透射波束纵向位移随入射波强度的变化关系,首次发现Goos-H?nchen位移随入射光强度的改变呈双稳态变化,提出了双稳态位移的概念。当入射波强度从较大值减小时,Goos-H?nchen位移被大大增强,在低阈值附近达到最大值。详细讨论了Kerr缺陷膜的厚度、线性折射率、入射波频率以及入射角对双稳态位移的影响,发现双稳态位移的峰值随非线性材料线性折射率的成倍增长而减小。当光子晶体结构和入射角确定时,双稳态位移取决于入射波频率偏离线性缺陷模频率的程度。随着入射波频率逐渐接近线性缺陷模频率,位移峰值急剧增大,但当入射波频率非常接近线性缺陷模频率甚至超过线性缺陷模频率时,双稳态位移消失。
(4)研究了亚波长缺陷膜对含Kerr类型非线性缺陷的一维光子晶体缺陷模频率附近透射波束双稳态位移特性的调制作用。研究表明双负折射率亚波长缺陷膜能明显改变双稳态位移特性。随着磁导率绝对值的增加,双稳态阈值增大,位移峰值却减小,回滞曲线上下两部分间的距离先是变得越来越小,直到两部分重合在一起,而后随着磁导率绝对值的增加,原来位于回滞曲线下面的部分移动到了上面,而原来上面的那部分却移动到了下面,并且随着磁导率绝对值的增加两部分间的距离增大。研究还发现,亚波长缺陷膜和Kerr缺陷膜的前后位置次序对双稳态位移的阈值和峰值产生剧烈影响,并且磁导率的绝对值越大,影响越明显。对于(AB) 3 ADCA( BA)3结构,当亚波长缺陷膜磁导率的绝对值较大时,双稳态位移的方向突然从向上翘变为向下翘,并且随着入射光强的变化,位移大部分变为负值。这些特性都是普通右手材料所不具备的,这主要是由于亚波长材料的负折射率和非线性介质内有效折射率随入射波强度的缓慢变化共同作用造成的。亚波长空气薄膜的引入,对光子晶体禁带边缘的反射谱线基本上没影响,但能够大大增强光子晶体禁带边缘的Goos-H?nchen位移。并且,禁带的上边缘和下边缘处一边为正值,另一边为负值,任何一边位移都是正负相间隔。当更换亚波长空气薄膜和非线性薄膜的位置次序时,禁带下边缘的位移由正值变为负值,而负值却变为正值,在禁带的上边缘,情形却恰恰相反。
所取得的理论结果对新型光学器件(特别是光子技术中缺少的光逻辑元件、记忆存储元件和光转换器等)的设计与开发具有一定的指导作用。
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.
引文
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