二维光子晶体带隙与慢光特性研究及结构优化设计
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摘要
随着光通信的发展,光器件的小型化和易于控制性越来越成为人们追求的目标,这就对光通信器件的集成度要求越来越高,然而现有的光器件还无法满足这个需求。光子晶体的概念提出之后,其以独特的带隙和慢光性能使得设计具有更高集成度和更好性能的光通信器件成为可能。本文主要针对二维光子晶体带隙和慢光特性进行了研究,设计了具有更大绝对带隙的光子晶体和具有更小群速度的光子晶体慢光波导结构,初步分析了慢光在全光缓存中的应用,并设计了光子晶体慢光实验平台,对制作的光子晶体波导慢光特性进行了测试。具体在以下几个方面展开工作并进行创新：
(1)针对三种常见的介质柱横截面分别为正六边形,正方形和圆形的二维光子晶体,提出了一种增大光子绝对带隙的方法。通过对介质柱截面形状进行变形,即在直角坐标系下,增大X方向长度为原来长度的p倍,并以原点为中心旋转角度φ。通过调整p和φ大小来降低其结构对称性,对其进行了大量的仿真分析,得到了具有更大的绝对带隙的光子晶体结构。改变结构之前最大绝对带隙率约为5.3%,改变结构之后,对于三种介质柱三角晶格结构的光子晶体,最大绝对带隙率均能达到12%以上,尤其对于正方柱三角晶格光子晶体,最大绝对带隙率达到15.1%。这种增大带隙的方法在其他文献中尚未被提及,为以后设计类似结构的大带隙光子晶体提供了一个重要参考。
(2)通过平面波展开法中的超胞算法对光子晶体线缺陷波导结构的慢光特性进行了研究。当缺陷柱半径小于光子晶体介质柱半径时,随着缺陷柱半径的增加,导模中心频率向低频移动,群速度也越来越小；当增大介质柱的介电常数时,导模有相同的变化规律。针对这种现象,本论文从介电常数在平面波展开法中的作用出发进行了探讨。然后研究了缺陷柱位置对导模慢光的影响,通过上下平移缺陷柱,得到具有更好线性的导模,此时群速度曲线相对平坦,色散值也更小。最后得到结论：缺陷柱的大小和介电常数的变化更多的是影响导模的慢光值,而通过调整缺陷柱上下平移的距离则能达到减小慢光群速度色散特性的目的。
(3)通过改变缺陷腔的结构,研究了二维光子晶体耦合腔波导慢光的变化情况,得到了具有极小慢光群速度的光子晶体耦合腔波导结构。首先对普通结构光子晶体CCW慢光特性进行了计算,随着腔间距离的增大,腔间耦合系数越小,CCW的慢光群速度越来越小；还计算了改变普通结构的微腔中心缺陷柱半径后的CCW慢光值,得到单独减小微腔缺陷柱尺寸并不能得到更小的慢光值的结论。定义慢光因子为导模最大群速度与真空中光速的比值,然后通过改变微腔中心缺陷柱和周围四个缺陷柱半径的方法设计新型结构的CCW,在中心缺陷柱半径为零的情况下得到慢光因子最小值为5.89x10-4；将中心缺陷柱尺寸影响考虑进去之后,通过调整周围四个缺陷柱,得到最小慢光因子为3.26x10-4,这大约是对应普通缺陷腔结构慢光因子的1/10。另外,当固定周围四个缺陷柱半径在某些范围内时,慢光因子随中心缺陷柱半径的变化很小,而且慢光因子值也很小。结合光子晶体的制作可知,这种结构在制作中对精度要求可以相对降低很多,从而具有很好的应用价值。
(4)结合慢光缓存的应用,通过紧束缚法原理介绍了CCW结构对应的慢光缓存参数计算方法,对耦合腔波导的比特长度和缓存容量等进行计算分析,看到CCW慢光缓存中延迟时间和缓存容量是相互制约的,即腔间距的增大,一方面使得耦合系数增大,从而减小了群速度,另一方面却使得导模带宽变小且比特长度增加,从而减小了缓存容量。通过对不同结构进行计算,在9.78cm的光子晶体CCW长度上实现了1μs的延迟,延迟时间大约是类似文献中结果的3倍,缓存容量达到3.3kbit。通过进一步分析得出,对于CCW慢光结构,当微腔间距较小时,系统具有较小的比特长度,从而缓存容量较大,此时对于慢光缓存具有较大的应用价值；而当微腔间距较大时,系统具有较大的比特长度,此时虽然缓存容量较小,却具有更小的慢光群速度,使得慢光时延较大,这种结构更适合用于对光与物质之间作用时间要求较长的非线性效应等应用中。
(5)结合测量光子晶体波导慢光的需求,对慢光实验平台的测试原理进行了分析,确认了通过测试光在光子晶体波导中相位变化来计算等效折射率变化的方法,并在此基础上设计了实验平台。用聚焦离子束方法(FIB)进行光子晶体波导制作,并对制作的W1型光子晶体波导进行慢光测试,得到其群折射率曲线。针对1560nm处的群折射率,通过光示波器进行延迟验证,得到4.7ps左右的延迟,与群折射率曲线结果吻合。
All-optical buffer is essential in the realization of all-optical network scheme and it plays a key role in all-optical switching system. The development of all-optical network has to breakthrough the technology of all-optical buffer. Two-dimensional (2D) photonic crystal (PhC) and its slow light properties provide many advantages to the development of the technology of all-optical buffer. The slow light testbed is designed and the slow light properties of the fabricated PCW are measured. To be specific, the contents and main results in this thesis are described as follows:
1. For three typical sorts of conventional 2D photonic crystals with dielectric rod's cross sections'shapes of hexagon, square and circular, a novel method for increasing improving the PBG of the photonic crystals is proposed. It achieves the design goal by increasing the length in X direction to be p times and rotating shapes with angleφ. The symmetry of the structures are decreased through changing the values of p andφp. Through the extensive simulations using planar wave expansion method, we find that improved PBG rate can reach up to 12% due to the photonic crystals of the three types of dielectric rod with triangular lattice. Especially for photonic crystals of rectangle rod with triangular lattice, the max PBG rate can reach 15.1%. This method provides us an important reference to design the PhC structure with better absouluty PBG. It is innovative, and currently there is no work about this to our knowledge.
2. The characteristics of slow light in PhC line defect waveguide structure is studied with supercell algorithm of PWE. When the radius of defect rod is smaller than the one of PhC dielectric rod, the central frequency of guided mode transfers to lower frequency and its group velocity gets smaller and smaller as the increase of radius of defect rod; The guided mode changes the same as the increase of dielectric constant of dielectric rod. With this observation, a discussion is set out from the function of dielectric constant in PWE. Then the effect of position of defect rod on guided mode slow light is studied, and the guided mode with better linearity which represents that the curve of group velocity is more smooth and the GVD is smaller is obtained through shifting the defect rod up and down. To sum up, the size of defect rod and the change of dielectric constant mostly effects on the value of group velocity, while the change of the position of the defect rod optimizes the GVD of slow light.
3. Through modifying the structure of the defedted cavity, we study the variation of the group velocity of the slow light in the 2D PhC CCW and get the CCW strucuter with ultro-small group velocity. Firstly we calculate the group velocity of the normal PhC CCW and find that the group velocity and coupling coefficient decrease as the distance between coupled cavities increases. The group velocity of the CCW structure is also calculated by changing cetral defect rod's radius only and we find that this can't reduce the group velocity. Then we design new CCW structure through modifying the radii of the central rod and around four rods. The slow light factor can reach 5.89×10-4 by varying the radii of other four rods when the radius of the central rod is zero. Ultra small slow light factor 3.26×10-4, which is about 1/10 of that of corresponding normal CCW, can be gotten if we modify the five rods at the same time. We also find that the variation of the slow light factor caused by the changing of the radius of the central rod is very small when the radii of the around four rods are set within a certain range. Considering the manufacture of PhC, this type of CCW structure has great application value since it reduces the demand of the precision.
4. Combined with the application of slow light buffers, the corresponding computation method of CCW structure is introduced through the principle of tight binding method. The BIT length of coupled cavity waveguide and buffering capacity etc. are analyzed to obtain that the delay time and buffering capacity in CCW slow light buffering restrict each other. This means that, on the one hand, the coupling coefficient gets larger as the increase of space between cavities to reduce the group velocity; on the other hand, the guided mode bandwidth gets narrower and the BIT length gets longer to reduce the buffering capacity. The delay time of 1μs in PhC CCW of 9.78cm is implemented through calculation on different structures and it is 3 times larger than similar literatures. Buffering capacity can reach 3.3kbit. Moreover, the analytic results on CCW slow light structures shows that, when the space between cavities is smaller, the system gains smaller BIT length to increase the buffering capacity, which is of great applied values to slow light buffering; when the space between cavities is larger, the system gains larger nic crystals with a triangular lattice of air holes", J. Opt. Soc. Am. B, Vol.20, 2003,p.19221926.
Olivier S, Smith C J M, Rattier M, et al., "Miniband transmission in a photonic crystal coupled-resonator optical waveguide", Opt. Lett., Vol.26, between (?) of measurement of PhC slow light, we analyze the test principle of the slow light testbed and decide to measure the change of the equivalent dielectric constant by testing the variation of the phase in PCW. Based on the analysis, we design the testbed. The W1 PCW is fabricated with focused ion beam (FIB) method. The obtained results demonstrate that the group index curve measured with the phase-delay method has the exact same trend with that in simulations. The time-delay of the pulse is also measured, and it fits for the theoretical result calculated according to the group index with the phase-delay method, witch is about 4.7ps.
(1)针对三种常见的介质柱横截面分别为正六边形,正方形和圆形的二维光子晶体,提出了一种增大光子绝对带隙的方法。通过对介质柱截面形状进行变形,即在直角坐标系下,增大X方向长度为原来长度的p倍,并以原点为中心旋转角度φ。通过调整p和φ大小来降低其结构对称性,对其进行了大量的仿真分析,得到了具有更大的绝对带隙的光子晶体结构。改变结构之前最大绝对带隙率约为5.3%,改变结构之后,对于三种介质柱三角晶格结构的光子晶体,最大绝对带隙率均能达到12%以上,尤其对于正方柱三角晶格光子晶体,最大绝对带隙率达到15.1%。这种增大带隙的方法在其他文献中尚未被提及,为以后设计类似结构的大带隙光子晶体提供了一个重要参考。
(2)通过平面波展开法中的超胞算法对光子晶体线缺陷波导结构的慢光特性进行了研究。当缺陷柱半径小于光子晶体介质柱半径时,随着缺陷柱半径的增加,导模中心频率向低频移动,群速度也越来越小；当增大介质柱的介电常数时,导模有相同的变化规律。针对这种现象,本论文从介电常数在平面波展开法中的作用出发进行了探讨。然后研究了缺陷柱位置对导模慢光的影响,通过上下平移缺陷柱,得到具有更好线性的导模,此时群速度曲线相对平坦,色散值也更小。最后得到结论：缺陷柱的大小和介电常数的变化更多的是影响导模的慢光值,而通过调整缺陷柱上下平移的距离则能达到减小慢光群速度色散特性的目的。
(3)通过改变缺陷腔的结构,研究了二维光子晶体耦合腔波导慢光的变化情况,得到了具有极小慢光群速度的光子晶体耦合腔波导结构。首先对普通结构光子晶体CCW慢光特性进行了计算,随着腔间距离的增大,腔间耦合系数越小,CCW的慢光群速度越来越小；还计算了改变普通结构的微腔中心缺陷柱半径后的CCW慢光值,得到单独减小微腔缺陷柱尺寸并不能得到更小的慢光值的结论。定义慢光因子为导模最大群速度与真空中光速的比值,然后通过改变微腔中心缺陷柱和周围四个缺陷柱半径的方法设计新型结构的CCW,在中心缺陷柱半径为零的情况下得到慢光因子最小值为5.89x10-4；将中心缺陷柱尺寸影响考虑进去之后,通过调整周围四个缺陷柱,得到最小慢光因子为3.26x10-4,这大约是对应普通缺陷腔结构慢光因子的1/10。另外,当固定周围四个缺陷柱半径在某些范围内时,慢光因子随中心缺陷柱半径的变化很小,而且慢光因子值也很小。结合光子晶体的制作可知,这种结构在制作中对精度要求可以相对降低很多,从而具有很好的应用价值。
(4)结合慢光缓存的应用,通过紧束缚法原理介绍了CCW结构对应的慢光缓存参数计算方法,对耦合腔波导的比特长度和缓存容量等进行计算分析,看到CCW慢光缓存中延迟时间和缓存容量是相互制约的,即腔间距的增大,一方面使得耦合系数增大,从而减小了群速度,另一方面却使得导模带宽变小且比特长度增加,从而减小了缓存容量。通过对不同结构进行计算,在9.78cm的光子晶体CCW长度上实现了1μs的延迟,延迟时间大约是类似文献中结果的3倍,缓存容量达到3.3kbit。通过进一步分析得出,对于CCW慢光结构,当微腔间距较小时,系统具有较小的比特长度,从而缓存容量较大,此时对于慢光缓存具有较大的应用价值；而当微腔间距较大时,系统具有较大的比特长度,此时虽然缓存容量较小,却具有更小的慢光群速度,使得慢光时延较大,这种结构更适合用于对光与物质之间作用时间要求较长的非线性效应等应用中。
(5)结合测量光子晶体波导慢光的需求,对慢光实验平台的测试原理进行了分析,确认了通过测试光在光子晶体波导中相位变化来计算等效折射率变化的方法,并在此基础上设计了实验平台。用聚焦离子束方法(FIB)进行光子晶体波导制作,并对制作的W1型光子晶体波导进行慢光测试,得到其群折射率曲线。针对1560nm处的群折射率,通过光示波器进行延迟验证,得到4.7ps左右的延迟,与群折射率曲线结果吻合。
All-optical buffer is essential in the realization of all-optical network scheme and it plays a key role in all-optical switching system. The development of all-optical network has to breakthrough the technology of all-optical buffer. Two-dimensional (2D) photonic crystal (PhC) and its slow light properties provide many advantages to the development of the technology of all-optical buffer. The slow light testbed is designed and the slow light properties of the fabricated PCW are measured. To be specific, the contents and main results in this thesis are described as follows:
1. For three typical sorts of conventional 2D photonic crystals with dielectric rod's cross sections'shapes of hexagon, square and circular, a novel method for increasing improving the PBG of the photonic crystals is proposed. It achieves the design goal by increasing the length in X direction to be p times and rotating shapes with angleφ. The symmetry of the structures are decreased through changing the values of p andφp. Through the extensive simulations using planar wave expansion method, we find that improved PBG rate can reach up to 12% due to the photonic crystals of the three types of dielectric rod with triangular lattice. Especially for photonic crystals of rectangle rod with triangular lattice, the max PBG rate can reach 15.1%. This method provides us an important reference to design the PhC structure with better absouluty PBG. It is innovative, and currently there is no work about this to our knowledge.
2. The characteristics of slow light in PhC line defect waveguide structure is studied with supercell algorithm of PWE. When the radius of defect rod is smaller than the one of PhC dielectric rod, the central frequency of guided mode transfers to lower frequency and its group velocity gets smaller and smaller as the increase of radius of defect rod; The guided mode changes the same as the increase of dielectric constant of dielectric rod. With this observation, a discussion is set out from the function of dielectric constant in PWE. Then the effect of position of defect rod on guided mode slow light is studied, and the guided mode with better linearity which represents that the curve of group velocity is more smooth and the GVD is smaller is obtained through shifting the defect rod up and down. To sum up, the size of defect rod and the change of dielectric constant mostly effects on the value of group velocity, while the change of the position of the defect rod optimizes the GVD of slow light.
3. Through modifying the structure of the defedted cavity, we study the variation of the group velocity of the slow light in the 2D PhC CCW and get the CCW strucuter with ultro-small group velocity. Firstly we calculate the group velocity of the normal PhC CCW and find that the group velocity and coupling coefficient decrease as the distance between coupled cavities increases. The group velocity of the CCW structure is also calculated by changing cetral defect rod's radius only and we find that this can't reduce the group velocity. Then we design new CCW structure through modifying the radii of the central rod and around four rods. The slow light factor can reach 5.89×10-4 by varying the radii of other four rods when the radius of the central rod is zero. Ultra small slow light factor 3.26×10-4, which is about 1/10 of that of corresponding normal CCW, can be gotten if we modify the five rods at the same time. We also find that the variation of the slow light factor caused by the changing of the radius of the central rod is very small when the radii of the around four rods are set within a certain range. Considering the manufacture of PhC, this type of CCW structure has great application value since it reduces the demand of the precision.
4. Combined with the application of slow light buffers, the corresponding computation method of CCW structure is introduced through the principle of tight binding method. The BIT length of coupled cavity waveguide and buffering capacity etc. are analyzed to obtain that the delay time and buffering capacity in CCW slow light buffering restrict each other. This means that, on the one hand, the coupling coefficient gets larger as the increase of space between cavities to reduce the group velocity; on the other hand, the guided mode bandwidth gets narrower and the BIT length gets longer to reduce the buffering capacity. The delay time of 1μs in PhC CCW of 9.78cm is implemented through calculation on different structures and it is 3 times larger than similar literatures. Buffering capacity can reach 3.3kbit. Moreover, the analytic results on CCW slow light structures shows that, when the space between cavities is smaller, the system gains smaller BIT length to increase the buffering capacity, which is of great applied values to slow light buffering; when the space between cavities is larger, the system gains larger nic crystals with a triangular lattice of air holes", J. Opt. Soc. Am. B, Vol.20, 2003,p.19221926.
Olivier S, Smith C J M, Rattier M, et al., "Miniband transmission in a photonic crystal coupled-resonator optical waveguide", Opt. Lett., Vol.26, between (?) of measurement of PhC slow light, we analyze the test principle of the slow light testbed and decide to measure the change of the equivalent dielectric constant by testing the variation of the phase in PCW. Based on the analysis, we design the testbed. The W1 PCW is fabricated with focused ion beam (FIB) method. The obtained results demonstrate that the group index curve measured with the phase-delay method has the exact same trend with that in simulations. The time-delay of the pulse is also measured, and it fits for the theoretical result calculated according to the group index with the phase-delay method, witch is about 4.7ps.
引文
验平台。用聚焦离子束方法(FIB)进行光子晶体波导制作,并对制作的W1型光子晶体波导进行慢光测试,得到其群折射率曲线,并通过光示波器进行延迟验证。
第七章：总结。概括了本论文研究的主要内容,并对后续的研究工作进行了展望。
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以上是对正六边形,正方形和圆形介质柱的二维光子晶体带隙特性进行仿真计算,将数据汇总,结果如表3-1所示。从表中可以看出,通过改变三种介质柱形状,可以使得原本不存在绝对带隙的光子晶体结构出现绝对带隙或者使原本存在的绝对带隙变得更大。具体的,对于三种形状介质柱的三角晶格结构的光子晶体,通过改变结构,最大带隙率能达到12%以上,尤其对于正方柱三角晶格光子晶体,最大带隙率F max达到15.1%。因此可以看出,以上提出的对光子晶体介质柱截面进行变形的方法,是改善介质柱光子晶体结构而获得较好带隙特性的有效途径。
本章针对三种常见的介质柱横截面分别为正六边形,正方形和圆形的二维光子晶体,使用平面波展开法,通过改变占空比,分别对其四方晶格和三角晶格结构带隙特性进行了仿真分析,计算可知介质柱结构的光子晶体绝对带隙比较小。为了得到更大的绝对带隙,在直角坐标系下,对三种介质柱截面形状进行变形,即增大X方向长度为原来长度的p倍,并以原点为中心旋转角度φ。通过调整p和φ大小来降低其结构对称性,使用平面波展开法,对其进行了详细的仿真分析后可知,结构改变后的光子晶体具有较大的带隙率。对于三种介质柱的三角晶格结构的光子晶体,最大带隙率能达到12%以上,尤其对于正方柱三角晶格光子晶体,最大带隙率达到15.1%。本章提出的增大介质柱结构二维光子晶体绝对带隙的方法为以后设计类似结构的大带隙光子晶体提供了一个重要参考,即只需要把介质柱的形状做上述相应变化,再结合具体条件和要求,就能得到较理想的带隙特性。该方法在其他文献中尚未被提及,具有一定的创新性和实用参考价值。
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由于光子晶体的微结构特性以及传输光为红外波段,光子晶体波导慢光的测试对实验条件的要求非常苛刻。本章结合测量光子晶体波导慢光的需求,首先对慢光实验平台的测试原理进行了分析,确认了通过测试光在光子晶体波导中相位变化来计算等效折射率变化的方法,并在此基础上设计了实验平台。然后对平台中所需相应器件的参数需求和设备选取进行了详细阐述,并确认了最终方案。然后用FIB方法进行了光子晶体样品制作,对新型PCW结构的透射功率进行测量,确认了其稳定性和可重复性,并分析了环境对结果的影响；然后主要针对W1光子晶体波导传输特性进行了实验测试,得出了对应的群折射率曲线,与仿真结果相比具有相同的变化趋势。最后通过时域测量光脉冲的方法证实了W1波导光脉冲较脊波导光脉冲具有时间延迟。本章确认并证实了一种测量光子晶体慢光的方法,为以后进行光子晶体慢光的研究提供了很好的基础。
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第七章：总结。概括了本论文研究的主要内容,并对后续的研究工作进行了展望。
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以上是对正六边形,正方形和圆形介质柱的二维光子晶体带隙特性进行仿真计算,将数据汇总,结果如表3-1所示。从表中可以看出,通过改变三种介质柱形状,可以使得原本不存在绝对带隙的光子晶体结构出现绝对带隙或者使原本存在的绝对带隙变得更大。具体的,对于三种形状介质柱的三角晶格结构的光子晶体,通过改变结构,最大带隙率能达到12%以上,尤其对于正方柱三角晶格光子晶体,最大带隙率F max达到15.1%。因此可以看出,以上提出的对光子晶体介质柱截面进行变形的方法,是改善介质柱光子晶体结构而获得较好带隙特性的有效途径。
本章针对三种常见的介质柱横截面分别为正六边形,正方形和圆形的二维光子晶体,使用平面波展开法,通过改变占空比,分别对其四方晶格和三角晶格结构带隙特性进行了仿真分析,计算可知介质柱结构的光子晶体绝对带隙比较小。为了得到更大的绝对带隙,在直角坐标系下,对三种介质柱截面形状进行变形,即增大X方向长度为原来长度的p倍,并以原点为中心旋转角度φ。通过调整p和φ大小来降低其结构对称性,使用平面波展开法,对其进行了详细的仿真分析后可知,结构改变后的光子晶体具有较大的带隙率。对于三种介质柱的三角晶格结构的光子晶体,最大带隙率能达到12%以上,尤其对于正方柱三角晶格光子晶体,最大带隙率达到15.1%。本章提出的增大介质柱结构二维光子晶体绝对带隙的方法为以后设计类似结构的大带隙光子晶体提供了一个重要参考,即只需要把介质柱的形状做上述相应变化,再结合具体条件和要求,就能得到较理想的带隙特性。该方法在其他文献中尚未被提及,具有一定的创新性和实用参考价值。
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本章通过平面波展开法中的超胞算法对光子晶体线缺陷波导结构的慢光特性进行了研究。当缺陷柱半径小于光子晶体介质柱半径时,随着缺陷柱半径的增加,导模中心频率向低频移动,群速度也越来越小；当增大介质柱的介电常数时,导模有相同的变化规律,针对这种现象,从介电函数在平面波展开法中的作用出发进行了探讨。然后研究了缺陷柱位置对导模慢光的影响,通过上下平移缺陷柱,得到具有更好线性的导模,此时群速度曲线相对平坦,色散值也更小。总的来说,缺陷柱的大小和介电常数的变化更多的是影响导模的慢光值,而缺陷柱位置的变化则能优化慢光的群速度色散特性。
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由于光子晶体的微结构特性以及传输光为红外波段,光子晶体波导慢光的测试对实验条件的要求非常苛刻。本章结合测量光子晶体波导慢光的需求,首先对慢光实验平台的测试原理进行了分析,确认了通过测试光在光子晶体波导中相位变化来计算等效折射率变化的方法,并在此基础上设计了实验平台。然后对平台中所需相应器件的参数需求和设备选取进行了详细阐述,并确认了最终方案。然后用FIB方法进行了光子晶体样品制作,对新型PCW结构的透射功率进行测量,确认了其稳定性和可重复性,并分析了环境对结果的影响；然后主要针对W1光子晶体波导传输特性进行了实验测试,得出了对应的群折射率曲线,与仿真结果相比具有相同的变化趋势。最后通过时域测量光脉冲的方法证实了W1波导光脉冲较脊波导光脉冲具有时间延迟。本章确认并证实了一种测量光子晶体慢光的方法,为以后进行光子晶体慢光的研究提供了很好的基础。
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