光子晶体自准直现象及其应用研究
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摘要
光子晶体是一种人工周期介质结构，在集成光学、全光通信等领域有着广泛的应用。最近几年，光子晶体的异常色散特性引起了越来越多的关注，成为一个新的研究热点，主要包括负折射、自准直、超棱镜等效应。其中，自准直效应为控制光的传输提供了一种崭新的方法，在集成光学中有着重要应用。本文对光子晶体中的自准直现象做了系统研究和深入分析，采用理论分析与数值计算相结合的方法，对光子晶体的可调自准直、宽带全角自准直、偏振无关的全角自准直以及宽带自准直亚波长成像等特性进行了深入研究，提高了光子晶体的自准直性能。并基于自准直效应，设计了多种分束器和光开关等光子晶体器件。本文主要完成了如下几个方面的工作：
（1）从色散曲面与等频线分析入手，系统研究了光子晶体自准直效应原理，讨论了最大自准直角与等频线的关系。分析了自准直虚拟波导的传输特性，并计算了入射角对虚拟波导传输性能的影响。
（2）提出并设计了自准直光束的T型、Y型以及1×3分束器。首先通过在正方晶格光子晶体中引入一个V型空气隙，设计了T型自准直光束分束器与1×3分束器。然后通过在三角晶格光子晶体中引入线缺陷，实现了自准直光束的60°弯曲；并通过引入V型线缺陷，设计了Y型自准直光束分束器与1×3分束器。目前自准直光束的分束形式单一，设计的T型与Y型分束器，使自准直光束有了更灵活的分束方式，以满足不同情形的应用。设计的1×3分束器可以将自准直光束一次性分成三束，不但效率高于普通的两个1×2分束器的组合，而且结构也更紧凑。
（3）优化设计了基于空气环光子晶体的自准直光束偏振分束器。这种分束器可以通过选择合适的内环与外环半径，更为便捷地调节TE模与TM模的自准直频率，提高偏振无关的自准直带宽，因而具有更高的设计自由度，在设计阶段可以根据情况灵活地调节参数以达到最佳的性能。
（4）研究了基于液晶材料与电磁感应透明材料光子晶体的可调自准直特性，并设计了自准直光开关。首先研究了液晶旋转角对自准直频率的影响，并基于液晶光子晶体的带隙可调性和自准直特性，设计了自准直光子晶体光开关。然后研究了基于半导体量子阱电磁感应透明材料光子晶体的可调自准直特性，并设计了基于电磁感应透明材料光子晶体的全光开关。
（5）成功实现了基于二维菱形晶格光子晶体的宽带全角自准直、偏振无关的全角自准直以及自准直亚波长成像。首先计算了二维菱形晶格光子晶体的第一布里渊区及高对称点，并对其平面波展开法做了详细的推导。接着分析了菱形晶格光子晶体的带隙特性，并讨论了介质填充率、晶格角对带隙特性的影响。然后，基于菱形晶格光子晶体的独特性质，通过参数优化，实现了带宽为17.42%的宽带全角自准直，并对偏振无关的全角自准直进行了探讨。最后，研究了菱形晶格光子晶体的宽带自准直亚波长成像特性。
Photonic crystals (PCs) are periodic dielectric structures, which have been widelyused in the scientific and engineering fields, such as the integrated optics and all-opticalcommunications. In recent years, the unusual dispersion properties of PCs, including thenegative refraction, self-collimation (SC), and super prism, have attracted more andmore interest and become an active research area. Among them, the SC effect provides abrand-new way of controlling the light propagation and plays an important role in theintegrated optics. In this dissertation, the SC phenomenon is studied systematically andthoroughly. With theoretical analyses and numerical calculations, the SC characteristicsof the PCs are studied in detail, including the tunable SC, broadband all-angle SC,polarization-independent all-angle SC, and broadband subwavelength imagingproperties. These studies improve the SC performance in PCs. Some useful PC devicesare proposed based on the SC effect, such as the beam splitters, polarization beamsplitters (PBS) and optical switches. The main works are as follows:
(1) By analyzing the dispersion surfaces and equi-frequency contours (EFCs), thefundamental principle of the SC effect in PCs is studied in detail. The relationshipbetween the maximum self-collimating angle and the EFCs is discussed. A virtualself-collimating waveguide is designed and the transmission properties are analyzed.The impact of the incident angle on the transmission performance is discussed.
(2) A T-shaped, a Y-shaped and two one-to-three beam splitters are proposed. Atfirst, by introducing a V-shaped air gap into a square-lattice PC, a T-shaped and aone-to-three beam splitters are proposed. Then, a60°beam bending for self-collimatedbeam is realized by introducing a line defect into a triangular-lattice PC. With aV-shaped defect instead of the line defect, a Y-shaped and a one-to-three beam splittersare presented. These splitters provide more flexibility in the splitting ways for theself-collimated beams which are expected to satisfy more applications. the proposedone-to-three beam splitters, which can split light beam into three sub-beams in one go,are more compact and efficient than the combination of two one-to-two splitters.
(3) A PBS is optimally designed based on the SC effect in the two-dimensional (2D) annular PCs. The self-collimating frequency for both TE and TM modes can be adjustedeasily by choosing proper inner and outer radii of the air ring. The bandwidth forpolarization-independent SC can also be enhanced. Such structures provide moreflexibility in the design of PBS. The optimum performance can be achieved by adjustingthe parameters freely in the design stage.
(4) The tunabilities of SC in PCs based on the liquid-crystal (LC) materials andelectromagnetically induced transparent (EIT) materials are investigated. Firstly, theimpact of the twist angle of LCs on the self-collimating frequency is studied. An opticalswitch for self-collimated beams is proposed with LC PCs based on the tunability of thebandgap properties and SC effect. Then, the tunable SC in PCs that made of EITmaterials is studied and an all-optical switch is designed.
(5) The broadband all-angle SC, polarization-independent all-angle SC, andbroadband subwavelength imaging are realized in the2D rhombic-lattice PCs. Firstly,the first Brillouin zone (FBZ) and the high symmetrical points are calculated. The planewave expansion method in such structures is deduced. The bandgap properties areanalyzed. The impacts of the filling ratio and the lattice angle on the bandgap propertiesare discussed. Then, by optimizing the parameters, the all-angle SC with a broadbandwidth of17.42%is realized in the rhombic-lattice PCs. Meanwhile, thesimultaneous SC for both TE and TM modes is extended to all-angle operation in suchstructures. At last, the broadband subwavelength imaging properties in rhombic-latticePCs are also investigated.
（1）从色散曲面与等频线分析入手，系统研究了光子晶体自准直效应原理，讨论了最大自准直角与等频线的关系。分析了自准直虚拟波导的传输特性，并计算了入射角对虚拟波导传输性能的影响。
（2）提出并设计了自准直光束的T型、Y型以及1×3分束器。首先通过在正方晶格光子晶体中引入一个V型空气隙，设计了T型自准直光束分束器与1×3分束器。然后通过在三角晶格光子晶体中引入线缺陷，实现了自准直光束的60°弯曲；并通过引入V型线缺陷，设计了Y型自准直光束分束器与1×3分束器。目前自准直光束的分束形式单一，设计的T型与Y型分束器，使自准直光束有了更灵活的分束方式，以满足不同情形的应用。设计的1×3分束器可以将自准直光束一次性分成三束，不但效率高于普通的两个1×2分束器的组合，而且结构也更紧凑。
（3）优化设计了基于空气环光子晶体的自准直光束偏振分束器。这种分束器可以通过选择合适的内环与外环半径，更为便捷地调节TE模与TM模的自准直频率，提高偏振无关的自准直带宽，因而具有更高的设计自由度，在设计阶段可以根据情况灵活地调节参数以达到最佳的性能。
（4）研究了基于液晶材料与电磁感应透明材料光子晶体的可调自准直特性，并设计了自准直光开关。首先研究了液晶旋转角对自准直频率的影响，并基于液晶光子晶体的带隙可调性和自准直特性，设计了自准直光子晶体光开关。然后研究了基于半导体量子阱电磁感应透明材料光子晶体的可调自准直特性，并设计了基于电磁感应透明材料光子晶体的全光开关。
（5）成功实现了基于二维菱形晶格光子晶体的宽带全角自准直、偏振无关的全角自准直以及自准直亚波长成像。首先计算了二维菱形晶格光子晶体的第一布里渊区及高对称点，并对其平面波展开法做了详细的推导。接着分析了菱形晶格光子晶体的带隙特性，并讨论了介质填充率、晶格角对带隙特性的影响。然后，基于菱形晶格光子晶体的独特性质，通过参数优化，实现了带宽为17.42%的宽带全角自准直，并对偏振无关的全角自准直进行了探讨。最后，研究了菱形晶格光子晶体的宽带自准直亚波长成像特性。
Photonic crystals (PCs) are periodic dielectric structures, which have been widelyused in the scientific and engineering fields, such as the integrated optics and all-opticalcommunications. In recent years, the unusual dispersion properties of PCs, including thenegative refraction, self-collimation (SC), and super prism, have attracted more andmore interest and become an active research area. Among them, the SC effect provides abrand-new way of controlling the light propagation and plays an important role in theintegrated optics. In this dissertation, the SC phenomenon is studied systematically andthoroughly. With theoretical analyses and numerical calculations, the SC characteristicsof the PCs are studied in detail, including the tunable SC, broadband all-angle SC,polarization-independent all-angle SC, and broadband subwavelength imagingproperties. These studies improve the SC performance in PCs. Some useful PC devicesare proposed based on the SC effect, such as the beam splitters, polarization beamsplitters (PBS) and optical switches. The main works are as follows:
(1) By analyzing the dispersion surfaces and equi-frequency contours (EFCs), thefundamental principle of the SC effect in PCs is studied in detail. The relationshipbetween the maximum self-collimating angle and the EFCs is discussed. A virtualself-collimating waveguide is designed and the transmission properties are analyzed.The impact of the incident angle on the transmission performance is discussed.
(2) A T-shaped, a Y-shaped and two one-to-three beam splitters are proposed. Atfirst, by introducing a V-shaped air gap into a square-lattice PC, a T-shaped and aone-to-three beam splitters are proposed. Then, a60°beam bending for self-collimatedbeam is realized by introducing a line defect into a triangular-lattice PC. With aV-shaped defect instead of the line defect, a Y-shaped and a one-to-three beam splittersare presented. These splitters provide more flexibility in the splitting ways for theself-collimated beams which are expected to satisfy more applications. the proposedone-to-three beam splitters, which can split light beam into three sub-beams in one go,are more compact and efficient than the combination of two one-to-two splitters.
(3) A PBS is optimally designed based on the SC effect in the two-dimensional (2D) annular PCs. The self-collimating frequency for both TE and TM modes can be adjustedeasily by choosing proper inner and outer radii of the air ring. The bandwidth forpolarization-independent SC can also be enhanced. Such structures provide moreflexibility in the design of PBS. The optimum performance can be achieved by adjustingthe parameters freely in the design stage.
(4) The tunabilities of SC in PCs based on the liquid-crystal (LC) materials andelectromagnetically induced transparent (EIT) materials are investigated. Firstly, theimpact of the twist angle of LCs on the self-collimating frequency is studied. An opticalswitch for self-collimated beams is proposed with LC PCs based on the tunability of thebandgap properties and SC effect. Then, the tunable SC in PCs that made of EITmaterials is studied and an all-optical switch is designed.
(5) The broadband all-angle SC, polarization-independent all-angle SC, andbroadband subwavelength imaging are realized in the2D rhombic-lattice PCs. Firstly,the first Brillouin zone (FBZ) and the high symmetrical points are calculated. The planewave expansion method in such structures is deduced. The bandgap properties areanalyzed. The impacts of the filling ratio and the lattice angle on the bandgap propertiesare discussed. Then, by optimizing the parameters, the all-angle SC with a broadbandwidth of17.42%is realized in the rhombic-lattice PCs. Meanwhile, thesimultaneous SC for both TE and TM modes is extended to all-angle operation in suchstructures. At last, the broadband subwavelength imaging properties in rhombic-latticePCs are also investigated.
引文
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