Study On Self-collimation Effect In Photonic Crystals And Its Applications

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.