Study On Energy Band And Defects In Kagome Lattice

The Kagome lattice is made up of staggered triangles,each vertex connected to two adjacent hexagonal artificial optical microstructures known as photonic crystals.Due to its novel properties such as topological flat band and Dirac band,it has important application prospects in quantum Hall effect,quantum spin liquid,condensed matter physics,all-optical integrated circuit,laser and so on,and is one of the research hotspots in recent years.In this dissertation,Kagome lattice energy bands and defects are studied based on the plane wave expansion(PWE)method and the finite-difference timedomain(FDTD)method.Main work is as follows:1.Based on the plane wave expansion method and supercell method,the energy band structure and defect mode of Kagome lattice composed of germanium cylinder with “point-ring defect” model were calculated by Matlab software.The structure of“point-ring defect” determines the number of defect modes and their degeneration.The frequency width,the coupling of defect modes and the movement of defect frequencies can be regulated by using the two distance structure parameters of "point-ring defect".The energy localization of defect modes is related to the parity of the number of symmetry axes of "point-ring defect".The photon is well localized at the "point ring defect" with an even symmetry axis.This research will provide a new idea for the study of photonic crystal point defects and contribute to the development of resonators and narrow-band filters.2.Based on the plane wave expansion and finite-difference time-domain method,line defect modes in Kagome lattice are calculated by Bandsolve module of Rsoft software.The Fullwave module was used to analyze the transmission spectrum of line defects and simulate the transmission dynamics of beams of different wavebands in the Kagome lattice waveguide.The line defect structure was optimized by changing the parameters of the defective medium cylinder(radius and position)and inserting a new dielectric column in the center of the original dielectric column,resulting in a few-mode(two modes)Kagome lattice waveguide with wide bandwidth(0.08888ωa/2πc).The results improve the study of Kagome lattice line defects and provide a new thought for the design of waveguide structures,which implements the large capacity,long distance signal transmission.The Kagome lattice waveguide with wide bandwidth and fewmode will have important applications in photonic integration.3.The transmission characteristics of the 60° bend in Kagome lattice are analyzed and the frequency divider based on Kagome lattice is designed.A filter with good channel isolation is implemented in Kagome lattice by controling the coupling between point defects and waveguides.The research provides ideas for the design of Kagome lattice waveguide devices and lay the foundation for the fabrication of photonic crystal devices with good properties.