Research On Finite Element Method For Several Kinds Of Periodic Structures And Its Application In Photonic Crystal Waveguides

Photonic crystal is a class of artificial material with periodic permittivity or permeability,which has the photonic band gap.Various photonic crystal devices prepared by using the existence of the photonic band gap have become a research hotspot in recent years due to their high integration,good optical performance,large transmission capacity and small volume.In practice,using the applicable numerical calculation methods are easy and efficient to numerically research the performance of photonic crystal devices without expensive research tools and complex operation.In this thesis,the two-dimensional photonic crystal device structures have been studied by using the finite element analysis and numerical simulation.Based on the finite element method,we have constructed the mathematical models for the calculation of photonic band gap structure,the analysis of photonic crystal waveguide bends and beam splitters in two-dimensional photonic crystals.The transmission performance of waveguide bends and beam splitters has been numerically simulated,and two simple and efficient optimization methods have been proposed to optimize the photonic crystal waveguide bends and beam splitters,respectively.For the design and optimization of two-dimensional photonic crystal waveguide bends,a mathematical model for the structure analysis has been constructed,and the transmission performance of waveguide bends has been numerically simulated and analysed.A simple and effective optimization design method has been proposed to improve the transmission performance of waveguide bends,and the effectiveness of the optimization method has been verified by waveguide bends with different structures and materials.Specifically,we have designed and optimized silicon photonic crystal waveguide bends of 60°,Z-shaped,Y-shaped and 120°,for a two-dimensional photonic crystal with a triangular lattice.For the two-dimensional gallium antimonide photonic crystal with a triangular lattice,we have completed the optimization design of three photonic crystal waveguide bends,namely 60°,Z-shaped and Y-shaped waveguide bends.The success of the optimized design for these waveguide structures with different materials and shapes fully shows that the design method we proposed,for optimization of photonic crystal waveguide bends,is simple and effective.For the design and optimization of the beam splitters in two-dimensional photonic crystals,we have constructed the mathematical model of the beam splitter analysis,using the finite element method to complete the numerical simulations of Y-shaped beam splitters.An optimization algorithm based on alternating iterative algorithm has been used to improve the transmission performance of the 1 × 2,1 × 4 Y-shaped beam splitters,based on gallium antimonide.The numerical simulations of two Y-shaped beam splitters fully demonstrated the practicability and effectiveness of the optimization method.In this thesis,the photonic band gaps of photonic crystals for several new materials and the structural design optimization of photonic crystal waveguide bends and beam splitters have been studied by using the finite element method.The numerical results show that the optimization design methods we proposed are simple and efficient,which provide new ideas and techniques for optimizing the optical structure design.Gallium antimonide has been used to design the photonic crystal,waveguide bend and beam splitter structures,which provided a theoretical and numerical experimental support for the application of new dielectric materials in photonic crystal devices.