Numerical Simulation And Optimization Of Photonic Crystal Microcavity Using Finite Element Methods

Photonic crystals(PhCs)are optical materials with good light control properties,which have the advantages of high integration and low volume when they use to make optical devices.Photonic crystal microcavity which has strong practical significance is one of the important applications.Numerical method research is an important means to understand the characteristics of microcavity.In this thesis,two-dimensional photonic crystal microcavity is investigated by finite element method(FEM).Firstly,the mathematical simulation method of electromagnetic wave propagation in 2D photonic crystal microcavity is studied.Finite element program design and numerical simulation are carried out via COMSOL software.The wave equation is derived from Maxwell’s equations,and FEM is used to solve it.Then,we could obtain band structure for twodimensional PhCs in TE and TM modes.Furthermore,PML boundary condition is added to simulate infinite space,which be meaningful to solve the microcavity numerically.By analyzing the influence of the radius of center defect and dielectric constant,it shows that the variation of radius and dielectric constant can increase the Q factor by 9 times and 2 times at most respectively.Both methods presented in the thesis reduce the modal area,a better microcavity structure is obtained compared to the original structure.Secondly,we further study the numerical simulation of 2D dispersive photonic crystal microcavity.We solve the problems including the band gap solution of dispersive crystals and the numerical simulation of dispersive microcavity.For a 2D dispersive photonic crystal whose permittivity is dependent on frequency,its band structure problem is formulated as a nonlinear eigenvalue problem.In this case,we present a novel method in which we choose approximate solutions as the initial value for iteration and solve this nonlinear problem based on inverse iteration method.Consequently,the band structure of dispersive photonic crystal can be obtained numerically.In addition,the dispersive photonic crystal microcavities whose dielectric function of medium is expressed by Drude model are constructed,which are solved by the algorithm investigated in this thesis numerically.Numerical results show that two dispersive microcavities given have excellent performance,whose theoretical value of Q-quality factor can reach 105.In this thesis,the numerical simulation of 2D photonic crystal microcavity is completed by FEM,and the performance of microcavity is optimized by adjusting the structural parameters.Our work provides theoretical basis for 2D dispersion microcavity which be helpful to the application of it in the future.