The Research Of Photonic Crystal Properties Based On The Precise Integration Time Domain

The optical crystal,with its unique characters such as “photonic band gap” and“photonic localization”,has been widely used in optical waveguides,optical fibers,filters,light emitting diodes,microwave antennas and so on.The analysis of the transmission characteristics and defect mode characteristics in photonic crystal is very important,and it has theoretical significance for the structural design and performance optimization of various optical devices.So seeking accurate and stable numerical methods become a focus research field.In this paper,the transmission characteristics and defect mode characteristics of photonic crystal are analyzed and calculated based on the precise integration method in time domain.The main contributions are as follows.(1)A precise integration time domain method is proposed to solve the transmission characteristics of photonic crystals,and its accuracy and stability are analyzed.From the first order Maxwell equations,the Yee cell differential technique is employed to discrete the Maxwell equations in the spatial domain.Then the discretized Maxwell equations with absorption boundary conditions and the expression of excitation source are rewritten in the standard form of the first order ordinary differential equation.According to the precise division of time step and the additional theorem of exponential matrix,the high precision integration is used to solve the homogeneous solution.To obtain the discretized electric and magnetic fields,the particular solution must be solved based on excitation and then be added to the homogeneous solution.The transmission characteristics of photonic crystals are obtained by the Flourier transformation.Practical calculation of photonic crystals is carried out by the precise integration time domain and the results are compared with those of the finite difference time domain method and the fourth order Ronge Kutta method.Compared with the finite difference time domain method,the precise integration time domain method has the characteristics of accurate and stable,which not only overcomes the limitation of the Courant stability condition on the time step,and the calculation accuracy is not affected by the time step.Compared with the fourth order Runge Kutta method,the precise integration time domain method is more accurate,stable and efficient.The presented method provides a new effective analytical method for the transmission characteristics of photonic crystals.(2)The defect mode properties of photonic crystals with doping defect layer are researched by the precise integration time domain method.The influence of cycles,optical thicknesses and refractive index of defect layer on the defect mode characteristics are systematically discussed.A photonic crystal model with doping defect structure is established,and the formula of the defect mode quality factor is given.based on the precise integration time domain algorithm,the defect mode characteristics of the photonic crystal containing defect layer are simulated.The defect mode quality factor of photonic crystal with defect is solved by the precise integration time domain and the results are compared with those of the finite difference time domain method.Numerical results show the proposed method can accurately and stably analyze the defect mode characteristics of photonic crystal.The influence of cycles,optical thicknesses and refractive index of defect layer on the defect mode characteristics are analyzed in detail.It is found that the quality factor and transmission peak of the defect mode are significantly affected by the number of cycles,optical thickness and the refractive index,and the position of defect mode is determined only by the optical thickness of defect layer.According to the relationship between quality factor and defect peak,the fabrication of high performance optical devices is also discussed.