Analysis Of Photonic Crystal Transmission Characteristics Based On Optimized Symplectic Multi-resolution Time-domain Method

Photonic crystal is a new type of synthetic material which is composed by two or more media with different dielectric constants arranged periodically in space.Its two main characteristics are the existence of local characteristics and photonic band gap,which makes it have high theoretical research value and broad industrial application prospect in the field of science and technology at present and in the future.In recent years,the great improvement of computer performance has provided methods for the processing of complex data.Various new numerical methods have appeared in the theory of computational electromagnetism.In the process of studying the transmission characteristics of photonic crystals,the traditional finite-difference time-domain(Finite-Difference Time-domian,FDTD)method has low calculation accuracy and large dispersion error.In view of this phenomenon,the symplectic multi-resolution time-domain(Symplectic Multi-Resolution Time-Domain,S-MRTD)method is applied to the numerical simulation of photonic crystals for the first time in this paper.The S-MRTD method introduces symplectic integral technique and wavelet scale function difference approximation in time and space respectively.In the long-term electromagnetic simulation,not only the internal symplectic structure of maxwell's equations is maintained in time direction,but also the numerical calculation accuracy is improved in space,and the numerical dispersion error is reduced.In this paper,the symplectic operators of symplectic multi-resolution time-domain method is optimized.On this basis,the optimized symplectic multi-resolution time-domain method is introduced into the photonic crystal to analyze and discuss the transmission spectrum and band gap range of the photonic crystal.In order to study the transmission characteristics of photonic crystals by optimizing the symplectic multi-resolution method,the following works are carried out in detail:(1)This paper introduces the significance of this topic,briefly introduces photonic crystals,and explains the continuous optimization and innovation of the FDTD method.The basic characteristics,manufacturing methods and theoretical research methods of photonic crystals are described in detail.Finally,some industrial applications of photonic crystals are listed.(2)From the basic multi-resolution time-domain analysis method and the basic theoretical knowledge of symplectic integral technology,The iterative formula of photonic crystal with S-MRTD method is derived.The absorption boundary condition of the perfectly matched layer is introduced,and the iterative formula of the perfectly matched layer absorption boundary condition based on the split-field technique is given.Then,the influence of the number of PML(Perfectly Matched Layer)layers are verified by using a dipole radiation example,and a suitable PML layers is selected.Finally,a Gaussian pulse excitation source suitable for studying photonic crystal is selected.(3)On the basis of(2),two methods for optimizing symplectic operators are presented:optimization of symplectic operators by error function and time reversible constraints and optimization of symplectic operators by growth factor and time reversible constraints.Then according to the dispersion equation of the S-MRTD,the maximum values of the time stability and stability constant of each order symplectic operator are discussed in detail.The comparisons of symplectic operators used in some literatures are cited,and the relative phase velocity error changes with spatial resolution and spherical angle are simulated respectively.The optimized symplectic operator is verified by the square cylinder conductor scattering.Finally,an optimal set of 4-stage 3-order symplectic operators is selected.(4)Firstly,the optimized symplectic multi-resolution time-domain method is applied to photonic crystals,and the advantages and disadvantages of the method and the traditional FDTD method in time domain are discussed.The simulation results verify that the proposed method outperforms the FDTD method in terms of computation time and cpu memory consumption.Then,based on the simulation of the example,the effects of period number?dielectric ratio ? dielectric layer thickness ratio ? material position on the band gapcharacteristics of the photonic crystal are discussed.Subsequenlty,the method is introduced into the ternary dielectric layer photonic crystal.The difference of band gap structure characteristics between ternary dielectric layer photonic crystal and two kinds of dielectric layer photonic crystal and the influence of dielectric constant of outermost dielectric on the band gap are observed.Compared with two dielectric layer photonic crystals,increasing one dielectric layer can change the band gap width and amount.Finally,the band gap characteristics of photonic crystals with defects are discussed,from the simplest single defect layer to the mirror symmetry photonic crystals structure and then to a multi-defect photonic crystals geometry.The band gap of photonic crystal structure with mirror defect has a peak value of nearly 40% higher than that of single defect layer photonic crystals,which can be applied to the manufacture of ultra-narrow band filter.