Study On The Propagation Characteristics Of Pulses In Nonlinear Media Based On FDTD Algorithm

With the development of computer technology,the computing ability of computers has been greatly improved.It has been applied more and more widely in the field of computational electromagnetics.Many complex electromagnetic problems can be effectively solved by using emerging and continuously improved numerical methods.Thus,the subject of computational electromagnetics has been formed,and a variety of methods for calculating electromagnetics have been extended.In 1966,Yee proposed the Finite-difference Time-domain algorithm.Its characteristics are simple,easy to implement,and convenient for parallelism.It is widely applied to solve the computational electromagnetic problems of complex models.In recent years,scholars have been studying various dispersive materials and nonlinear materials frequently,and more and more nonlinear materials have been added into the structure,which is used to enhance the properties of materials.For example,adding Kerr nonlinear material into photonic crystal can form soliton wave,which is of great significance for lossless optical fiber communication.Therefore,the theoretical analysis of the dispersive material and nonlinear material is particularly important.In this thesis,we first deduce the basic iterative equation of FDTD algorithm from the Maxwell equation,and analyze the numerical stability condition and boundary condition of the algorithm.Then,based on the FDTD algorithm,combined with the auxiliary differential equations,we use the existing dispersion models and nonlinear models(such as Kerr nonlinearity and Raman nonlinearity),to form an auxiliary differential equation FDTD algorithm.The above models can be effectively solved by using this algorithm.In this thesis,we also use the algorithm to numerically simulate the pulse propagation problem in photonic crystals doped with nonlinear materials,and finds that soliton waves are formed under the interaction of pulse broadening and self-phase modulation.Then,for the nonlinear problem in two-level atomic system,the Maxwell-Bloch equation needs to be solved.Therefore,the FDTD algorithm is combined with the predictive-correction method to construct the predictive-correction FDTD algorithm and program the algorithm.This method can be used to analyze the self-induced transparency effcets of 2? pulses without using any approximation(slow-wave approximation and the rotating-wave approximation),as well as to study the important influence of time-dependent non-linearity on the temporal evolution of two-level atomic systems.The effect of using the time derivative can be used to design an ultra-fast,single-cycle pump pulse that can completely reverse the two-level atom system.