Research On The Finite-difference Time-domain Algorithm For The Electromagnetic Characteristics Of Periodic Structures

Periodic structure refers to objects formed by periodic arrangement of specific media in space.Because of its special properties,the study of its electromagnetic properties has always been a hot topic in the field of electromagnetics.Periodic structures have been widely used in frequency selective surfaces,periodic array antennas,random rough surfaces,and so on.The finite difference time domain algorithm has the advantages of simple principle and easy programming.It has been widely applied in the analysis of periodic structures in many fields of electromagnetic applications.When the plane wave is incident perpendicularly,there is no time delay.The periodic boundary condition can be adopted directly,and the field value inside the boundary is replaced by the field value inside the boundary.When the plane wave is oblique incidence,there is a phase delay in the space of the electromagnetic field,and there is a field value of the future time in the use of the periodic boundary conditions.So the traditional finite difference time domain method is difficult to deal with the periodic structure of the plane wave under the oblique incidence condition.The main idea of this method is to introduce new intermediate variables to replace the original electric field and the unknown quantity of the magnetic field,so as to construct a new expression between the unknown quantities so as to eliminate the phase shift on the boundary of the periodic structure.The main work of this paper is to introduce some basic theories of the analysis of periodic structures in the finite difference time domain algorithm,including the basic FDTD iterative formula,the absorbing boundary condition,the one and two dimensional Floquet theorem and the periodic boundary conditions,and deduce the iterative formula of the FDTD algorithm for the splitting of the splitting field under the plane wave oblique incidence.Finally,with the introduction of the dispersive medium,the convolution formula of three common dispersive media,Debye,Drude and Lorentz dispersive medium,and the recursive iterative formula of the auxiliary differential equation method are derived,and the convolution method and auxiliary differential equation method suitable for any dispersive medium are derived.