Analysis Of Thin-layer Artificial Electromagnetic Structures By Finite-difference Time-domain Method Based On Surface Impedance Boundary Conditions

In recent years,metasurfaces have gradually replaced metamaterials due to their low loss and cost,and have become a research hotspot in scientific research.However,the metasurface has a sub-wavelength thickness,and a fine mesh is required for modeling and simulation using a time-domain numerical method such as finite-difference time-domain method,which will occupy a large amount of computer memory and consume a long simulation time.Therefore,an efficient electromagnetic simulation method is urgently needed to analyze metasurface structures.Based on the predecessors,metasurfaces are equivalent as impedance surfaces in this paper,and the metasurface structures are replaced by surface impedance boundary conditions,and further a finite-difference time-domain algorithm based on surface impedance boundary conditions is proposed to analyze metasurface structures.The main work of this paper is as follows:In chapter two,the basic theory of the finite-difference time-domain algorithm is introduced,including the three-dimensional iterative formula of the electromagnetic field components and the stability conditions to be satisfied during the iteration.At the same time,a finite-difference time-domain algorithm based on generalized sheet transition conditions for analyzing metasurface structures is proposed,and the accuracy of the method is verified by a numerical example.In chapter three,the finite-difference time-domain method applied surface impedance boundary conditions to graphene structures is introduced.Because the surface impedance of graphene can be expressed by the reciprocal of its surface conductivity,when dealing with the dispersion problems,only surface conductivity in the form of Drude model is needed to characterize graphene in the surface impedance boundary conditions.Then the effects of different chemical potentials and carrier relaxation times on the electromagnetic properties of graphene are analyzed using the method mentioned above.And a broadband absorber is further designed.It can achieve an absorption bandwidth of about 0.82 THz at central frequency about 1.68 THz.In chapter four,the FDTD method based on the surface impedance boundary condition(SIBC)is introduced in detail.Firstly,combining with the equivalent transmission line circuit model,the reflective metasurface is equivalent to an effective impedance surface,and the GSTC method is used to extract the surface impedance of the metasurface.For the equivalent surface impedance,the vector fitting technique is used to synthesize it into a rational fraction accumulation form.Furthermore,the FDTD method based on impenetrable and penetrable surface impedance boundary condition are proposed,respectively,and the accuracy of these methods is verified by a series of numerical examples.In the process of FDTD iterative solution,the surface impedance boundary conditions are used to replace the metasurface,which greatly reduces the transverse and longitudinal mesh grids,and saves the computer memory and simulation time.Finally,the simulation accuracy of SIBC-FDTD method under different coupling conditions is discussed through the simulation analysis of reflectarray.The simulation results show that the method proposed in this paper has higher accuracy when the coupling between elements is weak,while the simulation accuracy of the method proposed in this paper is reduced when the coupling between elements is strong.