Research On Calculation Accuracy Of Medium Dispersion Model For Finite-difference Time-domain Algorithm

Finite-Difference Time-Domain(FDTD)has been developed into a mature engineering electromagnetic numerical method for dealing with non-uniform and anisotropic dispersive media.When the physical mechanism of the electromagnetic interaction of metal micro-nano composite structures is studied using the FDTD algorithm,due to the characteristics of sub-wavelength micro-nano structures such as "field localization" and "mode resonance",the calculation results are extremely sensitive to the changes of physical parameters of medium such as dispersion.The approximate error of the algorithm parameters due to the mismatch of accuracy may be further amplified in the local resonance environment,and even the pseudo-valued parasitic fields may be caused.The frequency-dependent metal dielectric coefficient is a key medium parameter with dispersion characteristics in FDTD calculation.To a large extent,the calculation accuracy of the algorithm is determined by the accuracy of the description of the metal dielectric coefficient by the dispersion model.The approximate validity of the commonly used dispersion relation Drude or Drude-Lorentz model is only applicable to a limited frequency range.Since FDTD is a wide-band solution method,the obvious medium dispersion model errors will be caused by this dispersion distortion.In this thesis,the FDTD calculation accuracy of the basic dispersion model is analyzed and verified through numerical experiments,and the effects of the Drude model,the Drude-lorentzs model and the L4(4-Lorentz-pole pairs)model on the dielectric coefficient of gold and silver media are explored.Then the Drude2cp(critical point)model is studied in depth,and its calculation accuracy is analyzed by an example.The influence of media dispersion model error on the calculation accuracy of the FDTD algorithm is mainly discussed.The main research works are of this paper as follows:1.The typical dielectric dispersion model is discussed and analyzed.The RC-FDTD algorithm,the Z-FDTD algorithm and the ADE-FDTD algorithm used to deal with dispersive media are also discussed and analyzed,and the calculation accuracy characteristics of each algorithm are analyzed.The calculation accuracy of the FDTD algorithm is analyzed,and three kinds of errors in the calculation process of FDTD are discussed: algorithm errors,hardware calculation errors,and medium dispersion model errors.The reasons for the different errors are explained.2.The propagation of electromagnetic wave in dispersion medium is simulated and analyzed by numerical examples.The numerical experiments show that: in the basic dispersion model,the calculation accuracy of the TRC-FDTD algorithm and the ADE-FDTD algorithm is equivalent,which is superior to the Z-FDTD algorithm.But there is a certain deviation between them and the analytical solution.3.As an important foundation of the FDTD algorithm,the metal dielectric coefficient dispersion model and its algorithm implementation method are analyzed.The effect of the Lorentz resonance term on the dielectric coefficient of the gold and silver medium is discussed in detail.It is proved through numerical experiments that the accuracy of the fitting number of the Lorentz resonance term and the dielectric coefficient is not a linear correspondence relationship.Simply adding the Lorentz term does not further improve the accuracy of the dielectric coefficient,but the complexity of the FDTD algorithm implementation is greatly increased.4.The electronic state characteristics of the metal are analyzed and summarized by the band theory,and the dielectric coefficient model is imported.The dielectric coefficient Drude2 cp model is obtained and compared with two typical metal dispersion correction models such as the L4 model and the Drude-2lorentz model.Numerical experiments show that the calculation accuracy of the Drude2 cp model is the highest and the error between it and the real dielectric coefficient of gold and silver medium is the smallest.The Drude2 cp model not only can more accurately describe the complex dielectric effects caused by transitions between metal asymmetric linear bands,but also reduce the introduction of multiple Lorentz terms at resonance points,which makes the expression of dielectric coefficient more concise and facilitates the implementation of FDTD algorithm.5.The basic idea of implementing the Drude2 cp material plug-in has been elaborated,and the plug-in is imported into the material library of Lumerical FDTD software.The calculation accuracy of the Drude2 cp model in the wavelength range of 200 nm to 1000 nm is verified by an example analysis of the transmission enhancement of a three-dimensional silvermicro-nano composite structure.Experiments show that the calculation accuracy of the Drude2 cp model at low frequency is similar to that of the Drude model,and the calculation accuracy of the Drude2 cp model at high frequencies is superior to the Drude model and the Drude-2lorentz model.