Study Of FDTD For Dispersive Media And Related Problems Based On DSP

The transient electromagnetic problems with dispersive medium play an important role in stealth technology, bio-electromagnetics, and many other areas. Combination of digital signal processing (DSP) theory and technology, the Finite-Difference Time-Domain (FDTD) algorithms for dispersive medium and related problems are studied and a number of practical issues are analyzed using the proposed new methods.Combining with the Semi-Analytical Recursive Convolution (SARC) algorithm in DSP techniques, a novel FDTD update formulas for the analysis of electromagnetic characteristic of dispersive objects is proposed, namely as SARC-FDTD algorithm in here. In this scheme, the absolute stability, high accuracy, less storage and high effectiveness are retained, and a unified update formulation for general dispersive media, i.e., Debye, Drude, Lorentz and hybrid model is possessed. The SARC FDTD can therefore be applied to the analysis of general dispersive media provided that the poles and corresponding residues in dispersive medium model of interest are given. The complex derivation of coefficients in update formulas for the specified dispersive model is not requested and the separate treatment for a variety of dispersion media model in the existing RC-FDTD method is avoided.A novel SARC-FDTD algorithm for the dispersive medium described with high order rational fraction model based on the cascade implementation of Infinite Impulse Response (IIR) filter in DSP techniques is presented. The rational fraction is one of the dispersive models that can accurately and efficiently approximate to the complicated variation of the parameters of dispersive medium with the frequency. In this method, the high-order rational fraction model in frequency domain is firstly expressed as the product of a series low-order rational fraction and is further transformed into the convolution of a series complex exponential function responding to the each low-order rational fractions in time domain. Finally, the convolution is solved by the SARC-FDTD. The FDTD analysis of transient electromagnetic problems for dispersive medium with high-order rational fraction and asymptotic stability model is solved. It is applied to the analysis of dielectric described with wide-band Lorentz model, narrow-band Lorentz model and border-line case.An improved Z transformation is presented and improved FDTD method is implemented. The classical impulse invariance method in Z-transform theory is found to be incorrect and inaccurate when the impulse response is discontinuous at initial time t=0. Such inaccuracy results in higher numerical errors if it is used to develop the update equations for frequency-dependent FDTD. Thorough discussion of corrected impulse invariance method in the realm of Z-transform, a novel ZT-FDTD update formulas for dispersive media is discussed by the relation of polarization P with electric field E. Compared with the commonly used ZT-FDTD, the storage variables in the improved ZT-FDTD are reduced and high accuracy is achieved for dispersive media which exhibit discontinuity at t=0 in the time domain susceptibility function.An improved shifted operator (SO) FDTD method for general dispersive medium based on the implementation of IIR filter in DSP techniques is presented. Combining with the improved state-space equation of transposed direct-â…¡structure of IIR filter and cascade implementation, the update formulas of improved SO-FDTD are obtained. Compared with the commonly used SO-FDTD, the storage variables in the improved SO-FDTD are reduced by 33% and computational efficiency is also increased. The simple coefficients for high-order rational fraction model can be obtained in the novel scheme.A novel SO-FDTD scheme for high-order Debye, Lorentz and Drude dispersion model is presented as well. The transformation of low-order rational fraction into high-order form in commonly used SO-FDTD is avoided and derivation of the update formulas is simplified. A unified update formula is possessed for three typical kinds of dispersive model i.e. Debye, Lorentz and Drude medium and is suitable for dealing with high-order dispersive media as well as the hybrid model media. The general computational program can be conveniently developed.The novel Uniaxial Perfectly matched layers (UPML) absorbing boundary and Complex Frequency-Shifted PML (CFS-PML) absorbing boundary based on improved SO-FDTD and SARC-FDTD are presented and is suitable for truncating the FDTD computational domain for calculation of dispersive medium. Combined with the proposed SO-FDTD and SARC-FDTD, the implementation of PML is not only independent for the truncated medium, and the FDTD update formula in PML region is a unified form for the different dispersive medium.A unified FDTD update formulas simultaneously applied to SARC, Auxiliary Differential Equation (ADE), improved Z transform and improved SO algorithm is proposed. The inconvenience bringing with the different FDTD formulas for the above several algorithm is avoided. In this scheme, the coefficients in the unified update formulas are obtained providing the dispersion model parameters are specified. Then, FDTD calculation using the user-familiar FDTD algorithm can be conveniently carried out.