An Extended Newmark-FDTD Method for Complex Dispersive Media

Yu-Qiang Zhang,Peng-Ju Yang

doi:10.1155/2018/1573512

Yu-Qiang Zhang, Peng-Ju Yang

Open Access

https://doi.org/10.1155/2018/1573512

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Abstract

Based on polarizability in the form of a complex quadratic rational function, a novel finite-difference time-domain (FDTD) approach combined with the Newmark algorithm is presented for dealing with a complex dispersive medium. In this paper, the time-stepping equation of the polarization vector is derived by applying simultaneously the Newmark algorithm to the two sides of a second-order time-domain differential equation obtained from the relation between the polarization vector and electric field intensity in the frequency domain by the inverse Fourier transform. Then, its accuracy and stability are discussed from the two aspects of theoretical analysis and numerical computation. It is observed that this method possesses the advantages of high accuracy, high stability, and a wide application scope and can thus be applied to the treatment of many complex dispersion models, including the complex conjugate pole residue model, critical point model, modified Lorentz model, and complex quadratic rational function.

Highlights

The finite-difference time-domain (FDTD) method has been widely used to study electromagnetic (EM) wave interaction with a wide variety of materials due to its robustness and its ability to calculate accurate broadband response via a single simulation [1, 2]
For the typical dispersive FDTD approaches, the recursive convolution (RC) method and Z transform (ZT) method are not convenient to deal with the high-order models such as modified Lorentz (m-Lo) and quadratic complex rational function (QCRF)
The NewmarkFDTD method is further extended to the high-order model so that it can be used as a general approach for dispersive media, to treat with Debye, Drude, and Lorentz media, and to deal with complex dispersion models including complex-conjugate pole-residue (CCPR), critical point (CP), m-Lo, and QCRF media

Summary

Introduction

The finite-difference time-domain (FDTD) method has been widely used to study electromagnetic (EM) wave interaction with a wide variety of materials due to its robustness and its ability to calculate accurate broadband response via a single simulation [1, 2]. The Newmark algorithm was originally used for the numerical solution of structural dynamics and was introduced into the finite-element time-domain (FETD) method for electromagnetic simulations [13,14,15]. It is introduced into the analysis of the dispersive FDTD computation in 2014 for the unified treatment of the Debye, Drude, and Lorentz medium [16,17,18]. The NewmarkFDTD method is further extended to the high-order model so that it can be used as a general approach for dispersive media, to treat with Debye, Drude, and Lorentz media, and to deal with complex dispersion models including CCPR, CP, m-Lo, and QCRF media. The computational accuracy and stability are investigated from the two aspects of theory and numerical computation, and higher accuracy and stability are shown

Extended Newmark-FDTD Method

Analysis of Accuracy and Stability

Numerical Verification

Conclusion