Efficient FDTD algorithms for dispersive Drude‐critical points media based on bilinear z‐transform

Prokopidis, Konstantinos P.; Zografopoulos, Dimitrios C.

doi:10.1049/el.2013.0198

Cited by 11 publications

(20 citation statements)

References 9 publications

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“…where , and are constant coefficients related to the dispersive model parameters, then the frequency-domain wave-equation can be written in terms of the electric field and the current density, for example, as (2) where is the speed of light and the current density is given by (3) Using the inverse Fourier transform, (2) and (3) …”

Section: Formulationsmentioning

confidence: 99%

“…I N recent years, a new dispersive model, known as modified Lorentz (m-Lo) [1] model, has been successfully used for modeling accurately frequency-dependent dielectric functions in the finite difference time domain (FDTD) algorithm [2], [3]. In this context, two auxiliary differential equation (ADE) schemes have been used in the m-Lo FDTD implementation: one is based on the D-E ADE [2], while the other is based on the J-E ADE [3] ADE scheme.…”

Section: Introductionmentioning

confidence: 99%

“…In this context, two auxiliary differential equation (ADE) schemes have been used in the m-Lo FDTD implementation: one is based on the D-E ADE [2], while the other is based on the J-E ADE [3] ADE scheme. Very recently, the stability of these ADE schemes was studied by the combination of the von Neumann and the Routh-Hurwitz criterion [4].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Equivalence of the Stability of the D-E and J-E ADE-FDTD Schemes for Implementing the Modified Lorentz Dispersive Model

Ramadan

2015

IEEE Microw. Wireless Compon. Lett.

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Recently, the stability of the D-E and the J-E auxiliary differential equation (ADE) schemes, which are used in implementing the modified Lorentz dispersive model in the finite difference time domain (FDTD) algorithm, has been studied by Prokopidis and Zografopoulos and it has been concluded that "the J-E implementation is proven more restrictive compared to D-E" and "the D-E implementation is more robust in terms of stability," In order to avoid drawing inaccurate conclusions regarding the J-E ADE-FDTD scheme in general, it is shown in this comment that if the bilinear frequency approximation technique is used in the FDTD discretization of the J-E ADE scheme, one can obtain the same stability polynomial as that of the D-E ADE scheme, and therefore, the same stability conditions will be applied. Hence, the stability limitations of the ADE scheme are based on the FDTD discretization methodology rather than the ADE-method itself. Finally, a numerical example carried out in a one-dimensional domain shows that the presented J-E ADE implementation is numerically stable as well as accurate as the D-E ADE counterpart.Index Terms-Auxiliary differential equation (ADE), bilinear frequency approximation, finite difference time domain (FDTD), modified Lorentz model, Routh-Hurwitz, stability analysis, von Neumann.

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Section: Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Equivalence of the Stability of the D-E and J-E ADE-FDTD Schemes for Implementing the Modified Lorentz Dispersive Model

Ramadan

2015

IEEE Microw. Wireless Compon. Lett.

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“…In the analysis of dispersive materials using the FDTD approach, it is required that the variation of dielectric parameters with frequency is modeled efficiently and accurately. In recent years, some novel dispersive models have been introduced, for example, the complex-conjugate pole-residue (CCPR) model [3], critical point (CP) model [4], modified Lorentz (m-Lo) model [5], and quadratic complex rational function (QCRF) model [6]. Some hybrid dispersion models, such as the DrudeLorentz model [7,8] and Drude-CP model [4,9], were also usually adopted.…”

Section: Introductionmentioning

confidence: 99%

An Extended Newmark-FDTD Method for Complex Dispersive Media

Zhang

2018

International Journal of Antennas and Propagation

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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.

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“…Recently, a permittivity dispersion model based on critical points (CPs) in conjunction with a single Drude term, namely the Drude-critical point (DCP) model, has been shown to describe more efficiently the dispersion of metals in the infrared and visible spectra [22] than the traditional Drude or Drude-Lorentz models, and it has been efficiently implemented in the FDTD method [23][24][25][26]. In addition, the full LC anisotropy can also be incorporated by proper definition of the permittivity tensor [27,28].…”

Section: Introductionmentioning

confidence: 99%

Rigorous broadband investigation of liquid-crystal plasmonic structures using finite-difference time-domain dispersive-anisotropic models

2013

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A finite-difference time-domain scheme is proposed for the rigorous study of liquid-crystal photonic and plasmonic structures. The model takes into account the full-tensor liquid-crystal anisotropy as well as the permittivity dispersion of all materials involved. Isotropic materials are modeled via a generalized critical points model, while the dispersion of the liquid-crystal indices is described by Lorentzian terms. The validity of the proposed scheme is verified via a series of examples, ranging from transmission through liquid-crystal waveplates and cholesteric slabs to the plasmonic response of arrays of gold nanostripes with a liquid-crystal overlayer and the dispersive properties of metal-liquid-crystal-metal plasmonic waveguides. Results are directly compared with reference analytical or frequency-domain numerical solutions.

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Efficient FDTD algorithms for dispersive Drude‐critical points media based on bilinear z‐transform

Cited by 11 publications

References 9 publications

On the Equivalence of the Stability of the D-E and J-E ADE-FDTD Schemes for Implementing the Modified Lorentz Dispersive Model

On the Equivalence of the Stability of the D-E and J-E ADE-FDTD Schemes for Implementing the Modified Lorentz Dispersive Model

An Extended Newmark-FDTD Method for Complex Dispersive Media

Rigorous broadband investigation of liquid-crystal plasmonic structures using finite-difference time-domain dispersive-anisotropic models

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