scholarly journals An Extended Newmark-FDTD Method for Complex Dispersive Media

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yu-Qiang Zhang ◽  
Peng-Ju Yang
Keyword(s):  
Rational Function ◽  
Time Domain ◽  
Fdtd Method ◽  
Polarization Vector ◽  
Dispersive Media ◽  
Complex Conjugate ◽  
Time Stepping ◽  
Two Sides ◽  
Difference Time ◽  
Complex Dispersion

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.

scholarly journals Time-Domain Studies of General Dispersive Anisotropic Media by the Complex-Conjugate Pole–Residue Pairs Model

2021 ◽  
Vol 11 (9) ◽  
pp. 3844
Author(s):  
Konstantinos P. Prokopidis ◽  
Dimitrios C. Zografopoulos
Keyword(s):  
Time Domain ◽  
Electromagnetic Wave Propagation ◽  
Frequency Dispersion ◽  
Magnetized Plasma ◽  
Dispersive Media ◽  
Complex Conjugate ◽  
Pole Residue ◽  
Permittivity And Permeability ◽  
Arbitrary Frequency ◽  
Difference Time

A novel finite-difference time-domain formulation for the modeling of general anisotropic dispersive media is introduced in this work. The method accounts for fully anisotropic electric or magnetic materials with all elements of the permittivity and permeability tensors being non-zero. In addition, each element shows an arbitrary frequency dispersion described by the complex-conjugate pole–residue pairs model. The efficiency of the technique is demonstrated in benchmark numerical examples involving electromagnetic wave propagation through magnetized plasma, nematic liquid crystals and ferrites.

scholarly journals Newmark-FDTD Formulation for Modified Lorentz Dispersive Medium and Its Equivalence to Auxiliary Differential Equation-FDTD with Bilinear Transformation

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Hongjin Choi ◽  
Jeahoon Cho ◽  
Yong Bae Park ◽  
Kyung-Young Jung
Keyword(s):  
Differential Equation ◽  
Numerical Stability ◽  
Dispersive Medium ◽  
Fdtd Method ◽  
Dispersive Media ◽  
Complex Conjugate ◽  
Dispersion Models ◽  
Bilinear Transformation ◽  
Quadratic Complex ◽  
Difference Time

The finite-difference time-domain (FDTD) method has been popularly utilized to analyze the electromagnetic (EM) wave propagation in dispersive media. Various dispersion models were introduced to consider the frequency-dependent permittivity, including Debye, Drude, Lorentz, quadratic complex rational function, complex-conjugate pole-residue, and critical point models. The Newmark-FDTD method was recently proposed for the EM analysis of dispersive media and it was shown that the proposed Newmark-FDTD method can give higher stability and better accuracy compared to the conventional auxiliary differential equation- (ADE-) FDTD method. In this work, we extend the Newmark-FDTD method to modified Lorentz medium, which can simply unify aforementioned dispersion models. Moreover, it is found that the ADE-FDTD formulation based on the bilinear transformation is exactly the same as the Newmark-FDTD formulation which can have higher stability and better accuracy compared to the conventional ADE-FDTD. Numerical stability, numerical permittivity, and numerical examples are employed to validate our work.

Padé Approximation Method for FDTD Modeling of Wave Propagation in Dispersive Media

2012 ◽  
Vol 268-270 ◽  
pp. 1585-1588
Author(s):  
Wei Chen
Keyword(s):  
Wave Propagation ◽  
Approximation Method ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Padé Approximation ◽  
Fdtd Method ◽  
Dispersive Media ◽  
Pade Approximation ◽  
Air Muscle ◽  
Difference Time

A finite-difference time-domain (FDTD) method for simulating wave propagation in Cole-Cole dispersive media was presented. The main difficulty of the proposed way was the appearance of fractional time derivatives in the FDTD equation. The Padé approximation method was employed to solve this problem. The expansion of the fractional time derivatives could deal with this model. The comparison of analytical and calculated the reflection of a plasma proves the validity of the method. Then apply this method to calculate the reflection of the air-muscle interface.

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