Modeling of dispersive media in ADI-FDTD method with complex-conjugate pole residue pairs

2021 ◽  
Author(s):  
Konstantinos Prokopidis ◽  
Dimitrios Zografopoulos
Keyword(s):  
Fdtd Method ◽  
Dispersive Media ◽  
Complex Conjugate ◽  
Pole Residue

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.

Complex-conjugate Pole-residue Pair-Based FDTD Method for Assessing Ultrafast Transient Plasmonic Near Field

Plasmonics ◽  
2019 ◽  
Vol 15 (2) ◽  
pp. 495-505
Author(s):  
Tadele Orbula Otomalo ◽  
Fabrice Mayran de Chamisso ◽  
Bruno Palpant
Keyword(s):  
Near Field ◽  
Fdtd Method ◽  
Residue Pair ◽  
Complex Conjugate ◽  
Pole Residue

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.

A Polynomial Chaos Method for Dispersive Electromagnetics

2015 ◽  
Vol 18 (5) ◽  
pp. 1234-1263 ◽  
Author(s):  
Nathan L. Gibson
Keyword(s):  
Polynomial Chaos ◽  
Fdtd Method ◽  
Debye Model ◽  
Dispersive Media ◽  
Dielectric Parameters ◽  
Polarization Model ◽  
Computational Framework ◽  
Spatial Dimensions ◽  
Yee Scheme ◽  
Polynomial Chaos Expansions

AbstractElectromagnetic wave propagation in complex dispersive media is governed by the time dependent Maxwell's equations coupled to equations that describe the evolution of the induced macroscopic polarization. We consider “polydispersive” materials represented by distributions of dielectric parameters in a polarization model. The work focuses on a novel computational framework for such problems involving Polynomial Chaos Expansions as a method to improve the modeling accuracy of the Debye model and allow for easy simulation using the Finite Difference Time Domain (FDTD) method. Stability and dispersion analyzes are performed for the approach utilizing the second order Yee scheme in two spatial dimensions.

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