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The finite-difference time-domain (FDTD) method is a widely used numerical technique for simulating electromagnetic wave interactions with complex media. Various efficient approaches have been used to analyze complex media, and the surface impedance boundary condition (SIBC) is one of the most powerful techniques in FDTD simulations, allowing efficient electromagnetic modeling of lossy materials. However, conventional SIBC-FDTD formulations face challenges when analyzing lossy dispersive materials because of the assumption of frequency-independent relative permittivity and conductivity in the inverse Laplace transform. To address this, we propose a dispersion-modeling approach for the surface impedance of lossy dispersive materials. Additionally, to reduce grid errors in the FDTD discrete domain, we introduce the surface admittance boundary condition (SABC) for lossy dispersive materials. We investigated the numerical accuracy by deriving the numerical surface impedance and admittance for the proposed surface boundary condition (SBC)-FDTD formulations. In addition, we determined the numerical stability conditions of the SBC-FDTD formulations using the von Neumann method combined with the Routh-Hurwitz criterion. Numerical examples validate both the numerical accuracy and stability of the proposed SBC-FDTD formulations. Our findings enhance the understanding and application of the SBC in FDTD simulations, especially for lossy dispersive materials, and provide insights for future research and electromagnetic modeling in various fields. [ABSTRACT FROM AUTHOR]

The finite-difference time-domain (FDTD) method has been widely used for the electromagnetic analysis of complex dispersive media. The shift-operator (SO)-FDTD or auxiliary differential equation (ADE)-FDTD formulation has been mainly employed for dusty plasma. Each FDTD formulation has its pros and cons. SO-FDTD is accurate but not computationally efficient. ADE-FDTD needs fewer computational resources, but its accuracy is poor. Here, we propose an accurate and efficient FDTD formulation for dusty plasma, based on the bilinear transform (BT). We perform a comprehensive study on the numerical permittivity and the computational efficiency for three FDTD formulations. Numerical examples are employed to illustrate that the proposed BT-FDTD outperforms the previously reported FDTD formulations for dusty plasma. In addition, based on the proposed BT-FDTD simulations, the effect of dust particles on EM wave propagation is investigated in the GHz band and the THz band. [ABSTRACT FROM AUTHOR]

The complex-conjugate pole-residue (CCPR) model has been popularly adopted because CCPR-finite-difference time domain (FDTD) can reduce the memory requirement with the help of complex conjugate property of auxiliary variables. To fully utilize CCPR-FDTD, it is of great necessity to investigate its numerical stability since the FDTD method is conditionally stable. Nonetheless, the numerical stability conditions of CCPR-FDTD have not been studied because its derivation is not straightforward. In this communication, the numerical stability conditions of CCPR-FDTD are systematically derived by combining the von Neumann method with Routh–Hurwitz criterion. It is found that the numerical stability conditions of CCPR-FDTD are the same as those of the modified Lorentz-FDTD with bilinear transform. Moreover, the numerical accuracy of CCPR-FDTD is studied, and numerical examples are employed to validate this work. [ABSTRACT FROM AUTHOR]

Finite-difference time domain (FDTD) has been widely used to analyze electromagnetic wave interaction with dispersive media. It is of great necessity to incorporate a dispersion model into FDTD formulation for electromagnetic wave analysis of dispersive media. Recently, it was reported that the modified Lorentz model can cover Debye, Drude, Lorentz, critical point, and quadratic complex rational function models. In this work, it is illustrated that the modified Lorentz model can also cover the complex-conjugate pole-residue model which is one of the most popular dispersion models. Modified Lorentz-based dispersive FDTD has not been thoroughly studied, especially for numerical aspects. In this work, we investigate auxiliary differential equation (ADE)-FDTD formulations for the modified Lorentz model based on electric flux density (D), current (J), or polarization (P). We perform a comprehensive study on memory requirement, the number of arithmetic operations, numerical stability, and numerical permittivity for the above three ADE-FDTD formulations. In addition, the bilinear transformation (BT) is incorporated into modified Lorentz-based FDTD formulations and it will be shown that the utilization of the BT can lead to better performance in terms of numerical stability and numerical accuracy. Numerical examples are used to demonstrate our work. [ABSTRACT FROM AUTHOR]

In this work, we present a dispersive finite-difference time-domain (FDTD) algorithm using a four-pole complex rational function (CRF). For the sake of a better curve fitting of the four-pole CRF dispersion model, we use a particle swarm optimization technique. We also discuss an efficient memory storage strategy using a state-space approach. The numerical aspects of four-pole CRF-FDTD, the numerical accuracy and the numerical stability, are investigated in detail. Numerical examples are used to validate four-pole CRF-FDTD and numerical stability issues are discussed in detail. We also discuss the computational accuracy and the computational efficiency of an arbitrary $N$-pole CRF-FDTD. [ABSTRACT FROM PUBLISHER]

This article presents an accurate finite-difference time domain (FDTD) dispersive modelling suitable for complex dispersive media. A quadratic complex rational function (QCRF) is used to characterise their dispersive relations. To obtain accurate coefficients of QCRF, in this work, we use an analytical approach and a particle swarm optimisation (PSO) simultaneously. In specific, an analytical approach is used to obtain the QCRF matrix-solving equation and PSO is applied to adjust a weighting function of this equation. Numerical examples are used to illustrate the validity of the proposed FDTD dispersion model. [ABSTRACT FROM PUBLISHER]

Recently, based on a quadratic complex rational function, a simple and accurate finite-difference time-domain algorithm was introduced for the study of electromagnetic wave propagation in dispersive media. It is of great necessity to investigate the numerical stability of the quadratic complex rational function–finite-difference time-domain to fully utilize this finite-difference time-domain algorithm. In this work, using the von Neumann method with the Routh–Hurwitz criterion, the numerical stability conditions of the quadratic complex rational function–finite-difference time-domain are investigated. It is shown that the numerical stability conditions of the quadratic complex rational function–finite-difference time-domain are not same as those of the conventional finite-difference time-domain schemes. [ABSTRACT FROM AUTHOR]

Recently, based on a quadratic complex rational function, an attractive finite-difference time-domain algorithm was suggested for dispersive modeling of complex media because it is accurate and easy to implement. To fully utilize the quadratic complex rational function finite-difference time-domain, it is essential to investigate its numerical errors based on an exact mathematical approach. Toward this purpose, the exact expression of the numerical permittivity is first derived. From this numerical permittivity, the numerical dispersion, numerical dissipation, and numerical anisotropy inherent to the quadratic complex rational function finite-difference time-domain are examined. Numerical examples illustrate that the numerical errors of the quadratic complex rational function finite-difference time-domain is almost same as those of the nondispersive finite-difference time-domain. [ABSTRACT FROM AUTHOR]

We propose a dispersive finite-difference time domain (FDTD) suitable for the electromagnetic analysis of human tissues. The dispersion relation of biological tissues is characterized by a quadratic complex rational function (QCRF) that leads to an accurate FDTD algorithm in 400 MHz–3 GHz. QCRF coefficients are extracted by applying the complex-curve fitting technique, without initial guess. Numerical examples are used to illustrate the computational accuracy and stability of QCRF-based FDTD. [ABSTRACT FROM PUBLISHER]