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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]

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]

Enhanced transmission through a circular aperture surrounded by concentric surface corrugations in a conducting plane is investigated. A boundary-value problem of electromagnetic wave scattering from a circular aperture surrounded by concentric surface corrugations is rigorously solved based on the Hankel transform, eigenfunction expansion, and mode-matching method. The transmission coefficient is represented in a fast-convergent series that is amenable to numerical analysis. Computation is performed to illustrate the transmission behaviors in terms of the geometries of the concentric corrugations. The effects of the higher-order modes on the transmission coefficients are also discussed. [ABSTRACT FROM AUTHOR]