Lorentz Dispersive Media Research Articles

An improved two‐dimensional (2,4) finite‐difference time‐domain method for Lorentz dispersive media

AbstractThe credible solution of discretized Maxwell's equations in spaces occupied by Lorentz dispersive media is the main subject of this work. Specifically, we introduce a finite‐difference time‐domain (FDTD) algorithm with a typical (2,4) structure that features dispersion‐relation‐preserving characteristics and produces reduced numerical errors in two‐dimensional electromagnetic simulations, compared to the standard approach with similar computational requirements. We consider the case of dispersive media with non‐vanishing absorption coefficients and investigate different options for the suitable modification of the spatial approximations, so that the accomplished accuracy is optimized for a given computational overhead. The properties of the proposed FDTD technique are thoroughly examined, both theoretically and in numerical tests, and the performance upgrade compared with the conventional solution is assessed.

ADE-FDTD method for study of two-dimensional electromagnetic wave propagation in lossy lorentz medium

In order to study the reflection of electromagnetic wave in Lorentz medium layer, the finite difference time domain method of auxiliary differential equation (ADE-FDTD) is used to derive the difference formula of two-dimensional TM wave propagating in lossy Lorentz medium, and the reflection coefficient of reflection field is calculated in one-dimensional case. The calculated reflection coefficients coincide very well, which shows that the derived propagation formula of two-dimensional TM wave in lossy Lorentz medium is correct. In addition, the reflection of plane electromagnetic wave by infinite high Lorentz medium layer is also simulated. The results show that the reflection of plane electromagnetic wave by Lorentz dispersive medium layer is correct.

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

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.

Effective CNAD- and ADE-Based CFS-PML Formulations for Truncating the Dispersive FDTD Domains

An effective and unsplit-field implementation of the complex frequency-shifted perfectly matched layer (CFS-PML) based on the Crank-Nicolson-approximate-decoupling (CNAD) and the auxiliary differential equation (ADE) method is proposed to truncate the dispersive finite-difference time-domain (FDTD) domains. The proposed formulations take full advantage of the capacity of the CFS-PML for attenuating evanescent waves and reducing late-time reflections. Furthermore, the proposed formulations have an advantage of the unconditional stability of the original CN-FDTD method. Two numerical tests have been carried out to validate the proposed formulations in the two-dimensional FDTD domains composed of the linear Debye and the Lorentz dispersive media, respectively. It is shown in the numerical tests that the proposed formulations can not only increase the time step size over the Courant–Friedrichs–Lewy (CFL) limit as compared with the conventional FDTD, but also hold good absorbing performance.

Analysis of transient wave propagation in an arbitrary frequency-dispersive media using the associated laguerre functions in the FDTD-MOD method

In this work, we present a marching-on-in-degree (MOD) method in a finite difference time-domain (FDTD) framework for analyzing transient electromagnetic responses in a general dispersive media.The two issues related to the finite difference approximation of the time derivatives and the time-consuming convolution operations are handled analytically using the properties of the associated Laguerre functions. The basic idea here is that we fit the transient nature of the fields, the flux densities, the permittivity and the permeability with a finite sum of orthogonal associated Laguerre functions. Through this novel approach, not only the time variable can be decoupled analytically from the temporal variations but also the final computational form of the equations is transformed from FDTD to a FD formulation through a Galerkin testing. We also propose a second MOD formulation based on the Helmholtz wave equation. Representative numerical examples are presented for transient wave propagation in general Debye, Drude, or a Lorentz dispersive medium. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:925–930, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26696

라게르 함수를 이용한 일반적인 분산 매질의 시간 영역 해석

In this paper, we present a marching-on-in-degree(MOD) finite difference method(FDM) based on the Helmholtz wave equation for analyzing transient electromagnetic responses in a general dispersive media. The two issues related to the finite difference approximation of the time derivatives and the time consuming convolution operations are handled analytically using the properties of the Laguerre functions. The basic idea here is that we fit the transient nature of the fields, the flux densities, the permittivity with a finite sum of orthogonal Laguerre functions. Through this novel approach, not only the time variable can be decoupled analytically from the temporal variations but also the final computational form of the equations is transformed from finite difference time-domain(FDTD) to a finite difference formulation through a Galerkin testing. Representative numerical examples are presented for transient wave propagation in general Debye, Drude, and Lorentz dispersive medium.

Electromagnetic Signal Propagation in a Lorentz Dispersive Medium

Electromagnetic Signal Propagation in a Lorentz Dispersive Medium

New FDTD-based method for computing the Lorentz dispersive media

We apply the shift-operator finite-difference time-domain (SO-FDTD) method to the calculation of the Lorentz dispersive media. The Lorentz-medium permittivity is written as a rational fractional function, and the relation between D and E is derived in a time domain. The high efficiency and accuracy of the method is demonstrated by calculating the reflection and transmission of the electromagnetic plane wave impinging on a Lorentz-dispersive-medium slab. The results obtained with the help of the SOFDTD method are compared with analytical results. The SO-FDTD method is proved to have high efficiency and accuracy in computing the Lorentz dispersive media.

Analysis of stability and dispersion in a finite element method for Debye and Lorentz dispersive media

AbstractWe study the stability properties of, and the phase error present in, a finite element scheme for Maxwell's equations coupled with a Debye or Lorentz polarization model. In one dimension we consider a second order formulation for the electric field with an ordinary differential equation for the electric polarization added as an auxiliary constraint. The finite element method uses linear finite elements in space for the electric field as well as the electric polarization, and a theta scheme for the time discretization. Numerical experiments suggest the method is unconditionally stable for both Debye and Lorentz models. We compare the stability and phase error properties of the method presented here with those of finite difference methods that have been analyzed in the literature. We also conduct numerical simulations that verify the stability and dispersion properties of the scheme. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009

TEMPORAL CAVITY OSCILLATIONS CAUSED BY A WIDE-BAND WAVEFORM

Excitation of the electromagnetic fields by a wide-band current surge, which has a beginning in time, is studied in a cavity bounded by a closed perfectly conducting surface. The cavity is filled with Debye or Lorentz dispersive medium. The fields are presented as the modal expansion in terms of the solenoidal and irrotational cavity modes with the time-dependent modal amplitudes, which should be found. Completeness of this form of solution has been proved earlier. The systems of ordinary differential equations with time derivative for the modal amplitudes are derived and solved explicitly under the initial conditions and in compliance with the causality principle. The solutions are obtained in the form of simple convolution (with respect to time variable) integrals. Numerical examples are exhibited as well.

Direct Integration of the Constitutive Relations for Modeling Dispersive Metamaterials using the Finite Difference Time-domain Technique

A brief and self-consistent presentation for the integration of the Maxwell equations is present to study dielectric and magnetic dispersive materials using the Finite Difference Time-Domain technique. The methodology is based on a direct application of the Fourier Transform of the constitutive relations using complex variable. We study Drude and Lorentz dispersive media. We present results for the light reflection of a pulse impinging metamaterials where ε(ω) and μ(ω) are both dispersive.

Analyzing the stability of the FDTD technique by combining the von Neumann method with the Routh-Hurwitz criterion

This paper addresses the problem of stability analysis of finite-difference time-domain (FDTD) approximations for Maxwell's equations. The combination of the von Neumann method with the Routh-Hurwitz criterion is proposed as an algebraic procedure for obtaining analytical closed-form stability expressions. This technique is applied to the problem of determining the stability conditions of an extension of the FDTD method to incorporate dispersive media previously reported in the literature. Both Debye and Lorentz dispersive media are considered. It is shown that, for the former case, the stability limit of the conventional FDTD method is preserved. However, for the latter case, a more restrictive stability limit is obtained. To overcome this drawback, a new scheme is presented, which allows the stability limit of the conventional FDTD method to be maintained.

Stability and phase error analysis of FD-TD in dispersive dielectrics

Four FD-TD extensions for the modeling of pulse propagation in Debye or Lorentz dispersive media are analyzed through studying the stability and phase error properties of the coupled difference equations corresponding to Maxwell's equations and to the equations for the dispersion. For good overall accuracy the author shows that all schemes should be run at their Courant stability limit, and that the timestep should finely resolve the medium timescales. Particularly, for Debye schemes it should be at least /spl Delta/t=10/sup /spl minus/3//spl tau/, while for Lorentz schemes it should be /spl Delta/t=10/sup /spl minus/2//spl tau/, where /spl tau/ is a typical medium relaxation time. A numerical experiment with a Debye medium confirms this. The author has determined that two of the discretizations for Debye media are totally equivalent. In the Lorentz medium case the author establishes that the method that uses the polarization differential equation to model dispersion is stable for all wavenumbers, and that the method using the local-in-time constitutive relation is weakly unstable for modes with wavenumber k such that k/spl Delta/x>/spl pi//2.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>