Frequency-dependent FDTD methods using Z transforms

The frequency-dependent finite-difference time-domain method (FD) ²TD method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent. However, as researchers search for more elaborate applications, the formulation of the (FD)²TD methods becomes more complex. In this work, the mathematics of the (FD) ²TD method is developed using Z transform theory. This has the advantages of presenting a clearer formulation, and allowing researchers to draw on the literature of systems analysis and signal processing disciplines     

A frequency-dependent FDTD method for biological applications

A frequency-dependent finite-difference time-domain (FD)² TD method for calculating the response of pulses in plasma or water has recently been described. This method is an advance over the traditional finite-difference time-domain (FDTD) method in that it allows for the frequency dependence of these two media. The modification of the (FD)²TD method to obtain broadband frequency information in 3D biological applications is discussed. The implementation of this method is described, and its accuracy is verified by comparison with analytic solutions using the Bessel function expansion. The use of this method is illustrated by an example of the 3D simulation of a hyperthermia treatment using two applicators over a frequency range of 40 to 200 MHz     

The use of the frequency-dependent finite-difference time-domainmethod for induced current and SAR calculations for a heterogeneousmodel of the human body

This paper describes the use of the previously formulated frequency-dependent finite-difference time-domain ((FD)²TD) method for analysis of an anatomically based heterogeneous man model exposed to ultra-wide-band electromagnetic pulse sources. The human tissues' electrical permittivities, ϵ_i*(ω) are described by Debye equations with two relaxation constants, and the equation D(t)=ϵ*(ω))E(t) is converted to a finite-difference equation along with the Maxwell's equations used by the standard FDTD method. Using a single run with a broad-band pulse excitation, the (FD) ²TD method is used to calculate mass normalized rates of energy deposition (specific absorption rates or SARs) and induced currents in the man model over a broad band of frequencies. Time-domain coupling of a representative ultrashort pulse of subnanosecond rise time and nanosecond pulse duration to the human body is also examined     

Currents induced in the human body for exposure to ultrawidebandelectromagnetic pulses

The frequency-dependent finite-difference time-domain [(FD)² TD] method is used to calculate internal electric fields and induced current densities in a 1.31-cm resolution anatomically-based model of the human body for exposure to ultrawideband vertically polarized electromagnetic pulses (EMPs). From a single (FD)²TD simulation, two ultrawideband pulses with frequencies up to 1500 MHz are examined using a convolution technique. The complex permittivities ϵ*(τ) for the various tissues are known to vary a great deal over the wide bandwidth of these two pulses. In the (FD) ²TD formulation, these frequency-dependent ϵ*(τ) are described by the best-fit second-order Debye equations for the sixteen tissues that are used to define the anatomically based model. The vertical currents passing through several sections of the body are compared for a shoe-wearing model standing on a perfectly conducting ground plane, and a barefoot model suspended in air. For the first pulse, currents on the order of 1 to 4 mA per V/m of incident fields are calculated with the highest values calculated for the sections through the bladder and slightly above it. For the second pulse, currents on the order of 4 mA per V/m of incident fields were calculated     

Low-complexity Cole-Cole expression for modelling human biological tissues in (FD)/sup 2/TD method

It is always crucial to have an accurate human tissue model for bio-electromagnetic analysis by using the frequency-dependent finite-difference time-domain ((FD)²TD) method. A new approach is proposed that constructs a new Debye-type equation to perform the Cole-Cole dispersion in the (FD)²TD method. The proposed approach is extremely flexible and promising in representing different human tissues, and the same strategy can be applied to different frequency spectra. The proposed equation provides precise outcomes, but requires only a simple implementation. The results obtained can be found to be particularly important in analysing the interaction between electromagnetic waves and human biological tissues     

A multi-relaxation (FD)2-TD method for modelingdispersion in biological tissues

Pulse excitation in FD-TD provides multifrequency results with a single run of the code. The introduction of the Frequency Dependent FD-TD ((FD)²-TD) has also recently provided a means to deal with dispersive materials on condition that they had a first order permittivity. The authors present a multirelaxation approach to widen the (FD)²TD applicability to materials with more complex permittivity such as biological tissues     

A frequency-dependent finite-difference time-domain formulation for dispersive materials

The traditional finite-difference time-domain (FDTD) formulation is extended to include a discrete time-domain convolution, which is efficiently evaluated using recursion. The accuracy of the extension is demonstrated by computing the reflection coefficient at an air-water interface over a wide frequency band including the effects of the frequency-dependent permittivity of water. Extension to frequency-dependent permeability and to three dimensions is straightforward. The frequency dependent FDTD formulation allows computation of electromagnetic interaction with virtually any material and geometry (subject only to computer resource limitations) with pulse excitation. Materials that are highly dispersive, such as snow, ice, plasma, and radar-absorbing material, can be considered efficiently by using this formulation.<>     

Frequency-dependent FDTD modeling of optically controlleddielectric resonators

A theoretical analysis is carried out to describe the performance of optically controlled dielectric resonators. A previously developed frequency-dependent finite-difference-time domain (FDTD) formulation has been used to estimate the effect that solid state plasmas have on the resonant frequency on dielectric resonators. Optical generation of plasmas in contact with dielectric resonators is being considered here as a possible means of controlling the resonator's frequency. The effect that carrier diffusion and recombination-generation have on plasma permittivity and penetration depth are taken into account in this analysis. The results are compared with measurement and are shown to yield a quantitative estimate of the optically induced dielectric resonator frequency shift as a function of the illumination, properties of the plasma host semiconductor, and the properties of the dielectric resonator     

Nonstandard FDTD Method for Wideband Analysis

The nonstandard (NS) FDTD algorithm can compute electromagnetic propagation with very high accuracy on a coarse grid, but only for monochromatic or narrow-band signals. We have developed a wideband (W) NS-FDTD algorithm that overcomes this limitation. In NS-FDTD special finite difference operators are used to make the numerical dispersion isotropic, which is then corrected by a frequency-dependent factor. In WNS-FDTD the numerical dispersion is modeled as frequency-dependent electrical permittivity and magnetic permeability, and the Yee algorithm is augmented by correction terms in the time domain. We demonstrate the high accuracy of WNS-FDTD in example problems, and show that it gives better results than both the standard (S) FDTD and the FDTD(2,4) algorithms.      

Complete FDTD analysis of microwave heating processes infrequency-dependent and temperature-dependent media

It Is well known that the temperature rise in a material modifies its physical properties and, particularly, its dielectric permittivity. The dissipated electromagnetic power involved in microwave heating processes depending on ε(ω), the electrical characteristics of the heated media must vary with the temperature to achieve realistic simulations. In this paper, we present a fast and accurate algorithm allowing, through a combined electromagnetic and thermal procedure, to take into account the influence of the temperature on the electrical properties of materials. First, the temperature dependence of the complex permittivity ruled by a Debye relaxation equation is investigated, and a realistic model is proposed and validated. Then, a frequency-dependent finite-differences time-domain ((FD)²TD) method is used to assess the instantaneous electromagnetic power lost by dielectric hysteresis. Within the same iteration, a time-scaled form of the heat transfer equation allows one to calculate the temperature distribution in the heated medium and then to correct the dielectric properties of the material using the proposed model. These new characteristics will be taken into account by the EM solver at the next iteration. This combined algorithm allows a significant reduction of computation time. An application to a microwave oven is proposed     

A Study on the Stability and Numerical Dispersion of the Lumped-Network FDTD Method

The lumped-network finite-difference time-domain (LN-FDTD) technique is an extension of the conventional FDTD method that enables the incorporation of linear one-port LNs in a single FDTD cell. This paper studies the stability and the numerical dispersion of this technique. To this end, an isotropic medium that is uniformly loaded with LNs in the $x$-direction is considered as a working model. The stability analysis, based on the von Neumann method, is performed for general $M$th-order LNs and closed-form stability conditions are derived for some particular cases. The numerical dispersion relation is obtained for plane-wave propagation in the proposed LN-loaded medium. It is shown that LNs can be interpreted in terms of an effective frequency-dependent permittivity and, as a consequence, the LN-loaded medium can be viewed as a uniaxial medium. The numerical admittance of the LNs is also obtained showing that, as a side-effect of the time discretization, the LN parameters become frequency-dependent, e.g. for the resistor case, the resistance becomes a function of the frequency.      

Piecewise linear current density recursive convolution FDTD implementation for anisotropic magnetized plasmas

The piecewise linear current density recursive convolution (PLCDRC) finite-difference time-domain (FDTD) method for isotropic dispersive media greatly improves accuracy over recursive convolution (RC) and current density recursive convolution (CDRC) FDTD approaches but retains its speed and efficiency advantages. This letter extends this approach to anisotropic magnetoactive plasmas which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient solutions of electromagnetic wave propagation in anisotropic magnetoactive plasmas. The high efficiency and accuracy of the method are confirmed by computing the reflection and transmission through a magnetized plasma layer, with the direction of propagation parallel to the direction of the biasing field. A comparison to frequency-domain analytic results and CDRC FDTD results is included.     

Finite-difference time-domain analysis of gyrotropic media. I.Magnetized plasma

When subjected to a constant magnetic field, both plasmas and ferrites exhibit anisotropic constitutive parameters. For electronic plasmas this anisotropy must be described by using a permittivity tensor in place of the usual scalar permittivity. Each member of this tensor is also very frequency dependent. A finite-difference time-domain formulation which incorporates both anisotropy and frequency dispersion, enabling the wideband transient analysis of magnetoactive plasma, is described. Results are shown for the reflection and transmission through a magnetized plasma layer, with the direction of propagation parallel to the direction of the biasing field. A comparison to frequency-domain analytic results is included     

Analysis of microstrip patch antennas using finite difference timedomain method

The study of microstrip patch antennas is directly treated in the time domain, using a modified finite-difference time-domain (FDTD) method. Assuming an appropriate choice of excitation, the frequency dependence of the relevant parameters can readily be found using the Fourier transform of the transient current. The FDTD method allows a rigorous treatment of one or several dielectric interfaces. Different types of excitation can be taken into consideration (coaxial, microstrip lines, etc.). Plotting the spatial distribution of the current density gives information about the resonance modes. The usual frequency-dependent parameters (input impedance, radiation pattern) are given for several examples     

A general method for FDTD modeling of wave propagation in arbitraryfrequency-dispersive media

A general formulation is presented for finite-difference time-domain (FDTD) modeling of wave propagation in arbitrary frequency-dispersive media. Two algorithmic approaches are outlined for incorporating dispersion into the FDTD time-stepping equations. The first employs a frequency-dependent complex permittivity (denoted Form-1), and the second employs a frequency-dependent complex conductivity (denoted Form-2). A Pade representation is used in Z-transform space to represent the frequency-dependent permittivity (Form-1) or conductivity (Form-2). This is a generalization over several previous methods employing either Debye, Lorentz, or Drude models. The coefficients of the Pade model may be obtained through an optimization process, leading directly to a finite-difference representation of the dispersion relation, without introducing discretization error. Stability criteria for the dispersive FDTD algorithms are given. We show that several previously developed dispersive FDTD algorithms can be cast as special cases of our more general framework. Simulation results are presented for a one-dimensional (1-D) air/muscle example considered previously in the literature and a three-dimensional (3-D) radiation problem in dispersive, lossy soil using measured soil data     

非均匀等离子体覆盖目标隐身研究

推导了各向同性等离子体中的FDTD分段线性递归卷积（PLRC）计算式，首次将PLRC FD^2TD方法用于仿真电磁波与等离子体的相互作用，对垂直入射的非均匀等子体简化隐身模型进行了时域和频域研究。数值结果表明，等离子体包层可以极大地减少雷达目标的电磁回波能量。     

A novel dispersive FDTD formulation for modeling transient propagation in chiral metamaterials

Chiral media engineered for applications at microwave frequencies can be described as metamaterials composed of randomly oriented helices (with sizes typically less than a wavelength) embedded within an achiral background that is characterized by its permittivity and permeability. Chiral metamaterials embody properties of magnetoelectric coupling and polarization rotation. Chiral media are also highly dispersive and no effective full-wave time domain formulation has been available to simulate transient propagation through such an important class of metamaterials. A new finite-difference time-domain (FDTD) technique is introduced in this paper to model the interaction of an electromagnetic wave with isotropic dispersive chiral metamaterials, based on the implementation of a wavefield decomposition technique in conjunction with the piecewise-linear recursive convolution method. This formulation represents the first of its kind in the FDTD community. The FDTD model is validated by considering a one-dimensional example and comparing the simulations with available analytical results. Moreover, the FDTD technique is also used to investigate the propagation of electromagnetic waves through multilayered metamaterial slabs that include dispersive chiral and double-negative media. Hence, this model enables the investigation of complex dispersive metamaterials with magnetoelectric coupling and double-negative behavior as well as facilitates the exploitation of their unique properties for a variety of possible applications.     

A finite-difference time-domain method applied to anisotropicmaterial

The popularity of the finite-difference time-domain (FDTD) method stems from the fact that it is not limited to a specific geometry and it does not restrict the constitutive parameters of a scatterer. Furthermore, it provides a direct solution to problems with transient illumination, but can also be used for harmonic analysis. However, researchers have limited their investigation to materials that are either isotropic or that have diagonal permittivity, conductivity, and permeability tensors. The authors derive the necessary extension to the FDTD equations to accommodate nondiagonal tensors. Excellent agreement between FDTD and exact analytic results is obtained for a one-dimensional anisotropic scatterer     

FDTD-PLRC Technique for Modeling of Anisotropic-Dispersive Media and Metamaterial Devices

The goal of this paper is to develop a versatile computational engine based on the finite-difference time-domain (FDTD) technique to comprehensively demonstrate the broadband behaviors of devices designed utilizing anisotropic-dispersive metamaterials. In this regard, the frequency-dependent behavior of dispersive materials is incorporated into the FDTD equations with the use of a piecewise linear recursive convolution (PLRC) approach. The FDTD domain is effectively terminated utilizing convolutional perfectly matched layered (CPML) absorbing walls, which are derived from the complex frequency-shifted (CFS) formulation. The CPML has the advantage that it operates only on the filed intensities and has nothing to do with the and constitutive relationships. The CPML is also highly absorptive to both propagating and evanescent waves. Therefore, it would be of great interest for terminating metamaterials having complex constitutive parameters. The developed method is also capable of characterizing periodic configurations illuminated by normal incident plane waves. The FDTD engine is successfully validated through the analyses of several complex metamaterials. The design and characterization of novel devices such as a patch antenna printed on metasubstrate with anisotropic epsiv (omega) - mu (omega)parameters, an electrically small antenna embedded in negative permittivity resonator, and an anisotropic-dispersive self-biased hexagonal ferrite-coupled line (FCL) circulator are highlighted.     

FDTD Simulation of Electromagnetic Reflection of Conductive Plane Covered with Imhomogeneous Time-Varying Plasma

A finite-difference time-domain (FDTD) algorithm is applied to study the electromagnetic reflection of conduction plane covered with inhomogeneous, collision, warm, time-varying plasma. The collision frequency of plasma is a function of electron density and plasma temperature. Under the one-dimensional case, transient electromagnetic propagation through various plasmas have been obtained, and the reflection coefficient of EM wave through inhomogeneous time-varying plasma (ITVP), homogeneous time-varying plasma (HTVP) and inhomogeneous plasma (IP) are calculated under different conditions. The results illustrate that a plasma cloaking system can successfully absorb the incident EM wave.