Propagation in linear dispersive media: finite differencetime-domain methodologies

Finite difference time-domain (FDTD) methodologies are presented for electromagnetic wave propagation in two different kinds of linear dispersive media: an Nth order Lorentz and an Mth order Debye medium. The temporal discretization is accomplished by invoking the central difference approximation for the temporal derivatives that appear in the first-order differential equations. From this, the final equations are temporally advanced using the classical leapfrog method. One-dimensional scattering from a dielectric slab is chosen for a test case. Provided that the maximum operating frequency times the time step is small and that the wave is adequately resolved in space, as shown in the error analysis, the agreement between the computed and exact solutions will be excellent. The attached data, which are associated with the four pole Lorentz dielectric and the five pole Debye medium, verify this assertion     

Propagation of short optical pulses in dispersive medium

A theoretical analysis of the propagation of transform-limited short pulses in the medium of oscillators (Lorentz model) is presented. In particular, a temporal-modes expansion of the propagating field is introduced for the nonresonance and the resonance cases. It is shown that the medium dispersion causes severe distortions in the pulse shape. The proper choice of medium parameters and/or spectral filtering of the different temporal modes may allow the formation of arbitrary pulse shapes     

Stability and phase error analysis of FD-TD in dispersivedielectrics

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 Δt=10^-3τ, while for Lorentz schemes it should be Δt=10^-2τ, where τ 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 kΔx>π/2     

Maxwellian material-based absorbing boundary conditions for lossymedia in 3-D

A two time-derivative Lorentz material (2TDLM), which has been shown previously to be the correct Maxwellian medium choice to match an absorbing layer to a lossy region, is extended here to a complete absorbing boundary condition (ABC) for three-dimensional (3-D) finite-difference time-domain (FDTD) simulators. The implementation of the lossy 2TDLM (L2TDLM) ABC is presented. It is shown that in contrast to the one-dimensional (1-D) and two-dimensional (2-D) versions, the full 3-D ABC requires a three time-derivative Lorentz material in the edge and corner regions to achieve a rigorous matching of the resulting Maxwellian absorbing layer to the lossy medium. The 3-D ABC implementation thus requires the introduction of an auxiliary field to handle the edge and corner regions to achieve a state-space form of the update equations in the ABC layers. Fully 3-D examples including pulsed dipole radiation and pulsed Gaussian beam propagation in lossless and lossy materials as well as pulse propagation along a microstrip over lossless and lossy materials are included to illustrate the effectiveness of the L2TDLM ABC     

Two time-derivative Lorentz material (2TDLM) formulation of aMaxwellian absorbing layer matched to a lossy medium

A two time-derivative Lorentz material (2TDLM) is introduced to define polarization and magnetization fields that lead to an absorbing layer that can be matched to a lossy dielectric medium. The 2TDLM is a generalization of the successful uniaxial polarization and magnetization time-derivative Lorentz material (TDLM) which has been introduced as an absorbing boundary condition for simulation regions dealing with lossless materials. Expressions are derived to describe the propagation of an arbitrary plane wave in this 2TDLM Maxwellian absorbing material. They are used to study the scattering from a semi-infinite 2TDLM half-space of an arbitrary plane wave incident upon it from a lossy isotropic dielectric medium. Matching conditions are derived which produce reflectionless transmission through such an interface for any angle of incidence and frequency. Numerical tests are given which demonstrate the effectiveness of the resulting 2TDLM absorbing layer     

含色散增益介质光子晶体微腔的光学特性

为了理解光子晶体微腔的光学传输特性,探讨微腔的折射率对缺陷模放大特性和谐振频率的影响,采用时域有限差分法计算了含洛伦兹色散介质一维光子晶体微腔的透射谱,分析、比较了不同光子晶体微腔的透射谱。结果表明,微腔折射率的大小决定缺陷模的谐振频率,而介质色散特性将导致缺陷模频率的移动。另外,当通过复介电常数的虚部引入光学增益后,缺陷模在增益介质中被放大,其阈值特性和缺陷折射率的大小密切相关。模拟结果证明通过合理的选择微腔中介质折射率的大小,可以改善微腔的光学特性,降低激光器的阈值。     

The invariance of the Maxwell equations which is used in the solution of problems of technical electromagnetics

The solution of a boundary electromagnetic problem with impedance boundary conditions is considered using the method based on the invariance of the Maxwell equations to the Lorentz transformations. The results of solution of problems about the wave propagation in a circular waveguide with imperfectly conducting bounding surfaces are compared.     

High-order compact schemes for dispersive media

Staggered high-order compact (HOC) finite difference schemes are developed for modelling electromagnetic wave propagation in dispersive media. The main advantage of HOC schemes is their very low dispersion error, which is dominant in low-order methods. The high accuracy of HOC schemes is demonstrated by examples of wave propagation through first-order Debye and Lorentz media in one dimension.     

Numerical studies on soliton propagation in dielectric media by thenonlinear Lorentz computational model

Soliton propagation in the dielectric media has been simulated by using the nonlinear Lorentz computational model, which was recently developed to study the propagation of electromagnetic waves in a linear and a nonlinear dielectric. The model is constructed by combining a microscopic model used in the semi-classical approximation for dielectric media and the particle model developed for plasma simulations. The carrier wave frequency is retained in the simulation so that not only the envelope of the soliton but also its phase can be followed in time. It is shown that the model may be useful for studying pulse propagation in the dielectric media     

洛伦兹光束通过一阶轴对称光学系统的传输变换特性

从广义惠更斯-菲涅耳衍射积分出发,导出了洛伦兹光束通过一阶轴对称光学系统传输变换的解析公式.给出了洛伦兹光束的束宽、瑞利长度和发散角的表达式,讨论了这些参量通过自由空间的变换规律.结果表明,洛伦兹光束的瑞利长度大于高斯光束的瑞利长度,洛伦兹光束光斑半径的扩展速度慢于高斯光束,洛伦兹光束的远场发散角小于高斯光束的远场发散角.结果还表明,自由空间中洛伦兹光束的束宽、瑞利长度和发散角的变化规律与高斯光束相应参量的变化规律相同.     

An enhanced transmission line model for conductors with arbitrary cross sections

An enhanced transmission line model (ETL) has been recently proposed to describe the propagation along two parallel wires with circular cross sections up to wavelengths comparable to the distance between the wires. In this paper, a general ETL model is proposed to describe the propagation along interconnects consisting of wires with arbitrary cross sections. Since the ETL model has the same simplicity of the standard transmission line model, it allows investigating high-frequency effects, like radiation and dispersion, with a computational cost which is sensibly lower than that required by a full-wave numerical simulation. The ETL model is obtained, with suitable approximations, starting from a full-wave analysis of the propagation problem and using an integral formulation based on the electromagnetic potentials satisfying the Lorentz gauge. Some case studies are carried out and discussed, including a benchmark test with existing literature, performed to check the validity and accuracy of the proposed model.     

Reciprocity, discretization, and the numerical solution of directand inverse electromagnetic radiation and scattering problems

The author gives a formulation, based on Lorentz reciprocity, that unifies the finite element method (FEM) and the integral equation models. Wave propagation and scattering problems in electromagnetics have to be addressed with the aid of numerical techniques. Many of these methods can be envisaged as being discretized versions of appropriate weak formulations of the pertinent operator (differential or integral) equations. For the relevant problems as formulated in the time Laplace-transform domain it is shown that the Lorentz reciprocity theorem encompasses all known weak formulations, while its discretization leads to the discretized forms of the corresponding operator equations, in particular to their finite-element and integral-equation modeling schemes. Both direct (forward) and inverse problems are discussed     

The reflected impulse response of a Lorentz medium

The wave reflected from a Lorentz medium when illuminated by a transverse electric polarized plane wave with impulsive time dependence is expressed as an infinite sum of spherical Bessel functions. This solution is useful in numerical calculation for small and intermediate values of time. For small values of time the Lorentz medium solution simplifies to the result for the impulse response of a cold plasma.     

Tailoring double-negative metamaterial responses to achieve anomalous propagation effects along microstrip transmission lines

The design of a double-negative metamaterial loaded microstrip transmission line (DNG MTM-TL) to tailor the propagation characteristics at S- and C-band frequencies is presented. Guided-wave propagation along this DNG MTM-TL was studied numerically. The scattering parameters of the DNG MTM-TL were obtained with Ansoft's High Frequency Structure Simulator. A two-port network realization of the DNG MTM-TL is established. The effective permittivity and permeability for the DNG MTM-TL is extracted using this two-port network representation. It is shown that both a negative permittivity and a negative permeability and, hence, a negative index of refraction exist in the design frequency range. These material parameters are dispersive and conform to a two-time derivative Lorentz material model type of resonance behavior. This form of the index of refraction may be very suitable for applications dealing with phase and dispersion compensation along a microstrip transmission line.     

The Lorentz reciprocity theorem and range-dependent propagationmodeling

Modeling of electromagnetic propagation in the troposphere has been advanced in the last decade to the point where both the vertical and horizontal variation of refractivity can be accommodated readily. A hybrid ray-optics/parabolic equation model is utilized to predict propagation loss for a range-varying refractive structure to demonstrate the model obeys the Sommerfeld-Pfrang statement of the Lorentz reciprocity theorem     

Anisotropic dielectric properties of media containing aligned nonspherical scatterers

Electromagnetic wave propagation in a medium containing a random distribution of aligned, pair-correlated nonspherical scatterers is studied using theT-matrix to characterize the single scatterer response, the quasicrystalline approximation (QCA) and the correlation function. The resulting dispersion equation for the average medium is numerically solved as a function of frequency and the direction of propagation. Numerical results are presented for the attenuation of electromagnetic waves versus frequency, concentration, and direction of propagation.     

A summary and systematic analysis of FDTD algorithms for linearlydispersive media

This paper examines the most popular advances in the FDTD algorithm development, as applied to electromagnetic wave propagation in linearly dispersive media. Several methodologies are presented, and comparisons are made in order to demonstrate the strengths and weaknesses of the various approaches. In particular, direct-integration and recursive-convolution schemes, associated with wave propagation in a cold plasma, Debye dielectrics, and Lorentz materials, are considered     

A Highly Accurate FDTD Model for Simulating Lorentz Dielectric Dispersion

A highly accurate and numerically stable model of Lorentz dielectric dispersion for the finite-difference time-domain (FDTD) method is presented. The coefficients of the proposed model are optimally derived based on the Maclaurin series expansion (MSE) method and it is shown that the model is much better than the other four reported models in implementing the Lorentz dielectric dispersion with error of relative permittivity several orders lower. The model's stability and performance are also analyzed when it is incorporated into the practical second- and fourth-order accurate FDTD algorithms for an exemplified Lorentz medium. Interestingly, we find that all the mentioned models show nearly the same performance in the second-order algorithm due to its large intrinsic numerical dispersion and the superiority of the proposed MSE model begins to be manifested in the higher-order, say, fourth-order FDTD algorithms as implied by the governing numerical dispersion equations.      

单模光纤中洛伦兹脉冲传输特性研究

为了研究洛伦兹脉冲各参量在光纤中传输的演化特性,从麦克斯韦方程出发,建立光纤非线性传输方程,采用变分法进行了理论分析和数值模拟,得到了洛伦兹脉冲参量随传输距离的演化方程组以及振幅与脉宽、脉宽与啁啾之间的两个重要约束关系;并进一步得出了脉宽随传输距离演化的解析解;描绘了脉宽随传输距离演化的图形。结果表明,脉宽和振幅间满足绝热关系,初始啁啾会对洛伦兹脉冲的保形传输产生影响。     

Analysis of Non-WSSUS Fading Dispersive Channel Model

1Introduction Basically,whenthepropagationcharacteristicsofra diomobilecommunicationsarestudied[1],italways comestheWSSUSmodel,introducedbyBello[2]first ly,whichregardstheradiomobilechannelasafully stochasticchannelandassumestheuncorrelateddisper sivitybo…