Accurate FDTD modelling for dispersive media using rational function and particle swarm optimisation

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.     

An Alternative Algorithm for Both Narrowband and Wideband Lorentzian Dispersive Materials Modeling in the Finite-Difference Time-Domain Method

In this study, an alternative algorithm is proposed for modeling narrowband and wideband Lorentzian dispersive materials using the finite-difference time-domain (FDTD) method. Previous algorithms for modeling narrowband and wideband Lorentzian dispersive materials using the FDTD method have been based on a recursive convolution technique. They present two different and independent algorithms for the modeling of the narrowband and wideband Lorentzian dispersive materials, known as the narrowband and wideband Lorentzian recursive convolution algorithms, respectively. The proposed alternative algorithm may be used as a general algorithm for both narrowband and wideband Lorentzian dispersive materials modeling with the FDTD method. The second-order motion equation for the Lorentzian materials is employed as an auxilary differential equation. The proposed auxiliary differential-equation-based algorithm can also be applied to solve the borderline case dispersive electromagnetic problems in the FDTD method. In contrast, the narrowband and wideband Lorentzian recursive convolution algorithms cannot be used for the borderline case. A rectangular cavity, which is partially filled with narrowband and wideband Lorentzian dispersive materials, is presented as a numerical example. The time response of the electric field z component is used to validate and compare the results     

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

We assess the performance of three unconditionally stable finite-difference time-domain (FDTD) methods for the modeling of doubly dispersive metamaterials: 1) locally one-dimensional FDTD; 2) locally one-dimensional FDTD with Strang splitting; and (3) alternating direction implicit FDTD. We use both double-negative media and zero-index media as benchmarks.      

洛伦兹介质电磁特性分析的通用FDTD方法

针对窄带、宽带及其临界情况时洛伦兹介质对应不同时域表达式而导致的递归卷积、Z变换等常用色散介质FDTD方法的更新公式无法通用问题,提出一种改进的移位算子FDTD方法,该方法保持了原方法概念简明、推导简单的优点,减少了内存占用,提高了计算速度,对窄带、宽带及其临界情况洛伦兹介质具有完全相同的更新公式。最后,通过具体算例验证了算法的有效性。     

Z-transform theory and the FDTD method

In implementing the finite-difference time-domain (FDTD) method on materials which are dispersive or nonlinear, the relationship between the flux density and the electric field can be the most complicated part of the problem. Because the FDTD method is a sampled time-domain method, this relationship can be can be looked upon as a digital filtering problem. The Z transform is typically used in digital filtering and signal processing problems. The paper illustrates the use of the Z transform in implementing the FDTD method where complicated dispersive or nonlinear materials are involved     

Thru characteristics of a coaxial gap (FDTD model and measurements)

Thru characteristics of a coaxial cable interrupted by a small gap are modeled and measured. Finite-difference time-domain (FDTD) modeling is applied in cylindrical coordinates to semirigid coaxial cable and to the intervening gap material. Both dispersive and nondispersive gap materials are investigated. Gap loss and phase shift are accurately predicted by this two-dimensional model which accounts for TEM and TM modes in the gap and coaxial apertures. An application of the model is to establish reference data for thin sample permittivity or moisture measurements     

FDTD Maxwell's equations models for nonlinear electrodynamics andoptics

This paper summarizes algorithms which extend the finite-difference time-domain (FDTD) solution of Maxwell's equations to nonlinear optics. The use of the FDTD in this field is novel. Previous modeling approaches were aimed at modeling optical-wave propagation in electrically long structures such as fibers and directional couplers, wherein the primary flow of energy is along a single principal direction. However, the FDTD is aimed at modeling compact structures having energy flow in arbitrary directions. Relative to previous methods, the FDTD achieves robustness by directly solving, for fundamental quantities, the optical E and H fields in space and time rather than performing asymptotic analyses or assuming paraxial propagation and nonphysical envelope functions. As a result, it is almost completely general. It permits accurate modeling of a broad variety of dispersive and nonlinear media used in emerging technologies such as micron-sized lasers and optical switches     

An FDTD algorithm with perfectly matched layers for generaldispersive media

A three-dimensional (3-D) finite difference time domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) is presented for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of coordinate-stretching variables. We extend the recursive convolution (RC) and piecewise linear recursive convolution (PLRC) approaches to arbitrary dispersive media in a more general form. The algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media, i.e., Lorentz medium, unmagnetized plasma, and Debye medium. Excellent agreement between the FDTD results and analytical solutions is obtained for all testing cases with both RC and PLRC approaches. We demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine-like objects, cylinders, and spheres buried in a dispersive half-space and the mapping of a curved interface. Because of their generality, the algorithm and computer program can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media     

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     

An Improved Implicit Split-Step Algorithm for Dispersive Band-Limited FDTD Applications

An improved unconditionally stable envelope finite difference time domain (FDTD) algorithm is presented for modeling open region dispersive band-limited electromagnetic applications. The algorithm is based on incorporating the split-step implicit FDTD scheme into the stretched coordinates perfectly matched layer absorbing boundary conditions. Numerical examples carried out in 2-D domains are included to show the validity of the proposed formulations.      

ADE-FDTD Scattered-Field Formulation for Dispersive Materials

This letter presents a scattered-field formulation for modeling dispersive media using the finite-difference time-domain (FDTD) method. Specifically, the auxiliary differential equation method is applied to Drude and Lorentz media for a scattered field FDTD model. The present technique can also be applied in a straightforward manner to Debye media. Excellent agreement is achieved between the FDTD-calculated and exact theoretical results for the reflection coefficient in half-space problems.     

Analysis on the Calculation of Plasma Medium with Parallel SO‐FDTD Method

This paper introduces a novel parallel shift operator finite‐difference time‐domain (SO‐FDTD) method for plasma in the dispersive media. We calculate the interaction between the electromagnetic wave of various frequencies and non‐magnetized plasma by using the parallel SO‐FDTD method. Then, we compare the results, which are calculated with serial and parallel SO‐FDTD executions to obtain the speedup ratio and validate the parallel execution. We conclude that the parallel SO method has almost the same precision as the serial SO method, while the parallel approach expands the scope of memory and reduces the CPU time.     

DC power-bus design using FDTD modeling with dispersive media andsurface mount technology components

DC power-bus modeling in high-speed digital design using the finite-difference time-domain (FDTD) method is demonstrated herein. The dispersive character of the dielectric layers used in printed circuit board substrates is taken into account in this study. In particular, FR-4 is considered. The complex permittivity of the dielectric is approximated by a Debye model. A wide-band frequency response (100 MHz-5 GHz) is obtained through a single FDTD simulation. Good agreement is achieved between the modeled and measured results for a typical dc power-bus structure with multiple surface mount technology (SMT) decoupling capacitors placed on the printed circuit board (PCB). The FDTD method is then applied to investigate some general approaches of power-bus noise decoupling     

Generalized analysis of stability and numerical dispersion in thediscrete-convolution FDTD method

A simple technique is described for determining the stability and numerical dispersion of finite-difference time-domain (FDTD) calculations that are linear, second-order in space and time, and include dispersion by the discrete convolution method. The technique is applicable to anisotropic materials. Numerical examples demonstrate the accuracy of the technique for several anisotropic and/or dispersive materials     

Multispecies ADI-FDTD Algorithm for Nanoscale Three-Dimensional Photonic Metallic Structures

The unconditionally stable alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is extended to model multispecies dispersive media for simulation of nanoscale three-dimensional metallic structures based on optical plasmon resonances. Examples involving modeling of Au nanoparticles show that the proposed ADI-FDTD yields improved computational performance versus standard FDTD in highly refined grids and for moderate Courant numbers     

Frequency dispersive materials for 3-D hybrid solvers in time domain

The recursive convolution method to treat linear dispersive materials in the finite difference time domain (FDTD) is here generalized to an explicit finite volume solver and an implicit finite element solver. Both solvers are interfaced to FDTD resulting in two hybrid solvers. The stability of the solvers is analyzed and the accuracy is demonstrated in several scattering cases, where a plane wave illuminates a sphere with complex permittivity. Excellent agreement with the analytical Mie series solution is obtained for materials of Debye and Lorentz type as well as for a material consisting of two Lorentz poles.     

Wide-band Lorentzian media in the FDTD algorithm

This paper considers the case of a wide-band Lorentzian (WBL) algorithm in the finite-difference time-domain (FDTD) modeling of dispersive media. It is shown herein that the WBL model is a physically meaningful and practically useful case of the frequency behavior of materials along with the Debye and narrow-band Lorentzian (NBL). The recursive convolution algorithms for the finite-difference time-domain technique for NBL and WBL models differ. The Debye model, which is suitable for comparatively low-frequency dispersive materials, may not have sufficient number of parameters for describing the wide-band material, especially if this material exhibits pronounced absorption at higher frequencies. It is shown that the Debye model can be used, if the Q-factor of the linear circuit analog corresponding to the Lorentzian model of the material is less than approximately 0.8. If the quality factor is in the limits of about 0.81, the NBL model must be applied. The NBL model is suitable for dielectrics exhibiting resonance effects in the microwave frequency range. The WBL model is typical for composites filled with conducting fibers.     

A New FDTD Formulation for Wave Propagation in Biological Media With Cole–Cole Model

The finite-difference time-domain (FDTD) method has been widely used to simulate the electromagnetic wave propagation in biological tissues. The Cole-Cole model is a formulation which can describe many types of biological tissues accurately over a very wide frequency band. However, the implementation of the Cole-Cole model using the FDTD method is difficult because of the fractional order differentiators in the model. In this letter, a new FDTD formulation is presented for the modeling of electromagnetic wave propagation in dispersive biological tissues with the Cole-Cole model. The Z-transform is used to represent the frequency dependent dielectric properties. The fractional order differentiators in the Cole-Cole model is approximated by a polynomial. The coefficients of the polynomial are found using a least-squares fitting method     

BI-FDTD: a novel finite-difference time-domain formulation for modeling wave propagation in bi-isotropic media

This paper presents a newly developed finite-difference time-domain (FDTD) technique, referred to as BI-FDTD, for modeling electromagnetic wave interactions with bi-isotropic (BI) media. The theoretical foundation for the BI-FDTD method will be developed based on a wavefield decomposition. The main advantage of this approach is that the two sets of wavefields are uncoupled and can be viewed as propagating in an equivalent isotropic medium, which makes it possible to readily apply conventional FDTD analysis techniques. The BI-FDTD scheme will also be extended to include the dispersive nature of chiral media, an important subclass of bi-isotropic media. This extension represents the first of its kind in the FDTD community. Validations of this new model are demonstrated for a chiral half-space and a chiral slab.     

Response of realistic soil for GPR applications with 2-D FDTD

The three-dimensional (3D), wideband, bistatic ground penetrating radar (GPR) scatter response of rough, realistic ground is efficiently and accurately simulated using a hybrid high resolution 3D and large area two-dimensional (2D) finite difference time domain (FDTD) model. The 3D computation carefully models the transmitting and receiving antennas, while the 2D FDTD models wave propagation between the antennas and the scattering by the soil below them. The FDTD soil model considers realistic frequency dependent (dispersive) soil with Gaussian height variations. The modeling results are compared to experiments performed with the Geo-Centers, Inc., Newton, MA, commercially available GPR system used for mine detection. Despite the simplicity of the 2D model, the results of the simulation and the experiment agree quite well