Dispersive Finite-difference Time-domain Method Research Articles

Parallel Dispersive FDTD Method Based on the Quadratic Complex Rational Function

Recently, the quadratic complex rational function (QCRF) function was proposed for accurate finite-difference time-domain (FDTD) dispersive modeling. First, this letter discusses two implementations of QCRF-FDTD to a zeroth-order temporal derivative term and it is observed that the numerical accuracy of the double averaging implementation is better than that of the direct implementation. Second, this work presents a fast QCRF-FDTD algorithm by employing a parallel processing algorithm. The proposed parallel QCRF-FDTD is validated in terms of the speedup fact and the computational accuracy. Finally, we analyze the shielding effectiveness of large-scale concrete structures by using our parallel QCRF-FDTD.

A new high order dispersive FDTD method for Drude material with complex interfaces

In this paper, motivated by the needs of tracking the transient change in the regularity of the electromagnetic fields across a Drude interface, we propose a new Maxwell–Drude formulation for transverse magnetic problems with inhomogeneous Drude dispersive materials. Based on the auxiliary differential equation approach, the proposed formulation couples the wave equation for the electric component with Maxwell’s equations for the magnetic components. A new finite-difference time-domain (FDTD) algorithm is introduced for solving the proposed Maxwell–Drude system, in which the time dependent jump conditions across the Drude interface are enforced through the matched interface and boundary (MIB) method. The proposed FDTD method achieves a second order of accuracy in solving Drude interfaces with fluctuating curvatures and non-smooth corners based on a simple Yee lattice, while it can be generalized to up to sixth order in dealing with a straight Drude interface. Therefore, the proposed FDTD method is more accurate and cost-efficient than the classical FDTD methods for Drude material with complex interfaces.

Elliptic cylindrical pseudo-optical black hole for omnidirectional light absorber

An elliptic cylindrical omnidirectional light absorber forming a pseudo-optical black hole is studied both analytically and numerically. The conditions for permittivity tensors to trap optical rays are obtained from semiclassical analysis of the ray optic Hamiltonian. The dispersive finite-difference time-domain method is used to study the performance of these light-absorbing structures numerically. It is found that the permittivity of the structure in the form (1/sinhu u)≥(a/r)n traps the light ray efficiently into the elliptic absorber for n≥2, where u is the radial elliptic coordinate and a is the focal distance.

Accurate modeling of the scattering of 2D cloaks using dispersive FDTD method with higher-order algorithm

A higher-order dispersive finite-difference time-domain (FDTD) method has been proposed to accurately model cloaking structures. In the proposed method, the higher-order FDTD scheme with second-order accuracy in time and fourth-order in space has combined with the shift operator algorithm. The exotic electromagnetic parameters of the cloaks are taken into account using shift operator based on dispersive FDTD method. The introduction of the higher-order algorithm would reduce the numerical dispersion of the FDTD method and guarantee a coarser grid during the simulation. Numerical results have indicated that the proposed method is more accurate than the available method maintaining the same grid size. Scattering width of different kinds of simplified cylindrical cloaks including thickness and loss is presented and this could serve for a further study on this subject.

Dispersive FDTD analysis of induced electric field in human models due to electrostatic discharge

Contact currents flow from/into a charged human body when touching a grounded conductive object. An electrostatic discharge (ESD) or spark may occur just before contact or upon release. The current may stimulate muscles and peripheral nerves. In order to clarify the difference in the induced electric field between different sized human models, the in-situ electric fields were computed in anatomically based models of adults and a child for a contact current in a human body following ESD. A dispersive finite-difference time-domain method was used, in which biological tissue is assumed to obey a four-pole Debye model. From our computational results, the first peak of the discharge current was almost identical across adult and child models. The decay of the induced current in the child was also faster due mainly to its smaller body capacitance compared to the adult models. The induced electric fields in the forefingers were comparable across different models. However, the electric field induced in the arm of the child model was found to be greater than that in the adult models primarily because of its smaller cross-sectional area. The tendency for greater doses in the child has also been reported for power frequency sinusoidal contact current exposures as reported by other investigators.

Investigation of image magnification properties of hyperlenses formed by a tapered array of metallic wires using a spatially dispersive finite-difference time-domain method in cylindrical coordinates

In this paper, the spatially dispersive finite-difference time-domain (FDTD) method in cylindrical coordinates is applied to model the hyperlenses formed by a tapered array of metallic wires. The hyperlens device is modeled using the effective medium theory as a frequency and spatially dispersive dielectric. The gradual increase in spacing between wires along the radial direction of the physical structure is represented by the reduction of plasma frequency of the effective medium. Simulation results show that the image transfer and magnification capability of the hyperlens is insensitive to its transverse dimension. A seven-fold magnification of a subwavelength source distribution transferred to a distance of three wavelengths is demonstrated using a hyperlens with high plasma frequency at its front interface.

고차모드 시간영역 유한차분법을 이용한 원통형 메타물질 Slab의 해석

본 논문에서는 고차모드 시간영역 유한차분법(FDTD)을 이용하여 원통형 메타물질 Slab의 주파수 영역 특성을 정확하게 구하는 방법을 연구하였다. 메타물질의 해석방법에는 분산매질 FDTD방정식이 가장 광범위하게 사용되는데 주파수 분산특성을 갖는 유전율과 투자율 모델을 가정하기 때문에, 주파수 응답특성을 구하기 위해서는 주파수 영역에서 차분방정 식을 전개해야 한다. 본 논문에서는 고차모드 FDTD 방법을 유도하여 기존의 분산매질 FDTD 방법과 비교하여 유전체물질에서는 동일한 결과를 얻을 수 있지만 메타물질 해석에서는 오차가 발생을 한다는 것을 확인하였다. 원통형 메타물질 Slab을 해석하기 위해서 고차모드 FDTD 방법을 이용하면 계산오차를 줄일 수 있고 정확한 주파수 특성을 얻을 수 있다. 본 논문에서 제안한 방법을 사용하면 메타물질을 이용한 다양한 회로구조에 대하여 정 확한 주파수 특성을 얻을 수 있다. In this paper, the higher order FDTD(Finite-Difference Time-Domain) method is used to obtain the frequency response characteristics of the cylindrical metamaterial slab. FDTD method is one of strongest electromagnetic numerical method which is widely used to analyze the metamaterial structure because of its simplicity and the dispersive FDTD equation which has the dispersive effective dielectric constant and permeability are derived to analyze the metamaterials. This derived dispersive FDTD equation has no errors in analyzing the dielectric materials but there are some time and frequency errors in case of analyzing the metamaterials. We used the higher order FDTD method to obtain the accurate frequency response of the metamaterials. Comparisons between the dispersive FDTD method and the higher order FDTD method are performed in this paper also. From the results, we concluded that more accurate frequency response for various metamaterials applications can be obtained using the proposed method in this paper.

A Radially-Dependent Dispersive Finite-Difference Time-Domain Method for the Evaluation of Electromagnetic Cloaks

A radially-dependent dispersive finite-difference time-domain (FDTD) method is proposed to simulate electromagnetic cloaking devices. The Drude dispersion model is applied to model the electromagnetic characteristics of the cloaking medium. Both lossless and lossy cloaking materials are examined and their operating bandwidth investigated. It is demonstrated that the perfect ldquoinvisibilityrdquo of electromagnetic cloaks is only available for lossless metamaterials and within an extremely narrow frequency band.

Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures

This paper proposes a radial dependent dispersive finite-difference time-domain method for the modeling of electromagnetic cloaking structures. The permittivity and permeability of the cloak are mapped to the Drude dispersion model and taken into account in dispersive FDTD simulations. Numerical simulations demonstrate that under ideal conditions, objects placed inside the cloak are 'invisible' to external electromagnetic fields. However for the simplified cloak based on linear transformations, the back scattering has a similar level to the case of a PEC cylinder without any cloak, rendering the object still being 'visible'. It is also demonstrated numerically that the simplified cloak based on high-order transformations can indeed improve the cloaking performance.

Finite-Difference Time-Domain Study of Guided Modes in Nano-Plasmonic Waveguides

A conformal dispersive finite-difference time-domain (FDTD) method is developed for the study of one-dimensional (1-D) plasmonic waveguides formed by an array of periodic infinite-long silver cylinders at optical frequencies. The curved surfaces of circular and elliptical inclusions are modelled in orthogonal FDTD grid using effective permittivities (EPs) and the material frequency dispersion is taken into account using an auxiliary differential equation (ADE) method. The proposed FDTD method does not introduce numerical instability but it requires a fourth-order discretisation procedure. To the authors' knowledge, it is the first time that the modelling of curved structures using a conformal scheme is combined with the dispersive FDTD method. The dispersion diagrams obtained using EPs and staircase approximations are compared with those from the frequency domain embedding method. It is shown that the dispersion diagram can be modified by adding additional elements or changing geometry of inclusions. Numerical simulations of plasmonic waveguides formed by seven elements show that row(s) of silver nanoscale cylinders can guide the propagation of light due to the coupling of surface plasmons.

The effect of the 2-D Laplacian operator approximation on the performance of finite-difference time-domain schemes for Maxwell’s equations

The behavior of the finite-difference time-domain method (FDTD) is investigated with respect to the approximation of the two-dimensional Laplacian, associated with the curl–curl operator. Our analysis begins from the observation that in a two-dimensional space the Yee algorithm approximates the Laplacian operator via a strongly anisotropic 5-point approximation. It is demonstrated that with the aid of a transversely extended-curl operator any 9-point Laplacian can be mapped onto FDTD update equations. Our analysis shows that the mapping of an isotropic Laplacian approximation results in an isotropic and less dispersive FDTD scheme. The properties of the extended curl are further explored and it is proved that a unity Courant number can be achieved without the resulting scheme suffering from grid decoupling. Additionally, the case of a 25-point isotropic Laplacian is examined and it is shown that the corresponding scheme is fourth order accurate in space and exhibits isotropy up to sixth order. Representative numerical simulations are performed that validate the theoretically derived results.

Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries

The accuracy of finite-difference time-domain (FDTD) modelling of left-handed metamaterials (LHMs) is dramatically improved by using an averaging technique along the boundaries of LHM slabs. The material frequency dispersion of LHMs is taken into account using auxiliary differential equation (ADE) based dispersive FDTD methods. The dispersive FDTD method with averaged permittivity along the material boundaries is implemented for a two-dimensional (2-D) transverse electric (TE) case. A mismatch between analytical and numerical material parameters (e.g. permittivity and permeability) introduced by the time discretisation in FDTD is demonstrated. The expression of numerical permittivity is formulated and it is suggested to use corrected permittivity in FDTD simulations in order to model LHM slabs with their desired parameters. The influence of switching time of source on the oscillation of field intensity is analysed. It is shown that there exists an optimum value which leads to fast convergence in simulations.

Modelling of Wave Propagation in Wire Media Using Spatially Dispersive Finite-Difference Time-Domain Method: Numerical Aspects

The finite-difference time-domain (FDTD) method is applied for modelling of wire media as artificial dielectrics. Both frequency dispersion and spatial dispersion effects in wire media are taken into account using the auxiliary differential equation (ADE) method. According to the authors' knowledge, this is the first time when the spatial dispersion effect is considered in the FDTD modelling. The stability of developed spatially dispersive FDTD formulations is analysed through the use of von Neumann method combined with the Routh-Hurwitz criterion. The results show that the conventional stability Courant limit is preserved using standard discretisation scheme for wire media modelling. Flat sub-wavelength lenses formed by wire media are chosen for validation of proposed spatially dispersive FDTD formulation. Results of the simulations demonstrate excellent sub-wavelength imaging capability of the wire medium slabs. The size of the simulation domain is significantly reduced using the modified perfectly matched layer (MPML) which can be placed in close vicinity of the wire medium. It is demonstrated that the reflections from the MPML-wire medium interface are less than -70 dB, that lead to dramatic improvement of convergence compared to conventional simulations.

Accurate modeling of the optical properties of left-handed media using a finite-difference time-domain method

This paper contains an important message regarding the numerical modeling of left-handed media (LHM) using the finite-difference time-domain (FDTD) method which remains at the moment one of the main techniques used in studies of these exotic materials. It is shown that conventional implementation of the dispersive FDTD method leads to an inaccurate description of evanescent waves in the LHM. This defect can be corrected using spatial averaging at the interfaces. However, a number of results obtained using the conventional FDTD method have to be reconsidered. For instance, accurate simulation of subwavelength imaging by the finite-sized slabs of left-handed media does not reveal the cavity effect reported by Chen [Phys. Rev. Lett. 92, 107404 (2004)]. Hence the finite transverse dimension of LHM slabs does not have significant effects on the subwavelength image quality, contrary to previous assertions.

Use of conjugate dielectric and metamaterial slabs as radomes

An interesting application of left-handed metamaterials is proposed and numerically verified. Specifically, a structure consisting of a conventional dielectric slab adjacent to a metamaterial slab of the same width but of opposite material characteristics, is used as a radome. The behaviour of the structure for normal as well as for oblique incidence is considered. The results are satisfactory in both cases. It is shown that cylindrical structures similar to the aforementioned straight structures could also be used as radomes. However, the behaviour of the structure is non-reciprocal for incoming and outgoing waves. The dispersive finite-difference time-domain method is applied to study all the structures and the numerical results verify that the straight conjugate slabs are transparent in normal incidence and reduce the reflections for oblique incidence, which are the desirable characteristics for a radome.

Dispersive FDTD characterisation of no phase-delay radio transmission over layered left-handed meta-materials structure

At the interface of two materials with different permittivity and permeability, evanescent waves are excited and will constrain perfect imaging using left-handed meta-materials (LHMs). The dispersive finite-difference time-domain method is used to demonstrate that multilayer stacks, which consist of thin alternating layers of conventional materials and LHMs, can guide evanescent waves with very little attenuation at microwave frequencies and over large stack thicknesses. In addition, such layered structures demonstrate zero phase-delay over the stack thickness, a property that may be applied to construct a no phase-delay transmission line for applications such as beam forming networks for antenna arrays.

Simulation of acoustic wave propagation in dispersive media with relaxation losses by using FDTD method with PML absorbing boundary condition

We present a method to incorporate the relaxation dominated attenuation into the finite-difference time-domain (FDTD) simulation of acoustic wave propagation in complex media. A dispersive perfectly matched layer (DPML) boundary condition, which is suitable for boundary matching to such a dispersive media whole space, is also proposed to truncate the FDTD simulation domain. The numerical simulation of a Ricker wavelet propagating in a dispersive medium, described by second-order Debye model, shows that the Ricker wavelet is attenuated in amplitude and expanded in time in its course of propagation, as required by Kramers-Kronig relations. The numerical results also are compared to exact solution showing that the dispersive FDTD method is accurate and that the DPML boundary condition effectively dampens reflective waves. The method presented here is applicable to the simulation of ultrasonic instrumentation for medical imaging and other nondestructive testing problems with frequency dependent, attenuating media.