Accurate Finite-difference Time-domain Research Articles

Efficient Recursive Convolution Schemes for the Accurate FDTD Modeling of Graphene Interband Contribution via Complex Conjugate Pairs

The accurate time-domain numerical modeling of graphene surface conductivity due to the interband contribution is presented in this paper. Initially, the lower frequency limit for the interband conductivity inclusion is studied, highlighting that even in the far-infrared regime it should not be ignored. Then, a precise vector-fitting technique is utilized to decompose the analytical conductivity function into complex conjugate pairs. Every pair is connected to a complex surface current, while the frequency dispersion is evaluated via a proper recursive convolution scheme. Finally, a straightforward algebraic manipulation is conducted to eliminate the complex terms from the update equations of the electromagnetic components, concerning the finite-difference time-domain (FDTD) algorithm. The precision and efficiency of the proposed methodology are thoroughly validated by comparing the numerically extracted surface wave propagation characteristics to those obtained in terms of analytical expressions.

An Adaptive and Highly Accurate FDTD Mesh Generation Technique for Objects with Complex Edge Structures

In this paper, a triangular facets based, highly accurate, and adaptive finite-difference time-domain (FDTD) mesh generation technique is presented. There are two innovations in the implementation of this technique. One is adaptive mesh lines placement method. The mesh lines are automatically set to be dense where the object has fine structure and sparse where the object has rough structure based on the incremental placement of the triangular mesh vertices. The other is ray column tracing method. Ray columns in the normal direction of the coordinate plane are employed to intersect the surface facets to make the mesh generation results highly accurate. The generating FDTD results of the numerical examples show that the proposed technique can well-restore objects with complex edge structures. The simulation results are in good agreement with the theoretical results.

A Nonbalanced Staggered-Grid FDTD Scheme for the First-Order Elastic-Wave Extrapolation and Reverse-Time Migration

In this study, an efficient and accurate staggered-grid finite-difference time-domain (SG-FDTD) method to solve the two-dimensional first-order stress-velocity elastic wave equation is proposed. In the conventional implementation of the SGFD method, the same SGFD operator is used to approximate the spatial derivatives. However, we propose a numerical method based on mixed SGFD operators which are more efficient but similar in accuracy when compared to a uniform SGFD operator. We refer to the proposed method as the non-balanced SGFD numerical scheme which combines high-order SGFD operators with second-order SGFD operators. The suitability of the proposed scheme is verified by dispersion analysis. Through SGFD modeling and reverse time migration examples, we demonstrate that the proposed non-balanced scheme offers a similar level of accuracy with a lower computation cost compared to the time-consuming conventional SGFD method.

A prominent unified crosstalk model for linear and sub-threshold regions in mixed CNT bundle interconnects

With the feasibility to scale the devices and interconnects in highly sophisticated VLSI technology, the demand for high-speed and low-power e-applications have also subsequently increased stupendously. Based on the applications and requirements, a VLSI system is operated in different modes as linear or sub-threshold. A unified analytical model for describing both these linear and sub-threshold modes is highly desirable. This has been innovatively presented in the current paper. Moreover, the futuristic and emerging mixed carbon nanotube bundle (MCB) as interconnects for both linear and sub-threshold region of operations has been considered. The essential signal integrity analysis comprising of several crosstalk effects such as associated transient response, delay and power have been analyzed. To evaluate this, analytical model is formulated and proposed using accurate unconditionally-stable finite-difference time-domain (USFDTD) technique. Utilizing the proposed model, it is investigated that linear mode of operation is good for realizing high-speed systems while sub-threshold is a preferable operation for applications targeted for low-power. Comprehensively, it is envisaged that the average power-delay-product in MCB interconnects operating in sub-threshold region is low and reduced by 74% compared to corresponding linear region of operation. Also, it is demonstrated that the proposed unified USFDTD based model for MCB interconnects operating in different modes of operation is stable and not constricted by the Courant condition. At maximum allowable time step, the proposed model is nearly 10 and 25 times faster than the conventional FDTD analytical and HSPICE simulation models, respectively. The results reveal that USFDTD technique provides better accuracy than the FDTD technique. The different performance analyses are performed at 22 nm technology node.

Accurate and Efficient Finite-Difference Time- Domain Formulation of Dusty Plasma

The finite-difference time-domain (FDTD) method has been widely used for the electromagnetic analysis of complex dispersive media. The shift-operator (SO)-FDTD or auxiliary differential equation (ADE)-FDTD formulation has been mainly employed for dusty plasma. Each FDTD formulation has its pros and cons. SO-FDTD is accurate but not computationally efficient. ADE-FDTD needs fewer computational resources, but its accuracy is poor. Here, we propose an accurate and efficient FDTD formulation for dusty plasma, based on the bilinear transform (BT). We perform a comprehensive study on the numerical permittivity and the computational efficiency for three FDTD formulations. Numerical examples are employed to illustrate that the proposed BT-FDTD outperforms the previously reported FDTD formulations for dusty plasma. In addition, based on the proposed BT-FDTD simulations, the effect of dust particles on EM wave propagation is investigated in the GHz band and the THz band.

Perfectly Matched Layer for Accurate FDTD for Anisotropic Magnetized Plasma

In this work, we propose a stable perfectly matched layer (PML) for accurate finite-difference time-domain (FDTD) methods for analyzing electromagnetic wave propagation in the anisotropic magnetized plasma region. Toward this purpose, we apply the complex frequency-shifted PML systematically to the E-J collocated FDTD method. In specific, auxiliary PML variables are included in the matrix calculation involved in the final update equations of the E-J collocated FDTD method. Numerical examples are used to validate the proposed PML-FDTD for anisotropic magnetized plasma.

A simple and accurate FDTD based technique to determine equivalent complex permittivity of the multi-layered human tissue in MICS band

Abstract This paper proposes a methodology to determine the equivalent electrical properties of multilayered human tissue using the Finite Difference Time Domain (FDTD) method for dispersive media. In addition, the impact of fat layer thickness on the equivalent dielectric properties has also been critically analyzed. The effect of moisture content present in the skin layer has also been studied. The main advantage of the proposed method is that it can be used for any thickness and any number of layers of human tissue. The multilayer reflection and transmission coefficients of the human tissue are first calculated using the FDTD method and then the permittivity and conductivity are extracted using the Nicholson Ross Weir (NRW) Method. The results are validated analytically using the concept of transmission line analogy for plane wave propagation. The tool used is MATLAB. In this paper, a three-layered software model of the human chest for pacemaker applications has been analyzed in the Medical Implants Communication Service band (MICS). At the frequency of 403.5 MHz in the MICS band, the equivalent permittivity of 3 layered human tissue is approximately 43 and its conductivity is 0.41 s / m . Moreover, the effective permittivity, conductivity and tan delta loss decrease with the increase in fat layer thickness. These results form the basis for the development of phantom mixtures used for designing, testing and evaluation of implantable antenna and SAR measurements. The choice of using FDTD is because it is a very powerful tool for creating a numerical mixture.

An Accurate Three-Dimensional FDTD(2,4) Method on Face-Centered Cubic Grids With Low Numerical Dispersion

In this letter, a three-dimensional finite-difference time-domain (FDTD) method that is second-order in time and fourth-order in space on a face-centered cubic (FCC) grid, termed as FCC-FDTD(2,4), is proposed to solve the time-domain Maxwell's equations. The proposed method shows a much lower numerical dispersion error compared with the errors of other FDTD schemes, such as the FCC-FDTD(2,2) method, the FDTD(2,2) method, and the FDTD(2,4) method. This improvement in the numerical dispersion results from the FCC grid and the fourth-order scheme in space used in the proposed FCC-FDTD(2,4) method. Then, the Courant-Friedrichs-Lewy condition is given through spectral analysis, and an analytical numerical dispersion relation is obtained and comprehensively studied through numerical results with the FCC-FDTD(2,2) method, the FDTD(2,2) method, and the FDTD(2,4) method. Compared with the other three FDTD methods, the proposed method has much smaller numerical dispersion errors. Finally, the accuracy of the proposed method is further validated with other numerical examples.

A Finite-Difference Time-Domain Large-Signal Model for Silicon Photonics Modulators

A second-order accurate finite-difference time-domain (FDTD) model is, for the first time, proposed for efficient and reliable modeling of depletion-mode traveling-wave silicon photonics (SiP) modulators. After reviewing small signal and first-order large signal models for SiP modulators, we derive the second-order FDTD large-signal model for the staggered voltage and current fields in the p-n (PN) loaded transmission line with a series push-pull (SPP) circuit configuration. By modeling the non-even splitting distributive RF voltages on the two PNs, accurate propagation parameters of the two arms of a Mach-Zehnder interferometer (MZI) can be obtained to simulate modulated optical signals. The large signal simulations of 16-QAM SiP modulator at 64 Gbaud are used to demonstrate the application of the developed FDTD model.

Accurate and Efficient Finite-Difference Time-Domain Simulation Compared With CCPR Model for Complex Dispersive Media

Recently, it has received a great deal of attention to analyze the electromagnetic wave problems in dispersive media by using the finite-difference time-domain (FDTD) method. Accordingly, it is of great importance to employ a proper dispersion model which can fit the frequency-dependent permittivity of a medium considered. The reported dispersion models include Debye, Drude, Lorentz, modified Lorentz, quadratic complex rational function, complex-conjugate pole-residue (CCPR) models. The CCPR dispersion model has advantage over other dispersion models in the fact that accurate CCPR dispersion parameters can be simply extracted by using the powerful and robust vector fitting tool which has been widely used in the circuit theory. However, the arithmetic operation of CCPR-based FDTD implementation is involved with complex-valued numbers and thus its numerical computation is not efficient. In this work, we propose an accurate and efficient FDTD simulation for complex dispersive media. In specific, an accurate CCPR dispersion model is simply obtained using the vector fitting tool and then the CCPR dispersion model is converted to the modified Lorentz dispersion model which leads to the arithmetic operation of only real-valued numbers in its FDTD implementation. Numerical examples are used to illustrate the accuracy and efficiency of our dispersive FDTD simulation.

Hybrid Newmark-conformal FDTD modeling of thin spoof plasmonic metamaterials

The aim of this paper is to present a new efficient and accurate semi-implicit finite-difference time-domain (FDTD) method for modeling thin plasmonic metamaterials supporting spoof surface plasmons. The presented method is formulated by combining Yu–Mittra's conformal FDTD technique for dielectrics, the simplified conformal finite integration technique for perfectly electric conductors (PECs) and the Newmark-Beta method. The resultant scheme is magnetically implicit, has a more relaxed stability condition than that of Yee's FDTD scheme, and allows for accurate modeling of both PEC and dielectric curved surfaces. Energy conservation and stability of the presented scheme is theoretically proved with the energy inequality method. Its formulation can be generalized to a class of magnetically implicit FDTD schemes with weakly conditional and unconditional stability in a unified manner. The presented scheme is used to simulate thin structures supporting spoof surface plasmon polaritons and spoof localized surface plasmons, and also applied to recent plasmonic devices such as planar frequency splitter, ultrathin rainbow trapping device and compact planar metadisk with split-ring resonators. The accuracy and efficiency of the presented scheme are assessed in comparison with the conventional explicit and implicit FDTD methods, and their conformal variants.

An Unsymmetric FDTD Subgridding Algorithm With Unconditional Stability

To preserve accuracy in a grid with arbitrary subgrids, a finite-difference time-domain (FDTD) subgridding scheme, in general, would result in an unsymmetric numerical system. Such a numerical system can have complex-valued eigenvalues, which will render a traditional explicit time marching of FDTD absolutely unstable. In this paper, we develop an accurate FDTD subgridding algorithm suitable for arbitrary subgridding settings with arbitrary contrast ratios between the normal grid and the subgrid. Although the resulting system matrix is also unsymmetric, we develop a time-marching method to overcome the stability problem without sacrificing the matrix-free merit of the original FDTD. This method is general, which is also applicable to other subgridding algorithms whose underlying numerical systems are unsymmetric. The proposed FDTD subgridding algorithm is then further made unconditionally stable, thus permitting the use of a time step independent of space step. Extensive numerical experiments involving both 2- and 3-D subgrids with various contrast ratios have demonstrated the accuracy, stability, and efficiency of the proposed subgridding algorithm.

High-order accurate FDTD schemes for dispersive Maxwell’s equations in second-order form using recursive convolutions

Abstract We propose a novel finite-difference time-domain (FDTD) scheme for the solution of Maxwell’s equations in which linear dispersive effects are present. The method uses high-order accurate approximations in space and time for the dispersive Maxwell’s equations written as a second-order vector wave equation with a time-history convolution term. The modified equation approach is combined with the recursive convolution (RC) method to develop high-order approximations accurate to any desired order in space and time. High-order-accurate centered approximations of the physical Maxwell interface conditions are derived for the dispersive setting in order to fully restore accuracy at discontinuous material interfaces. Second- and fourth-order accurate versions of the scheme are presented and implemented in two spatial dimensions for the case of the Drude linear dispersion model. The stability of these schemes is analyzed. Finally, our approach is also amenable to curvilinear numerical grids if used with an appropriate generalized Laplace operator.

Accuracy and von Neumann stability of several highly accurate FDTD approaches for modelling Debye‐type dielectric dispersion

A comparative study of the accuracy and stability of several highly accurate finite-difference time-domain (FDTD) approaches, the bilinear transform (BT) approach, the modified Z-transform (MZT) approach and the piecewise linear recursive convolution (PLRC) approach, in modelling the Debye-type dielectric dispersion is conducted with the given numerical models of relative permittivities and compared with their theoretical counterpart. The obtained results from two examples in modelling liquid water and human muscle show that the newly proposed MZT approach has the highest accuracy in modelling the real part of complex permittivity, while the BT approach has the highest accuracy in modelling the imaginary part of permittivity. When combined with the second-order accurate FDTD algorithm, the MZT approach is a little more accurate than the BT and PLRC approaches. It is also demonstrated that all the three approaches are numerically stable with the von Neumann stability limits equal to or a little larger than the Courant stability limit.

Fractional Calculus Based FDTD Modeling of Layered Biological Media Exposure to Wideband Electromagnetic Pulses

Electromagnetic fields are involved in several therapeutic and diagnostic applications such as hyperthermia and electroporation. For these applications, pulsed electric fields (PEFs) and transient phenomena are playing a key role for understanding the biological response due to the exposure to non-ionizing wideband pulses. To this end, the PEF propagation in the six-layered planar structure modeling the human head has been studied. The electromagnetic field and the specific absorption rate (SAR) have been calculated through an accurate finite-difference time-domain (FDTD) dispersive modeling based on the fractional derivative operator. The temperature rise inside the tissues due to the electromagnetic field exposure has been evaluated using both the non-thermoregulated and thermoregulated Gagge’s two-node models. Moreover, additional parametric studies have been carried out with the aim to investigate the thermal response by changing the amplitude and duration of the electric pulses.

Solving the tensorial 3D acoustic wave equation: A mimetic finite-difference time-domain approach

Generating accurate numerical solutions of the acoustic wave equation (AWE) is a key computational kernel for many seismic imaging and inversion problems. Although finite-difference time-domain (FDTD) approaches for generating full-wavefield solutions are well-developed for Cartesian computational domains, several challenges remain when applying FDTD approaches to scenarios arguably best described by more generalized geometry. In particular, how best to generate accurate and stable FDTD solutions for scenarios involving grids conforming to complex topography or internal surfaces. We address these issues by developing a mimetic FDTD (MFDTD) approach that combines four key components: a tensorial 3D AWE, mimetic finite-difference (MFD) operators, fully staggered grids (FSGs), and MFD Robin boundary conditions (RBC). The tensorial formulation of the 3D AWE permits wave propagation to be specified on (semi-) analytically defined coordinate meshes designed to conform to complex domain boundaries. MFD operators allow for higher order FD stencils to be applied throughout the model domain, including the boundary region where implementing centered FD stencils can be problematic. The FSG approach combines wavefield information propagated on four complementary subgrids to ensure the existence of all wavefield gradients required for computing the tensorial Laplacian operator, and thereby avoids interpolation approximations. The RBCs are implemented with a flux-preserving mimetic boundary operator that forestalls introduction of nonphysical energy into the grid by enforcing underlying flux-conservation laws. After validating the 3D MFDTD scheme on a sheared Cartesian mesh, we generate 3D wavefield simulation examples for internal boundary (IB) and topographic coordinate systems. The numerical examples demonstrate that the MFDTD scheme is capable of providing accurate and low-dispersion impulse responses for scenarios involving distorted IB meshes conforming to water-bottom surfaces and topographic coordinate systems exhibiting 2.5 km of topographic relief and including steep (65°) slope angles.

Improved direct radiation pattern estimation in FDTD

Application of direct radiation pattern estimation in finite difference time domain (FDTD) simulation environment as an alternative to cumbersome near-to-far field transformation is considered. With the proposed improvement, direct estimation of the radiation pattern from the field strength samples in FDTD method becomes significantly less sensitive to the antenna geometry and thus more applicable to practically relevant cases. The main idea is to use field samples taken at two different radii to account for antenna geometry. The samples are taken at radii that are as close as possible to the antenna but still not too close to spoil the correctness of the results. The introduced improvement, combined with multigrid simulation domain and higher order accuracy FDTD formulations, reduces the necessary size of the computational domain, which directly leads to reduced memory consumption and a smaller error due to numerical dispersion.

Radiation Efficiency Enhancement of Graphene THz Antennas Utilizing Metamaterial Substrates

The radiation efficiency improvement of graphene plasmonic antennas via synthesized substrates with metamaterial resonators is introduced in this letter. Graphene, represented as an ultrathin layer, can support highly confined surface waves of significantly decreased wavelength compared to the vacuum one. Although this concept yields more compact devices, its applicability to graphene antennas is limited, due to the degradation of radiation efficiency. Thus, the effect of a substrate material on the surface-wave wavelength is thoroughly examined, while radiators of larger dimensions and enhanced efficiency are designed for an epsilon-negative medium. Also, a novel realistic metamaterial substrate is developed for graphene terahertz (THz) antennas, successfully verifying all theoretical estimations. Numerical results are extracted via an accurate finite-difference time-domain algorithm that treats graphene as an efficient surface boundary condition.

Terahertz electromagnetic field propagation in human tissues: A study on communication capabilities

A Body Area Nano-NETwork represents a system of biomedical nano-devices that, equipped with sensing, computing, and communication capabilities, can be implanted, ingested, or worn by humans for collecting diagnostic information and tuning medical treatments. The communication among these nano-devices can be enabled by graphene-based nano-antennas, which generate electromagnetic waves in the Terahertz band. However, from a perspective of the electromagnetic field propagation, human tissues generally introduce high losses that significantly impair the communication process, thus limiting communication ranges. In this context, the aim of this contribution is to study the communication capabilities of a Body Area Nano-NETwork, by carefully taking into account the inhomogeneous and disordered structure offered by biological tissues. To this end, the propagation of Pulsed Electric Fields in a stratified media stack made up by stratum corneum, epidermis, dermis, and fat has been carefully modeled. First, electric and magnetic fields, as well as the Poynting vector, have been calculated through an accurate Finite-Difference Time-Domain dispersive modeling based on the fractional derivative operator. Second, path loss and molecular absorption noise temperature have been evaluated. Finally, channel capacity and the related transmission ranges have been estimated by using some baseline physical interfaces. Moreover, the comparison with respect to reference values already available in the literature is presented too. Obtained results clearly highlight that new research efforts are needed to ensure the considered communications due to the severe impairment suffered by electromagnetic waves.

Second-Order Accurate FDTD Method for Nonuniform Plasma at Multilayer Interfaces

The second-order accurate finite-difference time domain (FDTD) method for nonuniform nonmagnetized plasma at multilayer interfaces is proposed based on the PLJERC scheme and Taylor series. The definition of the accuracy order of difference equations is given and a brief demonstration is presented to illustrate that the FDTD equations at the discontinuous interface based on the reflection coefficient theory is only first-order accurate. Second-order accurate FDTD equations are deduced according to the effective electron density at the interface both for the H-i-E case and the E-i-H case. A reflection coefficient test is done on a PEC slab covered by multilayer nonmagnetized plasma to validate the accuracy of the proposed FDTD method. Calculation results show that the reflection coefficient obtained by the proposed method coincides with that of the analytic methods well and the proposed method has higher accuracy than the conventional FDTD method. The reflection characteristics of the multilayer plasma with four typical electron density distribution profiles and versus incident angle, frequency, and electron collision frequency are analyzed by the proposed method.