Finite-difference Time-domain Solution Research Articles

Radiofrequency Dosimetry in Subjects Implanted with Metallic Structures Undergoing MRI: a Numerical Study

A numerical study to investigate the effects of the exposure to radiofrequency (RF) field on biological tissues implanted with thin metallic structures has been carried out, using the finite difference time domain (FDTD) solution technique. The particular case of the RF used in the clinical 1.5 T magnetic resonance imaging (MRI) scanners has been studied. The results of the model show that the presence of a metallic wire yields to a significant increase in the local specific absorption rate (SAR) and in temperature around the implant. Present standards or guidelines do not specifically address this problem and use threshold levels and methods to define safe exposure conditions that cannot apply to reveal high SAR gradients, such as the ones generated by thin metallic implanted objects. In particular, an averaging mass of 10 g, typically used for SAR calculation to evaluate the effect of RF exposure of biological tissues, is too big if compared to the SAR gradient generated by thin metallic structures. The SAR estimation according to this method cannot be considered a reliable indicator to evaluate the potential damage due to the RF induced heating at the interface between the implant and biological tissues. Five wires of different lengths and thicknesses were simulated and the SAR at the wire tip was evaluated over 10g, 1g, 0.1g averaging mass: the SAR underestimation related to the 10g and 1g masses, compared to 0.1g mass, was greater than 90 % and 60 %, respectively. In conclusion, present standards cannot be applied to thin metallic implants. The amount of averaging mass should be chosen as a function of the dimension of the implanted object and of the SAR gradient that is generated around it. At the same time, the averaging volume has to be not too small to be just a single “hot spot”, not relevant for the evaluation of potential tissue damage due to RF exposure.

Introducing Nonuniform Grids into the FDTD Solution of the Transmission-Line Equations by Renormalizing the Per-Unit-Length Parameters

A challenging aspect of using the finite-difference time-domain (FDTD) method to solve nonuniform transmission-line equations is to choose a discretization grid with an adequate spatial resolution. When the per-unit-length parameters have strong variations, an efficient problem-solving strategy requires the use of a nonuniform discretization grid. This paper presents a nonuniform gridding method that makes use of an analytically defined coordinate transformation to map a nonuniformly spaced grid onto a uniformly spaced grid where the standard FDTD time stepping equations can be applied. This approach absorbs all the details of the nonuniform grid into effective or renormalized per-unit-length parameters.

Frequency Transformation of a Whistler Wave by A Collapsing Plasma Medium in a Cavity: FDTD Solution

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A whistler wave in a cavity filled with a magnetoplasma medium is strongly affected when the plasma source is switched-off. Due to such a collapse of the plasma, the whistler wave is converted to an electric- field-intensified higher frequency wave (with an order of magnitude upshift of the frequency). In principle, it is possible to transform a 2.45 GHz source radiation to 300 GHz Terahertz radiation, with significant strength of the electric field. Finite difference time domain (FDTD) technique is used to study the effect of the following parameters: the rate of collapse, spatial plasma-density profile, collision frequency as well as the switching angle. </para>

A New Carrier-Free Nonlinear FDTD Algorithm Suitable for the Moving Computational Window Technique

The model equations of the vectorial time-domain simulator of second-harmonic generation in integrated optical structures have been reformulated by extracting the signal carrier. The moving computational window technique is then used to ease the computational burden in the finite-difference time-domain solution. Results show that the technique provides considerable savings in computation power especially for long propagation distances.

Global modeling of carrier-field dynamics in semiconductors using EMC–FDTD

The interactions between carriers and fields in semiconductors at low frequencies (<100 GHz) can be adequately described by numerical solution of the Boltzmann transport equation coupled with Poisson’s equation. As the frequency approaches the THz regime, the quasi-static approximation fails and full-wave dynamics must be considered. Here, we review recent advances in global modeling techniques—numerical techniques that couple carrier dynamics with full wave dynamics. We focus on the coupling between the stochastic ensemble Monte Carlo (EMC) simulation of carrier transport and the finite-difference time-domain (FDTD) solution to Maxwell’s curl equations. We discuss the stability and accuracy requirements for different types of high-frequency excitation (wave illumination vs. ac bias), and present simulation results for the THz-regime conductivity of doped bulk silicon, ultrafast carrier dynamics and radiation patterns in GaAs filaments, and the ac response of GaAs MESFETs.

Inversion of crosshole seismic data in heterogeneous environments: Comparison of waveform and ray-based approaches

High-resolution tomographic imaging of the shallow subsurface is becoming increasingly important for a wide range of environmental, hydrological and engineering applications. Because of their superior resolution power, their sensitivity to pertinent petrophysical parameters, and their far reaching complementarities, both seismic and georadar crosshole imaging are of particular importance. To date, corresponding approaches have largely relied on asymptotic, ray-based approaches, which only account for a very small part of the observed wavefields, inherently suffer from a limited resolution, and in complex environments may prove to be inadequate. These problems can potentially be alleviated through waveform inversion. We have developed an acoustic waveform inversion approach for crosshole seismic data whose kernel is based on a finite-difference time-domain (FDTD) solution of the 2-D acoustic wave equations. This algorithm is tested on and applied to synthetic data from seismic velocity models of increasing complexity and realism and the results are compared to those obtained using state-of-the-art ray-based traveltime tomography. Regardless of the heterogeneity of the underlying models, the waveform inversion approach has the potential of reliably resolving both the geometry and the acoustic properties of features of the size of less than half a dominant wavelength. Our results do, however, also indicate that, within their inherent resolution limits, ray-based approaches provide an effective and efficient means to obtain satisfactory tomographic reconstructions of the seismic velocity structure in the presence of mild to moderate heterogeneity and in absence of strong scattering. Conversely, the excess effort of waveform inversion provides the greatest benefits for the most heterogeneous, and arguably most realistic, environments where multiple scattering effects tend to be prevalent and ray-based methods lose most of their effectiveness.

Photonic nanojet-enabled optical data storage

We show that our recently reported microwave photonic jet technique for detection of deeply subwavelength pits in a metal substrate can be extended to optical wavelengths for purposes of high-density data storage. Three-dimensional finite-difference time-domain computational solutions of Maxwell's equations are used to optimize the photonic nanojet and pit configuration to account for the Drude dispersion of an aluminum substrate in the spectral range near lambda= 400 nm. Our results show that nanojet-illuminated pits having lateral dimensions of only 50 nm x 80 nm yield a contrast ratio 27 dB greater than previously reported using a lens system for pits of similar area. Such pits are much smaller than BluRay features. The high detection contrast afforded by the photonic nanojet could potentially yield significant increases in data density and throughput relative to current commercial optical data-storage systems while retaining the basic geometry of the storage medium.

Numerical solution of Maxwell’s equations for anisotropic media using the Laguerre transform

We apply the spectral Laguerre transform in the time domain to solve 2D Maxwell’s equations for propagation of electromagnetic waves in lossy anisotropic media. The new algorithm is simple and efficient as Maxwell’s equations are reduced to a harmonic series of linear algebraic equations where the matrix is independent of the harmonic order and is the same for all harmonics. The efficiency of the algorithm is improved by fitting a specially introduced free parameter of the Laguerre transform. If it is large, the solution spectrum shifts toward higher harmonics which is formally equivalent to the case of ray approximation. The Laguerre solution is comparable with high-order accurate finite-difference time-domain (FDTD) solutions. The method is stable both in the region of the wavefield, where conductivity approaches zero and the spectral Fourier method is unstable, and in the high-conductivity region, where the explicit FDTD code requires a too small time step.

Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets

We report a means to detect deeply subwavelength pits in optical data-storage media by employing the recently observed giant backscattering perturbation phenomenon of the photonic jet. We conducted microwave experiments with dimensionally scaled-up pits and lands in a simulated optical data-storage device. These measurements were backed up by three-dimensional finite-difference time-domain computational solutions of Maxwell's equations. Results indicate that pits having a lateral area of 0.025 square wavelengths, i.e., much smaller than current BluRay™ device features, can be robustly detected with a contrast ratio approximately 28dB greater than that provided by a lens system.

Electromagnetic ray tracing model for line structures

In this paper, a model for electromagnetic scattering of line structures is established based on high frequency approximation approach - ray tracing. This electromagnetic ray tracing (ERT) model gives the advantage of identifying each physical field that contributes to the total solution of the scattering phenomenon. Besides the geometrical optics field, different diffracted fields associated with the line structures are also discussed and formulated. A step by step addition of each electromagnetic field is given to elucidate the causes of a disturbance in the amplitude profile. The accuracy of the ERT model is also discussed by comparing with the reference finite difference time domain (FDTD) solution, which shows a promising result for a single polysilicon line structure with width of as narrow as 0.4 wavelength.

FRACTAL-LIKE SQUARE LATTICE OF AIR HOLES

Fractal structures have been widely used in many fields of science, such as biology, physics and chemistry. In this article, we analyze the basic properties of a fractal-like square lattice of air holes, with most of the holes having a lattice constant of Λ while others are repeated with a lattice constant of 2Λ. We change the radii of these holes and analyze their effects on the bandgap regions and transmission properties. The analysis conducted here is based upon band diagrams and 2D Finite difference time-domain (FDTD) solution of the full-wave Maxwell's equations. We show that this structure provides flexibility in tuning the bandgap of the photonic crystal structure and we show the appearance of mini-bandgap regions along certain directions.

Analysis of thin-wire ground penetrating radar systems for buried target detection, using a hybrid MoM-FDTD technique

A hybrid method combining the finite difference time domain (FDTD) method and the method of moments (MoM) in the frequency domain is proposed to model the electromagnetic behavior of a realistic ground penetrating radar (GPR) system. The GPR is a non-destructive testing (NDT) technique. It consists of a broadband thin-wire vee-dipole antenna located in the vicinity of a lossy ground containing unexploded ordnances. In the solution of the problem, we identify two sub-problems, namely, the antenna problem and the ground buried object problem. Capabilities of the MoM for solution of the governing thin-wire electric field integral equation of the antenna problem and general FDTD solution of Maxwell's equations posed by the scattering of arbitrary shape objects in multilayered media are combined to efficiently and accurately simulate the electromagnetic operation of the system. The proposed simulation technique is validated against the original MoM solution of the problem. It is shown that the proposed hybrid technique exhibits superior performance based on both computation time and numerical accuracy compared with the conventional FDTD and MoM solution techniques. It is also shown that the position and size of the target, as well as the electromagnetic characteristics of the target, can be determined using a simple signal processing technique.

New regime map of the geometric optics approximation for scattering from random rough surfaces

The electromagnetic wave scattering from random roughness surfaces is a technologically important but challenging problem. There is a significant amount of interest in understanding the radiative properties of the rough surfaces for diverse applications. On one end, the rigorous models require the solutions of complex formulations of the Maxwell's equations or rely on various numerical schemes, which typically are computationally intensive. On the other hand, it has been found that the geometric optics (GO) ray tracing approximation method produces reasonably accurate radiative property predictions in some cases and with little computational effort. However, the latter ignores the wave interference and polarization effects, which are important when the wavelength is on the same order or larger than the geometrical length scale. It is therefore important to quantify the accuracy of the GO approximation. This study reports a new regime map based on the comparisons of the GO and finite-difference time-domain solutions.

Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data

Crosshole radar tomography is a useful tool in diverse investigations in geology, hydrogeology, and engineering. Conventional tomograms provided by standard ray-based techniques have limited resolution, primarily because only a fraction of the information contained in the radar data (i.e., the first-arrival times and maximum first-cycle amplitudes) is included in the inversion. To increase the resolution of radar tomograms, we have developed a versatile full-waveform inversion scheme that is based on a finite-difference time-domain solution of Maxwell’s equations. This scheme largely accounts for the 3D nature of radar-wave propagation and includes an efficient method for extracting the source wavelet from the radar data. After demonstrating the potential of the new scheme on two realistic synthetic data sets, we apply it to two crosshole field data sets acquired in very different geologic/hydrogeologic environments. These are the first applications of full-waveform tomography to observed crosshole radar data. The resolution of all full-waveform tomograms is shown to be markedly superior to that of the associated ray tomograms. Small subsurface features a fraction of the dominant radar wavelength and boundaries between distinct geological/hydrological units are sharply imaged in the full-waveform tomograms.

Full-Waveform Inversion of Crosshole Radar Data Based on 2-D Finite-Difference Time-Domain Solutions of Maxwell's Equations

Crosshole radar techniques are important tools for a wide range of geoscientific and engineering investigations. Unfortunately, the resolution of crosshole radar images may be limited by inadequacies of the ray tomographic methods that are commonly used in inverting the data. Since ray methods are based on high-frequency approximations and only account for a small fraction of the information contained in the radar traces, they are restricted to resolving relatively large-scale features. As a consequence, the true potential of crosshole radar techniques has yet to be realized. To address this issue, we introduce a full-waveform inversion scheme that is based on a finite-difference time-domain solution of Maxwell's equations. We benchmark our new scheme on synthetic crosshole data generated from suites of increasingly complex models. The full-waveform tomographic images accurately reconstruct the following: (1) the locations, sizes, and electrical properties of isolated subwavelength objects embedded in homogeneous media; (2) the locations and sizes of adjacent subwavelength objects embedded in homogeneous media; (3) abrupt media boundaries and average and stochastic electrical property variations of heterogeneous layered models; and (4) the locations, sizes, and electrical conductivities of water-filled tunnels and closely spaced subwavelength pipes embedded in heterogeneous layered models. The new scheme is shown to be remarkably robust to the presence of uncorrelated noise in the radar data. Several limitations of the full-waveform tomographic inversion are also identified. For typical crosshole acquisition geometries and parameters, small resistive bodies and small closely spaced dielectric objects may be difficult to resolve. Furthermore, electrical property contrasts may be underestimated. Nevertheless, the full-waveform inversions usually provide substantially better results than those supplied by traditional ray methods.

Debye Function Expansions of Complex Permittivity Using a Hybrid Particle Swarm-Least Squares Optimization Approach

With appropriate modifications, the finite-difference time-domain (FDTD) method can be used to analyze propagation through linear isotropic dispersive media. Although materials characterized by the Debye permittivity model can be analyzed accurately and efficiently using well established methods, the treatment of other types of frequency dependence is more difficult. This paper proposes the use of a weighted sum of Debye functions to approximate more general complex permittivity functions. A combination of the particle swarm optimization method and linear least squares optimization is used to find the relaxation frequencies and weights in the expansion, which can then be accommodated in the FDTD method using one of the established methods. Two key advantages of the proposed approach are that the relaxation frequencies are bandlimited and the weights are always positive. These two characteristics help to maintain the accuracy and stability of the FDTD solution. It is also shown that the correlation between the imaginary parts of two Debye functions is the same as that between the real parts.

A Review of Progress in FDTD Maxwell's Equations Modeling of Impulsive Subionospheric Propagation Below 300 kHz

Wave propagation at the bottom of the electromagnetic spectrum (below 300 kHz) in the Earth-ionosphere waveguide system has been an interesting and important area of investigation for the last four decades. Such wave propagation is characterized by complex phenomena involving nonhomogeneous and anisotropic media, and can result in resonances of the entire Earth-ionosphere cavity. In the spirit of this Special Issue, the goal of this paper is to call attention to emerging finite-difference time-domain computational solutions of Maxwell's equations for wave propagation below 300 kHz which promise to complement and extend previous analyses by pioneers such as Profs. Wait and Felsen. The following topical areas are discussed: long-range two-dimensional propagation, lightning sources and radiation, global propagation, Schumann resonances, hypothesized pre-seismic lithosphere sources and radiation, detection of deep underground resource formations, and remote sensing of localized ionospheric anomalies. We conclude with a prospectus for future research, especially in incorporating the physics of the anisotropic, nonhomogeneous magnetized plasma in a global planetary ionosphere.

FDTD Subcell Modeling of the Inner Conductor of the Coaxial Feed: Accuracy and Convergence Analysis

In this paper, we analyze the method of exciting and truncating the coaxial probe used to excite an electromagnetically coupled patch antenna. The goal of the analysis is to avoid the unstable and unreliable behavior of finite-difference time-domain (FDTD) solution. The model considered here is based on the subcell thin wire modeling of inner conductor of a coaxial probe. Two main categories of structures and excitation models are considered. In the first category, the truncated thin wire is separated from the absorbing boundary by two FDTD cells, for several excitation models and their location along the wire. In the second category, the thin wire is extended into the absorbing boundary, and both the hard and the resistive source models are investigated. The comparison of the results for the two aforementioned categories of the FDTD coaxial probe feeds may be of particular interest to computational electromagnetics community, as it may yield insight into the limitations of the most commercial software packages which do not allow for extension of the coaxial probe model into the absorbing boundary

Numerical modelling of electromagnetic waveguide effects on crosshole radar measurements

High-frequency electromagnetic (EM) wave propagation associated with borehole ground-penetrating radar (GPR) is a complicated phenomenon. To improve the understanding of the governing physical processes, we employ a finite-difference time-domain solution of Maxwell’s equations in cylindrical coordinates. This approach allows us to model the full EM wavefield associated with crosshole GPR surveys. Furthermore, the use of cylindrical coordinates is computationally efficient, correctly emulates the three-dimensional geometrical spreading characteristics of the wavefield, and is an effective way to discretise explicitly small-diameter boreholes. Numerical experiments show that the existence of a water-filled borehole can give rise to a strong waveguide effect which affects the transmitted waveform, and that excitation of this waveguide effect depends on the diameter of the borehole and the length of the antenna.

FDTD solutions for the distribution of radiation from dipoles embedded in dielectric particles

The finite-difference time-domain (FDTD) method is used to simulate the electromagnetic radiation emitted by an infinitesimal electric dipole embedded in a small particle with an arbitrary shape and internal composition. The far-field pattern of the radiation pertaining to dipoles embedded in a host particle is highly sensitive to the particle shape. Thus, it is possible to discriminate host particles according to their radiation patterns. The method reported here is also applicable to the study of induced Raman scattering and fluorescence phenomena and the detection of biological agents.