Finite-difference Time-domain Results Research Articles

Long Range Propagation of Lightning Pulses Using the FDTD Method

The numerical dispersion of the finite-difference time-domain (FDTD) method is a serious drawback in view of computing long range propagation of lightning pulses in the Earth-ionosphere waveguide. In this paper, it is shown that most of this dispersion can be removed by postprocessing the FDTD results. This makes possible the propagation of lightning pulses up to thousands of kilometres with reasonable computational times.

Simulation of ultrasound propagation through bovine cancellous bone using elastic and Biot’s finite-difference time-domain methods

The propagation of ultrasonic pulse waves in bovine cancellous bone has been numerically analyzed in two dimensions by using two finite-difference time-domain (FDTD) methods: the commonly used elastic FDTD method and an FDTD method extended with Biot's theory for a porous elastic solid saturated with viscous fluid. Both FDTD results were compared with the results of previous experiments by Hosokawa and Otani [J. Acoust. Soc. Am. 101, 558-562 (1997)], in which the Biot's fast and slow longitudinal waves were clearly identified. It was difficult to analyze both the fast and slow waves with the elastic FDTD method because of the inadequate 2D model of cancellous bone. On the other hand, in Biot's FDTD results that consider the pore fluid motion relative to the solid frame, both waves could be clearly observed. The experimental and simulated values of the speeds of these waves were in good agreement. Using the modified Biot's FDTD equations containing the possible attenuations for the fast wave other than the viscous loss due to the pore fluid motion, the amplitude ratio of the slow wave to the fast wave largely increased with the porosity, which also agrees with the experimental results.

Influence of Phantom Shell on SAR Measurement in 3-6 GHz Frequency Range

SUMMARY This paper presents the results of an investigation on the effect of a thin low-dielectric material (phantom shell) on measuring the Specific Absorption Rate (SAR) in the frequency range of 3 to 6 GHz. The International Electrotechnical Commission (IEC) has started to develop a SAR measurement procedure in order to cover such frequencies. In the procedure, the SAR is measured in a liquid phantom, which is a shell filled with tissue-equivalent liquid. Although the shell is thin and has low-dielectric properties, the influence of the phantom shell is thought to increase at higher frequencies. Therefore, an investigation using the transmission line model and the Finite-Difference Time-Domain (FD-TD) method was conducted. To verify the FD-TD results, measurements were also carried out. The calculation results using the FD-TD method agree well with the measurement results. If the frequency is higher, the SAR is affected by the shell even though the shell is thinner and has much lower dielectric properties than those of the tissue-equivalent liquid. Specifically, the SAR with the shell is approximately 1.3 times higher than without the shell at 5.2 GHz for the maximum case. The deviations in the loss and the thickness for the shell do not affect the SAR more than the relative permittivity.

Optimally Accurate Second-Order Time-Domain Finite-Difference Scheme for Acoustic, Electromagnetic, and Elastic Wave Modeling

Abstract. Numerical methods are extremely useful in solving real-life problems with complex materials and geometries. However, numerical methods in the time domain suffer from artificial numerical dispersion. Standard numerical techniques which are second-order in space and time, like the conventional Finite Difference 3-point (FD3) method, Finite-Difference Time-Domain (FDTD) method, and Finite Integration Technique (FIT) provide estimates of the error of discretized numerical operators rather than the error of the numerical solutions computed using these operators. Here optimally accurate time-domain FD operators which are second-order in time as well as in space are derived. Optimal accuracy means the greatest attainable accuracy for a particular type of scheme, e.g., second-order FD, for some particular grid spacing. The modified operators lead to an implicit scheme. Using the first order Born approximation, this implicit scheme is transformed into a two step explicit scheme, namely predictor-corrector scheme. The stability condition (maximum time step for a given spatial grid interval) for the various modified schemes is roughly equal to that for the corresponding conventional scheme. The modified FD scheme (FDM) attains reduction of numerical dispersion almost by a factor of 40 in 1-D case, compared to the FD3, FDTD, and FIT. The CPU time for the FDM scheme is twice of that required by the FD3 method. The simulated synthetic data for a 2-D P-SV (elastodynamics) problem computed using the modified scheme are 30 times more accurate than synthetics computed using a conventional scheme, at a cost of only 3.5 times as much CPU time. The FDM is of particular interest in the modeling of large scale (spatial dimension is more or equal to one thousand wave lengths or observation time interval is very high compared to reference time step) wave propagation and scattering problems, for instance, in ultrasonic antenna and synthetic scattering data modeling for Non-Destructive Testing (NDT) applications, where other standard numerical methods fail due to numerical dispersion effects. The possibility of extending this method to staggered grid approach is also discussed. The numerical FD3, FDTD, FIT, and FDM results are compared against analytical solutions.

Finite difference time domain Simulation of the Earth-ionosphere resonant cavity: Schumann resonances

This paper presents a numerical approach to study the electrical properties of the Earth's atmosphere. The finite-difference time-domain (FDTD) technique is applied to model the Earth's atmosphere in order to determine Schumann resonant frequencies of the Earth. Three-dimensional spherical coordinates are employed and the conductivity profile of the atmosphere versus height is introduced. Periodic boundary conditions are implemented in order to exploit the symmetry in rotation of the Earth and decrease computational requirements dramatically. For the first time, very accurate FDTD results are obtained, not only for the fundamental mode but also for higher order modes of Schumann resonances. The proposed method constitutes a useful tool to obtain Schumann resonant frequencies, therefore to validate electrical models for the terrestrial atmosphere, or atmospheres of other celestial bodies.

The effect of interfacial roughness on the normal incidence bandgap of one-dimensional photonic crystals

As discussed previously, interfacial roughness in one-dimensional photonic crystals (1DPCs) can have a significant effect on their normal reflectivity at the quarter-wave tuned wavelength. We report additional finite-difference time-domain (FDTD) simulations that reveal the effect of interfacial roughness on the normal-incidence reflectivity at several other wavelengths within the photonic bandgaps of various 1DPC quarter-wave stacks. The results predict that both a narrowing and red-shifting of the bandgaps will occur due to the roughness features. These FDTD results are compared to results obtained when the homogenization approximation is applied to the same structures. The homogenization approximation reproduces the FDTD results, revealing that this approximation is applicable to roughened 1DPCs within the parameter range tested (rms roughnesses < 20% and rms wavelengths < 50% of the photonic crystal periodicity) across the entire normal incidence bandgap.

Characteristics of ultraband printed slot antenna using FDTD method

A cross-shaped microstripline-fed printed slot antenna with wide bandwidth is presented in this paper. The proposed antenna is analyzed using the finite-difference time-domain (FDTD) method. It was found that the bandwidth of the antenna depends highly on the characteristics of the proposed antenna, which depend highly on the design parameters (ls, Ws, offset, lu, and ld). We also compare the optimized offset/Ws ratio and the calculated bandwidth of RT-5880 substrate for slot width Ws. When Ws is 32 mm, the optimized offset/Ws ratio is 0.344, and the calculated bandwidth is 3.744 MHz (112.6%). The experimental bandwidth of this antenna is from 1.85 to 5.70 GHz, which is approximately 115.5%, for VSWR ≤ 2.0. The proposed antenna showed triresonance characteristics due to the wide bandwidth. Experimental data for the return loss and the radiation pattern of the antenna are also presented, and are in good agreement with the FDTD results. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 162–165, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20576

Optical Scattering from Isolated Metal Nanoparticles and Arrays

Near-field scanning optical microscopy (NSOM) is used to explore the optical scattering from isolated metal nanoparticles (MNPs) and arrays of MNPs. The optical excitation source is an evanescent wave created through total internal reflection of a continuous wave laser beam at the sample−air interface. For optical excitation of isolated Ag and Au MNPs, experimental results show that the scattered light propagates into the far field at an angle of 19° from the substrate. Finite-difference time-domain (FDTD) calculations are used to study simpler but related metallic nanowire systems under evanescent wave excitation. The FDTD results are found to be similar to the experimental results, indicating the generality of the scattering phenomenon. NSOM characterization of plasmonic arrays that consist of closely spaced Ag MNPs are subsequently reported. Confined optical signals within the array are observed along with a reduction in the far-field scattered signal. Simultaneous collection of the atomic force micros...

Analysis of the CDF biorthogonal MRTD method with application to PEC targets

We consider the biorthogonal Cohen-Daubechies- Feauveau (CDF) wavelet family in the context of a biorthogonal multiresolution time-domain (bi-MRTD) analysis. A disadvantage of previous bi-MRTD analyses is an inability to handle abrupt changes in material properties, particularly for a perfect electric conductor (PEC). A multiregion method is proposed to address PEC targets. The proposed method is based on the fact that the CDF bi-MRTD may be viewed as a linear combination of several conventional finite-difference time-domain (FDTD) solutions. The implementation of the connecting surface is also simplified. Several numerical results are presented, with comparison to analytic and FDTD results.

Analysis of coplanar LiNbO3 waveguide structures applicable to electrooptic modulator with FDTD method

AbstractThe 3D finite‐difference time‐domain (FDTD) method and the 2D quasi‐static formulation have been used to calculate the characteristic impedance and the microwave effective index of coplanar waveguide structures on lithium niobate (LiNbO3) single‐crystal substrates with a yttria‐stabilized zirconia (YSZ) or SiO2 buffer layer. The results shown can be a good source to predict the modulator characteristics. The effects of the thin buffer layer and anisotropy of the LiNbO3 crystal (x‐cut and z‐cut) are discussed. The comparison between the FDTD and quasi‐static results shows good agreement. In this paper, the efficient modeling technique of the FDTD method for the coplanar waveguide (CPW) structures based on an anisotropic substrate with a thin buffer layer is developed. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 234–237, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11178

Numerical and experimental investigation of an ultrawideband ridged pyramidal horn antenna with curved launching plane for pulse radiation

We report the numerical analysis and experimental characterization of an ultrawideband (UWB) antenna designed for radiating short microwave pulses. The antenna consists of a pyramidal horn, a ridge, and a curved launching plane terminated with resistors. The pyramidal horn is connected to the outer conductor of the coaxial feed and serves as the ground plane. The curved launching plane is connected to the central conductor of the coaxial feed. Detailed three-dimensional finite-difference time-domain (FDTD) simulations have been conducted to assist with the characterization of the antenna. FDTD results are compared with experimental data and are shown to be in good agreement. We demonstrate that the antenna exhibits a very low voltage standing wave ratio (/spl les/1.5) over a wide frequency range from 1 to 11 GHz and a very high fidelity (/spl ges/0.92). The spatial distribution of radiated energy is characterized both in the time domain, using transient field observations at various angles, as well as in the frequency domain, using single-frequency far-field radiation patterns. We conclude that this antenna offers high-fidelity transmission and reception of ultrashort microwave pulses with minimal distortion.

Waveguides in finite-height two-dimensional photonic crystals

We present a three-dimensional (3-D) finite-difference time-domain (FDTD) analysis of the transmission and the waveguiding properties of dielectric structures of finite height. A two-dimensional (2-D) photonic-crystal geometry is used for lateral confinement, and traditional waveguiding by dielectric mismatch is used for vertical confinement. We investigate different types of waveguide in photonic crystals with a finite height. We examine the dependence of the guiding properties on the lengths of the holes that constitute the photonic crystal and the widths of the layers of the waveguide. The role of the filling ratio of the holes and the dielectric constants of the upper and the lower layers for the guiding properties is presented. Also, a comparison between the 3-D and the 2-D FDTD results is given.

Dispersion analysis of multilayer cylindrical transmission lines containing magnetized ferrite substrates

Recently, there has been a growing interest in using cylindrical transmission lines that contain magnetized ferrite material in a variety of applications. In this paper, the finite-difference time-domain (FDTD) method (in cylindrical coordinates) and the spectral-domain analysis (SDA) are used to calculate the propagation characteristics of cylindrical transmission lines that contain magnetized ferrite material. The magnetization can be either in the longitudinal or azimuthal directions. Specifically, the cylindrical microstrip line, and the cylindrical coplanar waveguide printed on magnetized ferrite substrate are analyzed. Both the FDTD and SDA results are in very good agreement. In addition, the results are compared to those of planar structures by taking the radius of the substrate to be large enough such that the curvature effect is negligible.

Application of the FDTD for the optimization of broad-band transitions between different types of transmission lines

We present the application of an optimizer-coupled finite-difference time-domain (FDTD) simulator for the optimal design of waveguide transitions. The software package contains a standard FDTD algorithm and common optimization routines. The illustrated approach is a very efficient way for various design problems of wave-guide discontinuities. Several types of transitions in an unusual aligned geometry were investigated. A broad-band minimization of reflection losses up to 14 GHz was achieved. Close agreement has been obtained between FDTD results and measurement over a wide frequency range.

A new heuristic diffraction coefficient for lossy dielectric wedges at normal incidence

A new heuristic diffraction coefficient is proposed for dielectric wedges with losses. This new diffraction coefficient, based on the uniform theory of diffraction (UTD), is valid for incidence orthogonal to the edge and when losses are such that the field transmitted through the wedge can be neglected. This applicability range fits typical scenarios for urban propagation models. Our results are compared to those predicted by using the diffraction coefficients of R.J. Luebbers (see IEEE Trans. Antennas Propagat., vol.AP-32, p.70-76, 1984) and P.D. Holm (see IEEE Trans. Antennas Propagat., vol.48, p.1211-19, 2000), and the rigorous diffraction coefficient (RDC) of G.D. Maliuzhinets (see Sov. Phys. Dokl., vol.3, no.4, p.752-5, 1958). Comparisons with a diffraction coefficient derived from the finite-difference time-domain (FDTD) simulations are also presented for right angle wedges. Parallel and perpendicular field polarizations are tested. The new heuristic diffraction coefficient shows clear improvement in agreement with the RDC and the FDTD results. Moreover, the proposed diffraction coefficient is as simple to compute as Luebbers' and Holm's coefficients.

Wide-Band T-Shaped Microstrip-Fed Twin-Slot Array Antenna

A numerical simulation and an experimental implementation of T-shaped microstrip-fed printed slot array antenna are presented in this paper. The proposed antenna with relative permittivity 4.3 and thickness 1.0mm is analyzed by the finite-difference time-domain (FDTD) method. The dependence of design parameters on the bandwidth characteristics is investigated. The measured bandwidth of twin-slot array antenna is from 1.37 GHz to 2.388 GHz, which is approximately 53.9 % for return loss less than or equal to -10 dB. The bandwidth of twin-slot is about 1.06 % larger than that of single-slot antenna. The measured results are in good agreement with the FDTD results.

Finite difference time domain analysis of cylindrical coplanar waveguide circuits

There is a growing interest in using cylindrical transmission line structures in microwave applications. In this paper, the finite difference time domain (FDTD) method is used to characterize several three-dimensional cylindrical coplanar waveguide (CCPW) geometries. Specifically, a CCPW series stub and a three-section CCPW filter are studied both theoretically and experimentally. Moreover, CCPW gap is characterized and the FDTD results are compared to those obtained using conformal mapping techniques. Effective absorbing boundary conditions are employed to truncate the FDTD mesh at the end walls and the outer radial boundary.

An FDTD algorithm with perfectly matched layers for general dispersive 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 revised formulation of modal absorbing and matched modal source boundary conditions for the efficient FDTD analysis of waveguide structures

A revised formulation of modal absorbing and matched modal source boundary condition is proposed for the efficient analysis of a waveguide circuit with the finite-difference time-domain (FDTD) method. The formulation is based on a suitable translation operator modeling, in time domain, the propagation in a uniform hollow waveguide. By applying this operator, a multimodal absorbing boundary condition is obtained. Moreover, a source algorithm is developed that generates a given incident wave, while absorbing each modal component reflected from a discontinuity. The source is capable of separating incident and reflected waves without requiring any presimulation of long uniform waveguides. The validity and effectiveness of the formulation is verified by means of three numerical experiments. The first two refer to waveguide discontinuities. In these cases, the FDTD results are compared to mode-matching results. The third example is a transition from waveguide to printed circuit transmission line. The numerical simulation is compared with published experimental results. The presented examples show that the generalized scattering matrix of a waveguide circuit can be evaluated accurately in the smallest computational space allowed by the structure.

Characterization of a single-step microstrip discontinuity in a substrate using the finite-difference time-domain method

A single-step microstrip discontinuity in a substrate is characterized using the finite-difference time-domain (FDTD) method, and an equivalent circuit model has been developed. The microstrip discontinuity newly introduced in this paper has a substrate thickness change in the longitudinal direction with a uniform strip width. The discontinuity has applications in patch antenna feed design and interconnections between microwave circuit modules. The simulation results are compared with those computed by HFSS to show good agreement. An equivalent circuit developed from the FDTD results, which is accurate within 2.4% in magnitudes of S11 and S21, can be applied for computer-aided designs. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 245–248, 2000.