A high definition, finite difference time domain method

A high definition, finite difference time domain (HD-FDTD) method is presented in this paper. This new method allows the FDTD method to be efficiently applied over a very large frequency range including low frequencies, which are problematic for conventional FDTD methods. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and has been verified against analytical solutions within the frequency range 50 Hz-1 GHz. As an example of the lower frequency range, the method has been applied to the problem of induced eddy currents in the human body resulting from the pulsed magnetic field gradients of an MRI system. The new method only requires approximately 0.3% of the source period to obtain an accurate solution. (C) 2003 Elsevier Science Inc. All rights reserved.

Finite-difference time-domain-based studies of MRI pulsed field gradient-induced eddy currents inside the human body

In modern magnetic resonance imaging (MRI), patients are exposed to strong, rapidly switching magnetic gradient fields that, in extreme cases, may be able to elicit nerve stimulation. This paper presents theoretical investigations into the spatial distribution of induced current inside human tissues caused by pulsed z-gradient fields. A variety of gradient waveforms have been studied. The simulations are based on a new, high-definition, finite-difference time-domain method and a realistic inhomogeneous 10-mm resolution human body model with appropriate tissue parameters. it was found that the eddy current densities are affected not only by the pulse sequences but by many parameters such as the position of the body inside the gradient set, the local biological material properties and the geometry of the body. The discussion contains a comparison of these results with previous results found in the literature. This study and the new methods presented herein will help to further investigate the biological effects caused by the switched gradient fields in a MRI scan. (C) 2002 Wiley Periodicals, Inc.

An object-oriented designed finite-difference time-domain simulator for electromagnetic analysis and design in MRI - application to high field analyses

This paper presents a finite-difference time-domain (FDTD) simulator for electromagnetic analysis and design applications in MRI. It is intended to be a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The pro-ram has been constructed in an object-oriented framework. The design procedure is detailed and the numerical solver has been verified against analytical solutions for simple cases and also applied to various field calculation problems. In particular, the simulator is demonstrated for inverse RF coil design, optimized source profile generation, and parallel imaging in high-frequency situations. The examples show new developments enabled by the simulator and demonstrate that the proposed FDTD framework can be used to analyze large-scale computational electromagnetic problems in modern MRI engineering. (C) 2004 Elsevier Inc. All rights reserved.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

Characterization of ultra wideband antennas for personal communication devices using finite difference time domain technique

The current mobile networks don't offer sufficient data rates to support multimedia intensive applications in development for multifunctional mobile devices. Ultra wideband (UWB) wireless technology is being considered as the solution to overcome data rate bottlenecks in the current mobile networks. UWB is able to achieve such high data transmission rates because it transmits data over a very large chunk of the frequency spectrum. As currently approved by the U.S. Federal Communication Commission it utilizes 7.5 GHz of spectrum between 3.1 GHz and 10.6 GHz. ^ Successful transmission and reception of information data using UWB wireless technology in mobile devices, requires an antenna that has linear phase, low dispersion and a voltage standing wave ratio (VSWR) ≤ 2 throughout the entire frequency band. Compatibility with an integrated circuit requires an unobtrusive and electrically small design. The previous techniques that have been used to optimize the performance of UWB wireless systems, involve proper design of source pulses for optimal UWB performance. The goal of this work is directed towards the designing of antennas for personal communication devices, with optimal UWB bandwidth performance. Several techniques are proposed for optimal UWB bandwidth performance of the UWB antenna designs in this Ph.D. dissertation. ^ This Ph.D. dissertation presents novel UWB antenna designs for personal communication devices that have been characterized and optimized using the finite difference time domain (FDTD) technique. The antenna designs reported in this research are physically compact, planar for low profile use, with sufficient impedance bandwidth (>20%), antenna input impedance of 50-Ω, and an omni-directional (±1.5 dB) radiation pattern in the operating bandwidth. ^

Customization of the design of antenna using genetic algorithm and finite-difference time-domain technique

Antenna design is an iterative process in which structures are analyzed and changed to comply with certain performance parameters required. The classic approach starts with analyzing a "known" structure, obtaining the value of its performance parameter and changing this structure until the "target" value is achieved. This process relies on having an initial structure, which follows some known or "intuitive" patterns already familiar to the designer. The purpose of this research was to develop a method of designing UWB antennas. What is new in this proposal is that the design process is reversed: the designer will start with the target performance parameter and obtain a structure as the result of the design process. This method provided a new way to replicate and optimize existing performance parameters. The base of the method was the use of a Genetic Algorithm (GA) adapted to the format of the chromosome that will be evaluated by the Electromagnetic (EM) solver. For the electromagnetic study we used XFDTD™ program, based in the Finite-Difference Time-Domain technique. The programming portion of the method was created under the MatLab environment, which serves as the interface for converting chromosomes, file formats and transferring of data between the XFDTD™ and GA. A high level of customization had to be written into the code to work with the specific files generated by the XFDTD™ program. Two types of cost functions were evaluated; the first one seeking broadband performance within the UWB band, and the second one searching for curve replication of a reference geometry. The performance of the method was evaluated considering the speed provided by the computer resources used. Balance between accuracy, data file size and speed of execution was achieved by defining parameters in the GA code as well as changing the internal parameters of the XFDTD™ projects. The results showed that the GA produced geometries that were analyzed by the XFDTD™ program and changed following the search criteria until reaching the target value of the cost function. Results also showed how the parameters can change the search criteria and influence the running of the code to provide a variety of geometries.

Coarse-grid higher order finite-difference time-domain algorithm with low dispersion errors

Higher order (2,4) FDTD schemes used for numerical solutions of Maxwell`s equations are focused on diminishing the truncation errors caused by the Taylor series expansion of the spatial derivatives. These schemes use a larger computational stencil, which generally makes use of the two constant coefficients, C-1 and C-2, for the four-point central-difference operators. In this paper we propose a novel way to diminish these truncation errors, in order to obtain more accurate numerical solutions of Maxwell`s equations. For such purpose, we present a method to individually optimize the pair of coefficients, C-1 and C-2, based on any desired grid size resolution and size of time step. Particularly, we are interested in using coarser grid discretizations to be able to simulate electrically large domains. The results of our optimization algorithm show a significant reduction in dispersion error and numerical anisotropy for all modeled grid size resolutions. Numerical simulations of free-space propagation verifies the very promising theoretical results. The model is also shown to perform well in more complex, realistic scenarios.

Characterization and modeling of multi-conductor transmission line using Finite-difference Time-Domain method

A two-dimensional, 2D, finite-difference time-domain (FDTD) method is used to analyze two different models of multi-conductor transmission lines (MTL). The first model is a two-conductor MTL and the second is a threeconductor MTL. Apart from the MTL's, a three-dimensional, 3D, FDTD method is used to analyze a three-patch microstrip parasitic array. While the MTL analysis is entirely in time-domain, the microstrip parasitic array is a study of scattering parameter Sn in the frequency-domain. The results clearly indicate that FDTD is an efficient and accurate tool to model and analyze multiconductor transmission line as well as microstrip antennas and arrays.

Principal Component Analysis of Results Obtained from Finite-Difference Time-Domain Algorithms

Finite-Differences Time-Domain (FDTD) algorithms are well established tools of computational electromagnetism. Because of their practical implementation as computer codes, they are affected by many numerical artefact and noise. In order to obtain better results we propose using Principal Component Analysis (PCA) based on multivariate statistical techniques. The PCA has been successfully used for the analysis of noise and spatial temporal structure in a sequence of images. It allows a straightforward discrimination between the numerical noise and the actual electromagnetic variables, and the quantitative estimation of their respective contributions. Besides, The GDTD results can be filtered to clean the effect of the noise. In this contribution we will show how the method can be applied to several FDTD simulations: the propagation of a pulse in vacuum, the analysis of two-dimensional photonic crystals. In this last case, PCA has revealed hidden electromagnetic structures related to actual modes of the photonic crystal.

Buried-object detection using free-space time-domain near-field measurements

The detection of buried objects using time-domain freespace measurements was carried out in the near field. The location of a hidden object was determined from an analysis of the reflected signal. This method can be extended to detect any number of objects. Measurements were carried out in the X- and Ku-bands using ordinary rectangular pyramidal horn antennas of gain 15 dB. The same antenna was used as the transmitter and recei er. The experimental results were compared with simulated results by applying the two-dimensional finite-difference time-domain(FDTD)method, and agree well with each other. The dispersi e nature of the dielectric medium was considered for the simulation.

Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Long-range and high-resolution correlation optical time-domain reflectometry utilizing an all optical chaotic source

A high resolution optical time domain reflectometry (OTDR) based on an all-fiber chaotic source is demonstrated. We analyze the key factors limiting the operational range of such an OTDR, e.g., integral Rayleigh backscattering and the fiber loss, which degrade the optical signal to noise ratio at the receiver side, and then the guideline for counter-act such signal fading is discussed. The experimentally demonstrated correlation OTDR presents ability of 100km sensing range and 8.2cm spatial resolution (1.2 million resolved points), as a verification of the theoretical analysis. To the best of our knowledge, this is the first time that correlation OTDR measurement is performed over such a long distance with such high precision.

Long-range and high-precision correlation optical time-domain reflectometry utilizing an all-fiber chaotic source

We propose a long range, high precision optical time domain reflectometry (OTDR) based on an all-fiber supercontinuum source. The source simply consists of a CW pump laser with moderate power and a section of fiber, which has a zero dispersion wavelength near the laser's central wavelength. Spectrum and time domain properties of the source are investigated, showing that the source has great capability in nonlinear optics, such as correlation OTDR due to its ultra-wide-band chaotic behavior, and mm-scale spatial resolution is demonstrated. Then we analyze the key factors limiting the operational range of such an OTDR, e. g., integral Rayleigh backscattering and the fiber loss, which degrades the optical signal to noise ratio at the receiver side, and then the guideline for counter-act such signal fading is discussed. Finally, we experimentally demonstrate a correlation OTDR with 100km sensing range and 8.2cm spatial resolution (1.2 million resolved points), as a verification of theoretical analysis.

Optimization of a label-free biosensor vertically characterized based on a periodic lattice of high aspect ratio SU-8 nano-pillars with a simplified 2D theoretical model

We have recently demonstrated a biosensor based on a lattice of SU8 pillars on a 1 μm SiO2/Si wafer by measuring vertically reflectivity as a function of wavelength. The biodetection has been proven with the combination of Bovine Serum Albumin (BSA) protein and its antibody (antiBSA). A BSA layer is attached to the pillars; the biorecognition of antiBSA involves a shift in the reflectivity curve, related with the concentration of antiBSA. A detection limit in the order of 2 ng/ml is achieved for a rhombic lattice of pillars with a lattice parameter (a) of 800 nm, a height (h) of 420 nm and a diameter(d) of 200 nm. These results correlate with calculations using 3D-finite difference time domain method. A 2D simplified model is proposed, consisting of a multilayer model where the pillars are turned into a 420 nm layer with an effective refractive index obtained by using Beam Propagation Method (BPM) algorithm. Results provided by this model are in good correlation with experimental data, reaching a reduction in time from one day to 15 minutes, giving a fast but accurate tool to optimize the design and maximizing sensitivity, and allows analyzing the influence of different variables (diameter, height and lattice parameter). Sensitivity is obtained for a variety of configurations, reaching a limit of detection under 1 ng/ml. Optimum design is not only chosen because of its sensitivity but also its feasibility, both from fabrication (limited by aspect ratio and proximity of the pillars) and fluidic point of view. (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)