The Finite-Difference Time-Domain (FDTD) method has been used extensively in electromagnetic field modeling because of its ability to robustly handle interactions of fields with complex heterogeneous structures. In particular, the total/scattered field formulation has allowed for efficient implementation of arbitrarily directed uniform plane waves, consequently facilitating efficient modeling of far-field scattering problems. The total/scattered approach is not restricted to plane waves and can be expanded to any waveforms that can be described in analytical or semi-analytical form. While existing formulations of FDTD have been immensely successful, they are not well suited to problems that involve near field scattering/interaction problems, where both the source and object are in the same domain but at a substantial distance from each other. This is due to the exceedingly high demands for computational resources that may result from the domain size, and/or dramatically different requirements for the mesh density in the source and object areas. One solution to this problem is to separate the domain into source and scatterer regions coupled by surface boundary radiation conditions. However, this method can incur large storage requirements for calculation of the radiation conditions. A specific near-field situation of interest to the utility industry is the case of workers near high voltage powerlines. In this instance, the field pattern takes on a cylindrical, transverse electromagnetic character. More general radiating sources can be accurately represented in the near-field by using spherical wave expansions, which are often used to represent antennas measured on test ranges. Successful implementation of these analytic solutions is feasible within the FDTD framework, and would allow for the illumination of the scatterer modeled at a considerably lower cost than in the standard approach. This thesis presents a method where these non-uniform, near-field, sources can be implemented implicitly as source conditions in an existing FDTD method. The specific case of powerline fields is described first, followed by the more general case of spherical waves. The analytic solution for powerline fields is implemented to show that near-field source configuration can be successfully modeled implicitly with accurate and efficient results. The method is validated by comparing with known analytic solutions, with very good accuracy being achieved. Then, a specific example of a human under a powerline close by is modeled to examine predictions made earlier under the assumption of a plane wave source condition. For a similar powerline source configuration, results of organ dosimetry predict that induced fields are from ten to sixty percent greater than predicted with the plane wave source. This same approach is applied to model a more general and difficult problem, namely spherical waves as sources in the total/scattered FDTD, called the SW-FDTD. Since transverse properties of spherical modes are known, the behavior of a mode can be represented on a one-dimensional radial grid. Thus, much like the plane wave sources in the FDTD method, the spherical wave modes are time-stepped on one-dimensional staggered electric/magnetic field source grids in the radial direction, representing mode propagation in free space. Spherical wave modes can then be interpolated and summed on the Huygens’ surface to represent the total field of the source, thus providing the coupling between the complex source and a scatterer using one-dimensional grids. It is assumed that the object of interest is beyond the reactive near-field of the source, and therefore there is no significant coupling between source and object. The SW-FDTD method is validated by comparing simulations with several analytic solutions that increase in complexity, demonstrating very good accuracy. Issues relating to the numerical implementation are discussed, including the effects of numerical dispersion, stability, and simple Mur first order boundary conditions. Incorporation of the method as a source condition in an existing FDTD program, and validation of this synthesis, show that the SW-FDTD method can implictly model sources as accurately as explicit models do. The efficiency, and the reduction of errors remain issues for further research to improve the overall utility of the SW-FDTD method. / Graduate

Dissertation submitted in compliance with the requirements for Master's Degree in Technology: Electrical Engineering (Light Current), Durban Institute of Technology, 2002. / Modern society as a whole seems destined to have an ever-increasing demand for power for both industrial and domestic use, as continued population growth means that cities, suburbs and industrial areas become larger and denser. At the same time the trend toward increased productivity in all segments of industry is influencing the development and techniques employed at locating faults in power cables and networks to ensure only limited downtime and reduced direct and indirect costs associated with the location of faults / M

Plasmonic structures are utilized in many applications ranging from bio-medicine to solar energy generation and transfer. Numerical schemes capable of solving equations of classical electrodynamics have been the method of choice for characterizing scattering properties of such structures. However, as dimensions of these plasmonic structures reduce to nanometer scale, quantum mechanical effects start to appear. These effects cannot be accurately modeled by available classical numerical methods. One of these quantum effects is the tunneling, which is observed when two structures are located within a sub-nanometer distance of each other. At these small distances electrons “jump" from one structure to another and introduce a path for electric current to flow. Classical equations of electrodynamics and the schemes used for solving them do not account for this additional current path. This limitation can be lifted by introducing an auxiliary tunnel with material properties obtained using quantum models and applying a classical solver to the structures connected by this auxiliary tunnel. Early work on this topic focused on quantum models that are generated using a simple one-dimensional wave function to find the tunneling probability and assume a simple Drude model for the permittivity of the tunnel. These tunnel models are then used together with a classical frequency domain solver. In this thesis, a time domain surface integral equation solver for quantum corrected analysis of transient plasmonic interactions is proposed. This solver has several advantages: (i) As opposed to frequency domain solvers, it provides results at a broad band of frequencies with a single simulation. (ii) As opposed to differential equation solvers, it only discretizes surfaces (reducing number of unknowns), enforces the radiation condition implicitly (increasing the accuracy), and allows for time step selection independent of spatial discretization (increasing efficiency). The quantum model of the tunnel is obtained using density functional theory (DFT) computations, which account for the atomic structure of materials. Accuracy and applicability of this (quantum corrected) time domain surface integral equation solver will be shown by numerical examples.

No description available.

The Finite-Difference Time-Domain (FDTD) method has become a very powerful tool for the analysis of propagating electromagnetic waves. It involves the discretization of Maxwell's equations in both time and space that leads to a numerical solution of the wave propagation problem in the time domain. The technique's main benefits are that it permits the description of wave propagation in non-uniform media, it can easily accommodate a wide range of boundary conditions, and it can be used to model nonlinear effects as well as the wave behaviour near localized structures or material defects. In this study, we extend this technique to mechanical wave propagation in piezoelectric crystals. It is observed to give large reflection artefacts generated by the computational boundaries which interfere with the desired wave propagation. To solve this problem, the renowned absorbing boundary condition called perfectly matched layer (PML) is used. PML was first introduced in 1994 for electromagnetic wave propagation. Our research has further developed this idea for acoustic wave propagation in piezoelectric crystals. The need to improve the large reflection artefacts by introducing a finite thickness PML has reduced acoustic wave reflection occurring due to practical errors to less than 0.5 %. However, it is found that PML can generate numerical instabilities in the calculation of acoustic fields in piezoelectric crystals. Theses observations are also discussed in this report. / Thesis / Master of Applied Science (MASc)

Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Recent progress in laser and semiconductor technology has allowed for far easier generation and measuring of coherent terahertz radiation, a previously difficult region in the radiation spectrum to coherently generate. Time based terahertz spectroscopy is a rather unique form of spectroscopy. Not only is it time based, but the electric field is measured instead of the intensity. This allows for the measurement of the complex refractive index. From this one can obtain certain details of the structure and environment of the sample being studied. A terahertz time-domain spectroscopy setup was constructed during this project. This setup used low temperature grown GaAs photoconductive antennae, with multiple antenna size options available for both the receiving and transmitting antennae. After the construction and alignment of this setup, the antennae were characterized. Lastly measurements were performed on the background, sugar and silicon to demonstrate the capabilities of the system. It was found that the measured terahertz electric field amplitude increased with the intensity of the pump pulse and that the amplitude of the measured terahertz electric field was dependent on the polarization of the pump pulse. As the size of the antenna was increased so too did the amplitude of the measured electric field and conversely the bandwidth of the measured terahertz electric field decreased with the increase of antenna size. This held true for both the transmitting and receiving antennae. / AFRIKAANSE OPSOMMING: Danksê onlangse tegnologiese onwikkelings in lasers en halfgeleier het dit veel makliker geraak om terahertz straling te genereer wat fase samehangendheid toon. Voor hierdie ontwikkelings was straling in hierdie spektrale gebied moeilik om te genereer op ’n wyse wat fase samehangendheid toon. Tyd verwante terahertz spektroskopie is taamlik uniek, aangesien die metings in tyd geneem word en die elektriese veld amplitude word pleks van die intensiteit gemeet. Een van die voordele van hierdie metode is dat dit toelaat vir die meeting van die komplekse brekingsindeks van monsters. Dit is moontlik om van die komplekse brekingsindeks strukturele en omgewings eienskappe van die monster af te lei. Gedurende die projek was ’n tyd verwante terahertz spektroskopie sisteem gebou wat gebaseer was op lae temperatuur gegroeide GaAs foto-geleidende antennas. Die sisteem bevat vier antennas van verskillende groottes aan beide die sender en ontvanger kant. Die antennas was gekarakteriseer na die bou en belyning van die terahertz sisteem en meetings was gedoen op die agtergrond, suiker en silikon om die sisteem se vermoë te demonstreer. Dit was gevind dat die amplitude van die gemete terahertz elektriese veld groter geraak het soos die intensiteit van die pomp puls verhoog was en dat die die amplitude van die gemete terahertz electriese veld afhanklik was van die polarisasie van die pomp puls. Die amplitude van van die gemete terahertz elektriese veld het gegroei met die grootte van die antenna, maar hoe groter die antenna geraak het, hoe kleiner was die bandwydte van die gemete terahertz elektriese veld. Hierdie was die geval vir beide die sender en ontvanger antennas.

This work presents an investigation into the optical scattering of heterogeneous cells with an application to two-photon imaging, optical scattering measurements and STED imaging. Using the finite difference time-domain (FDTD) method, the full-wave scattering by many cells containing multiple organelles with varying indices of refraction is computed. These simulations were previously limited to single cells for reasons of computational cost. A superposition approximation that uses the coherent linear superposition of FDTD-determined farfield scattering patterns of small numbers of cells to estimate the scattering from a larger tissue was developed and investigated. It was found that for the approximation to be accurate, the scattering sub-problems must at minimum extend along the incident field propagation axis for the full depth of the tissue, preserving the scattering that takes place in the direction of propagation. The FDTD method was used to study the scattering effects of multiple inhomogeneous cells on the propagation of a focused Gaussian beam with an application to two-photon imaging. It was found that scattering is mostly responsible for the reduction in two-photon fluorescence signal as depth is increased. It was also determined that for the chosen beam parameters and the cell and organelle configurations used, the nuclei are the dominant scatterers. FDTD was also utilized in an investigation of cellular scattering effects on the propagation of a common depletion beam used in STED microscopy and how scattering impacts the image obtained with a STED microscope. An axial doughnut beam was formulated and implemented in FDTD simulations, along with a corresponding focused Gaussian beam to simulate a fluorescence excitation beam. It was determined that the depletion beam will maintain a well-defined axial null in spite of scattering, although scattering will reduce the resulting fluorescence signal with focal depth. / text

No description available.

<p>Domain decomposition method provides a solution for the very large electromagnetic</p><p>system which are impossible for single domain methods. Discontinuous Galerkin</p><p>(DG) method can be viewed as an extreme version of the domain decomposition,</p><p>i.e., each element is regarded as one subdomain. The whole system is solved element</p><p>by element, thus the inversion of the large global system matrix is no longer necessary,</p><p>and much larger system can be solved with the DG method compared to the</p><p>continuous Galerkin (CG) method.</p><p>In this work, the DG method is implemented on a subdomain level, that is, each subdomain contains multiple elements. The numerical flux only applies on the</p><p>interfaces between adjacent subdomains. The subodmain level DG method divides</p><p>the original large global system into a few smaller ones, which are easier to solve,</p><p>and it also provides the possibility of parallelization. Compared to the conventional</p><p>element level DG method, the subdomain level DG has the advantage of less total</p><p>DoFs and fexibility in interface choice. In addition, the implicit time stepping is </p><p>relatively much easier for the subdomain level DG, and the total CPU time can be</p><p>much less for the electrically small or multiscale problems.</p><p>The hybrid of elements are employed to reduce the total DoF of the system.</p><p>Low-order tetrahedrons are used to catch the geometry ne parts and high-order</p><p>hexahedrons are used to discretize the homogeneous and/or geometry coarse parts.</p><p>In addition, the non-conformal mesh not only allow dierent kinds of elements but</p><p>also sharp change of the element size, therefore the DoF can be further decreased.</p><p>The DGTD method in this research is based on the EB scheme to replace the</p><p>previous EH scheme. Dierent from the requirement of mixed order basis functions</p><p>for the led variables E and H in the EH scheme, the EB scheme can suppress the</p><p>spurious modes with same order of basis functions for E and B. One order lower in</p><p>the basis functions in B brings great benets because the DoFs can be signicantly</p><p>reduced, especially for the tetrahedrons parts.</p><p>With the basis functions for both E and B, the EB scheme upwind </p><p>ux and</p><p>EB scheme Maxwellian PML, the eigen-analysis and numerical results shows the</p><p>eectiveness of the proposed DGTD method, and multiscale problems are solved</p><p>eciently combined with the implicit-explicit hybrid time stepping scheme and multiple</p><p>kinds of elements.</p><p>The EB scheme DGTD method is further developed to allow arbitrary anisotropic</p><p>media via new anisotropic EB scheme upwind </p><p>ux and anisotropic EB scheme</p><p>Maxwellian PML. The anisotropic M-PML is long time stable and absorb the outgoing</p><p>wave eectively. A new TF/SF boundary condition is brought forward to</p><p>simulate the half space case. The negative refraction in YVO4 bicrystal is simulated</p><p>with the anisotropic DGTD and half space TF/SF condition for the rst time with</p><p>numerical methods.</p> / Dissertation

by Ronald Siu-kwong, Ip. / "June 1999." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (p. 89-94). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.