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In order to accurately describe the behavior of an antenna, one needs to understand the radiation mechanisms that govern its operation. One way to gain such an insight is to view the fields and currents present on a radiating structure. Unfortunately, in close proximity to an antenna empirical techniques fail because the measurement probe alters the operation of the radiating structure. Computational methods offer a solution to this problem. By simulating the operation of an antenna, one can obtain electromagnetic field data near (or even internal to) a radiating structure. However, these computationally intense techniques often generate extremely large data sets that cannot be adequately interpreted using traditional graphical approaches. A visualization capability is developed that allows an analysis of the above-mentioned data sets. With this technique, the data is viewed from a unique, global perspective. This format is well suited for analytical investigations as well as debugging during modeling and simulation. An illustrative example is provided in the context of a rectangular microstrip patch antenna. A comparison is performed between the visualized data and the theory of operation for the microstrip patch in order to demonstrate that radiation mechanisms can be obtained visually. An additional analysis tool is developed using Gabor filters and image-processing techniques. This tool allows one to detect and filter electromagnetic waves propagating with different velocities (both speed and direction). By doing so, each mode of an antenna can be analyzed independently. The fields of a multi-moded, open-ended rectangular waveguide are analyzed in order to demonstrate the effectiveness of these techniques. / Master of Science

The Transmission Line Matrix (TLM) method is an existing and established mathematical method for conducting computational electromagnetic (CEM) simulations. TLM models Maxwell s equations by discretising the contiguous nature of an environment and its contents into individual small-scale elements and it is a computationally intensive process. This thesis focusses on parallel processing optimisations to the TLM method when considering the opposing ends of the contemporary computing hardware spectrum, namely large-scale computing systems versus small-scale mobile computing devices. Theoretical aspects covered in this thesis are: The historical development and derivation of the TLM method. A discrete random variable (DRV) for rain-drop diameter,allowing generation of a rain-field with raindrops adhering to a Gaussian size distribution, as a case study for a 3-D TLM implementation. Investigations into parallel computing strategies for accelerating TLM on large and small-scale computing platforms. Implementation aspects covered in this thesis are: A script for modelling rain-fields using free-to-use modelling software. The first known implementation of 2-D TLM on mobile computing devices. A 3-D TLM implementation designed for simulating the effects of rain-fields on extremely high frequency (EHF) band signals. By optimising both TLM solver implementations for their respective platforms, new opportunities present themselves. Rain-field simulations containing individual rain-drop geometry can be simulated, which was previously impractical due to the lengthy computation times required. Also, computationally time-intensive methods such as TLM were previously impractical on mobile computing devices. Contemporary hardware features on these devices now provide the opportunity for CEM simulations at speeds that are acceptable to end users, as well as providing a new avenue for educating relevant user cohorts via dynamic presentations of EM phenomena.

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

<p>In this thesis we study hybrid numerical methods to be usedin computational electromagnetics. We restrict the methods tospectral domain and scattering problems. The hybrids consist ofcombinations of Boundary Element Methods and Geometrical Theoryof Diffraction.</p><p>In the thesis three hybrid methods will be presented. Onemethod has been developped from a theoretical idea to anindustrial code. The two other methods will be presented mainlyfrom a theoretical perspective. We will also give shortintroductions to the Boundary Element Method and theGeometrical Theory of Diffraction from a theoretical andimplementational point of view.</p><p><b>Keywords:</b>Maxwell’s equations, Geometrical Theoryof Diffraction, Boundary Element Method, Hybrid methods,Electromagnetic Scattering</p>

A set of tools are proposed for the efficient modeling of several classes of problems related to periodic structures in microwave and optical regimes with Finite-Difference Time-Domain method. The first category of problems under study is the interaction of non-periodic sources and printed elements with infinitely periodic structures. Such problems would typically require a time-consuming simulation of a finite number of unit cells of the periodic structures, chosen to be large enough to achieve convergence. To alleviate computational cost, the sine-cosine method for the Finite-Difference Time-Domain based dispersion analysis of periodic structures is extended to incorporate the presence of non-periodic, wideband sources, enabling the fast modeling of driven periodic structures via a small number of low cost simulations. The proposed method is then modified for the accelerated simulation of microwave circuit geometries printed on periodic substrates. The scheme employs periodic boundary conditions applied at the substrate, to dramatically reduce the computational domain and hence, the cost of such simulations. Emphasis is also given on radiation pattern calculation, and the consequences of the truncated computational domain of the proposed method on the computation of the electric and magnetic surface currents invoked in the near-to-far-field transformation. It has been further demonstrated that from the mesh truncation point of view, the scheme, which has a unified form regardless dispersion and conductivity, serves as a much simpler but equally effective alternative to the Perfectly Matched Layer provided that the simulated domain is periodic in the direction of termination. The second category of problems focuses on the efficient characterization of nonlinear periodic structures. In Finite-Difference Time-Domain, the simulation of these problems is typically hindered by the fine spatial and time gridding. Originally proposed for linear structures, the Alternating-Direction Implicit Finite-Difference Time-Domain method, as well as a novel spatial filtering method, are extended to incorporate nonlinear media. Both methods are able to use time-step sizes beyond the conventional stability limit, offering significant savings in simulation time.

A set of tools are proposed for the efficient modeling of several classes of problems related to periodic structures in microwave and optical regimes with Finite-Difference Time-Domain method. The first category of problems under study is the interaction of non-periodic sources and printed elements with infinitely periodic structures. Such problems would typically require a time-consuming simulation of a finite number of unit cells of the periodic structures, chosen to be large enough to achieve convergence. To alleviate computational cost, the sine-cosine method for the Finite-Difference Time-Domain based dispersion analysis of periodic structures is extended to incorporate the presence of non-periodic, wideband sources, enabling the fast modeling of driven periodic structures via a small number of low cost simulations. The proposed method is then modified for the accelerated simulation of microwave circuit geometries printed on periodic substrates. The scheme employs periodic boundary conditions applied at the substrate, to dramatically reduce the computational domain and hence, the cost of such simulations. Emphasis is also given on radiation pattern calculation, and the consequences of the truncated computational domain of the proposed method on the computation of the electric and magnetic surface currents invoked in the near-to-far-field transformation. It has been further demonstrated that from the mesh truncation point of view, the scheme, which has a unified form regardless dispersion and conductivity, serves as a much simpler but equally effective alternative to the Perfectly Matched Layer provided that the simulated domain is periodic in the direction of termination. The second category of problems focuses on the efficient characterization of nonlinear periodic structures. In Finite-Difference Time-Domain, the simulation of these problems is typically hindered by the fine spatial and time gridding. Originally proposed for linear structures, the Alternating-Direction Implicit Finite-Difference Time-Domain method, as well as a novel spatial filtering method, are extended to incorporate nonlinear media. Both methods are able to use time-step sizes beyond the conventional stability limit, offering significant savings in simulation time.

In this thesis we study hybrid numerical methods to be usedin computational electromagnetics. We restrict the methods tospectral domain and scattering problems. The hybrids consist ofcombinations of Boundary Element Methods and Geometrical Theoryof Diffraction. In the thesis three hybrid methods will be presented. Onemethod has been developped from a theoretical idea to anindustrial code. The two other methods will be presented mainlyfrom a theoretical perspective. We will also give shortintroductions to the Boundary Element Method and theGeometrical Theory of Diffraction from a theoretical andimplementational point of view. <b>Keywords:</b>Maxwell’s equations, Geometrical Theoryof Diffraction, Boundary Element Method, Hybrid methods,Electromagnetic Scattering / NR 20140805

Yes / Potential demodulating ability in biological tissue exposed to Radio Frequency (RF) signals intrinsically requires an unsymmetrical diode-like nonlinear response in tissue samples. This may be investigated by observing possible generation of the second harmonic in a cavity resonator designed to have fundamental and second harmonic resonant frequencies with collocated antinodes. Such a response would be of interest as being a mechanism that could enable demodulation of information-carrying waveforms having modulating frequencies in ranges that could interfere with cellular processes. Previous work has developed an experimental system to test for such responses: the present work reports an electric circuit model devised to facilitate calibration of any putative nonlinear RF energy conversion occurring within a nonlinear test-piece inside the cavity. The method is validated computationally and experimentally using a well-characterised nonlinear device. The variations of the reflection coefficients of the fundamental and second harmonic responses of the cavity due to adding nonlinear and lossy material are also discussed. The proposed model demonstrates that the sensitivity of the measurement equipment plays a vital role in deciding the required input power to detect any second harmonic signal, which is expected to be very weak. The model developed here enables the establishment of a lookup table giving the level of the second harmonic signal in the detector as a function of the specific input power applied in a measurement. Experimental results are in good agreement with the simulated results. / Engineering and Physical Science Research Council through Grant EP/E022936A

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