Doctor of Philosophy / Department of Physics / Christopher M. Sorensen / This work presents a microphysical model of the classical interaction of electromagnetic waves with arbitrary single and multiple particles. The model is based on the volume integral equation solution to the macroscopic time-harmonic Maxwell equations. The integral is discretized over a particle's volume. The near and far-field scattered wave is then described by the secondary radiation from the discretized elements. The physical origin of the angular structure of the scattered wave is characterized by the superposition of these secondary waves. A graphical technique is developed to visualize how this superposition relates to the physical features of a particle, e.g., its size, shape, and refractive index. Numerical and analytical implementations of the model are presented for spherical and spheroidal particles and fractal-like spherical-particle aggregates. The connection between the reflection symmetry of a particle and the polarization state of its far-field scattered wave is illustrated. The model is used to explain the cause of the angular power-law patterns in a particle's scattered intensity. An analysis of the internal field distribution in fractal-like aggregates is performed and the results are compared to the Rayleigh-Debye-Gans theory. Extinction and the optical theorem are examined within the context of the model, resulting in a new understanding for the physical mechanism causing extinction and implications regarding its measurement. The culmination of this work is the unification of multiple scattering-concepts, often regarded as distinct, and the resulting insight afforded by the unified microphysical picture. This unified view is shown to reveal a new and simple explanation for the famous extinction paradox.

Visualizações imersivas são muito valiosas para melhorar a compreensão de uma variedade de fenômenos físicos, que podem ser eventualmente modelados na forma discreta e simulados por computador. Dentre possíveis aplicações podemos utilizar a visualização imersiva como ferramenta pedagógica para percepção aumentada de tópicos complexos, ou como uma poderosa ferramenta de apoio analítico para ajudar os engenheiros a interpretarem os resultados de projetos. Este projeto de pesquisa aborda o uso da visualização imersiva de campos eletromagnéticos, especificamente os campos gerados por redes sem fio, largamente utilizadas no cotidiano como é o caso das redes IEEE 802.11 (Wi-Fi). Para tanto este trabalho propõe métodos novos para visualizar, em tres dimensões, campos eletromagnéticos variantes no tempo e distribuições de parâmetros interessantes relacionados a redes sem fio. Para atingir este objetivo, uma versão aprimorada do método de diferenças finitas no domínio do tempo (FDTD) é desenvolvido: o método FDTD de alta ordem e malha grosseira (Coarse Grid Higher Order FDTD, CGHO-FDTD). Portanto, soluções numéricas muito precisas, mais rápidas, e computacionalmente mais eficientes das equações de Maxwell podem ser obtidas. Os cálculos numéricos podem ser ainda mais rápidos pelo uso de computação paralela em um aglomerado de computadores. As características de domínio de tempo facilitam a criação de instantâneos de campos eletromagnéticos que estão se propagando, e desta maneira é possível criar figuras e animações tridimensionais que podem ser usadas para explicar alguns dos seguintes fenômenos físicos comuns em redes sem fio: difração, reflexão, e atenuação. Para que aumente a percepção física ainda mais, visualizações imersivas são feitas em um ambiente de realidade virtual. Por fim, a ferramenta desenvolvida também pode ser usada para criar distribuições muito detalhadas de parâmetros importantes que afetam o desempenho em uma rede sem fio. É mostrado que simulações de um ambiente fechado para prever a distribuição de potência de uma rede sem fio do tipo IEEE 802.11 (Wi-Fi), estão de acordo com as medidas. / Immersive visualizations are very valuable in order to improve the understanding of a variety of physical phenomena that can be modeled numerically and simulated by computers. Amongst the possible applications, we could utilize immersive visualizations as a pedagogical tool for enhanced perception of complex topics, or as a powerful tool that helps engineers interpret the outcome of simulations. This research project approaches the use of immersive visualizations of electromagnetic fields, especially fields generated by wireless networks widely utilized in the everyday life, as is the case for networks of the type IEEE 802.11 (Wi-Fi). For such a purpose this work proposes new methods to three-dimensionally visualize time-varying electromagnetic fields, and distributions of interesting parameters related to wireless networks. To achieve these objectives, a better version of the finite-difference time-domain (FDTD) method is developed: the Coarse Grid Higher Order FDTD (CGHO-FDTD) method. Thus highly accurate, faster and more computationally efficient numerical solutions of Maxwells equations can be obtained. The numerical calculations are made even faster by the use of parallel computing on a cluster of computers. The characteristics of the time domain facilitate the creation of snapshots of the propagating electromagnetic fields, and in this manner it is possible to create three-dimensional figures and animations that can be used to explain some of the following common physical effects found in wireless networks: diffraction, reflection, and attenuation. To further enhance the perception of the physics, immersive visualizations are carried out in a virtual reality environment. Finally, the developed tool can also be used to create highly detailed distributions of important parameters that affect the performance in wireless networks. It is shown that simulations to predict the power distribution in an indoor wireless network of the type IEEE 802.11 (Wi-Fi), agree very well with measurements.

This study is performed as a partial aid to a larger study that aims to determine if electromagnetic fields produced by underwater power cables have any effect on marine species. In this study, a new numerical method for calculating magnetic fields around subsea power cables is presented and tested. The numerical method is derived from electromagnetic theory, and the program, Matlab, is implemented in order to run the simulations. The Matlab code is validated by performing a series of tests in which the theoretical code is compared with other previously validated magnetic field solvers. Three main tests are carried out; two of these tests are physical and involve the use of a magnetometer, and the third is numerical and compares the code with another numerical model known as Ansys. The data produced by the Matlab code remains consistent with the measured values from both the magnetometer and the Ansys program; thus, the code is considered valid. The validated Matlab code can then be implemented into other parts of the study in order to plot the magnetic field around a specific power cable. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

In this report, we study various nonlinear wave equations arising in mathematical physics and investigate the existence of solutions to these equations using variational methods. In particular, we look for particle-like traveling wave solutions known as solitary waves. This study is motivated by the prevalence of solitary waves in applications and the rich mathematical structure of the nonlinear wave equations from which they arise. We focus on a semilinear perturbation of Maxwell's equations and the nonlinear Klein - Gordon equation coupled with Maxwell's equations. Physical ramifications of these equations are also discussed.

Das Strahlungsfeld in einem absorbierenden, periodischen Dielektrikum ist kanonisch quantisiert worden. Dabei wurde ein eindimensionales Modell mit punktförmigen Streuern betrachtet, deren Polarisierbarkeit den Kramers-Kronig Relationen gehorcht. Es wurde ein Quantisierungsverfahren nach Knöll, Scheel und Welsch [1] verwendet, das als eine Ergänzung zum mikroskopischen Huttner-Barnett Schema [2] aufgefaßt werden kann und in dem auf der Basis der phänomenologischen Maxwell Gleichungen eine bosonische Rauschpolarisation als die Quelle des Feldes auftritt. Das Problem reduziert sich dabei auf die Bestimmung der klassischenGreens Funktion. Die Kramers-Kronig Relationen der komplexen Polarisierbarkeit der Punktstreuer sichert die korrekte Verknüpfung zwischen Dispersion und Absorption. Der Punktstreuer ist dabei ein idealisiertes Modell, um periodische Hintergrundmedien, denen das Strahlungsfeld ausgesetzt ist, zu beschreiben. Er bedarf jedoch eines Kompromisses, um die entsprechenden Rauschquellen zu konstruieren. Es konnte gezeigt werden, daß der Punktstreuer dasselbe Streuverhalten wie eine dünne Potentialschwelle besitzt und damit die technischen Schwierigkeiten für den Fall eines absorptiven Punktstreuers überwunden werden können. An Hand dieses Beispiels konnte das Quantisierungsschema nach Knöll, Scheel und Welsch auf periodische und absorbierende Strukturen angewendet werden. Es ist bekannt, daß die Bestimmung der Modenstruktur für den Fall der Modenzerlegung des Strahlungsfeldes ein rein klassisches Problem darstellt. Mit Ausnahme des Vakuums ist eine zweckmäßige Modenzerlegung nur dann durchführbar, wenn mit einer reellen Polarisierbarkeit die Absorption vernachlässigt werden kann. Aus den Kramers-Kronig Relationen wird klar, daß solch eine Annahme nur in bestimmten Intervallen des Frequenzspektrums gerechtfertigt werden kann. Es wurde gezeigt, daß auch das quantisierte Strahlungsfeld in Anwesenheit der Punktstreuer in eben solchen Intervallen in Quasimoden entwickelt werden kann, wenn man neue Quasioperatoren als Erzeuger und Vernichter einführt. Die bosonischen Vertauschungsrelationen dieser Operatoren konnten bestätigt werden. Die allgemeine Vertauschungsrelation kanonisch konjugierter Variablen im Sinne der kanonischen Quantisierung kann für das elektrische Feld und das Vektorpotential beibehalten werden. In der Greens Funktion sind sämtliche Informationen über die dispersiven und absorptiven Eigenschaften des Dielektrikums sowie über die räumliche Struktur enthalten. Die wesentlichen Merkmale werden dabei durch den Reflexionskoeffizienten nach Boedecker und Henkel [3] bestimmt, der das Reflexionsverhalten an einem unendlich ausgedehnten Halbraum aus periodisch angeordneten Punktstreuern beschreibt. Mit Hilfe des Transfermatrixformalismus war es möglich einen allgemeinen Zugang zum Reflexionsverhalten zunächst endlicher Strukturen zu erhalten. Die Ausdehnung auf den Halbraum mit Hilfe der Klassifizierung in Untergruppen der Transfermatrizen nach ermöglichte es, den Reflexionskoeffizienten nach Boedecker und Henkel [3] auch geometrisch plausibel zu machen. Ein wesentlicher Aspekt von periodischen Systemen ist die Translationssymmetrie, die im Fall unendlich ausgedehnter, verlustfreier Systeme auf eine ideale Bandstruktur führt. Mit Hilfe der Untergruppenklassifizierung kann im verlustfreien Fall die Geometrie der Anordnung indirekt mit der Bandstruktur verknüpft werden. Es konnte nachgewiesen werden, daß auch der einzelne Punktstreuer immer in einer dieser Untergruppen zu finden ist. Dabei besitzt die Bandstruktur der unendlich periodischen Anordnung dieser Streuer immer eine von der Polarisierbarkeit abhängige Bandkante und eine von der Polarisierbarkeit unabhängige Bandkante. Die Bandstruktur, die mit den verlustbehafteten Feldern einhergeht, ist eine doppelt komplexe. Alternativ zu dieser nur schwer zu interpretierenden Bandstruktur wurden die Feldfluktuationen selektiv nach reellen Frequenzen und Wellenzahlen sondiert. Es zeigt sich, daß Absorption besonders in der Nähe der Bandkanten die Bänder verbreitert. Die Ergebnisse, die mit Hilfe der lokalen Zustandsdichtefunktion gewonnen wurden, konnten dabei bestätigt werden. [1] S. Scheel, L. Knöll and D. G. Welsch, Phys.Rev. A 58, 700 (1998). [2] B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992). [3] G. Boedecker and C. Henkel, OPTICS EXPRESS 11, 1590 (2003). / A canonical scheme based on the phenomenological Maxwell equations in the presence of dielectric matter is used to quantize the electromagnetic field in a periodic and lossy linear dielectric. We focus on a one-dimensional model of point scatterers with given frequency-dependent complex permittivity, and construct an expansion of the field operators that is based on the Green function and preserves the canonical equal-time commutation relations. Translation symmetry is secured by working with an infinite lattice. The impact of absorption is examined using the local density of states and the decay rate of a phase-coherent dipole chain located inside the structure. Incidentally the model is used to bring about a geometrical interpretation of the reflection from multilayers

Airborne CW doppler proximity sensors are very sensitive, but leaks precise height measurement. It may be possible to estimate the heigth at the terminal phase (the case where the sensor is at a heigth close to ground) precisely by using the doppler shift and amplitude information. The thesis includes this novel concept with theoritical analysis and simulation results.

Electromagnetic wave scattering from a semi-infinite array of dipoles in free space is described by using asymptotic high frequency methods. An electric field integral expression is obtained and solved with asymptotic high frequency methods. An asymptotic field expression is obtained for a finite &times / infinite array of dipoles in free space. The analytical closed form expression for the array guided surface wave launching coefficient is obtained via a combination of an asymptotic high frequency analysis of a related reciprocal problem and Lorentz reciprocity integral formulation for the semi-infinite planar dipole array in which modified Kirchhoff approximation is used. The accuracy and the validity of the asymptotic analytical solutions are compared with the numerical solutions available in the literature before.

This thesis analyzes some aspects of electromagnetic wave propagation in double negative materials. Double negative materials have negative refractive indices. They are backward-wave materials. Plane waves undergo negative refraction at interfaces between double positive and double negative media. Causality principle implies these properties. High frequency plane wave scattering from a double negative infinitely long cylinder has been analyzed by using modified Watson transform, geometrical optics and Mie series. Mie series results and the modified Watson transform results have been found to be in good agreement. Hence, the physical mechanism of the scattering has been revealed.

Conventional fixed threshold detectors set a fixed threshold based on the overall statistical characteristics of the spatially uniform clutter over all ranges to give a specific probability of false alarm and detection. However, in radar applications clutter statistics are not known a priori. Constant False Alarm Rate (CFAR) techniques provide an adaptive threshold to estimate the clutter statistics and to distinguish targets from clutter. In Cell Averaging CFAR (CA-CFAR) the threshold is controlled by averaging the fixed size CFAR cells surrounding the cell under test. In this thesis, radar detection of targets in sea clutter modelled by compound Kdistribution is examined from a statistical detection viewpoint by Monte Carlo simulations. The performance of CA-CFAR processors is analysed under varying conditions of sea clutter spatial correlation and spikiness for several cases of false alarm probability, the length of cell size used in the CFAR processor and the number of pulses integrated prior to CA-CFAR processor. v The detection performance of CA-CFAR is compared with the performance of fixed threshold detection. The performance evaluations are quantified by CFAR loss. CFAR loss is defined as the increase in average signal to clutter ratio compared to that of fixed threshold, required to achieve a given probability of detection and probability of false alarm. Curves for CFAR loss to the spikiness and spatial correlation of clutter, number of pulses integrated and the length of cell size are presented.

I implemented and tested the method of Non-Linear Conjugate Gradients (NLCG) to invert magnetotelluric (MT) and radiomagnetotelluric (RMT) data in two dimensions. The forward problem and the objective function gradients were computed using finite-difference methods. The NLCG algorithm was applied to three field data sets to test the performance of the code. It was then compared to the inversion techniques of Occam and damped Occam considering the quality of the output resistivity models and the computation times. The implemented code was further investigated by testing two line search techniques to reduce the objective function along a given search direction. The first line search procedure was constrained to the first Wolfe condition, leading to a rather inexact line search. The second, more thorough line search, was additionally constrained to the second Wolfe condition. Three preconditioners were applied to the NLCG algorithm and their performance was analysed. The first preconditioner was set to the diagonal of the approximate Hessian matrix and updated every 20-th iteration. Preconditioners two and three were updated with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm using the identity matrix and the diagonal of the approximate Hessian matrix as start preconditioners, respectively. The tests showed that the method of NLCG is more efficient pertaining to computation times compared to the Gauss-Newton (GN) based techniques (Occam and damped Occam). For the two smaller data sets that were inverted, the NLCG inversion was two to four times faster than Occam and damped Occam. For the larger data set, the NLCG inversion converged more than one order of magnitude faster than the GN based inversion techniques. This is because GN methods require to evaluate the entire sensitivity matrix to update the model, whereas NLCG only needs to compute a matrix-vector product of the Jacobian. Moreover, expensive operations such as matrix products and direct inversions of linearised systems are avoided by NLCG. A limitation of the NLCG algorithm is that it is prone to converge to local minima due to the fixed Lagrange multiplier that is used in the penalty function. Occam inversion, which determines the optimal Lagrange multiplier as part of the inversion, did not show such problems. The line search tests of the NLCG algorithm showed that an inexact line search yields higher convergence per CPU time than a more exact line search. In accordance to previous studies, preconditioning accelerated the convergence of the NLCG algorithm considerably. The preconditioners updated with the BFGS algorithm achieved highest convergence. Choosing the identity matrix as a start preconditioner led to fast but unstable convergence. The reasons for that could not be determined completely. Taking the diagonal of the approximate Hessian as a start preconditioner instead of the identity matrix led to slower convergence for most of the inversion tests, but convergence could be stabilised. All the tests performed within this project led to a robust implementation of the NLCG algorithm. A default set-up pertaining to line search and preconditioning could be established. However, the NLCG set-up can be adjusted by the user to improve convergence for a specific data set. This makes the algorithm implemented in this thesis more flexible than previously introduced NLCG codes. Preconditioning can certainly still be improved with further tests. Moreover, a future project will be to extend the 2D code to 3D, where NLCG should perform especially well, because the number of model parameters is usually higher in 3D.