Thesis (M.S.)--Ohio State University, 2006. / Includes bibliographical references (leaves 61-63). Available online via OhioLINK's ETD Center

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 174-181). Available also in a digital version from Dissertation Abstracts.

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Numerical techniques for solving differential equations have been vigorously studied, and various techniques have been proposed and investigated for particular problems. Maxwell's equations are the system of partial differential equations which describe the behavior of electromagnetic fields. The methods for solving the equations should be properly chosen depending on the purpose of the analysis and the available computational resources. In this thesis, we propose a time-domain electromagnetic field modeling technique based on Haar wavelets. The multiresolution nature of the wavelets was used in the formulation, and a time stepping algorithm that is similar to the conventional finite-difference time-domain (FDTD) method was obtained. The proposed technique effectively models realistic structures by virtue of the multi-resolution property; the computational time is reduced approximately by half compared to the conventional FDTD method. In order to provide a comprehensive understanding of the proposed method, algorithms for one, two and three space dimensions were formulated, validated in terms of the accuracy, and actually applied to various realistic problems. Various boundary conditions have been formulated and implemented, and in addition, the following applications are addressed: S-parameter extraction for two-dimensional waveguide problems, combined with field singularity correction at metal edges and corners, resonant cavity analyses for validation purposes, and analyses of microwave passive devices with open boundaries such as microstrip low-pass filters and spiral inductors. An algorithm that needs half the computational effort is equivalent to hardware that is twice as fast. The purpose of this thesis is to make a contribution to the improvement of computational speed in electromagnetic time domain solutions. / Graduate

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Discussion begins with a brief account of atomic level-pumping and reasons why atomic coherence is typically not considered in cw work on optical interactions. This dissertation is divided into four parts: semiclassical treatments of one-photon electric- dipole atom-field single-mode interactions and multimode interactions, and corresponding treatments for the two-photon interaction. We present the effects of injected atomic coherence on the polarization of the medium, the slowly varying envelope wave equation, the single- and multiwave mixing coefficients, and weak field propagation in a homogeneously broadened two-level medium. Spatial and temporal phase matching of the injected coherence to a field mode is crucial throughout, since the field may not be able to remain in phase with the induced and injected polarizations. One-photon injected coherence contributes directly to the polarization at the atomic resonance frequency. The perfectly phase-matched case leads to a linear superposition of an exponentially decaying field (Beer's law) and a constant field driven by the injected coherence. The interaction of an injected coherence with a detuned field produces frequency-symmetric sidebands about the pump field polarization. The sideband spacing equals the atom-field detuning. To probe the injected coherence we inject a weak resonant field. The resulting three-wave mixing leads to multiwave mixing coefficients that are unaffected to first-order in the weak sidemodes, but the injected coherence adds inhomogeneous terms to the coupled-mode equations. For both single- and multimode interactions the injected coherence does not affect the exponential growth/decay of the sidemodes, but it supports a weak field that may propagate if properly phase matched. For two-photon media the injected coherence requires at least one field interaction in order to produce a polarization, which then appears in the single- and multiwave mixing coefficients. The exponential growth/decay rate is modified by the injected coherence. For a centrally-tuned pump the injected coherence contributes the standard multiwave mixing terms as well as additional effects. Four-wave mixing is discussed as a means of relaxing the spatial phase matching constraint on the injected coherence.

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Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains xviii, 182 p.; also includes graphics. Includes abstract and vita. Co-advisors: Robert Lee and Fernando L. Teixeira, Dept. of Electrical Engineering. Includes bibliographical references (p. 176-182).

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