published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

Many advances in technology ranging from biology and medicine through engineering and computer science to fundamental physics and chemistry depend upon the capability to control the fabrication of materials and devices at the submicron scale. Quantum mechanical effects become increasingly important to atomic and molecular interactions as the distances between neighbors decrease. These effects will provide materials and device designers with additional flexibility to establish properties of the designers choice, but the cost of this additional flexibility must be paid in the complexity of nonlinearities entering the interactions and the design process. The work presented here has provided several early results on three such interactions among closely-spaced submicron material structures: 1) the properties of superconductivity have been studied, 2) the properties of ferromagnetism have been studied, and 3) the interactions between superconductivity and ferromagnetism have been studied. Since our work was published, there has been considerable interest in all three of these wide-open areas and hundreds or thousands of additional results are now in the literature. We have used standard methods from the semiconductor industry as well as innovative methods to fabricate micron and submicron devices for observation. Standard optical lithography and standard electron beam lithography have been implemented to shape micron and submicron structures, respectively. Additionally, a laser interferometric lithography method has been invented and used to shape submicron structures. The materials used were vanadium, niobium, nickel, and/or permalloy. We have utilized SQUID magnetometry and Hall effect magnetometry to observe the properties of superconductor structures and superconductorferromagnetic mixed systems. We have used SQUID magnetometry and ferromagnetic resonance to observe the physical properties of ferromagnetic structures and the interactions between adjacent structures. Using these materials and methods we have discovered an unusual paramagnetic Meissner effect in thin Nb films that exists at igh-applied magnetic fields. We have discovered fluxoid matching anomalies at low sample temperature. And we have discovered interactions between electron exchange and magnetic dipole forces. Additionally, we have found clear evidence to support several past hypotheses advanced by other authors.

The derivation of nonlinear dispersive PDE, such as the nonlinear Schrödinger (NLS) or nonlinear Hartree equations, from many body quantum dynamics is a central topic in mathematical physics, which has been approached by many authors in a variety of ways. In particular, one way to derive NLS is via the Gross-Pitaevskii (GP) hierarchy, which is an infinite system of coupled linear non-homogeneous PDE. In this thesis we present two types of results related to obtaining NLS via the GP hierarchy. In the first part of the thesis, we derive a NLS with a linear combination of power type nonlinearities in R[superscript d] for d = 1, 2. In the second part of the thesis, we focus on considering solutions to the cubic GP hierarchy and we prove unconditional uniqueness of low regularity solutions to the cubic GP hierarchy in R[superscript d] with d ≥ 1: the regularity of solution in our result coincides with known regularity of solutions to the cubic NLS for which unconditional uniqueness holds. / text

The present work aims at studying the coupling between hydrodynamic fingering instabilities and chemical reactions at the interface between two miscible solutions. Hydrodynamic deformations of interfaces between two reactive fluids as well as flows induced by chemical reactions at the front between two initially steady fluids are encountered frequently in combustion, petroleum, chemical and pharmaceutical engineering. Most of the time, concrete applications imply a very large number of variables so that an understanding of the fundamental processes of chemo-hydrodynamic coupling is out of reach. Our goal is here to analyze a much simpler model system in which only one mechanism of hydrodynamic instability is at play and for which the chemical reactions can be modeled by a one or two-variable model. Buoyantly unstable, autocatalytic chemical fronts, are one such model system, which can be used as prototype to study the effects of the coupling between chemical reactions and hydrodynamic fingering instabilities. Fingering processes occur whenever a fluid of high mobility displaces a less mobile one in a porous medium. The initially planar interface looses then stability and a cellular fingering deformation of the interface is observed. Such an instability has been observed, for instance, in the iodate-arsenous acid and chlorite-tetrathionate reactions, autocatalytic redox reactions known to produce a change of density across a traveling front. Fingering happens there when the heavier solution lies on top of the lighter one in the gravity field. Our theoretical contribution to the analysis of fingering of chemical fronts focuses on different points which we detail in this thesis along the following outline. In chapter 2, we introduce fingering phenomena occurring in porous media and distinguish the situation of viscous and density fingering of pure non reactive fluids. Chapter 3 reviews the literature on coupling between fingering and chemical reactions before studying the linear stability conditions as well as nonlinear dynamics of density fingering of isothermal iodate-arsenous acid fronts. This prototype nonlinear redox reaction is the first one on which experimental results on fingering in spatially extended set-ups have been obtained. We next analyze in chapter 4 the density fingering of another front producing autocatalytic system i.e. the chlorite-tetrathionate reaction in order to address the influence of the chemical kinetics on the dynamics observed. The influence of the exothermicity of the reaction is then presented in chapter 5. Eventually, chapter 6 analyzes what happens if the kinetics is now bistable and further compares the situation of both viscous and density fingering of bistable fronts. We then conclude and present suggestions for future work in this subject at the frontier between nonlinear chemistry, hydrodynamics and engineering.

Motivés par les développements récents dans le domaine des nanosciences, nous étudions les propriétés statistiques et thermodynamiques des systèmes mésoscopiques. En particulier, nous nous concentrons sur les résultats connus sous le nom de théorèmes de fluctuation. Ces relations donnent des prédictions sur le comportement de différents quantités dynamiques dans des situations loin de l'équilibre, tout en tenant compte des fluctuations de l'évolution temporelle. La première partie de notre étude est consacrée aux relations existants entre les fluctuations et la théorie de la réponse. Nous commençons par dériver une relation fonctionnelle pour les systèmes quantiques forcés dans le temps qui généralise l'égalité de Jarzynski et dont l'expansion en l'intensité du forçage permet de retrouver les résultats de la réponse linéaire. Nous poursuivons ensuite ces considérations en nous intéressant aux états stationnaires de non-équilibre. Ceci est réalisé dans le cadre des processus stochastiques, dans lequel nous dérivons une relation de fluctuation pour les courants de non-équilibre traversant le système. Cette relation lie explicitement les fluctuations aux forces thermodynamiques, ce qui nous permet de développer ses conséquences au niveau de la théorie de la réponse non-linéaire. De cette manière, nous obtenons de nouvelles relations liant fluctuations et coefficients de réponse dans le régime non-linéaire. Dans la deuxième partie de ce travail, nous développons une connexion récente liant l'irréversibilité au désordre dynamique. Nous présentons des résultats expérimentaux montrant que la production d'entropie s'exprime comme la différence de deux quantités mesurant la brisure de symétrie sous renversement du temps au niveau du désordre temporel. Nous étudions ensuite les conséquences de cette relation dans le contexte de l'énergétique du traitement de l'information. En particulier, nous présentons une généralisation du principe de Landauer pour l'effaçage d'information. De la même manière, nous relions la dissipation à la génération d'information par les entités biologiques.

This dissertation presents the results of experimental research on the nonlinear refraction in InSb and the experimental demonstration of two nonlinear etalon devices using InSb as the active material. The first portion of the dissertation considers the Dynamic Burstein-Moss Shift model for nonlinearities in narrow-gap semiconductors. The physics and the equations are reviewed, and limitations in describing intensity dependent refraction in a semiconductor are considered. These limitations arise from the nonlinear dependence of charge carrier density upon irradiance. The second portion of the dissertation presents experimental measurements made on the nonlinear refraction of InSb at temperatures between 80 K and 182 K, for wavelengths from 5.75 μm to 6.10 μm, where the photon energy lay in the band tail below 100 cm⁻¹. Measurements of the linear absorption were first made with an infrared spectrometer for temperatures from 80 K to 300 K. The nonlinearity was measured by analyzing the transmission through InSb etalons. Nonlinear transmission curves were digitized and stored with an IBM PC-XT, then a curve fit was performed using the nonlinear refractive index as a fiting parameter. Observations are reported of increasing absorption, due in part to a thermal shift of the absorption edge. The second portion of the work presents the theory and demonstration of a bistable etalon using an edge-injected control beam. Plane-wave nonlinear etalon theory is used to describe the operation of such a device, illustrating the way in which switching and logic gate operation can be obtained. Two devices based on this concept are demonstrated: the 3-port device using a single control beam, and the 2SON gate using two control beams to perform two-input logic operation. The extension of the 2SON gate to an array of pixels, and some considerations for optimizing array performance, are considered. Two appendices follow the body of the dissertation, the first describing the preparation of the InSb etalon samples, and the second detailing several procedures for maintenance and operation of the CO laser used.

The rigorous descriptions of linear and nonlinear guided wave theory are given together with a geometrical description that helps in the understanding of the physical phenomena taking place. The nonlinear waveguide discussed in this dissertation is composed of a linear thin film and substrate with a cladding material whose refractive index varies with the intensity of the light. Experimentally, this was accomplished, by placing an oriented liquid crystal (highly nonlinear but extremely slow) on top of a thin film glass waveguide. When the liquid crystal used was K15, light-induced mode cutoff was observed. The TE(,0) mode became leaky as the guided wave power was increased. This was a consequence of the light-induced increase in refractive index due to thermal effects. This behaviour was studied as a function of temperature. Light by light modulation was also accomplished with this setup. The theory of the linear and nonlinear prism coupler and the first experimental investigations on the nonlinear prism coupler are given. The nonlinear prism coupler used was obtained by depositing a small amount of MBBA liquid crystal in the gap beween the input coupling prism and the thin film. The basic properties of the nonlinear prism coupler were demonstrated experimentally and the results obtained were verified to have their origin in the temperature component of the nonlinear index of refraction. Good qualitative agreement between the theory developed and experiments were obtained. Bistability and switching in a thin film waveguide with a K18 liquid crystal cladding has been demonstrated for the first time. These experiments made use of the interesting phenomena associated with the nematic to isotropic phase transition. Such behaviour was satisfactorily explained by the intense light scattering associated with the critical opalescence that accompanies such a phase transition in a liquid crystal. Both the TE(,0) and the TM(,0) modes were found to exhibit such behaviour.

This dissertation studies the physics of room-temperature optical nonlinearities in GaAs and their application to the optical logic gates. The microscopic origins of the room-temperature optical nonlinearities in GaAs are investigated experimentally and theoretically. The data of nonlinear absorption measurement are analyzed in the framework of a semiconductor plasma theory in combination with excitation-dependent line broadening. The importance of the plasma screening of the continuum-state Coulomb enhancement and band filling are emphasized for GaAs at room temperature. Optical bistability and optical logic gating are direct consequences of the nonlinear refractive index changes in etalons. The nonlinear index changes are directly measured by a new technique of observing the Fabry-Perot transmission peak shift using the self-photoluminescence as a broad-band source. The validity of a Kramers-Kronig technique under quasi-steady state conditions is crosschecked by an independent measurement of Δn under identical pumping conditions. Thermal index changes are also directly measured to establish the criteria on the temperature stability condition that is needed for reliable operation of devices based on dispersive nonlinearities. Optical logic gates based on dispersive optical nonlinearities may be the critical components of an all-optical computer in the future. Five optical logic functions are demonstrated in a nonlinear GaAs/AlGaAs MQW etalon. Specially designed dielectric mirrors are used to observe low-energy (3-pJ) operation of optical logic gates. Parallel operation using as many as eight optical logic devices is achieved with Wollaston prisms. Toward practical devices, optical logic gating using diode lasers is demonstrated in a setup much smaller than the usual argon-laser pumped dye laser setup. The cycle time of optical logic devices is limited, not by the switch-on time, but by the switch-off time which depends on the carrier relaxation rather than the switch-on time. To reduce the carrier relaxation time windowless GaAs is employed to take advantage of the faster surface recombination of carriers at the GaAs/dielectric mirror interface compared to that at the GaAs/GaAlAs interface. The speed and effectiveness of the windowless GaAs are compared with those of the proton-bombarded GaAs as optical logic gates.

This dissertation reports on the development of a nonlinear surface spectroscopy and the observation of nonlinear optical phenomena using sputtered zinc oxide waveguides. The first is known as Surface Coherent Raman Spectroscopy, or SCRS, and is capable of monolayer sensitivity. The second, discovered during the development of SCRS, is optical limiting and a previously unobserved form of optical switching based on an absorptive nonlinear coupling mechanism. Overviews of the theories of waveguiding, linear coupling, and SCRS are given. Experiments showing that the spectrum of a monolayer coverage of molecules on the surface of a metal oxide waveguide can be obtained using SCRS are reported. For this purpose ZnO waveguides were fabricated using rf magnetron sputtering; the details of which are presented. The results of the characterization of these films, using an optical loss technique, Rutherford backscattering, and X-ray diffraction, are also presented. Experiments are described and data are presented to show the existence of optical limiting and optical switching phenomena in ZnO waveguides. The experimental dependence of these phenomena on input pulse energy, wavelength, temporal pulse width, and type of distributed coupling mechanism is described. Existing nonlinear distributed coupler theory is extended to include the effect of an absorptive nonlinearity and the results of this theory are used to explain some of the characteristic features of the experimental results. A value of n₂ ≅ 2 x 10⁻¹⁶ m²/W for the nonlinear coefficient of sputtered ZnO films is obtained.

Because of their compatibility with the planar concept of integrated optics, grating couplers offer the most satisfactory means of coupling light into thin film optical waveguides. The purpose of this dissertation has been to study the behaviour, both theoretically and experimentally, and fabrication of grating couplers in nonlinear waveguides. A theory of nonlinear grating couplers is presented based on a coupled-mode approach. The dependence of coupling efficiency on incident beam intensity, beam size, beam position, incident angle, chirp rate, and waveguide losses have been examined all in the presence of nonlinearities in the waveguide. It is reported that, in the presence of nonlinearities, the coupling efficiency decreases with increasing incident power. Different ways of optimizing the coupling efficiency at high incident power levels are presented. These include adjusting the beam size, the coupling angle, and chirping the grating. A new technique is reported for fabrication of regular period, chirped, and curved photoresist gratings. The experimental arrangement is essentially based on Lloyd's mirror fringes and is characterized by its stability, simplicity, and versatility. We also report on successful use of Reactive Ion-Beam Etching (RIBE) with C₂F₆ gas in producing very smooth and deep gratings with high aspect ratios in different waveguide structures. Experimental coupling efficiencies of up to 40% are reported in polystyrene waveguides using etched grating couplers. Experiments are reported in support of the theoretical findings of this dissertation using a polystyrene waveguide with thermal nonlinearity.