D.Ing. / Please refer to full text to view abstract

In this thesis I will introduce a novel nonlinear optical microscopy method to address some of the shortcomings in the current nonlinear optical microscopy literature and offer a supplement to traditional fluorescent microscopy for label free optical biomedical imaging. In order to demonstrate this method I describe a method for the generation of a numerical sample of collagen fibrils, produce a set of numerical diffraction measurements. I introduce a novel Ptychography model for the simultaneous reconstruction of the components of the nonlinear optical susceptibility tensor and demonstrate the results of this model using numerically generated measurements from a numerical collagen sample. I additionally use the recovered information from Ptychography to retrieve new information about the structure of a sample.

The organic-metal interface is ubiquitous in a wide variety of natural environments and industrial applications. As a result, the interfacial chemistry has been studied for many decades. Specifically, the surfactant-metal interfaces play an important role in the prevention of metallic corrosion where surface active corrosion inhibitors are often used as a prevention method. Development of a spectroscopic method based on vibrational sum frequency generation, specifically for metal interfaces, is carried out with the goal of elucidating the surface structure of these molecules. The contribution to the signalarising from the metal substrate often plays a crucial role in the quantitative analysis of spectra. By adopting a phase-resolved detection scheme, the polar orientation of the organic molecule adsorbed on metal surfaces is experimentally obtained. Furthermore,the development of a novel acquisition scheme is demonstrated where the incident angle is scanned while simultaneously measuring the magnitude and phase of the nonlinear response. This enables the separation of all contributions to the nonlinear susceptibility tensor governing the response. Such an approach is especially useful when the conventional nonlinear vibrational technique is inaccessible in beam polarizations where the infrared field is perpendicular to the plane of incidence, due to the infrared surface selection rule of metals. Finally, this approach is used to examine the structure of a surfactant on iron surfaces. / Graduate / 2022-09-08

It is found here that the state of a network of coupled ordinary differential equations is partially localizable through a pair of contractive ideal subspaces, chosen from dual complete lattices related to the synchrony and synchronization of cells within the network. The first lattice is comprised of polydiagonal subspaces, corresponding to synchronous activity patterns that arise from functional equivalences of cell receptive fields. This lattice is dual to a transdiagonal subspace lattice ordering subspaces transverse to these network-compatible synchronies. Combinatorial consideration of contracting polydiagonal and transdiagonal subspace pairs yields a rich array of dynamical possibilities for structured networks. After proving that contraction commutes with the lattice ordering, it is shown that subpopulations of cells are left at fixed potentials when pairs of contracting subspaces span the cells' local coordinates - a phenomenon named glyph formation here. Treatment of mappings between paired states then leads to a theory of network-compatible sequence generation. The theory's utility is illustrated with examples ranging from the construction of a minimal circuit for encoding a simple phoneme to a model of the primary visual cortex including high-dimensional environmental inputs, laminar speficicity, spiking discontinuities, and time delays. In this model, glyph formation and dissolution provide one account for an unexplained anomaly in electroencephalographic recordings under periodic flicker, where stimulus frequencies differing by as little as 1 Hz generate responses varying by an order of magnitude in alpha-band spectral power. Further links between coupled-cell systems and neural dynamics are drawn through a review of synchronization in the brain and its relationship to aggregate observables, focusing again on electroencephalography. Given previous theoretical work relating the geometry of visual hallucinations to symmetries in visual cortex, periodic perturbation of the visual system along a putative symmetry axis is hypothesized to lead to a greater concentration of harmonic spectral energy than asymmetric perturbations; preliminary experimental evidence affirms this hypothesis. To conclude, connections drawn between dynamics, sensation, and behavior are distilled to seven hypotheses, and the potential medical uses of the theory are illustrated with a lattice depiction of ketamine xylazine anaesthesia and a reinterpretation of hemifield neglect.

Parametric down-conversion (PDC) is a nonlinear optical process widely used to generate pairs of photons. It occurs when an intense laser traverses an optical parametric amplifier (OPA). When the gain of the amplifier is increased, the number of downconverted photons increases exponentially: this is the high-gain regime of PDC. High-gain PDC is potentially a versatile tool for metrology. It is a source of highly-entangled states and bright squeezed states for applications in quantum information and interferometry. In addition, the high number of photons in high-gain PDC makes it possible to use diodes and cameras directly, instead of single-photon detectors and coincidence-counting apparatus. However, all the quantum-optical experimental methods need to be generalized or adapted for a high-photon flux. Most of the theoretical and experimental techniques used or developed in this thesis aim to address this transition from low to high-photon flux of PDC. I theoretically and experimentally provide strategies to harness the mode structure of PDC, bringing us steps closer to a usable source of bright squeezed vacuum for interferometry and quantum imaging. I present experimental progress in reducing the number of frequency modes of high-gain PDC, which is naturally broadband, and consequently highly multimode. Our theory for high-gain PDC generated in a nonlinear crystal provides a set of modes containing physically meaningful information, i.e. the pairwise quantum correlations between independant modes. In addition, I provide a thorough discussion on the limit of SU(1,1) interferometry in regards to internal loss and gain unbalancing. Finally, I tie the frequency spectrum of high-gain PDC to the properties of vacuum fluctuations, allowing to predict the number of photons from first principles, making it a powerful tool for spectroradiometry. Those developments are a springboard towards usable high-gain PDC for metrology.

The nonlinear dynamics of PWM DC-DC switching regulators operating in the continuous conduction mode are investigated. A quick review of the existing analysis techniques and their limitations is first presented. A discrete nonlinear time-domain model is derived for open-loop DC-DC converters. This model is then extended for closed-loop regulator systems implementing any type of compensation scheme. The equilibrium solutions of the closed-loop system are calculated and their stability is determined. The methods developed are used to study the dynamic behavior of a DC-DC buck regulator implementing different types of compensation design: proportional, integral, proportional-integral, and proportional-integral-derivative feedback control. A detailed bifurcation analysis of the dynamic solutions as a design or a control parameter is changed is presented. A period-doubling route to chaos is shown to exist in voltage-mode regulators, depending on the values of the parameters of the compensator and the input voltage. An investigation of the behavior of the converter in the instability regions has been carried out to shed light on its bifurcations. The interactions of input filters with DC-DC switching-mode regulators are investigated as well. It is shown that the small-signal averaged model widely used in the design of DC-DC regulators does not provide a complete understanding of the stability of the filter-regulator system. It can only provide the local borders of small-signal stable operation. The large-signal time-domain nonlinear averaged model is used to further understand the interaction on the slow scale using nonlinear analysis techniques. No fast scale interactions, however, can be predicted using this model. A complete nonlinear switching model is thus used to investigate the interaction of the filter and the regulator on all scales: fast and slow. / Master of Science

Self-trapped beams of light propagate while maintaining their initial intensity profile within a self-induced channel of high refractive index. When multiple self-trapped beams or filaments travel within the same medium, a diverse host of interactions are observed, including attraction, repulsion, fusion, annihilation, and birth. This thesis describes studies of interactions between large and small filament populations and/or beam-induced structures (waveguides) within polymer media. The understanding developed in this fundamental work was applied to design polymer cuboids – the cuboids that count – with computing-inspired functionality. First, the spontaneous self-organisation of randomly-seeded waveguides within a photopolymer material formed the basis of 3 operations: (i) data transfer; (ii) volumetric encoding; and (iii) binary arithmetic. The same material was used for 3D data storage using highly-intersecting waveguide lattices. The pursuit of enhanced capacity prompted an exploration of light coupling in waveguides with small angular separation and significant field of view overlap. Using multiple angled light sources, we successfully demonstrated single-step data writing and multiplexed data reading in these structures. Finally, we examined long-range interactions between 2 to 4 collinear beams within a spiropyran-functionalised hydrogel. The mechanism of refractive index increase in this medium – a light-induced volume contraction and expulsion of water – allowed beams to inhibit their neighbours’ self-trapping, with a clear relationship between number of neighbours and degree of inhibition. These observations were used to form the basis for an optical hydrogel NAND gate. / Thesis / Doctor of Philosophy (PhD)

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