Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

The terahertz frequency range is a relatively unstudied region of the electromagnetic spectrum. However with the emergence of numerous applications for terahertz light in diverse areas such as security scanning, biological imaging, gas spectroscopy and astrophysics there has been considerable recent growth in the volume of research activity in this area. The studies presented in this thesis aim to introduce the physics of surface plasmons to the terahertz frequency range, and on the way to use some of the unique capabilities of terahertz spectroscopy to try and find new information about fundamental surface-plasmon based electromagnetic structures. Four distinct experiments are described in this work, all of them underpinned by the technique of terahertz time-domain spectroscopy (Chapter 2). This is a very powerful and adaptable spectroscopic method which allows us to measure the electric field of pulsed terahertz radiation as a function of time. This in turn allows us to directly extract both phase and amplitude of the terahertz light as a function of frequency, over a broad frequency range. Furthermore, this method of terahertz spectroscopy can be combined with photoexcitation pulses of visible/NIR light which can be used to make dynamic changes to the properties of materials in the terahertz beam. The first experiment reported (Chapter 3) measures the propagation of coupled surface plasmons in a resonant slit cavity. We use terahertz time-domain spec- troscopy to determine the characteristics of the cavity resonances in a semiconductor slit near the surface plasma frequency of the material, where we are able to mea- sure very large red-shifts in the frequency of the cavity resonance. By considering the phase information which can be extracted directly from time-resolved terahertz measurements we are able to link the behaviour of the resonances to the propagation characteristics of the surface plasmon modes inside the slits. The second experiment (Chapter 4) is a more direct measurement of surface plasmons, propagated over the surface of a semiconductor wafer. We show that the electric field of the surface plasmon is confined to a subwavelength region around the surface, and that the confined field is useful for spectroscopy of very thin layers above the surface. We are able to measure films with thickness less than 1/600th of the wavelength of the terahertz light. After these two experiments with confined semiconductor surface plasmons we move on to a pair of experiments looking at terahertz surface modes mediating the transmission of light through holes in metal films. In the initial experiment (Chapter 5) we use the time-domain data from terahertz spectroscopy to determine the role that surface mode lifetime plays in modifying the amplitude and width of Extraor- dinary Optical Transmission (EOT) resonances, which arise from the periodicity of a hole-array lattice. By changing the temperature of the lossy dielectric semicon- ductor substrate we are able to modify the surface mode lifetime, and link this to the resonant transmission characteristics. In Chapter 6 we extend the hole array EOT experiment by making dynamic changes to the propagation of the surface mode which mediates the transmission. This is achieved by photo-exciting the semiconductor substrate inside the holes and forming a thin layer of material with high charge carrier density on the surface. Interaction of the surface mode with the photoexcited region quenches the resonant transmission. We show that by changing the hole size so that the surface-mode mediated transmission pathway predominates in the spectrum it is possible to use optical pulses to modulate the transmission of terahertz radiation with very high efficiency. In the conclusions (Chapter 7) we link together some of the insights and infer- ences which can be drawn from the above results, as well as evaluating the efficacy of the experimental and simulation methodology.

This doctoral thesis is comprised of five parts. The first three parts concern signal processing and electromagnetic modelling of multiport antennas. The last two parts concern signal processing and transmission line theory applied to wave splitting on transmission lines. In Part I, the spherical vector wave expansion of the electromagnetic field is used to completely characterize a multiport antenna. A general framework for modelling an antenna configuration based on measurement data and numerical computation is obtained. The generic electromagnetic model for arbitrary multiport antennas or vector sensors is applied in direction of arrival (DOA) estimation. Next, in Part II using the generic electromagnetic model (from Part I), we obtain the Cramér–Rao bound (CRB) for DOA and polarization estimation using arbitrary multiport antennas. In the Gaussian case, the CRB is given in terms of the transmission matrix, the spherical vector harmonics and its spatial derivatives. Numerical examples using an ideal Tripole antenna array and a non-ideal Tetrahedron antenna array are included. In Part III, the theory of optimal experiments is applied to a cylindrical antenna near-field measurement setup. The D-optimal (determinant) formulation using the Fisher information matrix of the multipole coefficients in the spherical wave expansion of the electrical field result in the optimal measurement positions. The estimation of the multipole coefficients and corresponding electric field using the optimal measurement points is studied using numerical examples and singular value analysis. Further, Part IV describes a Digital Directional Coupler (DDC), a device for wave splitting on a transmission line. The DDC is a frequency domain digital wave splitter based on two independent wide-band measurements of the voltage and the current. A calibration of the digital processor is included to account for the particular transmission line and the sensors that are employed. Properties of the DDC are analyzed using the CRB and an experiment where wave splitting was conducted on a coaxial–cable is accounted for. Finally, in Part V the DDC has been designed and implemented for wave splitting on a medium voltage power cable in a power distribution station using low cost wide–band sensors. Partial discharge measurements are conducted on cross–linked polyethylene insulated power cables. The directional separation capabilities of the DDC are visualized and utilized to separate multiple reflections from partial discharges based on the direction of travel.

Computational methods are a convenient resource to solve drawbacks of drug research such as high cost, time-consumption, and high risk of failure. In order to get an optimum search of new drugs we need to design a rational approach to analyze the molecular forces that govern the interactions between the drugs and their target molecules. The objective of this project is to get an understanding of the interactions between drugs and proteins at the molecular level. The interaction energy, when protein and drugs react, has two components: non-covalent and covalent. The former accounts for the ionic interactions, the later accounts for electron transfer between the reactants. We study each energy component using the most popular analysis tools in computational chemistry such as docking scoring, molecular dynamics fluctuations, electron density change, molecular electrostatic potential (MEP), density of states projections, and the transmission function. We propose the probability of transfer of electrons (transmission function) between reactants in protein-drug complexes as an alternative tool for molecular recognition and as a direct correlator to the binding affinity. The quadratic correlation that exists between the electron transfer rate and the electronic coupling strength of the reactants allow a clear distinguishability between ligands. Thus, in order to analyze the binding affinity between the reactants, a calculation of the electronic coupling between them is more suitable than an overall energetic analysis such as free reaction energy.

L'objectif de ce travail fut le développement de nouvelles méthodes pour aborder certainsproblèmes inverses en élasticité, en tirant parti de la présence d'un petit paramètre dans ces problèmespour construire des approximation asymptotiques d'ordre élevé.La première partie est consacrée à l'identification de la taille et la position d'une inhomogénéité$BTrue$ enfouie dans un domaine élastique tridimensionnel. Nous nous concentrons sur l'étude defonctions-co^uts $Jbb(Br)$ quantifiant l'écart entre $BTrue$ et une hétérogénéité ``test'' $Br$. Unetelle fonction-co^ut peut en effet être minimisée par rapport à tout ou partie des caractéristiques del'inclusion ``test'' $Br$ (position, taille, propriétés mécaniques ...) pour établir la meilleurecorrespondance possible entre $Br$ et $BTrue$. A cet effet, nous produisons un développement asymptotique de $Jbb$en la taille $incsize$ de $Br$, qui en constitue une approximation polynomiale plus aisée à minimiser. Cedéveloppement, établi jusqu'à l'ordre $O(incsize^6)$, est justifié par une estimation du résidu. Uneméthode d'identification adaptée est ensuite présentée et illustrée par des exemples numériques portant surdes obstacles de formes simples dans l'espace libre $Rbb^3$.L'objet de la seconde partie est de caractériser une inclusion microstructurée de longueur $ltot$, modéliséeen une dimension, composée de couches de deux matériaux alternés périodiquement, en supposant que les plusbasses de ses fréquences propres de transmission (TEs) sont connues. Ces fréquences sont les valeurs propres d'unproblème dit de transmission intérieur (ITP). Afin de disposer d'un modèle propiceà l'inversion, tout en prenant en compte les effets de la microstructure, nous nous reposons sur des approximationsde l'ITP exact obtenues par homogénéisation. A partir du modèle homogénéisé d'ordre 0, nous établissonstout d'abord une méthode simple pour déterminer les paramètres macroscopiques ($ltot$ et contrastes matériaux)d'une telle inclusion. Pour avoir accès à la période de la microstructure, nous nous intéressons ensuite àdes modèles homogénéisés d'ordre élevé, pour lesquels nous soulignons le besoin de conditions aux limitesadaptées. / The purpose of this work was to develop new methods to address inverse problems in elasticity,taking advantage of the presence of a small parameter in the considered problems by means of higher-order asymptoticexpansions.The first part is dedicated to the localization and size identification of a buried inhomogeneity $BTrue$ in a 3Delastic domain. In this goal, we focused on the study of functionals $Jbb(Br)$ quantifying the misfit between $BTrue$and a trial homogeneity $Br$. Such functionals are to be minimized w.r.t. some or all the characteristics of the trialinclusion $Br$ (location, size, mechanical properties ...) to find the best agreement with $BTrue$. To this end, weproduced an expansion of $Jbb$ with respect to the size $incsize$ of $Br$, providing a polynomial approximationeasier to minimize. This expansion, established up to $O(incsize^6)$ in a volume integral equations framework, isjustified by an estimate of the residual. A suited identification procedure is then given and supported by numericalillustrations for simple obstacles in full-space $Rbb^3$.The main purpose of this second part is to characterize a microstructured two-phases layered1D inclusion of length $ltot$, supposing we already know its low-frequency transmission eigenvalues (TEs). Thoseare computed as the eigenvalues of the so-called interior transmission problem (ITP). To provide a convenient invertiblemodel, while accounting for the microstructure effects, we then relied on homogenized approximations of the exact ITPfor the periodic inclusion. Focusing on the leading-order homogenized ITP, we first provide a straightforward method torecover the macroscopic parameters ($ltot$ and material contrast) of such inclusion. To access to the period of themicrostructure, higher-order homogenization is finally addressed, with emphasis on the need for suitable boundaryconditions.

Most applications in computer vision suffer from two major difficulties. The first is they are notoriously ridden with sub-optimal local minima. The second is that they typically require high computational cost to be solved robustly. The reason for these two drawbacks is that most problems in computer vision, even when well-defined, typically require finding a solution in a very large high-dimensional space. It is for these two reasons that multiscale methods are particularly well-suited to problems in computer vision. Multiscale methods, by way of looking at the coarse scale nature of a problem before considering the fine scale nature, often have the ability to avoid sub-optimal local minima and obtain a more globally optimal solution. In addition, multiscale methods typically enjoy reduced computational cost. This thesis applies novel multiscale active contour methods to several problems in computer vision, especially in simultaneous segmentation and reconstruction of tomography images. In addition, novel multiscale methods are applied to contour registration using minimal surfaces and to the computation of non-linear rotationally invariant optical flow. Finally, a methodology for fast robust image segmentation is presented that relies on a lower dimensional image basis derived from an image scale space. The specific advantages of using multiscale methods in each of these problems is highlighted in the various simulations throughout the thesis, particularly their ability to avoid sub-optimal local minima and their ability to solve the problems at a lower overall computational cost.

L'organisation des substances humiques à l'échelle moléculaire reste une question largement débattue, et à ce jour, il n'a pas été possible de trancher entre une structure polymérique en pelotte plus ou moins flexible et un assemblage supramoléculaire de molecules hétérogènes associées par des liaisons hydrogènes et des interactions hydrophobes. Dans cette thèse, nous étudions la reconformation induite par l'addition de tensio-actifs cationiques (Chlorure de C n-trimethylammonium) sur une série de substances humiques (acides fulvique et humiques) ainsi que sur de la matière organique naturelle contenue dans des eaux noires. Des mesures de turbidité, de diffusion de lumière, mobilité électrophorétique, tension de surface, spectroscopie de fluorescence, diffusion des neutrons aux petits angles, et cryomicroscopie à transmission, permettent de decrire les complexes formés entre le tensio-actif et la matière humique. L'association matière humique/tensio-actif dépend à la fois d'interactions d'origine électrostatique et hydrophobe. Une série de structures moléculaires, vésicules, disques, globules, pseudo-micelles, est observée en cryomicroscopie selon la concentration en surfactant. La séquence obtenue est cohérente avec un système catanionique, en d'autres termes une partie de la matière humique est amphiphile et s'organise en assemblage supramoléculaire. L'addition de tensio-actif modifie également fortement le spectre de fluorescence de la matière humique, les nouvelles bandes bien résolues présentes sur le spectre indiquant une restructuration majeure de l'assemblage supramoléculaire. / The structural organization of humic nanocolloids remains a matter of harsh debate, and surprisingly, it is yet not possible to decide between an arrangement of the humic matter in the form of randomly coiled macromolecules more or less connected, and a supramolecular organization of small heterogeneous molecules linked by hydrogen bonds and hydrophobic interactions. In this study, we investigate the reconformation induced by the addition of cationic surfactants (C n-trimethylammonium chloride) of varying alkyl chain length with a series of humic substances (HS) and Dissolved Organic matter (DOM) from two blackwater rivers of the Central Amazon. Turbidity measurements, Dynamic light scattering, electrophoretic mobility, surface tension, fluorescence spectroscopy, small angle neutron scattering and cryo-transmission electron microscopy (cryo-TEM), are combined to describe the Humic Substance/Surfactant complexes obtained. The association between the oppositely charged HS and cationic surfactant is driven by both electrostatic and hydrophobic interactions. A variety of molecular structures, unilamellar vesicles, disks, globules, spheroidal micelles, are visualized by cryo-TEM depending on surfactant concentration. Such sequence, consistent with those displayed by catanionic systems, provides an independent confirmation of both the amphiphilic nature of HS and of its supramolecular organization. In addition, the molecular rearrangement was investigated using single-scan fluorescence emission spectra spectroscopy, thus identifying the chemical groups responsible for the fluorescence properties in HS and DOM. The addition of cationic surfactant to HS/DOM unveils an unexpected fine structure of humic-like fluorescence through new emission peaks that are not evidenced in the references HS/DOM. An enhanced protein-like fluorescence indicating major restructuration and structural stacking/de-stacking is observed. All our results support a supramolecular organization of humic substances and DOM.