abstract: The study of subwavelength behavior of light and nanoscale lasing has broad potential applications in various forms of computation i.e. optical and quantum, as well as in energy engineering. Although this field has been under active research, there has been little work done on describing the behaviors of threshold and saturation. Particularly, how the gain-molecule behavior affects the lasing behavior has yet to be investigated. In this work, the interaction of surface-plasmon-polaritons (SPPs) and molecules is observed in lasing. Various phenomenologies are observed related to the appearance of the threshold and saturation regions. The lasing profile, as a visual delimiter of lasing threshold and saturation, is introduced and used to study various parametrical dependencies of lasing, including the number-density of molecules, the molecular thickness and the frequency detuning between the molecular transition frequency and the SPP resonant frequency. The molecular population distributions are studied in terminal and dynamical methods and are found to contain unexpected and theoretically challenging properties. Using an average dynamical analysis, the simulated spontaneous emission cascade can be clearly seen. Finally, theoretical derivations of simple 1D strands of dipoles are presented in both the exact and mean-field approximation, within the density matrix formalism. Some preliminary findings are presented, detailing the observed behaviors of some simple systems. / Dissertation/Thesis / Masters Thesis Chemical Engineering 2017

La diffraction d'une onde électromagnétique par une structure présentant des échelles d'espace petites devant la longueur d'onde est un phénomène complexe qui décrit à la fois l'interaction entre l'onde et la géométrie de la structure et la matière qui la constitue. Quand la fréquence n'est pas résonnante, l'onde incidente interagit faiblement avec des petites irrégularités de la structure. En langage mathématique, ceci se traduit par le fait que la différence entre les champs électromagnétiques de la structure perturbée et ceux de la structure de référence est de l'ordre de la perturbation. Par contre, quand la fréquence est résonante, le comportement de l'onde est très sensible aux petites déformations singulières de la géométrie de la structure. Cette sensibilité est susceptible d'être détectée dans les mesures du champ lointain, et est la brique de base de plusieurs capteurs et filtres plasmoniques. Dans ce projet de thèse nous nous sommes intéressés aux propriétés optiques de surfaces métalliques comportant des cavités sub-longueur d'onde distribués périodiquement ou non, et de couches métalliques minces. Ces structures possèdent des résonances électromagnétiques proches de l’axe réel, et sont capables de concentrer l’énergie électromagnétique dans des volumes bien inférieurs à la cubique de la longueur d’onde incidente. La compréhension de ce phénomène est un enjeu important pour le développement des spectroscoepies ultra-sensibles, mais aussi dans le domaine des bio-capteurs et de l’opto-électronique. En utilisant des techniques asymptotiques couplées avec des équations intégrales, nous avons déterminé le développement asymptotique des fréquences de résonance de ces structures quand le rapport entre l'échelle de la structuration spatiale et la longueur d'onde tend vers zéro. Les modèles asymptotiques dérivés sont beaucoup plus simples à étudier et à simuler et rendent parfaitement compte des résultats expérimentaux. Ils permettent de prédire les fréquences résonnantes, la quantité d’énergie localisée en fonction de la géométrie des structures et des propriétés des matériaux qui les constituent. / Rough metallic surfaces with subwavelength structurations possess extraordinary diffractive properties: at certain frequencies, one may observe fine localization and very large enhancement of the electromagnetic fields. The discovery of these phenomena has raised considerable interest as potential applications are numerous (optical switches, sensors, devices for microscopy). This behavior results from the combination of very complex interaction between the incident excitation, the geometry and the material properties of the scatterer. The main goal of this thesis is to better understand these phenomena from the mathematical point of view.In mathematical terms, the localization and concentration of the fields is the mark of a resonance phenomenon. In our context, the corresponding resonant field may be surface plasmons, i.e., waves that propagate along the interface of the grating, and that decay exponentially away from it. Another type of resonance is due to possible cavity modes. Thus, the study of these phenomena pertains to eigenvalue problems for the solutions of the Maxwell system, in geometric configurations where in the whole of a dielectric (generally air) and a metal are separated by an infinite rough interface.We are interested in particular micro-structured devices, namely metallic surfaces that contain rectangular grooves with sub-wavelength apertures, and thin plane layers. Configurations of this type can be manufactured quite precisely and have been subject to many experimental works. The simple geometry of these structures allows us to transform the eigenvalue problem for the Maxwell system into a nonlinear eigenvalue problem for an integral operator that depends on a small parameter, which, using tools from analytic perturbation of operators theory, lends itself to a precise asymptotic analysis. Precisely, we showed that the resonances of these structures converge tothe zeros of some explicit dispersion equations when the ratio between the roughness parameter and the wavelength tends to zero. These asymptotic models provide a precise localization of the resonances in the complex plane, and are suited for numerical approximation, shape and material optimization.

abstract: A proposed visible spectrum nanoscale imaging method requires material with permittivity values much larger than those available in real world materials to shrink the visible wavelength to attain the desired resolution. It has been proposed that the extraordinarily slow propagation experienced by light guided along plasmon resonant structures is a viable approach to obtaining these short wavelengths. To assess the feasibility of such a system, an effective medium model of a chain of Noble metal plasmonic nanospheres is developed, leading to a straightforward calculation of the waveguiding properties. Evaluation of other models for such structures that have appeared in the literature, including an eigenvalue problem nearest neighbor approximation, a multi- neighbor approximation with retardation, and a method-of-moments method for a finite chain, show conflicting expectations of such a structure. In particular, recent publications suggest the possibility of regions of invalidity for eigenvalue problem solutions that are considered far below the onset of guidance, and for solutions that assume the loss is low enough to justify perturbation approximations. Even the published method-of-moments approach suffers from an unjustified assumption in the original interpretation, leading to overly optimistic estimations of the attenuation of the plasmon guided wave. In this work it is shown that the method of moments approach solution was dominated by the radiation from the source dipole, and not the waveguiding behavior claimed. If this dipolar radiation is removed the remaining fields ought to contain the desired guided wave information. Using a Prony's-method-based algorithm the dispersion properties of the chain of spheres are assessed at two frequencies, and shown to be dramatically different from the optimistic expectations in much of the literature. A reliable alternative to these models is to replace the chain of spheres with an effective medium model, thus mapping the chain problem into the well-known problem of the dielectric rod. The solution of the Green function problem for excitation of the symmetric longitudinal mode (TM01) is performed by numerical integration. Using this method the frequency ranges over which the rod guides and the associated attenuation are clearly seen. The effective medium model readily allows for variation of the sphere size and separation, and can be taken to the limit where instead of a chain of spheres we have a solid Noble metal rod. This latter case turns out to be the optimal for minimizing the attenuation of the guided wave. Future work is proposed to simulate the chain of photonic nanospheres and the nanowire using finite-difference time-domain to verify observed guided behavior in the Green's function method devised in this thesis and to simulate the proposed nanosensing devices. / Dissertation/Thesis / M.S. Electrical Engineering 2013

Dans ce travail de Thèse de Doctorat, dans le contexte d’une application de filtrage optique pour la réalité augmentée des Viseurs Tête Haute (VTH), plusieurs possibilités de conception de filtres basés sur des résonances de nanoparticules métalliques sont explorées. Pour ce faire, une formulation de la Méthode des Éléments Finis (FEM) précédemment développée au sein de l’Institut Fresnel est appliquée à différentes structures électromagnétiques complexes. La validité des résultats de la FEM est alors vérifiée, dans une configuration extrêmement résonante d’un réseau bidimensionnel de nanocônes d’or illuminé dans des conditions d’absorption totale de la lumière incidente, par comparaison avec les résultats d’une autre méthode numérique complètement indépendante. Une fois validée dans cette configuration extrême, cette méthode a pu être utilisée afin de conduire une étude paramétrique sur deux types particuliers de réseaux de nanoparticules métalliques. Les résultats de cette étude paramétrique ont conduit aux designs de deux types de composant de filtrage de la lumière visible requis pour l’application VTH: celui de réseaux monodimensionnels de rubans d’argent permettant de réfléchir une partie du spectre lumineux pour une composante de polarisation de la lumière tout en étant globalement transparent pour l’autre composante de polarisation, et celui de réseaux bidimensionnels de nanocylindres à section elliptique permettant de réfléchir deux parties distinctes du spectre en fonction de la polarisation de la lumière incidente et ceci toujours avec des propriétés de transparence globale. Dans un dernier temps, une nouvelle formulation de la FEM est développée afin d’étendre cette méthode numérique au calcul des modes de résonance de ce type de nanostructures métalliques. En présence de structures incorporant des matériaux métalliques, dispersifs et dissipatifs, l’opérateur de Maxwell associé est non-linéaire en fréquence et non-Hermitien et donc difficile à aborder numériquement. Dans le but de linéariser cet opérateur vis-à-vis de la fréquence, le formalisme dit de “champs auxiliaires” a été implémenté numériquement aux éléments finis. La validité des résultats numériques obtenus est enfin vérifiée sur une cavité fermée puis sur différents cristaux photoniques bidimensionnels constitués de tiges métalliques de Drude. Enfin, dans le cas de structures ouvertes, une couche parfaitement adaptée (PML) dispersive est étudiée dans le cadre des problèmes modaux. / In this PhD, in the frame of a filtering application for augmented reality of Head-Up Display (HUD), several possibilities to design filters based on metallic nanoparticles resonances are explored. To do so, a Finite Element Method formulation previously developed within the Institut Fresnel is initially recalled and its implementation applied to various complex electromagnetic structures. The validity of its results is verified, in the particuliar case of an extremely resonant configuration consisting in a gold nanocones metallic grating illuminated in the condition of total absorption of light, by comparison with the results of another completely independent numerical method. Thus, the results of this implementation having been validated in this extreme configuration, they could then be used to conduct a parametric study on two particular types of metallic nanoparticles gratings significantly less resonant. The results of this parametric study have led to the design of both types of filtering component of the visible light required for the HUD application: the mono-dimensional silver ribbons gratings allowing to reflect a part of the visible spectrum for one polarization’s component of the light while being globally transparent for the other component, and that of two-dimensional silver nanocylinders of elliptic cross section allowing to reflect two distinct parts of the spectrum according to the polarization of incident light while still being globally transparent. In a last time, a new FEM formulation is developed in order to extend this numerical method to the resonances computation of this kind of metallic nanostructures. When metallic materials are involved into electromagnetic structures, the associated Maxwell operator is non-linear and non-Hermitian. The Eigenvalue problem to solve is practically impossible to implement into the FEM. In order to linearize the Maxwell operator toward the frequency, a formalism called “Auxiliary fields formalism” is introduced and implemented numerically. The validity of the results obtained through this implementation is then verified on a closed cavity and on several example of bi-dimensional photonic crystals made of Drude metallic rods. Finally, when tackling open structures, a dispersive perfectly matched layer (PML) is studied in the frame of eigenvalue problems.

Cette thèse a pour but d'étudier les effets quantiques apparaissant pour des agrégats métalliques de très petite taille en raison de l'augmentation du ratio surface/volume et de la discrétisation de la structure électronique. Mettre en avant ces effets demande une très grande qualité de fabrication des nanoparticules étudiées, monodisperse dans le cas idéal. Nous fabriquons des nanostructures en encapsulant des agrégats d'argent générés par une source magnétron dans des matrices solides, comme la silice ou l'alumine. Cette technique nous permet de contrôler indépendamment la composition des particules, leur taille, et leur concentration. Un spectre de masse quadripolaire a été mis en place et utilisé comme un filtre en taille pour obtenir une distribution plus étroite et précise.Les échantillons ont été caractérisés par deux techniques complémentaires : par spectroscopie optique à transmission avec des mesures sur des ensembles de particules, et par spectroscopie de perte d'énergie des électrons (EELS) sur des particules uniques, réalisée dans un microscope électronique à balayage par transmission. Bien qu'utilisant deux outils conceptuellement différents, ces deux méthodes mesurent les résonances plasmoniques des particules. Ce travail a donc pour objectif de relier théoriquement et expérimentalement ces deux méthodes dans le but de comprendre comment les propriétés physiques de ces petits agrégats de métaux nobles sont affectées par les effets quantiques / The aim of this thesis is to study quantum effects appearing in very small metallic clusters caused by the increasing surface/volume ratio and the discretization of the electronic structure. Investigating effects such as size dependencies demand a very high quality of the studied nanoparticles, monodisperse in the ideal case. We fabricate nanostructures by embedding silver clusters generated in a magnetron source in solid matrices, such as silica or alumina. This technique gives us full and independent control over the particle composition, size and concentration. A quadrupole mass spectrometer is used as a size filter to obtain a more precise and narrow distribution.Samples have been characterized with two complementary methods: optical transmission spectroscopy of ensembles of particles and electron energy loss spectroscopy (EELS) on single particles using a scanning transmission electron microscope. Although these two tools are conceptually different, they both measure the plasmonic resonances of metal nanoparticles. The objective of this work is to link theory and experiment in these two methods in order to understand how the physical properties of these small noble metal clusters are affected by quantum effects

Dans ce travail, la chimie supramoléculaire est utilisé pour créer des polymères triarylamine auto-assemblées affichant l’auto-assemblage, la conduction, et les propriétés plasmoniques. Deux classes de polymères triarylamine auto‐assemblées sont décrits en détail, y compris leurs propriétés d'auto-assemblage, structure à empiler, ainsi que le comportement électrochimique. En outre, l'application de ces matériaux à l'égard des cellules solaires organiques et spintronique moléculaire est examinée. Enfin, la capacité de ces fibres pour être utilisé dans des applications plasmoniques est détaillé, dans lequel les assemblages supramoléculaires sont présentés à quelques résonances plasmoniques de nanoparticules, agissent comme guides plasmoniques, et induisent l'ordre des nanoparticules plasmoniques à une interface liquide-liquide. Ces propriétés émergentes sont intimement liés aux interactions supramoléculaires démontrant ainsi de nouvelles applications de polymères supramoléculaires. / In this work, supramolecular chemistry is used to create self-assembled triarylamine polymers displaying novel self-assembly, conduction, and plasmonic properties. Two classes of self-assembled triarylamine polymers are described in detail, including their self-assembly properties, stacking structure, as well as electrochemical behavior. Additionally, the application of these materials towards organic solar cells and molecular spintronics is examined. Finally, the ability of these fibers to be used in plasmonic applications is detailed, wherein the supramolecular assemblies are shown to couple plasmonic nanoparticle resonances, act as plasmonic waveguides, and induce the ordering of plasmonic nanoparticles at a liquid-liquid interface. These emergent properties are intimately linked to the supramolecular interactions thereby demonstrating novel applications of supramolecular polymers.

Nous avons étudié la dynamique des électrons dans des réseaux de nanoparticules métalliques. Nous avons d'abord considéré le réseau le plus simple, c'est-à-dire le dimère de nanoparticules. Nous avons trouvé des fréquences propres du dimère hétérogène et ensuite nous avons appliqué l'approche du système quantique ouvert pour décrire les processus d’amortissement présents dans le système. Nous avons étudié deux processus d’amortissement qui dépendent de la taille des nanoparticules constituant le dimère: l'amortissement de Landau avec une proportionnalité inverse à la taille du système, et l’amortissement radiatif, proportionnel au volume du système. En utilisant les résultats de l'étude des dimères, nous avons étendu notre approche du système quantique ouvert pour étudier des chaînes de nanoparticules unidimensionnelles. Nous avons dérivé une équation maîtresse qui a été utilisée pour étudier la propagation des plasmons le long de la chaîne. Nous avons constaté que la propagation du plasmon est limitée que par les sources non radiatives d'amortissement. Enfin, nous avons dérivé l'expression analytique de la longueur de propagation d'un plasmon dans une chaîne de nanoparticules. / We studied the electron dynamics in metallic nanoparticle arrays. We first considered the simplestarray i.e. a nanoparticle dimer. We found the eigenfrequencies of the heterogeneous dimer andthen we applied the open quantum system approach to describe the decay processes present inthe system. We investigated two decay processes which depend on the size of the nanoparticlesbuilding up the dimer : the Landau damping, inversly proportional to the system-size, and radiationdamping, proportional to the volume of the system. Using the results of the dimer study weextended our open quantum system approach to study one-dimensional nanoparticle chains. Wederived a master equation and used it to investigate the propagation of plasmons along the chain.We found that the propagation of the plasmon is limited by the non-radiative sources of damping.Finally we derived an analytical expression for the propagation length of a plasmon in ananoparticle chain.

In this dissertation, advances in the fields of Photonics, and Plasmonics, and specifically, single cell analysis and waveguide sensing will be addressed. The first part of the dissertation is on Finite Difference Time Domain (FDTD) optimization and experimental demonstration of a nano-scale instrument that allows sensing at the cellular and subcellular levels. A new design of plasmonic coupler into a nanoscale waveguide is proposed and optimized using FDTD simulations. Following this, a subcellular nanoendoscope that can locally excite fluorescence in labelled cell organelles and collect the emitted fluorescent light for detailed spectrum analysis is fabricated and tested. The nanoendoscope has a sharp tapered tip of diameter ~ 50 nm that permits safe insertion into the cell that was confirmed by a number of viability experiments. FDTD analysis demonstrated that, with an optimized nanoendoscope taper profile, light emission and collection was very local. Thus, signal detection could be used for nano-photonic sensing of proximity of fluorophores. In further experiments, fluorescent signals were collected from individual organelles of living cells including: the nucleus of Acridine orange labelled human fibroblast cells, the nucleus of Hoechst stained live liver cells and the mitochondria of MitoTracker Red labelled MDA-MB-231 cells. In addition, this endoscope was inserted into a live organism, the nematode Caenorhabditis elegans, and in- vivo fluorescence signal was collected. Second, an innovative single step fabrication method of low loss polysilicon waveguides was developed as a potential platform for a number of photonic sensors. Optimization of a capacitively coupled plasma etching for the fabrication of a polysilicon waveguide with smooth sidewalls and low optical loss was demonstrated. A detailed experimental study on the influences of RF plasma power and chamber pressure on the roughness of the sidewalls of waveguides was conducted and waveguides were characterized using a scanning electron microscope. It was demonstrated that optimal combination of pressure (30 mTorr) and power (150 W) resulted in the smoothest sidewalls. The optical losses of the optimized waveguide were 4.1± 0.6 dB/ cm. Finally, an on-chip nanophotonic sensor for continuous blood coagulation analysis was proposed. The system was simulated using three-dimensional FDTD software. At first, the noise due to the presence of cells was calculated. Next, the design of a waveguide cladding-based filtering structure for elimination of the noise from cells was proposed and significantly decreased noise level was theoretically demonstrated.

The outstanding electrical and material properties of Graphene have made it a promising material for several fields of analog applications, though its zero bandgap precludes its application in digital and logic devices. With its remarkably high electron mobility at room temperature, Graphene also has strong potential for terahertz (THz) plasmonic devices. However there still are challenges to be solved to realize Graphene’s full potential for practical applications. In this dissertation, we investigate solutions for some of these challenges. First, to reduce the access resistances which significantly reduces the radio frequency (RF) performance of Graphene field effect transistors (GFETs), a novel device structure consisting of two additional contacts at the access region has been successfully modeled, designed, microfabicated/integrated, and characterized. The additional contacts of the proposed device are capacitively coupled to the device channel and independently biased, that induce more carriers and effectively reduce access resistance. In addition to that, in this dissertation, bandgap has been experimentally introduced to semi-metallic Graphene, by decorating with randomly distributed gold nano-particles and zinc oxide (ZnO) nano-seeds, where their interaction breaks its sublattice symmetry and opens up bandgap. The engineered bandgap was extracted from its temperature dependent conductivity characteristics and compared with reported theoretical estimation. The proposed method of device engineering combined with material bandgap engineering, on a single device, introduces a gateway towards high speed Graphene logic devices. Finally, THz plasmon generation and propagation in Graphene grating gate field effect transistors and Graphene plasmonic ring resonators have been investigated analytically and numerically to explore their potential use for compact, solid state tunable THz detectors.

We explore a new laboratory technique in the field of urinalysis promising a combination of speed and selectivity in support of urinary tract infection diagnosis. Laboratory experimentation demonstrates long range surface plasmon polaritons (LRSPP) waveguides as a useful biosensor to selectively detect gram negative bacteria or gram positive bacteria in human urine. The biosensor can detect bacteria at concentration of 105 CFU/ml, the internationally recommended threshold for diagnostic of urinary tract infection (UTI). Using a negative control solution at bacterial concentration 1000x higher than the targeted bacteria in urine with a weak concentration of constituents, the power ratio between the negative control signals to the target bacteria signal is measured to be 5.4. Thus we report a conclusive demonstration of the LRSPP waveguide biosensor selectivity to the gram of bacteria in human urine. In addition, the biosensor may prove useful as an alternative urinalysis test method to determine the urine specific gravity, to estimate proteinuria, and to detect biofilm formation on surfaces.