Different types of plasmonic nanostructures are proposed and examined experimentally and theoretically, with a view towards sensing applications. First, a self-assembly approach was developed to create arrays of well-ordered glass-supported gold nanoparticles (AuNPs) with controllable particle size and inter-particle spacing. Then, a periodic array of gold nano-disks (AuNDs) supported by a Bragg reflector was proposed and examined in a search for Fano resonances in its optical response. Arrays of heptamer-arranged nanoholes (HNH) in a thin gold film were also proposed and explored theoretically and experimentally, revealing a very rich spectrum of resonances, several exhibiting a Fano lineshape. A commercial implementation of the vectorial finite element method (FEM) was used to model our plasmonic structures. Taking advantage of the periodic nature of the structures, a unit cell containing a single element was modelled. The transmittance, reflectance or absorbance spectra were computed, and the associated electromagnetic fields were obtained by solving the vector wave equations for the electromagnetic field vectors throughout the structures, subject to the applicable boundary conditions, and the applied source fields. The sensing performance of the structures, based on the bulk sensitivity, surface sensitivity and figure of merit (FOM) was calculated. First, a novel bottom-up fabrication approach was applied (by our collaborators) to form a periodic array of AuNPs with controllable size over large areas on SiO2 substrates. In this method, self-assembly of block copolymer micelles loaded with metal precursors was combined with a seeding growth route to create ordered AuNPs of desired size. It was shown that this new fabrication method offers a new approach to tune the AuNP size and edge-to-edge inter-particle spacing while preserving the AuNP ordering. The optical characteristics of the AuNP arrays, such as their size, interparticle spacing, localized surface plasmon resonance (LSPR) wavelength, and bulk sensitivity, were examined, numerically and experimentally. This proposed novel fabrication method is applicable for low-cost mass-production of large-area arrays of high-quality AuNPs on a substrate for sensing applications. Then, we proposed and examined the formation of Fano resonances in a plasmonic-dielectric system consisting of uncoupled gold nano-disk (AuND) arrays on a quarter-wave dielectric stack. The mechanism behind the creation of Fano resonances was explained based on the coherent interference between the reflection of the Bragg stack and the LSPPs of the AuNDs. Fano parameters were obtained by fitting the computational data to the Fano formula. The bulk sensitivities and figure of merit of the Fano resonances were calculated. This plasmonic structure supports Fano resonances with a linewidth around 9 nm which is much narrower than the individual AuND LSPP bandwidth ( 80 nm) and the Bragg stack bandwidth ( 100 nm). Supporting Fano resonances with such a narrow linewidth, the structure has a great potential to be used for sensing applications. Also, this metallic-dielectric nanostructure requires no near-field coupling between AuNDs to generate the Fano resonances. So, the AuNDs can be located far enough from each other to simplify the potential fabrication process. The optical properties of HNH arrays on an SiO2 substrate were investigated, numerically and experimentally. Helium focused ion beam (HeFIB) milling was applied (by Dr. Choloong Hahn) to fabricate well-ordered and well-defined arrays of HNHs. Transmittance spectra of the structures were obtained as the optical response, which exhibits several Fano resonances. Then, the mechanism behind the formation of the Fano resonances was explained, and the sensing performance of the structure was inspected by measuring the bulk sensitivities. This array of nanohole cluster is exciting because it supports propagating SPPs and LSPPs, and also Wood’s anomaly waves, which makes the optical response very rich in excitations and spectral features. Also, as a periodic array of sub-wavelength metallic nanoholes, the system produces extraordinary optical transmission - highly enhanced transmission through (otherwise) opaque metallic films at specific wavelengths, facilitating measurement acquisition in transmission.

Recently, lattices - a mathematical representation of infinite discrete points in the Euclidean space, have become an effective way to describe and analyze communication systems especially system those that can be modeled as linear Gaussian vector channel model. Channel codes based on lattices are preferred due to three facts: lattice codes have simple structure, the code can achieve the limits of the channel, and they can be decoded efficiently using lattice decoders which can be considered as the Closest Lattice Point Search (CLPS). Since the time lattice codes were introduced to Multiple Input Multiple Output (MIMO) channel, Sphere Decoder (SD) has been an efficient way to implement lattice decoders. Sphere decoder offers the optimal performance at the expense of high decoding complexity especially for low signal-to-noise ratios (SNR) and for high- dimensional systems. On the other hand, linear and non-linear receivers, Minimum Mean Square Error (MMSE), and MMSE Decision-Feedback Equalization (DFE), provide the lowest decoding complexity but unfortunately with poor performance. Several studies works have been conducted in the last years to address the problem of designing low complexity decoders for the MIMO channel that can achieve near optimal performance. It was found that sequential decoders using backward tree 
search can bridge the gap between SD and MMSE. The sequential decoder provides an interesting performance-complexity trade-off using a bias term. Yet, the sequential decoder still suffers from high complexity for mid-to-high SNR values. In this work, we propose a new algorithm for Bidirectional Fano sequential Decoder (BFD) in order to reduce the mid-to-high SNR complexity. Our algorithm consists of first constructing a unidirectional Sequential Decoder based on forward search using the QL decomposition. After that, BFD incorporates two searches, forward and backward, to work simultaneously till they merge and find the closest lattice point to the received signal. We show via computer simulations that BFD can reduce the mid-to-high SNR complexity for the sequential decoder without changing the bias value.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20885号 / 理博第4337号 / 新制||理||1623(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 望月 拓郎, 教授 中島 啓, 教授 小野 薫 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

No abstract available

Previous studies have shown that it is possible for juvenile songbirds to learn songs through listening to prerecorded songs played back to them. What is not known however, is how this will differ from normal learning, both on neural level as well as on the bird as whole. In this project we have taken data from playback experiments and attempted to measure the differences in neuron spiking activity across two different contexts. Firstly, when the bird is only listening to playback recordings and secondly when the bird is listening to playback recordings on the same day as listening to a live tutor. We analysed the spiking activity with several different methods in order to establish a distinction between these contexts that could be seen across birds and across trials. The methods include analysing joint spiking events as binary spike trains, the Fano factor across trials as well as the variability of the spike rate. Our hypothesis was that the birds would learn more effectively on days when exposed to a live tutor, therefore, the playback days would show much higher and much more varied spiking data. From our results we found many cases when this hypothesis is true. However, it does not hold true for each of the birds, as some are offered similar results in either context. Therefore we believe that further study would be required to get conclusive results. Although, our results tend to favour the tutoring days it is only suggestive that this shows evidence of better learning. / Tidigare studier har visat att det är möjligt för unga sångfåglar att lära sig sånger genom att lyssna på förinspelade läten som spelas upp för dem. Vad som dock inte är känt är hur detta sätt kommer att skilja sig, jämfört med normalt lärande, både på neural nivå och på fågeln som helhet. I detta projekt har vi tagit data från ett uppspelningsexperiment och försökt mäta skillnaderna neuronspikande aktiviteter i två fall. I det första fallet lyssnar fågeln bara på inspelad fågelsång och i det andra fallet lyssnar fågeln på inspelad fågelsång samma dag som den lyssnar på en vuxen fågel som mentor. Vi analyserade spikningsaktiviteten med flera olika metoder för att finna en skillnad mellan dessa fall, som kan ses både mellan fåglar och mellan ollika försök. Metoderna inkluderar analys av gemensamma spikinghändelser som binära spiktåg, Fanofaktorn över försöken samt variationen i spikhastigheten. Vår hypotes var att fåglarna skulle lära sig mer effektivt på dagar när de utsattes för en vuxen fågel som mentor, därför skulle uppspelningsdagarna visa mycket högre och mycket mer varierad spikdata. Från våra resultat fann vi att i många fall där hypotesen är sann. Men den stämmer inte för alla fåglarna eftersom några fåglar hade liknande resultat för båda fallen. Därför tror vi att ytterligare studier krävs för att få tydliga resultat. Dock så tenderar våra resultat att gynna mentordagarna, även om det bara antyder att detta visar på bättre lärande.

No description available.

We first introduce the octonions as an eight dimensional vector space over a field of characteristic zero with a multiplication defined using a table. We also show that the multiplication rules for octonions can be derived from a special graph with seven vertices call the Fano Plane. Next we explain the Cayley-Dickson construction, which exhibits the octonions as the set of ordered pairs of quaternions. This approach parallels the realization of the complex numbers as ordered pairs of real numbers. The rest of the thesis is devoted to following a paper by N. Jacobson written in 1939 entitled "Cayley Numbers and Normal Simple Lie Algebras of Type G". We prove that the algebra of derivations on the octonions is a Lie algebra of type G_2. The proof proceeds by showing the set of derivations on the octonions is a Lie algebra, has dimension fourteen, and is semisimple. Next, we complexify the algebra of derivations on the octonions and show the complexification is simple. This suffices to show the complexification of the algebra of derivations is isomorphic to g_2 since g_2 is the only semisimple complex Lie algebra of dimension fourteen. Finally, we conclude the algebra of derivations on the octonions is a simple Lie algebra of type G_2. / Master of Science

No / The bandwidth of a microstrip patch antenna is expressed in terms of minimum achievable reflection coefficient using an equivalent circuit and the Bode-Fano theory. The bandwidth-reflection coefficient product is found to be proportional to antenna height and largely independent of feed probe position, for small bandwidths. The product can be computed directly from a numerical evaluation of the first-order Bode-Fano integral. Curves are presented showing how the product becomes limited by the feed probe inductance at very large bandwidths. It is concluded that this effect is unlikely to be a limit on the potential bandwidth of a practical patch antenna. If as a minimal correction the feed inductance is tuned out, the realized bandwidth with low order matching or optimal over-coupling shows the expected relationship to the theoretical limit.

Les recherches présentées dans ce mémoire ont été rendues possible grâce à la contribution financière du CRSNG, par à leur Programme de subventions à la découverte (SD) et leur Programme de bourses d’études supérieures du Canada au niveau de la maîtrise (BESC M); du FRQNT, par leur Programme de bourse de maîtrise (B1); et du CLS, par leur Graduate and Post-Doctoral Student Travel Support Program. / Le graphène est un nano-matériau très prometteur grâce à ses excellentes propriétés mécaniques, optiques et électriques. Toutefois, la plupart de ses applications les plus novatrices requièrent de l'altérer, mais la compréhension du graphène altéré est encore limitée. Certaines applications envisagées sont en optique infrarouge. Or, notre compréhension actuelle du graphène ne permet pas d’expliquer l’apparition des pics infrarouges qui sont observés dans les bicouches et dans les monocouches fonctionnalisées. Le comportement du graphène fonctionnalisé est particulièrement contre-intuitif, puisque l’ajout de greffons le rend plus transparent, et non pas plus opaque! Un modèle proposé par Bruno Rousseau, un étudiant post-doctorant du professeur Michel Côté à l'Université de Montréal, suggère une explication à ce phénomène: bien que les phonons du graphène ne puissent pas coupler directement avec la lumière, ils coupleraient indirectement avec celle-ci grâce à des collisions sur les électrons, qui eux, peuvent coupler avec les photons. Ce couplage indirect peut produire des interférences parfois constructives, parfois destructives, de telle sorte que ce mécanisme peut autant produire des pics d’absorbance que de transparence. Dans le cadre de ce mémoire, nous avons entrepris de vérifier expérimentalement la validité de ce modèle, et nous concluons qu’il semble prédire adéquatement le comportement de l’activité infrarouge des bicouches de graphène et des monocouches fonctionnalisées. Nous avons aussi étudié les méthodes par lesquelles nous synthétisions ces différents types de graphène afin de les optimiser. Enfin, nous avons déterminé des techniques, basées sur la spectroscopie Raman, permettant de bien caractériser l’intensité de l’altération causée par ces méthodes. / Graphene is a promising nanomaterials thanks to its excellent mechanical, optical and electrical properties. However, its most innovative applications require that it be altered, but the understanding altered graphene is still limited. Some applications are considered in infrared optics. However, our current understanding of graphene does not explain the appearance of the infrared peaks that are observed in bilayers and grafted monolayers. The behaviour of grafted graphene is especially baffling, since the addition of grafts makes it more transparent, not less! A model proposed by Bruno Rousseau, a postdoctoral student of Professor Michel Côté at Université de Montréal, suggests an explanation for this phenomenon: although the phonons of graphene cannot couple directly with light, they could couple indirectly through collisions with the electrons, which can couple with photons. This indirect coupling may produce constructive and destructive interference, depending on the conditions, so this mechanism can produce absorbance peaks as much as transparency peaks. In this master’s thesis, we have undertaken to experimentally verify the validity of this model, and we conclude that it seems to adequately predict the behaviour of the infrared activity of graphene bilayers and grafted monolayers. We also studied the methods by which we synthesized these different types of graphene to optimize them. Finally, we determined techniques based on Raman spectroscopy to characterize the intensity of the alteration induced by these methods.

Les nanotubes de carbone et le graphène sont des nanostructures de carbone hybridé en sp2 dont les propriétés électriques et optiques soulèvent un intérêt considérable pour la conception d’une nouvelle génération de dispositifs électroniques et de matériaux actifs optiquement. Or, de nombreux défis demeurent avant leur mise en œuvre dans des procédés industriels à grande échelle. La chimie des matériaux, et spécialement la fonctionnalisation covalente, est une avenue privilégiée afin de résoudre les difficultés reliées à la mise en œuvre de ces nanostructures. La fonctionnalisation covalente a néanmoins pour effet de perturber la structure cristalline des nanostructures de carbone sp2 et, par conséquent, d’affecter non seulement lesdites propriétés électriques, mais aussi les propriétés optiques en émanant. Il est donc primordial de caractériser les effets des défauts et du désordre dans le but d’en comprendre les conséquences, mais aussi potentiellement d’en exploiter les retombées. Cette thèse traite des propriétés optiques dans l’infrarouge des nanotubes de carbone et du graphène, avec pour but de comprendre et d’expliquer les mécanismes fondamentaux à l’origine de la réponse optique dans l’infrarouge des nanostructures de carbone sp2. Soumise à des règles de sélection strictes, la spectroscopie infrarouge permet de mesurer la conductivité en courant alternatif à haute fréquence des matériaux, dans une gamme d’énergie correspondant aux vibrations moléculaires, aux modes de phonons et aux excitations électroniques de faible énergie. Notre méthode expérimentale consiste donc à explorer un espace de paramètres défini par les trois axes que sont i. la dimensionnalité du matériau, ii. le potentiel chimique et iii. le niveau de désordre, ce qui nous permet de dégager les diverses contributions aux propriétés optiques dans l’infrarouge des nanostructures de carbone sp2. Dans un premier temps, nous nous intéressons à la spectroscopie infrarouge des nanotubes de carbone monoparois sous l’effet tout d’abord du dopage et ensuite du niveau de désordre. Premièrement, nous amendons l’origine couramment acceptée du spectre vibrationnel des nanotubes de carbone monoparois. Par des expériences de dopage chimique contrôlé, nous démontrons en effet que les anomalies dans lespectre apparaissent grâce à des interactions électron-phonon. Le modèle de la résonance de Fano procure une explication phénoménologique aux observations. Ensuite, nous établissons l’existence d’états localisés induits par la fonctionnalisation covalente, ce qui se traduit optiquement par l’apparition d’une bande de résonance de polaritons plasmons de surface (nanoantenne) participant au pic de conductivité dans le térahertz. Le dosage du désordre dans des films de nanotubes de carbone permet d’observer l’évolution de la résonance des nanoantennes. Nous concluons donc à une segmentation effective des nanotubes par les greffons. Enfin, nous montrons que le désordre active des modes de phonons normalement interdits par les règles de sélection de la spectroscopie infrarouge. Les collisions élastiques sur les défauts donnent ainsi accès à des modes ayant des vecteurs d’onde non nuls. Dans une deuxième partie, nous focalisons sur les propriétés du graphène. Tout d’abord, nous démontrons une méthode d’électrogreffage qui permet de fonctionnaliser rapidement et à haute densité le graphène sans égard au substrat. Par la suite, nous utilisons l’électrogreffage pour faire la preuve que le désordre active aussi des anomalies dépendantes du potentiel chimique dans le spectre vibrationnel du graphène monocouche, des attributs absents du spectre d’un échantillon non fonctionnalisé. Afin d’expliquer le phénomène, nous présentons une théorie basée sur l’interaction de transitions optiques intrabandes, de modes de phonons et de collisions élastiques. Nous terminons par l’étude du spectre infrarouge du graphène comportant des îlots de bicouches, pour lequel nous proposons de revoir la nature du mécanisme de couplage à l’œuvre à la lumière de nos découvertes concernant le graphène monocouche. / Carbon nanotubes and graphene are sp2 hybridized carbon nanostructures which electrical and optical properties raise considerable interest for the design of a new generation of electronic devices and optically active materials. However, many challenges remain before their implementation in industrial processes on a large scale. Materials chemistry, especially covalent functionalization, is a privileged avenue to resolve the difficulties related to the processing of these nanostructures. Covalent functionalization, however, disrupts the sp2 carbon nanostructures’ crystalline structure, and pertubs not only said electrical properties, but also the deriving optical properties. It is therefore essential to characterize the effects of defects and disorder in order to understand their consequences, but also to potentially exploit the benefits. This thesis deals with the optical properties in the infrared of carbon nanotubes and graphene, with the aim to understand and explain the fundamental mechanisms at the origin of the optical response in the infrared of sp2 carbon nanostructures. Subject to strict selection rules, infrared spectroscopy measures the high frequency AC conductivity of materials in an energy range corresponding to molecular vibrations, phonon modes and low energy electronic excitations. Our experimental method is therefore to explore a parameter space defined by the three axes that are i. the dimensionality of the material, ii. the chemical potential, and iii. the disorder level, which allows us to identify the various contributions to optical properties in the infrared of sp2 carbon nanostructures. At first, we focus on the infrared spectroscopy of single-walled carbon nanotubes as a function of doping and disorder level. We start by amending the commonly accepted origin of single-walled carbon nanotubes vibrational spectra. Using controlled chemical doping experiments, we show that the anomalies in the carbon nanotube spectra appear through electron-phonon interactions. The Fano resonance model provides a phenomenological explanation for the observations. Then, we establish the existence of localized states induced by covalent functionalization, which appear as a surface plasmon polariton resonance (nanoantenna) contributing to the terahertz conductivity peak. Control of the disorder level in carbon nanotube films allows us to observe the evolution of the nanoantenna resonance. We therefore conclude to an effective segmentation of the nanotubes by the grafts. Finally, we show that disorder activates phonon modes that are usually forbidden by infrared spectroscopy’s selection rules. Disorder-induced infrared activity originates from elastic collisions on defects that give access to phonon modes with non-zero wave vectors. In a second part, we focus on the properties of graphene. First, we demonstrate an electrografting method to rapidly functionalize graphene with high-density, regardless of the substrate. Subsequently, we use electrografting to show that disorder activates chemical potential dependent anomalies in the vibrational spectra of single-layer graphene. These anomalies are absent in the spectra of pristine samples. In order to explain this phenomenon, we present a theory based on the interaction of intraband optical transitions, phonon modes and elastic collisions. We conclude by studying the infrared spectra of graphene with bilayer islands, for which we propose to review the nature of the coupling mechanism in the light of our findings on single-layer graphene.