L’objectif de cette thèse est de concevoir et réaliser un amplificateur Raman fibré impulsionnel mono-fréquence à 1645 nm. Une telle source permettrait le développement futur d’un système LIDAR pour la caractérisation de panaches industriels de méthane. Cette application nécessite l’émission d’impulsions d’une durée de l’ordre de 100 ns et de plusieurs dizaines de µJ à haute cadence de répétition (10-100 kHz). Dans la fibre non linéaire utilisée pour l’amplification Raman, deux phénomènes principaux s’opposent à nos objectifs. D’une part, la diffusion Brillouin stimulée limite à la fois la puissance de la pompe et du signal amplifié. D’autre part, nous avons montré que l’amplification Raman s’accompagne d’un élargissement spectral non linéaire indésirable du signal. Pour mieux appréhender ces phénomènes, des expressions originales ont été établies pour la réflectivité Brillouin du signal et pour la phase non linéaire. Cette dernière a notamment permis de minimiser l’élargissement spectral du signal grâce à un choix pertinent de la forme des impulsions. Nous avons ensuite mis en œuvre plusieurs techniques d’augmentation du seuil Brillouin. Pour le signal, la solution retenue consiste à appliquer un profil longitudinal de contrainte mécanique à la fibre. Pour la pompe, nous avons procédé par élargissement spectral et comparé les résultats produits par une source multimode et par une source à dérive de fréquence. C’est cette deuxième solution que nous avons retenue dans la configuration finale. Le signal amplifié à 1645 nm atteint 27 µJ à 20 kHz pour une durée d’impulsion de 100 ns et une largeur spectrale de 10 MHz, répondant ainsi aux attentes pour le LIDAR envisagé. / The objective of this thesis work is to design and build a single-frequency Raman fiber amplifier at 1645 nm. Such an amplifier could form the basis of a future LIDAR system for industrial methane plume characterization. Emission of pulses about 100 ns long and a few tens of µJ at high repetition rate (10-100 kHz) is needed for this application. In the nonlinear fiber used for Raman amplification, two main phenomena oppose our objectives. On one hand stimulated Brillouin scattering limits the optical power of both the pump and the signal. On the other hand adverse spectral broadening of the signal due to Raman amplification has been demonstrated. To address these issues, original expressions have been derived for Brillouin reflectivity of the signal and for nonlinear phase. In particular, the latter has allowed minimization of the signal spectral broadening thanks to adapted pulse waveforms. Various Brillouin threshold increasing techniques have then been implemented. The signal threshold is increased by applying a longitudinal mechanical strain profile to the fiber. The pump threshold is increased through spectral broadening, using either a multimode source or a frequency-swept source. Our experimental study has shown that the latter was more suitable. In the final configuration, a 27 µJ source at 1645 nm with a 20 kHz repetition rate, a 100 ns pulse duration and a spectral width equal to 10 MHz has been achieved, meeting the requirements for the considered LIDAR system.

The optoelectronics industry continues to demand improved materials, devices and systems for the generation, transmission, detection, amplification and processing of optical signals. Heterojunction phototransistors (HPTs), in recent years, have attracted considerable interest for optical detection due to their intrinsic gain, low noise performance, high-frequency operation and process and the device layer compatibility with heterojunction bipolar transistors for high-speed optoelectronic monolithic microwave/millimetre-wave integrated circuit (OEMMIC) photoreceivers. A key performance parameter of HPTs is their spectral response (SR) which is critical in their usage in optical applications. The SR depends on several inherent factors including material absorption coefficient, refractive index, device structure, doping and temperature of operation along with the external factors such as bias voltage and the energy of incident radiation. The spectral response and optical characteristics of GaAs-based and InP-based sHPTs have been successfully predicted for the first time through an advanced absorption theoretical model. The model is based on the accurate prediction of photocarriers in the active layers of the phototransistor which, when related to the base current of the transistor in forward active mode, enables the prediction of optical characteristics. The importance of collection efficiency in accurate SR modelling is highlighted and the layer dependence of the optical flux absorption profile at near-band gap wavelengths is also investigated and its generalisation as a single-exponential has been refuted for GaAs-based HPTs. Analytical modelling of the spectral response has also been developed from the resolution of continuity equations that govern the excess optically generated minority carrier variation in the active layers of the HPT, taking into account the related physical parameters. Realistic boundary conditions have been considered for efficient device operation and a detailed optical flux absorption profile is constructed for accurate device modelling. This analytical model provides insight into the direct influence of various parameters (such as base width and carrier concentration) on the device performance, thus, providing a valuable optimization tool for the future design of HPTs in optical receivers. The measured results at 635 nm, 780 nm 808 nm and 850 nm for AlGaAs/GaAs HPTs and 980 nm, 1310 nm and 1550 nm for InP/InGaAs HPTs show good agreement with the predicted data, validating the proposed theoretical model. Finally, a detailed absorption model and photoresponse of double heterojunction phototransistors in a top/surface-illuminated orientation has been analyzed with a modified small-signal model. The effect of incident optical illumination on intrinsic small-signal parameters such as resistances and capacitances has been discussed and analyzed for photoresponse modelling.

For any two differential modules M and N over a graded differential k-algebra Λ (k a commutative ring), there Is a spectral sequence Er, called the Eilenberg-Moore spectral sequence, having the following properties: Er converges to Tor Λ (M,N) and E2=TorH(Λ) (H(M),H(N)). This algebraic set-up gives rise to a "geometric" spectral sequence in algebraic topology. Starting with a commutative diagram of topological spaces [diagram omitted] where B Is simply connected, one gets a spectral sequence Er converging to the cohomology H*(X xBY) of the space X xBY, and for which E₂=TorH*(B) (H*(X),H*(Y)). In this thesis we outline a generalization of the above geometric spectral sequence obtained, by first extending the category of topological spaces and then, extending the cohomology theory H* to this larger category. The convergence of the extended spectral sequence does not depend, on any topological conditions of the spaces involved. It follows algebraically from the way the exact couple (from which the spectral sequence Is derived) Is set up and from the Suspension Axiom of the extended cohomology theory. / Science, Faculty of / Mathematics, Department of / Graduate

no / Visual psychophysicists, who study object, color, and light perception, have a demand for software that produces complex but, at the same time, physically accurate stimuli for their experiments. The number of computer graphic packages that simulate the physical interaction of light and surfaces is limited, and mostly they require the purchase of a license. RADIANCE (Ward, 1994), however, is freely available and popular in the visual perception community, making it a prime candidate. We have shown previously that RADIANCE¿s simulation accuracy is greatly improved when color is coded by spectra, rather than by the originally envisaged RGB triplets (Ruppertsberg & Bloj, 2006). Here, we present a method for spectral rendering with RADIANCE to generate hyperspectral images that can be converted to XYZ images (CIE 1931 system) and then to machine-dependent RGB images. Generating XYZ stimuli has the added advantage of making stimulus images independent of display devices and, thereby, facilitating the process of reproducing results across different labs. Materials associated with this article may be downloaded from www.psychonomic.org.

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Aluminum is a non-essential trace element that accumulates in human bone tissue (Nayak, 2002). Its toxic effects are cumulative and result in painful forms of renal osteodystrophy, most notably a dynamic bone disease and osteomalacia, but also other forms of disease (Yokel, 2001; Cannata-Andia, 2002). Presently, histological tests of bone biopsies are the only approach for the diagnosis of aluminum-related pathologies (Malluche, 2002). Neutron Activation Analysis was proposed as an alternative method for quantifying aluminum. The Trace Element Group at McMaster University has developed an in vivo procedure for detecting aluminum levels in the bones of the hand, exploiting an accelerator-based approach. A minimum detectable limit (MDL) of 1.14mg of aluminum could be distinguished for a local dose to the hand of 48mSv (Pejovic-Milic, 2001). For the procedure to be clinically effective, the MDL should be comparable to the levels normally contained in healthy subjects (0.3-0.4 mg AI). Further refining of the method is therefore necessary. This dissertation presents an improved algorithm for data analysis, based on Spectral Decomposition. Following phantom measurements, a new MDL of(0.7±0.1)mg AI was reached for a local dose of (20±1)mSv, representing an improvement by a factor of 1.60±0.04. In addition, a time-dependent variant of this algorithm was proposed. The study also addresses the feasibility of a new data acquisition technique, the electronic rejection of the coincident events detected by the Nai(Tl) system. It is expected that the application of this technique, together with Spectral Decomposition Analysis, would provide an acceptable MDL for the method to be valuable in a clinical setting. / Thesis / Master of Science (MS)

The spectral theory of the Laplace operator has long been studied in connection with physics. It appears in the wave equation, the heat equation, Schroedinger's equation and in the expression of quantum effects such as the Casimir force. The Casimir effect can be studied in terms of spectral invariants computed entirely from the spectrum of the Laplace operator. It is these spectral invariants and their computation that are the object of study in the present work. The objective of this thesis is to present a computational framework for the spectral zeta function $\zeta(s)$ and its derivative on a Euclidean domain in $\mathbb{R}^2$, with rigorous theoretical error bounds when this domain is polygonal. To obtain error bounds that remain practical in applications an improvement to existing heat trace estimates is necessary. Our main result is an original estimate and proof of a heat trace estimate for polygons that improves the one of van den Berg and Srisatkunarajah, using finite propagation speed of the corresponding wave kernel. We then use this heat trace estimate to obtain a rigorous error bound for $\zeta(s)$ computations. We will provide numerous examples of our computational framework being used to calculate $\zeta(s)$ for a variety of situations involving a polygonal domain, including examples involving cutouts and extrusions that are interesting in applications. Our second result is the development a new eigenvalue solver for a planar polygonal domain using a partition of unity decomposition technique. Its advantages include multiple precision and ease of use, as well as reduced complexity compared to Finite Elemement Method. While we hoped that it would be able to contend with existing packages in terms of speed, our implementation was many times slower than MPSPack when dealing with the same problem (obtaining the first 5 digits of the principal eigenvalue of the regular unit hexagon). Finally, we present a collection of numerical examples where we compute the spectral determinant and Casimir energy of various polygonal domains. We also use our numerical tools to investigate extremal properties of these spectral invariants. For example, we consider a square with a small square cut out of the interior, which is allowed to rotate freely about its center.

International Telemetering Conference Proceedings / October 22-25, 2001 / Riviera Hotel and Convention Center, Las Vegas, Nevada / In current practice sensor data is digitized and input into computers, displays, and recorders. To try to reduce the volume of digitized data, our original hypothesis was that by selecting a subset of digital values from an over-sampled signal, we could improve signal identification and improve perhaps Nyquist performance. Our investigations did not lead to significant improvements but did clarify our thinking regarding the usage of digitized data.