Discrete Modeling of Granular Media: A NURBS-based Approach

This dissertation is concerned with the development of a new discrete element method (DEM) based on Non-Uniform Rational Basis Splines (NURBS). With NURBS, the new DEM is able to capture sphericity and angularity, the two particle morphological measures used in characterizing real grain geometries. By taking advantage of the parametric nature of NURBS, the Lipschitzian dividing rectangle (DIRECT) global optimization procedure is employed as a solution procedure to the closest-point projection problem, which enables the contact treatment of non-convex particles. A contact dynamics (CD) approach to the NURBS-based discrete method is also formulated. By combining particle shape flexibility, properties of implicit time-integration, and non-penetrating constraints, we target applications in which the classical DEM either performs poorly or simply fails, i.e., in granular systems composed of rigid or highly stiff angular particles and subjected to quasistatic or dynamic flow conditions. The CD implementation is made simple by adopting a variational framework, which enables the resulting discrete problem to be readily solved using off-the-shelf mathematical programming solvers. The capabilities of the NURBS-based DEM are demonstrated through 2D numerical examples that highlight the effects of particle morphology on the macroscopic response of granular assemblies under quasistatic and dynamic flow conditions, and a 3D characterization of material response in the shear band of a real triaxial specimen.

Scalable Methods for Deterministic Integration of Quantum Emitters in Photonic Crystal Cavities

We investigated four unique methods for achieving scalable, deterministic integration of quantum emitters into ultra-high Q{V photonic crystal cavities, including selective area heteroepitaxy, engineered photoemission from silicon nanostructures, wafer bonding and dimensional reduction of III-V quantum wells, and cavity-enhanced optical trapping. In these areas, we were able to demonstrate site-selective heteroepitaxy, size-tunable photoluminescence from silicon nanostructures, Purcell modification of QW emission spectra, and limits of cavity-enhanced optical trapping designs which exceed any reports in the literature and suggest the feasibility of capturing- and detecting nanostructures with dimensions below 10 nm. In addition to process scalability and the requirement for achieving accurate spectral- and spatial overlap between the emitter and cavity, these techniques paid specific attention to the ability to separate the cavity and emitter material systems in order to allow optimal selection of these independently, and eventually enable monolithic integration with other photonic and electronic circuitry.

We also developed an analytic photonic crystal design process yielding optimized cavity tapers with minimal computational effort, and reported on a general cavity modification which exhibits improved fabrication tolerance by relying exclusively on positional- rather than dimensional tapering. We compared several experimental coupling techniques for device characterization. Significant efforts were devoted to optimizing cavity fabrication, including the use of atomic layer deposition to improve surface quality, exploration into factors affecting the design fracturing, and automated analysis of SEM images. Using optimized fabrication procedures, we experimentally demonstrated 1D photonic crystal nanobeam cavities exhibiting the highest Q/V reported on substrate. Finally, we analyzed the bistable behavior of the devices to quantify the nonlinear optical response of our cavities.

Optical response of high-order band gap photonic crystal applying in-plane in one-dimensional integration

A new broadband filter, based on the high-order band gap in one-dimensional photonic crystal (PCs) of the form Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si, has been designed by the plane wave expansion method (PWEM) and transfer matrix method (TMM) and fabricated by lithography. The optical response of this filter to normal-incident and oblique-incident light proves that utilizing the high-order band gaps of PCs is an efficient method to lower the difficulties of fabricating PCs, increase the etching depth of semiconductor materials, and reduce the coupling loss at the interface between optical fibers and PC device. (c) 2007 Elsevier B.V. All rights reserved.

Monolithic integration of an InGaAsP-InP strained DFB laser and an electroabsorption modulator by ultra-low-pressure selective-area-growth MOCVD

The design and basic characteristics of a strained InGaAsP-InP multiple-quantum-well (MQW) DFB laser monolithically integrated with an electroabsorption modulator (EAM) by ultra-low-pressure (22 mbar) selective-area-growth (SAG) MOCVD are presented. A fundamental study of the controllability and the applicability of band-gap energy by using the SAG, method is performed. A large band-gap photoluminescence wavelength shift of 88 mn. was obtained with a small mask width variation (0-30 mu m). The technique is then applied to fabricate a high performance strained MQW EAM integrated with a DFB laser. The threshold current of 26 mA at CW operation of the device with DFB laser length of 300 mu m and EAM length of 150 mu m has been realized at a modulator bias of 0 V. The devices also exhibit 15 dB on/off ratio at an applied bias voltage of 5 V.

Monolithic integration of electroabsorption modulator and DFB laser for 10-Gb/s transmission

A strained InGaAsP-InP multiple-quantum-well DFB laser monolithically integrated with electroabsorption modulator by ultra-low-pressure (22 mbar) selective-area-growth is presented. The integrated chip exhibits superior characteristics, such as low threshold current of 19 mA, single-mode operation around 1550 nm range with side-mode suppression ratio over 40 dB, and larger than 16 dB extinction ratio when coupled into a single-mode fiber. More than 10 GHz modulation bandwidth is also achieved. After packaged in a compact module, the device successfully performs 10-Gb/s NRZ transmission experiments through 53.3 km of standard fiber with 8.7 dB dynamic extinction ratio. A receiver sensitivity of -18.9 dBm at bit-error-rate of 10(-1)0 is confirmed. (c) 2005 Elsevier B.V. All rights reserved.

High Q microring resonator in silicon-on-insulator rib waveguides - art. no. 68380J

A high quality (Q) factor microring resonator in silicon-on-insulator rib waveguides was fabricated by electron beam lithography, followed by inductively coupled plasma etching. The waveguide dimensions were scaled down to submicron, for a low bending loss and compactness. Experimentally, the resonator has been realized with a quality factor as high as 21,200, as well as a large extinction ratio 12.5dB at telecommunication wavelength near 1550nm. From the measured results, propagation loss in the rib waveguide is determined as low as 6.900/cm. This high Q microring resonator is expected to lead to high speed optical modulators and bio-sensing devices.

Hybrid integration and packaging of grating-coupled silicon photonics

This thesis covers both the packaging of silicon photonic devices with fiber inputs and outputs as well as the integration of laser light sources with these same devices. The principal challenge in both of these pursuits is coupling light into the submicrometer waveguides that are the hallmark of silicon-on-insulator (SOI) systems. Previous work on grating couplers is leveraged to design new approaches to bridge the gap between the highly-integrated domain of silicon, the Interconnected world of fiber and the active region of III-V materials. First, a novel process for the planar packaging of grating couplers with fibers is explored in detail. This technology allows the creation of easy-to-use test platforms for laser integration and also stands on its own merits as an enabling technology for next-generation silicon photonics systems. The alignment tolerances of this process are shown to be well-suited to a passive alignment process and for wafer-scale assembly. Furthermore, this technology has already been used to package demonstrators for research partners and is included in the offerings of the ePIXfab silicon photonics foundry and as a design kit for PhoeniX Software’s MaskEngineer product. After this, a process for hybridly integrating a discrete edge-emitting laser with a silicon photonic circuit using near-vertical coupling is developed and characterized. The details of the various steps of the design process are given, including mechanical, thermal, optical and electrical steps. The interrelation of these design domains is also discussed. The construction process for a demonstrator is outlined, and measurements are presented of a series of single-wavelength Fabry-Pérot lasers along with a two-section laser tunable in the telecommunications C-band. The suitability and potential of this technology for mass manufacture is demonstrated, with further opportunities for improvement detailed and discussed in the conclusion.

Development of germanium/silicon integration for near infrared detection

Silicon (Si) is the base material for electronic technologies and is emerging as a very attractive platform for photonic integrated circuits (PICs). PICs allow optical systems to be made more compact with higher performance than discrete optical components. Applications for PICs are in the area of fibre-optic communication, biomedical devices, photovoltaics and imaging. Germanium (Ge), due to its suitable bandgap for telecommunications and its compatibility with Si technology is preferred over III-V compounds as an integrated on-chip detector at near infrared wavelengths. There are two main approaches for Ge/Si integration: through epitaxial growth and through direct wafer bonding. The lattice mismatch of ~4.2% between Ge and Si is the main problem of the former technique which leads to a high density of dislocations while the bond strength and conductivity of the interface are the main challenges of the latter. Both result in trap states which are expected to play a critical role. Understanding the physics of the interface is a key contribution of this thesis. This thesis investigates Ge/Si diodes using these two methods. The effects of interface traps on the static and dynamic performance of Ge/Si avalanche photodetectors have been modelled for the first time. The thesis outlines the original process development and characterization of mesa diodes which were fabricated by transferring a ~700 nm thick layer of p-type Ge onto n-type Si using direct wafer bonding and layer exfoliation. The effects of low temperature annealing on the device performance and on the conductivity of the interface have been investigated. It is shown that the diode ideality factor and the series resistance of the device are reduced after annealing. The carrier transport mechanism is shown to be dominated by generation–recombination before annealing and by direct tunnelling in forward bias and band-to-band tunnelling in reverse bias after annealing. The thesis presents a novel technique to realise photodetectors where one of the substrates is thinned by chemical mechanical polishing (CMP) after bonding the Si-Ge wafers. Based on this technique, Ge/Si detectors with remarkably high responsivities, in excess of 3.5 A/W at 1.55 μm at −2 V, under surface normal illumination have been measured. By performing electrical and optical measurements at various temperatures, the carrier transport through the hetero-interface is analysed by monitoring the Ge band bending from which a detailed band structure of the Ge/Si interface is proposed for the first time. The above unity responsivity of the detectors was explained by light induced potential barrier lowering at the interface. To our knowledge this is the first report of light-gated responsivity for vertically illuminated Ge/Si photodiodes. The wafer bonding approach followed by layer exfoliation or by CMP is a low temperature wafer scale process. In principle, the technique could be extended to other materials such as Ge on GaAs, or Ge on SOI. The unique results reported here are compatible with surface normal illumination and are capable of being integrated with CMOS electronics and readout units in the form of 2D arrays of detectors. One potential future application is a low-cost Si process-compatible near infrared camera.

Semi-Lagrange time integration for PDE models of asian options

Semi-Lagrange time integration is used with the finite difference method to provide accurate stable prices for Asian options, with or without early exercise. These are combined with coordinate transformations for computational efficiency and compared with published results

Advanced product development integration architecture: an out-of-box solution to support distributed production networks

This paper presents novel collaboration methods implemented using a centralized client/server product development integration architecture, and a decentralized peer-to-peer network for smaller and larger companies using open source solutions. The product development integration architecture has been developed for the integration of disparate technologies and software systems for the benefit of collaborative work teams in design and manufacturing. This will facilitate the communication of early design and product development within a distributed and collaborative environment. The novelty of this work is the introduction of an‘out-of-box’ concept which provides a standard framework and deploys this utilizing a proprietary state-of-the-art product lifecycle management system (PLM). The term ‘out-of-box’ means to modify the product development and business processes to suit the technologies rather than vice versa. The key business benefits of adopting such an approach are a rapidly reconfigurable network and minimal requirements for software customization to avoid systems instability

Dynamic Network Mechanisms of Relational Integration

A prominent hypothesis states that specialized neural modules within the human lateral frontopolar cortices (LFPCs) support “relational integration” (RI), the solving of complex problems using inter-related rules. However, it has been proposed that LFPC activity during RI could reflect the recruitment of additional “domain-general” resources when processing more difficult problems in general as opposed to RI specifi- cally. Moreover, theoretical research with computational models has demonstrated that RI may be supported by dynamic processes that occur throughout distributed networks of brain regions as opposed to within a discrete computational module. Here, we present fMRI findings from a novel deductive reasoning paradigm that controls for general difficulty while manipulating RI demands. In accordance with the domain- general perspective, we observe an increase in frontoparietal activation during challenging problems in general as opposed to RI specifically. Nonetheless, when examining frontoparietal activity using analyses of phase synchrony and psychophysiological interactions, we observe increased network connectivity during RI alone. Moreover, dynamic causal modeling with Bayesian model selection identifies the LFPC as the effective connectivity source. Based on these results, we propose that during RI an increase in network connectivity and a decrease in network metastability allows rules that are coded throughout working memory systems to be dynamically bound. This change in connectivity state is top-down propagated via a hierarchical system of domain-general networks with the LFPC at the apex. In this manner, the functional network perspective reconciles key propositions of the globalist, modular, and computational accounts of RI within a single unified framework.

Special functions of Weyl groups and their continuous and discrete orthogonality

Cette thèse s'intéresse à l'étude des propriétés et applications de quatre familles des fonctions spéciales associées aux groupes de Weyl et dénotées $C$, $S$, $S^s$ et $S^l$. Ces fonctions peuvent être vues comme des généralisations des polynômes de Tchebyshev. Elles sont en lien avec des polynômes orthogonaux à plusieurs variables associés aux algèbres de Lie simples, par exemple les polynômes de Jacobi et de Macdonald. Elles ont plusieurs propriétés remarquables, dont l'orthogonalité continue et discrète. En particulier, il est prouvé dans la présente thèse que les fonctions $S^s$ et $S^l$ caractérisées par certains paramètres sont mutuellement orthogonales par rapport à une mesure discrète. Leur orthogonalité discrète permet de déduire deux types de transformées discrètes analogues aux transformées de Fourier pour chaque algèbre de Lie simple avec racines des longueurs différentes. Comme les polynômes de Tchebyshev, ces quatre familles des fonctions ont des applications en analyse numérique. On obtient dans cette thèse quelques formules de <>, pour des fonctions de plusieurs variables, en liaison avec les fonctions $C$, $S^s$ et $S^l$. On fournit également une description complète des transformées en cosinus discrètes de types V--VIII à $n$ dimensions en employant les fonctions spéciales associées aux algèbres de Lie simples $B_n$ et $C_n$, appelées cosinus antisymétriques et symétriques. Enfin, on étudie quatre familles de polynômes orthogonaux à plusieurs variables, analogues aux polynômes de Tchebyshev, introduits en utilisant les cosinus (anti)symétriques.