High-Speed Semiconductor Lasers based on Low-Dimensional Active Materials for Optical Telecommunication

The scope of this work is the fundamental growth, tailoring and characterization of self-organized indium arsenide quantum dots (QDs) and their exploitation as active region for diode lasers emitting in the 1.55 µm range. This wavelength regime is especially interesting for long-haul telecommunications as optical fibers made from silica glass have the lowest optical absorption. Molecular Beam Epitaxy is utilized as fabrication technique for the quantum dots and laser structures. The results presented in this thesis depict the first experimental work for which this reactor was used at the University of Kassel. Most research in the field of self-organized quantum dots has been conducted in the InAs/GaAs material system. It can be seen as the model system of self-organized quantum dots, but is not suitable for the targeted emission wavelength. Light emission from this system at 1.55 µm is hard to accomplish. To stay as close as possible to existing processing technology, the In(AlGa)As/InP (100) material system is deployed. Depending on the epitaxial growth technique and growth parameters this system has the drawback of producing a wide range of nano species besides quantum dots. Best known are the elongated quantum dashes (QDash). Such structures are preferentially formed, if InAs is deposited on InP. This is related to the low lattice-mismatch of 3.2 %, which is less than half of the value in the InAs/GaAs system. The task of creating round-shaped and uniform QDs is rendered more complex considering exchange effects of arsenic and phosphorus as well as anisotropic effects on the surface that do not need to be dealt with in the InAs/GaAs case. While QDash structures haven been studied fundamentally as well as in laser structures, they do not represent the theoretical ideal case of a zero-dimensional material. Creating round-shaped quantum dots on the InP(100) substrate remains a challenging task. Details of the self-organization process are still unknown and the formation of the QDs is not fully understood yet. In the course of the experimental work a novel growth concept was discovered and analyzed that eases the fabrication of QDs. It is based on different crystal growth and ad-atom diffusion processes under supply of different modifications of the arsenic atmosphere in the MBE reactor. The reactor is equipped with special valved cracking effusion cells for arsenic and phosphorus. It represents an all-solid source configuration that does not rely on toxic gas supply. The cracking effusion cell are able to create different species of arsenic and phosphorus. This constitutes the basis of the growth concept. With this method round-shaped QD ensembles with superior optical properties and record-low photoluminescence linewidth were achieved. By systematically varying the growth parameters and working out a detailed analysis of the experimental data a range of parameter values, for which the formation of QDs is favored, was found. A qualitative explanation of the formation characteristics based on the surface migration of In ad-atoms is developed. Such tailored QDs are finally implemented as active region in a self-designed diode laser structure. A basic characterization of the static and temperature-dependent properties was carried out. The QD lasers exceed a reference quantum well laser in terms of inversion conditions and temperature-dependent characteristics. Pulsed output powers of several hundred milli watt were measured at room temperature. In particular, the lasers feature a high modal gain that even allowed cw-emission at room temperature of a processed ridge wave guide device as short as 340 µm with output powers of 17 mW. Modulation experiments performed at the Israel Institute of Technology (Technion) showed a complex behavior of the QDs in the laser cavity. Despite the fact that the laser structure is not fully optimized for a high-speed device, data transmission capabilities of 15 Gb/s combined with low noise were achieved. To the best of the author`s knowledge, this renders the lasers the fastest QD devices operating at 1.55 µm. The thesis starts with an introductory chapter that pronounces the advantages of optical fiber communication in general. Chapter 2 will introduce the fundamental knowledge that is necessary to understand the importance of the active region`s dimensions for the performance of a diode laser. The novel growth concept and its experimental analysis are presented in chapter 3. Chapter 4 finally contains the work on diode lasers.

Magnetic interactions between transition metal impurities and clusters mediated by low-dimensional metallic hosts: A first principles theoretical investigation

The magnetic properties and interactions between transition metal (TM) impurities and clusters in low-dimensional metallic hosts are studied using a first principles theoretical method. In the first part of this work, the effect of magnetic order in 3d-5d systems is addressed from the perspective of its influence on the enhancement of the magnetic anisotropy energy (MAE). In the second part, the possibility of using external electric fields (EFs) to control the magnetic properties and interactions between nanoparticles deposited at noble metal surfaces is investigated. The influence of 3d composition and magnetic order on the spin polarization of the substrate and its consequences on the MAE are analyzed for the case of 3d impurities in one- and two-dimensional polarizable hosts. It is shown that the MAE and easy- axis of monoatomic free standing 3d-Pt wires is mainly determined by the atomic spin-orbit (SO) coupling contributions. The competition between ferromagnetic (FM) and antiferromagnetic (AF) order in FePtn wires is studied in detail for n=1-4 as a function of the relative position between Fe atoms. Our results show an oscillatory behavior of the magnetic polarization of Pt atoms as a function of their distance from the magnetic impurities, which can be correlated to a long-ranged magnetic coupling of the Fe atoms. Exceptionally large variations of the induced spin and orbital moments at the Pt atoms are found as a function of concentration and magnetic order. Along with a violation of the third Hund’s rule at the Fe sites, these variations result in a non trivial behavior of the MAE. In the case of TM impurities and dimers at the Cu(111), the effects of surface charging and applied EFs on the magnetic properties and substrate-mediated magnetic interactions have been investigated. The modifications of the surface electronic structure, impurity local moments and magnetic exchange coupling as a result of the EF-induced metallic screening and charge rearrangements are analysed. In a first study, the properties of surface substitutional Co and Fe impurities are investigated as a function of the external charge per surface atom q. At large inter-impurity distances the effective magnetic exchange coupling ∆E between impurities shows RKKY-like oscillations as a function of the distance which are not significantly affected by the considered values of q. For distances r < 10 Å, important modifications in the magnitude of ∆E, involving changes from FM to AF coupling, are found depending non-monotonously on the value and polarity of q. The interaction energies are analysed from a local perspective. In a second study, the interplay between external EF effects, internal magnetic order and substrate-mediated magnetic coupling has been investigated for Mn dimers on Cu(111). Our calculations show that EF (∼ 1eV/Å) can induce a switching from AF to FM ground-state magnetic order within single Mn dimers. The relative coupling between a pair of dimers also shows RKKY-like oscillations as a function of the inter-dimer distance. Their effective magnetic exchange interaction is found to depend significantly on the magnetic order within the Mn dimers and on their relative orientation on the surface. The dependence of the substrate-mediated interaction on the magnetic state of the dimers is qualitatively explained in terms of the differences in the scattering of surface electrons. At short inter-dimer distances, the ground-state configuration is determined by an interplay between exchange interactions and EF effects. These results demonstrate that external surface charging and applied EFs offer remarkable possibilities of manipulating the sign and strength of the magnetic coupling of surface supported nanoparticles.

Three-Dimensional Motion Estimation Using Shading Information in Multiple Frames

A new formulation for recovering the structure and motion parameters of a moving patch using both motion and shading information is presented. It is based on a new differential constraint equation (FICE) that links the spatiotemporal gradients of irradiance to the motion and structure parameters and the temporal variations of the surface shading. The FICE separates the contribution to the irradiance spatiotemporal gradients of the gradients due to texture from those due to shading and allows the FICE to be used for textured and textureless surface. The new approach, combining motion and shading information, leads directly to two different contributions: it can compensate for the effects of shading variations in recovering the shape and motion; and it can exploit the shading/illumination effects to recover motion and shape when they cannot be recovered without it. The FICE formulation is also extended to multiple frames.

Exploring Object Perception with Random Image Structure Evolution

We have developed a technique called RISE (Random Image Structure Evolution), by which one may systematically sample continuous paths in a high-dimensional image space. A basic RISE sequence depicts the evolution of an object's image from a random field, along with the reverse sequence which depicts the transformation of this image back into randomness. The processing steps are designed to ensure that important low-level image attributes such as the frequency spectrum and luminance are held constant throughout a RISE sequence. Experiments based on the RISE paradigm can be used to address some key open issues in object perception. These include determining the neural substrates underlying object perception, the role of prior knowledge and expectation in object perception, and the developmental changes in object perception skills from infancy to adulthood.

Two-dimensional Photonic Crystals Fabricated by Nanoimprint Lithography

We report on the process parameters of nanoimprint lithography (NIL) for the fabrication of two-dimensional (2-D) photonic crystals. The nickel mould with 2-D photonic crystal patterns covering the area up to 20mm² is produced by electron-beam lithography (EBL) and electroplating. Periodic pillars as high as 200nm to 250nm are produced on the mould with the diameters ranging from 180nm to 400nm. The mould is employed for nanoimprinting on the poly-methyl-methacrylate (PMMA) layer spin-coated on the silicon substrate. Periodic air holes are formed in PMMA above its glass-transition temperature and the patterns on the mould are well transferred. This nanometer-size structure provided by NIL is subjective to further pattern transfer.

Exploring Bit-Difference for Approximate KNN Search in High-dimensional Databases

In this paper, we develop a novel index structure to support efficient approximate k-nearest neighbor (KNN) query in high-dimensional databases. In high-dimensional spaces, the computational cost of the distance (e.g., Euclidean distance) between two points contributes a dominant portion of the overall query response time for memory processing. To reduce the distance computation, we first propose a structure (BID) using BIt-Difference to answer approximate KNN query. The BID employs one bit to represent each feature vector of point and the number of bit-difference is used to prune the further points. To facilitate real dataset which is typically skewed, we enhance the BID mechanism with clustering, cluster adapted bitcoder and dimensional weight, named the BID⁺. Extensive experiments are conducted to show that our proposed method yields significant performance advantages over the existing index structures on both real life and synthetic high-dimensional datasets.

Online Robust 3D Mapping Using Structure from Motion Cues

This paper presents a complete solution for creating accurate 3D textured models from monocular video sequences. The methods are developed within the framework of sequential structure from motion, where a 3D model of the environment is maintained and updated as new visual information becomes available. The camera position is recovered by directly associating the 3D scene model with local image observations. Compared to standard structure from motion techniques, this approach decreases the error accumulation while increasing the robustness to scene occlusions and feature association failures. The obtained 3D information is used to generate high quality, composite visual maps of the scene (mosaics). The visual maps are used to create texture-mapped, realistic views of the scene

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Precipitating convection in cold air: virtual potential temperature structure

Simulations of precipitating convection are used to illustrate the importance of the turbulent kinetic energy (TKE) budget in determining the virtual potential-temperature structure of the convecting atmosphere. Two sets of simulations are presented: in one the surface temperature was increased to simulate cold air flowing over a warmer surface and in the second a cooling profile, representing cold-air advection, was imposed. It is shown that the terms in the TKE budgets for both sets of simulations scale in the same way, but that the non-dimensional profiles are different. It is suggested that this is associated with the effects of sublimation of ice. It is shown that the magnitudes of the transport and precipitation terms in the virtual potential temperature budget are determined by the scaling of the TKE budget. Some implications of these results for parametrizations of moist convection are discussed. Copyright © 2007 Royal Meteorological Society

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

A singular vector perspective of 4DVAR: The spatial structure and evolution of baroclinic weather systems

The extent to which the four-dimensional variational data assimilation (4DVAR) is able to use information about the time evolution of the atmosphere to infer the vertical spatial structure of baroclinic weather systems is investigated. The singular value decomposition (SVD) of the 4DVAR observability matrix is introduced as a novel technique to examine the spatial structure of analysis increments. Specific results are illustrated using 4DVAR analyses and SVD within an idealized 2D Eady model setting. Three different aspects are investigated. The first aspect considers correcting errors that result in normal-mode growth or decay. The results show that 4DVAR performs well at correcting growing errors but not decaying errors. Although it is possible for 4DVAR to correct decaying errors, the assimilation of observations can be detrimental to a forecast because 4DVAR is likely to add growing errors instead of correcting decaying errors. The second aspect shows that the singular values of the observability matrix are a useful tool to identify the optimal spatial and temporal locations for the observations. The results show that the ability to extract the time-evolution information can be maximized by placing the observations far apart in time. The third aspect considers correcting errors that result in nonmodal rapid growth. 4DVAR is able to use the model dynamics to infer some of the vertical structure. However, the specification of the case-dependent background error variances plays a crucial role.

The structure of crystallisable copolymers of L-lactide, epsilon-caprolactone and glycolide

We apply a new X-ray scattering approach to the study of melt-spun filaments of tri-block and random terpolymers prepared from lactide, caprolactone and glycolide. Both terpolymers contain random sequences, in both cases the overall fraction of lactide units is similar to 0.7 and C-13 and H-1 NMR shows the lactide sequence length to be similar to 9-10. A novel representation of the X-ray fibre pattern as series of spherical harmonic functions considerably facilitates the comparison of the scattering from the minority crystalline phase with hot drawn fibres prepared from the poly(L-lactide) homopolymer. Although the fibres exhibit rather disordered structures we show that the crystal structure is equivalent to that displayed by poly(L-lactide) for both the block and random terpolymers. There are variations in the development of a two-phase structure which reflect the differences in the chain architectures. There is evidence that the random terpolymer includes non-lactide units in to the crystal interfaces to achieve a well defined two-phase structure. (c) 2005 Published by Elsevier Ltd.

Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

The two-dimensional anharmonic oscillator I: vibration-rotation constants of fulminic acid, HCNO

The lowest-wavenumber vibration of HCNO and DCNO, ν5, is known to involve a largeamplitude low-frequency anharmonic bending of the CH bond against the CNO frame. In this paper the anomalous vibrational dependence of the observed rotational constants B(v5, l5), and of the observed l-doubling interactions, is interpreted according to a simple effective vibration-rotation Hamiltonian in which the appropriate vibrational operators are averaged in an anharmonic potential surface over the normal coordinates (Q5x, Q5y). All of the data on both isotopes are interpreted according to a single potential surface having a minimum energy at a slightly bent configuration of the HCN angle ( 170°) with a maximum at the linear configuration about 2 cm−1 higher. The other coefficients in the Hamiltonian are also interpreted in terms of the structure and the harmonic and anharmonic force fields; the substitution structure at the “hypothetical linear configuration” determined in this way gives a CH bond length of 1.060 Å, in contrast to the value 1.027 Å determined from the ground-state rotational constants. We also discuss the difficulties in rationalizing our effective Hamiltonian in terms of more fundamental theory, as well as the success and limitations of its use in practice.

Can 4D-Var use dynamical information from targeted observations of a baroclinic structure?

Targeted observations are generally taken in regions of high baroclinicity, but often show little impact. One plausible explanation is that important dynamical information, such as upshear tilt, is not extracted from the targeted observations by the data assimilation scheme and used to correct initial condition error. This is investigated by generating pseudo targeted observations which contain a singular vector (SV) structure that is not present in the background field or routine observations, i.e. assuming that the background has an initial condition error with tilted growing structure. Experiments were performed for a single case-study with varying numbers of pseudo targeted observations. These were assimilated by the Met Office four-dimensional variational (4D-Var) data assimilation scheme, which uses a 6 h window for observations and background-error covariances calculated using the National Meteorological Centre (NMC) method. The forecasts were run using the operational Met Office Unified Model on a 24 km grid. The results presented clearly demonstrate that a 6 h window 4D-Var system is capable of extracting baroclinic information from a limited set of observations and using it to correct initial condition error. To capture the SV structure well (projection of 0.72 in total energy), 50 sondes over an area of 1×106 km2 were required. When the SV was represented by only eight sondes along an example targeting flight track covering a smaller area, the projection onto the SV structure was lower; the resulting forecast perturbations showed an SV structure with increased tilt and reduced initial energy. The total energy contained in the perturbations decreased as the SV structure was less well described by the set of observations (i.e. as fewer pseudo observations were assimilated). The assimilated perturbation had lower energy than the SV unless the pseudo observations were assimilated with the dropsonde observation errors halved from operational values. Copyright © 2010 Royal Meteorological Society