Spatial mode dynamics in wide-aperture quantum-dot lasers

We present a systematic theoretical study of spatial mode dynamics in wide-aperture semiconductor quantum-dot lasers within the Maxwell-Bloch formalism. Our opto-electro-thermal model self-consistently captures the essential dynamical coupling between field, polarization, and carrier density in both thermal and nonthermal regimes, providing detailed description of the complex spatiotemporal modal intensity structure and spectra in these novel devices and broad area edge-emitting lasers in general. Using linear stability analysis and high resolution adaptive-grid finite element numerical simulation, we show that in the nonthermal regime, the presence of inhomogeneous broadening in quantum-dot active media leads to suppressed filamentation and enhanced spatial coherence compared to conventional quantum well devices with comparable phase-amplitude coupling (alpha parameter). Increasing the degree of inhomogeneous broadening in the active medium leads to further improvement in spatial coherence. In the thermal regime, there is further suppression of filamentation in the inhomogeneously broadened quantum-dot active medium; however, the spatial coherence aided by inhomogeneous broadening is partly lost due to the effect of temperature on cavity detuning. We propose that device designs based on optimized inhomogeneous broadening of quantum-dot gain medium could ultimately lead to diffraction-limited outputs in the quasi-cw regime which are still very difficult to achieve in conventional wide-aperture designs

Modeling round-off error in the fast gradient method for predictive control

We present a method for determining the smallest precision required to have algorithmic stability of an implementation of the Fast Gradient Method (FGM) when solving a linear Model Predictive Control (MPC) problem in fixed-point arithmetic. We derive two models for the round-off error present in fixed-point arithmetic. The first is a generic model with no assumptions on the predicted system or weight matrices. The second is a parametric model that exploits the Toeplitz structure of the MPC problem for a Schur-stable system. We also propose a metric for measuring the amount of round-off error the FGM iteration can tolerate before becoming unstable. This metric is combined with the round-off error models to compute the minimum number of fractional bits needed for the fixed-point data type. Using these models, we show that exploiting the MPC problem structure nearly halves the number of fractional bits needed to implement an example problem. We show that this results in significant decreases in resource usage, computational energy and execution time for an implementation on a Field Programmable Gate Array

Horizon-independent preconditioner design for linear predictive control

First-order optimization solvers, such as the Fast Gradient Method, are increasingly being used to solve Model Predictive Control problems in resource-constrained environments. Unfortunately, the convergence rate of these solvers is significantly affected by the conditioning of the problem data, with ill-conditioned problems requiring a large number of iterations. To reduce the number of iterations required, we present a simple method for computing a horizon-independent preconditioning matrix for the Hessian of the condensed problem. The preconditioner is based on the block Toeplitz structure of the Hessian. Horizon-independence allows one to use only the predicted system and cost matrices to compute the preconditioner, instead of the full Hessian. The proposed preconditioner has equivalent performance to an optimal preconditioner in numerical examples, producing speedups between 2x and 9x for the Fast Gradient Method. Additionally, we derive horizon-independent spectral bounds for the Hessian in terms of the transfer function of the predicted system, and show how these can be used to compute a novel horizon-independent bound on the condition number for the preconditioned Hessian

Optical Bistability in Semiconductor Injection Lasers

This paper reviews optical bistability in semiconductor lasers, with particular reference to the potential switching speeds of the systems demonstrated to date. Devices which switch by redistributing a nearly constant number of carriers within the active region should be faster, though less stable, than systems whose transitions are attended by changes in carrier numbers. One system of the former type, the self-focused coupled cavity laser, is analysed in some detail and is compared with the twin stripe laser and the Fabry-Perot laser amplifier

Low-frequency fluctuations in a semiconductor laser with phase conjugate feedback

We analyze the dynamics of a semiconductor laser with phase conjugate optical feedback, using numerical simulations based on rate equations for the complex amplitude of the electric field and the carrier density. From this analysis we observe the presence of low-frequency fluctuations which are similar to those observed in a semiconductor laser with conventional optical feedback. The similarities and differences between phase conjugate and conventional optical feedback are discussed, and a mechanism for the appearance of low-frequency fluctuations in a semiconductor laser with phase conjugate feedback is suggested

Rocket observations of the ionosphere during the eclipse of 26 February 1979

Electron density profiles and energetic particle fluxes were determined from two rockets launched, respectively, at the beginning and end of totality during the solar eclipse of 26 February 1979. These, and one other rocket at the same time of day on 24 February 1979, were launched from near Red Lake, Ontario. The electron density profile from 24 February shows the electron density to be normal above 110 km, to rocket apogee. Below 110 km, the electron density is enhanced, by an order of magnitude in the D region, compared with data from Wallops Island at the same solar zenith angle (63 deg). The enhancement is qualitatively explained by the large flux of field aligned energetic particles observed on the same rocket. During totality (on 26 February) the electron density above 110 km to rocket apogee is reduced by a factor of about three. Below 110 km, the electron density is much greater than observed during previous eclipses. The particle flux measured on the 26 February was an order of magnitude less than that on the 24 February but showed greater variability, particularly at the higher energies (100 keV). A feature of the particle flux is that, for the two rockets that were separated horizontally by 38 km while above the absorbing region, the variations are uncorrelated

Process Mining of Disease Trajectories: A Feasibility Study

Modelling patient disease trajectories from evidence in electronic health records could help clinicians and medical researchers develop a better understanding of the progression of diseases within target populations. Process mining provides a set of well-established tools and techniques that have been used to mine electronic health record data to understand healthcare care pathways. In this paper we explore the feasibility for using a process mining methodology and toolset to automate the identification of disease trajectory models. We created synthetic electronic health record data based on a published disease trajectory model and developed a series of event log transformations to reproduce the disease trajectory model using standard process mining tools. Our approach will make it easier to produce disease trajectory models from routine health data

Two-photon absorption properties of commercial fused silica and germanosilicate glass at 264 nm

Using high-intensity femtosecond pulses at lambda=264 nm, we have measured the two-photon absorption (TPA) coefficient in three fused silica samples Suprasil, Herasil, Infrasil (Heraeus) and in 3.5 mol % Ge-doped fused silica. While in fused silica samples the TPA coefficient value is about 2x10(-11) cm/W, in germanosilicate glass it equals (42+/-3)x10(-11) cm/W. (C) 2002 American Institute of Physics. (DOI: 10.1063/1.1448387

Dynamics of traveling waves in the transverse section of a laser

We analyze the general features of the formation and interaction of transverse traveling waves and the appearance of filamentation in broad area semiconductor lasers with current profiling. For small apertures, the emitted profile is symmetric consisting of two counterpropagating transverse traveling waves, both emanating from the center of the device. For larger apertures, the emission becomes asymmetric as one of the traveling waves expands to occupy an increased area while the other occupies the remaining, smaller spatial region. In both devices, the pattern becomes unstable at higher injection currents due to optical filamentation, although an intermediate state is present in the wider device whereby the dominant wave undergoes a Hopf bifurcation before filamentation occurs