There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Artificial Neural Networks have dramatically improved performance for many machine learning tasks. We demonstrate a new architecture for a fully optical neural network that enables a computational speed enhancement of at least two orders of magnitude and three orders of magnitude in power efficiency over state-of-the-art electronics.

Deep learning with coherent nanophotonic circuits

: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

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Nonlinear Time Series Analysis.

Recent advances in physical reservoir computing: A review

Neurons in the brain behave as nonlinear oscillators, which develop rhythmic activity and interact to process information. Taking inspiration from this behaviour to realize high-density, low-power neuromorphic computing will require very large numbers of nanoscale nonlinear oscillators. A simple estimation indicates that to fit 108 oscillators organized in a two-dimensional array inside a chip the size of a thumb, the lateral dimension of each oscillator must be smaller than one micrometre. However, nanoscale devices tend to be noisy and to lack the stability that is required to process data in a reliable way. For this reason, despite multiple theoretical proposals and several candidates, including memristive and superconducting oscillators, a proof of concept of neuromorphic computing using nanoscale oscillators has yet to be demonstrated. Here we show experimentally that a nanoscale spintronic oscillator (a magnetic tunnel junction) can be used to achieve spoken-digit recognition with an accuracy similar to that of state-of-the-art neural networks. We also determine the regime of magnetization dynamics that leads to the greatest performance. These results, combined with the ability of the spintronic oscillators to interact with each other, and their long lifetime and low energy consumption, open up a path to fast, parallel, on-chip computation based on networks of oscillators.

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Neuromorphic computing with nanoscale spintronic oscillators

Static and dynamic characteristics of weakly index guided VCSELs in a multi-transverse mode regime are analyzed by using a model that takes into account all the transverse modes supported by the waveguide and a consistent spectral gain including many-body effects. Selection of a particular high order transverse mode by using azimuthal dependent current profiling can be obtained over a wide current range. The alternate current modulation of two orthogonal high order transverse modes is studied taking into account thermal effects. This current induced spatial switching leads to high frequency beam steering in the laser azimuthal direction.

High-frequency beam steering induced by transverse mode switching in VCSELs: optical gain effects

We report a first experimental study of the nonlinear dynamics of a 1550nm single-mode VCSEL when subject to orthogonal optical injection. The polarization resolved dynamics is mapped in the plane of frequency detuning versus injected power.

Nonlinear polarization dynamics induced by orthogonal optical injection in 1550 nm-Vertical-Cavity Surface-Emitting Lasers

The recent rapid advances in the performance of vertical cavity surface emitting lasers (VCSELs) give significant impetus to identifying practical applications of these devices in, for example, optical data links and two-dimensional optical switching. In looking towards such applications serious consideration must be given to basic device performance characteristics and specifically to their operating efficiencies, threshold currents and transverse mode structures. Recent work has indicated the role of spatial hole-burning effects in determining both the transverse mode structure and the wall-plug efficiencies of gain-guided VCSELs. We show that the strength of the in-built transverse mode waveguide in index-guided VCSELs exerts a dramatic influence on the excitation of transverse modes. The influence is, in particular, revealed by calculated light-current characteristics of index guided VCSELs.

Transverse mode selection and light-current characteristics in index-guided VCSELs

We investigate self-averaging properties in the transport of particles through random media. We show rigorously that in the subdiffusive anomalous regime transport coefficients are not self--averaging quantities. These quantities are exactly calculated in the case of directed random walks. In the case of general symmetric random walks a perturbative analysis around the Effective Medium Approximation (EMA) is performed.

Analysis of self-averaging properties in the transport of particles through random media.

Chaotic Lidar systems (CLIDAR) are used for high-resolution ranging. They are based on the correlation of a chaotic signal waveform with the signal that is reflected back from the target. We report a novel CLIDAR system based on the autocorrelation of the signal obtained by the superposition of the chaotic signal waveform and the signal that is reflected from the target. A simplified set-up with just one detector is required in contrast to the two detectors used in standard CLIDAR systems. Our experimental results are obtained with a 1550-nm vertical-cavity surface-emitting laser (VCSEL) with chaotic dynamics due to optical feedback. Our CLIDAR system provides an autocorrelation function with several sharp minima. The position of the target is obtained from the location of those minima. A theoretical analysis of the CLIDAR system is also presented. A rate equation model for the polarization of a VCSEL subject to optical feedback is the basis for the simulation of the CLIDAR system. A comparison between our theoretical and experimental results is performed, resulting in a good agreement in the chaotic signal but in a different sign of the CLIDAR signal.

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Luis Pesquera

Papers

High-frequency beam steering induced by transverse mode switching in VCSELs: optical gain effects

Nonlinear polarization dynamics induced by orthogonal optical injection in 1550 nm-Vertical-Cavity Surface-Emitting Lasers

Transverse mode selection and light-current characteristics in index-guided VCSELs

Analysis of self-averaging properties in the transport of particles through random media.

Free space ranging based on a chaotic long-wavelength VCSEL with optical feedback