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Ising machines are a promising non-von-Neumann computational concept for neural network training and combinatorial optimization. However, while various neural networks can be implemented with Ising machines, their inability to perform fast statistical sampling makes them inefficient for training neural networks compared to digital computers. Here, we introduce a universal concept to achieve ultrafast statistical sampling with analog Ising machines by injecting noise. With an opto-electronic Ising machine, we experimentally demonstrate that this can be used for accurate sampling of Boltzmann distributions and for unsupervised training of neural networks, with equal accuracy as software-based training. Through simulations, we find that Ising machines can perform statistical sampling orders-of-magnitudes faster than software-based methods. This enables the use of Ising machines beyond combinatorial optimization and makes them into efficient tools for machine learning and other applications.

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In photonic reservoir computing, semiconductor lasers with delayed feedback have shown to be suited to efficiently solve difficult and time-consuming problems. The input data in this system is often optically injected into the reservoir. Based on numerical simulations, we show that the performance depends heavily on the way that information is encoded in this optical injection signal. In our simulations we compare different input configurations consisting of Mach-Zehnder modulators and phase modulators for injecting the signal. We observe far better performance on a one-step ahead time-series prediction task when modulating the phase of the injected signal rather than only modulating its amplitude.

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We present a method to improve the performance of a reservoir computer by keeping the reservoir fixed and increasing the number of output neurons. The additional neurons are nonlinear functions, typically chosen randomly, of the reservoir neurons. We demonstrate the interest of this expanded output layer on an experimental opto-electronic system subject to slow parameter drift which results in loss of performance. We can partially recover the lost performance by using the output layer expansion. The proposed scheme allows for a trade-off between performance gains and system complexity.

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Photonic delay-based reservoir computing (RC) has gained considerable attention lately, as it allows for simple technological implementations of the RC concept that can operate at high speed. In this paper, we discuss a practical, compact and robust implementation of photonic delay-based RC, by integrating a laser and a 5.4 cm delay line on an InP photonic integrated circuit. We demonstrate the operation of this chip with 23 nodes at a speed of 0.87 GSa/s, showing performances that is similar to previous non-integrated delay-based setups. We also investigate two other post-processing methods to obtain more nodes in the output layer. We show that these methods improve the performance drastically, without compromising the computation speed.

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In optical communications the transmission bandwidth of single mode optical fibers is almost fully exploited. To further increase the capacity of a telecommunication link, multiplexing techniques can be applied across 5 physical dimensions: amplitude, quadrature, polarization, frequency and space, with all but the latter being nearly exhausted. We experimentally demonstrate the feasibility of an original space division multiplexing technique based on the classification of speckle patterns measured at the fiber's output. By coupling multiple optical signals into a standard multimode optical fiber, speckle patterns arise at the fiber's end facet. This is due to quasi-random interference between the excited modes of propagation. We show how these patterns depend on the parameters of the optical signal beams and the fiber length. Classification of the speckle patterns allows the detection of the independent signals: we can detect the state (i.e. on or off ) of different beams that are multiplexed in the fiber. Our results show that the proposed space division multiplexing on standard multimode fibers is robust to mode-mixing and polarization scrambling effects.

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Coherent Ising machines (CIMs) constitute a promising approach to solve computationally hard optimization problems by mapping them to ground state searches of the Ising model and implementing them with optical artificial spin-networks. However, while CIMs promise speed-ups over conventional digital computers, they are still challenging to build and operate. Here, we propose and test a concept for a fully programmable CIM, which is based on opto-electronic oscillators subjected to self-feedback. Contrary to current CIM designs, the artificial spins are generated in a feedback induced bifurcation and encoded in the intensity of coherent states. This removes the necessity for nonlinear optical processes or large external cavities and offers significant advantages regarding stability, size and cost. We demonstrate a compact setup for solving MAXCUT optimization problems on regular and frustrated graphs with 100 spins and can report similar or better performance compared to CIMs based on degenerate optical parametric oscillators.

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We discuss the design and characterization of a micro ring laser with on-chip filtered optical feedback. The laser and feedback section have been fabricated on a generic photonic integration platform using only standard building blocks. The filtering process in the feedback scheme is based on the reflection from a distributed Bragg reflector. We include several control pads in the feedback section which allows us to control separately the wavelength, the strength and the phase of the filtered feedback. By controlling the phase of the feedback, we can fine-tune the longitudinal mode selection and wavelength of the laser output, while changing the strength of the feedback allows us to control the power distribution between the two directions of the micro ring laser. Numerical simulations reproduce our experimental observations.

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We discuss the design and testing of a laser integrated with a long on-chip optical feedback section. The device and feedback section have been fabricated on a generic photonic integration platform using only standard building blocks. We have been able to integrate a 10 cm feedback length on a footprint of 5.5 mm2. By controlling the amount of feedback, we achieve chaotic dynamics in the long-cavity regime and show that the resulting dynamics is sufficiently complex in order to generate random bits based on the chaotic intensity fluctuation at a rate of 500 Mbits/s.

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We report on a novel speckle reduction scheme using microlens arrays as screen material for application in laser-based projection systems. The scheme is based on properly adjusting the coherence properties on the screen: when the coherence area on the microlens-array screen is smaller than the microlens footprint, there is no interference between the fields emitted by the different microlenses and as a result no speckle is formed. We measured and modelled the speckle properties of microlens arrays with regular and irregular structure and lens sizes, and also a paper screen for comparison. In the experiments, we tune the laser beam's spatial coherence by sending it through a rotating diffuser. We show the amount of speckle reduction that can be achieved, which mechanisms influence the observed speckle contrast and we discuss the limitations due to increased non-uniformity in the projected image.

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With the development of new applications using semiconductor ring lasers (SRLs) subject to optical feedback, the stability properties of their outputs becomes a crucial issue. We propose a systematic bifurcation analysis in order to properly identify the best parameter ranges for either steady or self-pulsating periodic regimes. Unlike conventional semiconductor lasers, we show that SRLs exhibit both types of outputs for large and well defined ranges of the feedback strength. We determine the stability domains in terms of the pump parameter and the feedback phase. We find that the feedback phase is a key parameter to achieve a stable steady output. We demonstrate that the self-pulsating regime results from a particular Hopf bifurcation mechanism referred to as bifurcation bridges. These bridges connect two distinct external cavity modes and are fully stable, a scenario that was not possible for diode lasers under the same conditions.

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We consider nonlinear rate equations appropriate for a quantum cascade laser subject to optical feedback. We analyze the conditions for a Hopf bifurcation in the limit of large values of the delay. We obtain a simple expression for the critical feedback rate that highlights the effects of key parameters such as the linewidth enhancement factor and the pump. All our asymptotic approximations are validated numerically by using a path continuation technique that allows us to follow Hopf bifurcation points in parameter space.

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Optical implementations of reservoir computing systems are very promising because of their high processing speeds and the possibility to process several tasks in parallel. These systems can be implemented using semiconductor lasers subject to optical delayed feedback and optical injection. While the amount of the feedback/injection can be easily controlled, it is much more difficult to control the optical feedback/injection phase. We present extensive numerical investigations of the influence of the feedback/injection phases on laser-based reservoir computing systems with feedback. We show that a change in the phase can lead to a strong reduction in the reservoir computing system performance. We introduce a new readout layer design that -at least for some tasks- reduces this sensitivity to changes in the phase. It consists in optimizing the readout weights from a coherent combination of the reservoir's readout signal and its delayed version rather than only from the reservoir's readout signal as is usually done.

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In a multi-disciplinary effort, we investigate the level of speckle that can be tolerated in a laser cinema projector based on a quality of experience experiment with movie clips shown to a test audience in a real-life movie theatre setting. We identify a speckle disturbance threshold by statistically analyzing the observers' responses for different values of the amount of speckle, which was monitored using a well-defined speckle measurement method. The analysis shows that the speckle perception of a human observer is not only dependent on the objectively measured amount of speckle, but it is also strongly influenced by the image content. The speckle disturbance limit for movies turns out to be substantially larger than that for still images, and hence is easier to attain.

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In this brief, we numerically demonstrate a photonic delay-based reservoir computing system, which processes, in parallel, two independent computational tasks even when the two tasks have unrelated input streams. Our approach is based on a single-longitudinal mode semiconductor ring laser (SRL) with optical feedback. The SRL emits in two directional optical modes. Each directional mode processes one individual task to mitigate possible crosstalk. We illustrate the feasibility of our scheme by analyzing the performance on two benchmark tasks: 1) chaotic time series prediction and 2) nonlinear channel equalization. We identify some feedback configurations for which the results for simultaneous prediction/classification indicate a good performance, but with slight degradation (as compared with the performance obtained for single task processing) due to nonlinear and linear interactions between the two directional modes of the laser. In these configurations, the system performs well on both tasks for a broad range of the parameters.

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We numerically show the quantitative relation between the chaos bandwidth enhancement and fast phase dynamics in semiconductor lasers with optical feedback and optical injection. The injection increases the coupling between the intensity and the phase leading to a competition between the relaxation oscillation (RO) frequency and the intrinsic response frequency of the phase. For large feedback strengths, it is found that the chaos bandwidth is determined by the intrinsic phase response frequency. For smaller feedback strengths, the system is not chaotic and its bandwidth is determined by the RO frequency.

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We investigate the square-wave (SW) self-modulation output of an edge-emitting diode laser subject to polarization rotated optical feedback in detail, both experimentally and theoretically. Our experimental results show that the 2τ-periodic SW, where τ is the delay of the feedback, coexists with other SW oscillations of shorter periods. We have found that these new SWs are specific harmonics of the fundamental one and their periods are P(n)≃2τ/(1+2n), where n is an integer. Numerical simulations and analytical studies of laser rate equations confirm the multistability of SW solutions. By adding a weak conventional optical feedback, we show that the switching between the different periodic SWs can be easily controlled. The delay of this feedback control is the key parameter determining the harmonic that is stabilized. Numerical simulations corroborate the effectiveness of our experimental control scheme.

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We study the perception of speckle by human observers in a laser projector based on a 40 persons survey. The speckle contrast is first objectively measured making use of a well-defined speckle measurement method. We statistically analyse the results of the user quality scores, revealing that the speckle perception is not only influenced by the speckle contrast settings of the projector, but it is also strongly influenced by the type of image shown. Based on the survey, we derive a speckle contrast threshold for which speckle can be seen, and separately we investigate a speckle disturbance limit that is tolerated by the majority of test persons.

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Semiconductor lasers subject to delayed optical feedback have recently shown great potential in solving computationally hard tasks. By optically implementing a neuro-inspired computational scheme, called reservoir computing, based on the transient response to optical data injection, high processing speeds have been demonstrated. While previous efforts have focused on signal bandwidths limited by the semiconductor laser's relaxation oscillation frequency, we demonstrate numerically that the much faster phase response makes significantly higher processing speeds attainable. Moreover, this also leads to shorter external cavity lengths facilitating future on-chip implementations. We numerically benchmark our system on a chaotic time-series prediction task considering two different feedback configurations. The results show that a prediction error below 4% can be obtained when the data is processed at 0.25 GSamples/s. In addition, our insight into the phase dynamics of optical injection in a semiconductor laser also provides a clear understanding of the system performance at different pump current levels, even below solitary laser threshold. Considering spontaneous emission noise and noise in the readout layer, we obtain good prediction performance at fast processing speeds for realistic values of the noise strength.

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In laser projection applications, laser light modules are often combined with rotating diffusers in order to reduce the appearance of speckle on the projection screen. The rotation of a diffuser in a laser beam generates a beam of partially coherent light. Propagation of this light through the different optical components constituting the laser projector is thus essential when investigating the appearance of speckle. In this paper, a computationally efficient simulation model is presented to propagate partially coherent light through a homogenizing rectangular light pipe. The light pipe alters the coherence properties of the light and different consequences are discussed. The outcomes of the simulation model are experimentally verified using a reversing wavefront Michelson interferometer.

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We report on an integrated approach to obtain multiwavelength emission from semiconductor ring lasers with filtered optical feedback. The filtered feedback is realized on-chip employing two arrayed-waveguide gratings to split/recombine light into different wavelength channels. Through experimental observations and numerical simulations, we find that the effective gain of the different modes is the key parameter which has to be balanced in order to achieve multiwavelength emission. This can be achieved by tuning the injection current in each amplifier.