Experimental reservoir computing with diffractively coupled VCSELs.

We present experiments on reservoir computing (RC) using a network of vertical-cavity surface-emitting lasers (VCSELs) that we diffractively couple via an external cavity. Our optical reservoir computer consists of 24 physical VCSEL nodes. We evaluate the system's memory and solve the 2-bit XOR task and the 3-bit header recognition (HR) task with bit error ratios (BERs) below 1% and the 2-bit digital-to-analog conversion (DAC) task with a root mean square error (RMSE) of 0.067.

Linear optical random projections without holography.

We introduce what we believe to be a novel method to perform linear optical random projections without the need for holography. Our method consists of a computationally trivial combination of multiple intensity measurements to mitigate the information loss usually associated with the absolute-square non-linearity imposed by optical intensity measurements. Both experimental and numerical findings demonstrate that the resulting matrix consists of real-valued, independent, and identically distributed (i.i.d.) Gaussian random entries. Our optical setup is simple and robust, as it does not require interference between two beams. We demonstrate the practical applicability of our method by performing dimensionality reduction on high-dimensional data, a common task in randomized numerical linear algebra with relevant applications in machine learning.

(3+1)D printed adiabatic 1-to-M broadband couplers and fractal splitter networks.

We experimentally demonstrate, based on a generic concept for creating 1-to-M couplers, single-mode 3D optical splitters leveraging adiabatic power transfer towards up to 4 output ports. We use the CMOS compatible additive (3+1)D flash-two-photon polymerization (TPP) printing for fast and scalable fabrication. Optical coupling losses of our splitters are reduced below our measurement sensitivity of 0.06 dB by tailoring the coupling and waveguides geometry, and we demonstrate almost octave-spanning broadband functionality from 520 nm to 980 nm during which losses remain below 2 dB. Finally, based on a fractal, hence self-similar topology of cascaded splitters, we show the efficient scalability of optical interconnects up to 16 single-mode outputs with optical coupling losses of only 1 dB.

Additive 3D photonic integration that is CMOS compatible.

Today, continued miniaturization in electronic integrated circuits (ICs) appears to have reached its fundamental limit at ∼2 nm feature-sizes, from originally ∼1 cm. At the same time, energy consumption due to communication becomes the dominant limitation in high performance electronic ICs for computing, and modern computing concepts such neural networks further amplify the challenge. Communication based on co-integrated photonic circuits is a promising strategy to address the second. As feature size has leveled out, adding a third dimension to the predominantly two-dimensional ICs appears a promising future strategy for further IC architecture improvement. Crucial for efficient electronic-photonic co-integration is complementary metal-oxide-semiconductor (CMOS) compatibility of the associated photonic integration fabrication process. Here, we review our latest results obtained in the FEMTO-ST RENATECH facilities on using additive photo-induced polymerization of a standard photo-resin for truly three-dimensional (3D) photonic integration according to these principles. Based on one- and two-photon polymerization (TPP) and combined with direct-laser writing, we 3D-printed air- and polymer-cladded photonic waveguides. An important application of such circuits are the interconnects of optical neural networks, where 3D integration enables scalability in terms of network size versus its geometric dimensions. In particular viaflash-TPP, a fabrication process combining blanket one- and high-resolution TPP, we demonstrated polymer-cladded step-index waveguides with up to 6 mm length, low insertion (∼0.26 dB) and propagation (∼1.3 dB mm-1) losses, realized broadband and low loss (∼0.06 dB splitting losses) adiabatic 1 to M couplers as well as tightly confining air-cladded waveguides for denser integration. By stably printing such integrated photonic circuits on standard semiconductor samples, we show the concept's CMOS compatibility. With this, we lay out a promising, future avenue for scalable integration of hybrid photonic and electronic components.

Injection locking and coupling the emitters of large VCSEL arrays via diffraction in an external cavity.

Networks of semiconductor lasers are the foundation of numerous applications and fundamental investigations in nonlinear dynamics, material processing, lighting, and information processing. However, making the usually narrowband semiconductor lasers within the network interact requires both high spectral homogeneity and a fitting coupling concept. Here, we report how we use diffractive optics in an external cavity to experimentally couple vertical-cavity surface-emitting lasers (VCSELs) in a 5×5 array. Out of the 25 lasers, we succeed to spectrally align 22, all of which we lock simultaneously to an external drive laser. Furthermore, we show the considerable coupling interactions between the lasers of the array. This way, we present the largest network of optically coupled semiconductor lasers reported so far and the first detailed characterization of such a diffractively coupled system. Due to the high homogeneity of the lasers, the strong interaction between them, and the scalability of the coupling approach, our VCSEL network is a promising platform for experimental investigations of complex systems, and it has direct applications as a photonic neural network.

Roadmap on Deep Learning for Microscopy.

Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap is written collectively by prominent researchers and encompasses selected aspects of how machine learning is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of machine learning for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.

Understanding and mitigating noise in trained deep neural networks.

Deep neural networks unlocked a vast range of new applications by solving tasks of which many were previously deemed as reserved to higher human intelligence. One of the developments enabling this success was a boost in computing power provided by special purpose hardware, such as graphic or tensor processing units. However, these do not leverage fundamental features of neural networks like parallelism and analog state variables. Instead, they emulate neural networks relying on binary computing, which results in unsustainable energy consumption and comparatively low speed. Fully parallel and analogue hardware promises to overcome these challenges, yet the impact of analogue neuron noise and its propagation, i.e. accumulation, threatens rendering such approaches inept. Here, we determine for the first time the propagation of noise in deep neural networks comprising noisy nonlinear neurons in trained fully connected layers. We study additive and multiplicative as well as correlated and uncorrelated noise, and develop analytical methods that predict the noise level in any layer of symmetric deep neural networks or deep neural networks trained with back propagation. We find that noise accumulation is generally bound, and adding additional network layers does not worsen the signal to noise ratio beyond a limit. Most importantly, noise accumulation can be suppressed entirely when neuron activation functions have a slope smaller than unity. We therefore developed the framework for noise in fully connected deep neural networks implemented in analog systems, and identify criteria allowing engineers to design noise-resilient novel neural network hardware.

Two-color optically addressed spatial light modulator as a generic spatiotemporal system.

Nonlinear spatiotemporal systems are the basis for countless physical phenomena in such diverse fields as ecology, optics, electronics, and neuroscience. The canonical approach to unify models originating from different fields is the normal form description, which determines the generic dynamical aspects and different bifurcation scenarios. Realizing different types of dynamical systems via one experimental platform that enables continuous transition between normal forms through tuning accessible system parameters is, therefore, highly relevant. Here, we show that a transmissive, optically addressed spatial light modulator under coherent optical illumination and optical feedback coupling allows tuning between pitchfork, transcritical, and saddle-node bifurcations of steady states. We demonstrate this by analytically deriving the system's dynamical equations in correspondence to the normal forms of the associated bifurcations and confirm these results via extensive numerical simulations. Our model describes a nematic liquid crystal device using nano-dimensional dichalcogenide (a-As 2S 3) glassy thin films as photo sensors and alignment layers, and we use device parameters obtained from experimental characterization. Optical coupling, for example, using diffraction, holography, or integrated unitary maps allows implementing a variety of system topologies of technological relevance for neural networks and potentially Ising or XY-Hamiltonian models with ultralow energy consumption.

Analysis of a Tubular Torsionally Resonating Viscosity-Density Sensor.

This paper discusses a state-of-the-art inline tubular sensor that can measure the viscosity-density of a passing fluid. In this study, experiments and numerical modelling were performed to develop a deeper understanding of the tubular sensor. Experimental results were compared with an analytical model of the torsional resonator. Good agreement was found at low viscosities, although the numerical model deviated slightly at higher viscosities. The sensor was used to measure viscosities in the range of 0.3-1000 mPa·s at a density of 1000 kg/m3. Above 50 mPa·s, numerical models predicted viscosity within ±5% of actual measurement. However, for lower viscosities, there was a higher deviation between model and experimental results up to a maximum of ±21% deviation at 0.3 mPa·s. The sensor was tested in a flow loop to determine the impact of both laminar and turbulent flow conditions. No significant deviations from the static case were found in either of the flow regimes. The numerical model developed for the tubular torsional sensor was shown to predict the sensor behavior over a wide range, enabling model-based design scaling.

Advancing Fourier: space-time concepts in ultrafast optics, imaging, and photonic neural networks.

The concepts of Fourier optics were established in France in the 1940s by Pierre-Michel Duffieux, and laid the foundations of an extensive series of activities in the French research community that have touched on nearly every aspect of contemporary optics and photonics. In this paper, we review a selection of results where applications of the Fourier transform and transfer functions in optics have been applied to yield significant advances in unexpected areas of optics, including the spatial shaping of complex laser beams in amplitude and in phase, real-time ultrafast measurements, novel ghost imaging techniques, and the development of parallel processing methodologies for photonic artificial intelligence.

Coupled Nonlinear Delay Systems as Deep Convolutional Neural Networks.

Neural networks are transforming the field of computer algorithms, yet their emulation on current computing substrates is highly inefficient. Reservoir computing was successfully implemented on a large variety of substrates and gave new insight in overcoming this implementation bottleneck. Despite its success, the approach lags behind the state of the art in deep learning. We therefore extend time-delay reservoirs to deep networks and demonstrate that these conceptually correspond to deep convolutional neural networks. Convolution is intrinsically realized on a substrate level by generic drive-response properties of dynamical systems. The resulting novelty is avoiding vector matrix products between layers, which cause low efficiency in today's substrates. Compared to singleton time-delay reservoirs, our deep network achieves accuracy improvements by at least an order of magnitude in Mackey-Glass and Lorenz time series prediction.

Dynamical complexity and computation in recurrent neural networks beyond their fixed point.

Spontaneous activity found in neural networks usually results in a reduction of computational performance. As a consequence, artificial neural networks are often operated at the edge of chaos, where the network is stable yet highly susceptible to input information. Surprisingly, regular spontaneous dynamics in Neural Networks beyond their resting state possess a high degree of spatio-temporal synchronization, a situation that can also be found in biological neural networks. Characterizing information preservation via complexity indices, we show how spatial synchronization allows rRNNs to reduce the negative impact of regular spontaneous dynamics on their computational performance.

Conditions for reservoir computing performance using semiconductor lasers with delayed optical feedback.

Photonic implementations of reservoir computing (RC) have been receiving considerable attention due to their excellent performance, hardware, and energy efficiency as well as their speed. Here, we study a particularly attractive all-optical system using optical information injection into a semiconductor laser with delayed feedback. We connect its injection locking, consistency, and memory properties to the RC performance in a non-linear prediction task. We find that for partial injection locking we achieve a good combination of consistency and memory. Therefore, we are able to provide a physical basis identifying operational parameters suitable for prediction.

Detecting Disordered Breathing and Limb Movement Using In-Bed Force Sensors.

We present and evaluate measurement fusion and decision fusion for recognizing apnea and periodic limb movement in sleep episodes. We used an in-bed sensor system composed of an array of strain gauges to detect pressure changes corresponding to respiration and body movement. The sensor system was placed under the bed mattress during sleep and continuously recorded pressure changes. We evaluated both fusion frameworks in a study with nine adult participants that had mixed occurrences of normal sleep, apnea, and periodic limb movement. Both frameworks yielded similar recognition accuracies of 72.1 ± âˆ¼  12% compared to 63.7 ± 17.4% for a rule-based detection reported in the literature. We concluded that the pattern recognition methods can outperform previous rule-based detection methods for classifying disordered breathing and period limb movements simultaneously.

Bidirectional private key exchange using delay-coupled semiconductor lasers.

We experimentally demonstrate a key exchange cryptosystem based on the phenomenon of identical chaos synchronization. In our protocol, the private key is symmetrically generated by the two communicating partners. It is built up from the synchronized bits occurring between two current-modulated bidirectionally coupled semiconductor lasers with additional self-feedback. We analyze the security of the exchanged key and discuss the amplification of its privacy. We demonstrate private key generation rates up to 11 Mbit/s over a public channel.

Non-24-Hour Sleep-Wake Disorder Revisited - A Case Study.

The human sleep-wake cycle is governed by two major factors: a homeostatic hourglass process (process S), which rises linearly during the day, and a circadian process C, which determines the timing of sleep in a ~24-h rhythm in accordance to the external light-dark (LD) cycle. While both individual processes are fairly well characterized, the exact nature of their interaction remains unclear. The circadian rhythm is generated by the suprachiasmatic nucleus ("master clock") of the anterior hypothalamus, through cell-autonomous feedback loops of DNA transcription and translation. While the phase length (tau) of the cycle is relatively stable and genetically determined, the phase of the clock is reset by external stimuli ("zeitgebers"), the most important being the LD cycle. Misalignments of the internal rhythm with the LD cycle can lead to various somatic complaints and to the development of circadian rhythm sleep disorders (CRSD). Non-24-hour sleep-wake disorders (N24HSWD) is a CRSD affecting up to 50% of totally blind patients and characterized by the inability to maintain a stable entrainment of the typically long circadian rhythm (tau > 24.5 h) to the LD cycle. The disease is rare in sighted individuals and the pathophysiology less well understood. Here, we present the case of a 40-year-old sighted male, who developed a misalignment of the internal clock with the external LD cycle following the treatment for Hodgkin's lymphoma (ABVD regimen, four cycles and AVD regimen, four cycles). A thorough clinical assessment, including actigraphy, melatonin profiles and polysomnography led to the diagnosis of non-24-hour sleep-wake disorders (N24HSWD) with a free-running rhythm of tau = 25.27 h. A therapeutic intervention with bright light therapy (30 min, 10,000 lux) in the morning and melatonin administration (0.5-0.75 mg) in the evening failed to entrain the free-running rhythm, although a longer treatment duration and more intense therapy might have been successful. The sudden onset and close timely connection led us to hypothesize that the chemotherapy might have caused a mutation of the molecular clock components leading to the observed elongation of the circadian period.

Interaction between Liénard and Ikeda dynamics in a nonlinear electro-optical oscillator with delayed bandpass feedback.

We report on experimental and theoretical analysis of the complex dynamics generated by a nonlinear time-delayed electro-optic bandpass oscillator. We investigate the interaction between the slow- and fast-scale dynamics of autonomous oscillations in the breather regime. We analyze in detail the coupling between the fast-scale behavior associated to a characteristic low-pass Ikeda behavior and the slow-scale dynamics associated to a Liénard limit-cycle. Finally, we show that when projected onto a two-dimensional phase space, the attractors corresponding to periodic and chaotic breathers display a spiral-like pattern, which strongly depends on the shape of the nonlinear function.

Reconfigurable semiconductor laser networks based on diffractive coupling.

Networks of optical emitters are highly sought-after, both for fundamental investigations as well as for various technological applications. We introduce and implement a novel scheme, based on diffractive optical coupling, allowing for the coupling of large numbers of optical emitters with adjustable weights. We demonstrate its potential by coupling emitters of a 2D array of semiconductor lasers with significant efficiency.

Minimal approach to neuro-inspired information processing.

To learn and mimic how the brain processes information has been a major research challenge for decades. Despite the efforts, little is known on how we encode, maintain and retrieve information. One of the hypothesis assumes that transient states are generated in our intricate network of neurons when the brain is stimulated by a sensory input. Based on this idea, powerful computational schemes have been developed. These schemes, known as machine-learning techniques, include artificial neural networks, support vector machine and reservoir computing, among others. In this paper, we concentrate on the reservoir computing (RC) technique using delay-coupled systems. Unlike traditional RC, where the information is processed in large recurrent networks of interconnected artificial neurons, we choose a minimal design, implemented via a simple nonlinear dynamical system subject to a self-feedback loop with delay. This design is not intended to represent an actual brain circuit, but aims at finding the minimum ingredients that allow developing an efficient information processor. This simple scheme not only allows us to address fundamental questions but also permits simple hardware implementations. By reducing the neuro-inspired reservoir computing approach to its bare essentials, we find that nonlinear transient responses of the simple dynamical system enable the processing of information with excellent performance and at unprecedented speed. We specifically explore different hardware implementations and, by that, we learn about the role of nonlinearity, noise, system responses, connectivity structure, and the quality of projection onto the required high-dimensional state space. Besides the relevance for the understanding of basic mechanisms, this scheme opens direct technological opportunities that could not be addressed with previous approaches.