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.

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.

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.

Delayed dynamical systems: networks, chimeras and reservoir computing.

We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques.

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.

Dependence of quality factor on surface roughness in crystalline whispering-gallery mode resonators.

We present an experimental study of the variation of quality factor (Q-factor) of WGM resonators as a function of surface roughness. We consider mm-size whispering-gallery mode resonators manufactured with fluoride crystals, featuring Q-factors of the order of 1 billion at 1550 nm. The experimental procedure consists of repeated polishing steps, after which the surface roughness is evaluated using profilometry by white-light phase-shifting interferometry, while the Q-factors are determined using the cavity-ring-down method.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme.

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.

Consistency in experiments on multistable driven delay systems.

We investigate the consistency properties in the responses of a nonlinear delay optoelectronic intensity oscillator subject to different drives, in particular, harmonic and self-generated waveforms. This system, an implementation of the Ikeda oscillator, is operating in a closed-loop configuration, exhibiting its autonomous dynamics while the drive signals are additionally introduced. Applying the same drive multiple times, we compare the dynamical responses of the optoelectronic oscillator and quantify the degree of consistency among them via their correlation.

Nonlinear Memory Capacity of Parallel Time-Delay Reservoir Computers in the Processing of Multidimensional Signals.

This letter addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking. First, an approximating reservoir model is presented in those frameworks that provides an explicit functional link between the reservoir architecture and its performance in the execution of a specific task. Second, the inference properties of the ridge regression estimator in the multivariate context are used to assess the impact of finite sample training on the decrease of the reservoir capacity.

Optimal nonlinear information processing capacity in delay-based reservoir computers.

Reservoir computing is a recently introduced brain-inspired machine learning paradigm capable of excellent performances in the processing of empirical data. We focus in a particular kind of time-delay based reservoir computers that have been physically implemented using optical and electronic systems and have shown unprecedented data processing rates. Reservoir computing is well-known for the ease of the associated training scheme but also for the problematic sensitivity of its performance to architecture parameters.

Laser chimeras as a paradigm for multistable patterns in complex systems.

A chimera state is a rich and fascinating class of self-organized solutions developed in high-dimensional networks. Necessary features of the network for the emergence of such complex but structured motions are non-local and symmetry breaking coupling. An accurate understanding of chimera states is expected to bring important insights on deterministic mechanism occurring in many structurally similar high-dimensional dynamics such as living systems, brain operation principles and even turbulence in hydrodynamics.

Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor.

We report the fabrication for the first time of a strontium fluoride (SrF(2)) whispering-gallery mode resonator with quality factor in excess of 1 billion. The millimeter-size disk-resonator is polished until the surface roughness decreases down to a root-mean square value of 1.2 nm, as measured with a vertical scanning profilometer.

Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications.

Optical Kerr frequency combs are known to be effective coherent multiwavelength sources for ultrahigh capacity fiber communications. These combs are the frequency-domain counterparts of a wide variety of spatiotemporal dissipative structures, such as cavity solitons, chaos, or Turing patterns (rolls). In this Letter, we demonstrate that Turing patterns, which correspond to the so-called primary combs in the spectral domain, are optimally coherent in the sense that for the same pump power they provide the most robust carriers for coherent data transmission in fiber communications using advanced modulation formats.

Mixed-mode oscillations in slow-fast delayed optoelectronic systems.

In this article, we investigate the dynamical behavior of breathers in optoelectronic oscillators from the standpoint of mixed-mode oscillations. In the phase space, these breathers are composite oscillations that are damped to the attractive branches of an invariant manifold. Our study shows that the emergence of breather dynamics is linked to the apparition of inflection points in the phase space, and we develop an analytical framework based on the Liénard reduction form in order to provide an analytical insight into this phenomenology.

Stochastic nonlinear time series forecasting using time-delay reservoir computers: performance and universality.

Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs.

Incoherent resonant seeding of modulation instability in optical fiber.

We report control of the spectral and noise properties of spontaneous modulation instability (MI) in optical fiber using an incoherent seed with power at the 10(-6) level relative to the pump. We sweep the seed wavelength across the MI gain band, and observe significant enhancement of MI bandwidth and improvement in the signal-to-noise ratio as the seed coincides with the MI gain peak. We also vary the seed bandwidth and find a reduced effect on the MI spectrum as the seed coherence decreases.

Microwave photonics systems based on whispering-gallery-mode resonators.

Microwave photonics systems rely fundamentally on the interaction between microwave and optical signals. These systems are extremely promising for various areas of technology and applied science, such as aerospace and communication engineering, sensing, metrology, nonlinear photonics, and quantum optics. In this article, we present the principal techniques used in our lab to build microwave photonics systems based on ultra-high Q whispering gallery mode resonators.

Complexity in electro-optic delay dynamics: modelling, design and applications.

Nonlinear delay dynamics have found during the last 30 years a particularly prolific exploration area in the field of photonic systems. Besides the popular external cavity laser diode set-ups, we focus in this article on another experimental realization involving electro-optic (EO) feedback loops, with delay. This approach has strongly evolved with the important technological progress made on broadband photonic and optoelectronic devices dedicated to high-speed optical telecommunications.

Slow-fast dynamics of a time-delayed electro-optic oscillator.

Square-wave oscillations exhibiting different plateau lengths have been observed experimentally by investigating an electro-optic oscillator. In a previous study, we analysed the model delay differential equations and determined an asymptotic approximation of the two plateaus. In this paper, we concentrate on the fast transition layers between plateaus and show how they contribute to the total period.

Virtual chimera states for delayed-feedback systems.

Time-delayed systems are found to display remarkable temporal patterns the dynamics of which split into regular and chaotic components repeating at the interval of a delay. This novel long-term behavior for delay dynamics results from strongly asymmetric nonlinear delayed feedback driving a highly damped harmonic oscillator dynamics. In the corresponding virtual space-time representation, the behavior is found to develop as a chimeralike state, a new paradigmatic object from the network theory characterized by the coexistence of synchronous and incoherent oscillations.

Strongly asymmetric square waves in a time-delayed system.

Time-delayed systems are known to exhibit symmetric square waves oscillating with a period close to twice the delay. Here, we show that strongly asymmetric square waves of a period close to one delay are possible. The plateau lengths can be tuned by changing a control parameter.

Photonic nonlinear transient computing with multiple-delay wavelength dynamics.

We report on the experimental demonstration of a hybrid optoelectronic neuromorphic computer based on a complex nonlinear wavelength dynamics including multiple delayed feedbacks with randomly defined weights. This neuromorphic approach is based on a new paradigm of a brain-inspired computational unit, intrinsically differing from Turing machines. This recent paradigm consists in expanding the input information to be processed into a higher dimensional phase space, through the nonlinear transient response of a complex dynamics excited by the input information.