Emergence of collapsed snaking related dark and bright Kerr dissipative solitons with quartic-quadratic dispersion.

We theoretically investigate the dynamics, bifurcation structure, and stability of dark localized states emerging in Kerr cavities in the presence of positive second- and fourth-order dispersion. In this previously unexplored regime, dark states form through the locking of uniform wave fronts, or domain walls, connecting two coexisting stable uniform states, and undergo a generic bifurcation structure known as collapsed homoclinic snaking. We characterize the robustness of these states by computing their stability and bifurcation structure as a function of the main control parameter of the system. Furthermore, we show that by increasing the dispersion of fourth order, bright localized states can be also stabilized.

Photonic reservoir computer based on frequency multiplexing.

Reservoir computing is a brain-inspired approach for information processing, well suited to analog implementations. We report a photonic implementation of a reservoir computer that exploits frequency domain multiplexing to encode neuron states. The system processes 25 comb lines simultaneously (i.e., 25 neurons), at a rate of 20 MHz. We illustrate performances on two standard benchmark tasks: channel equalization and time series forecasting. We also demonstrate that frequency multiplexing allows output weights to be implemented in the optical domain, through optical attenuation. We discuss the perspectives for high-speed, high-performance, low-footprint implementations.

Efficient type II second harmonic generation in an indium gallium phosphide on insulator wire waveguide aligned with a crystallographic axis.

We theoretically and experimentally investigate type II second harmonic generation in III-V-on-insulator wire waveguides. We show that the propagation direction plays a crucial role and that longitudinal field components can be leveraged for robust and efficient conversion. We predict that the maximum theoretical conversion is larger than that of type I second harmonic generation for similar waveguide dimensions and reach an experimental conversion efficiency of 12%/W, limited by the propagation loss.

Online Training of an Opto-Electronic Reservoir Computer Applied to Real-Time Channel Equalization.

Reservoir computing is a bioinspired computing paradigm for processing time-dependent signals. The performance of its analog implementation is comparable to other state-of-the-art algorithms for tasks such as speech recognition or chaotic time series prediction, but these are often constrained by the offline training methods commonly employed. Here, we investigated the online learning approach by training an optoelectronic reservoir computer using a simple gradient descent algorithm, programmed on a field-programmable gate array chip. Our system was applied to wireless communications, a quickly growing domain with an increasing demand for fast analog devices to equalize the nonlinear distorted channels. We report error rates up to two orders of magnitude lower than previous implementations on this task. We show that our system is particularly well suited for realistic channel equalization by testing it on a drifting and a switching channel and obtaining good performances.

Embodiment of Learning in Electro-Optical Signal Processors.

Delay-coupled electro-optical systems have received much attention for their dynamical properties and their potential use in signal processing. In particular, it has recently been demonstrated, using the artificial intelligence algorithm known as reservoir computing, that photonic implementations of such systems solve complex tasks such as speech recognition. Here, we show how the backpropagation algorithm can be physically implemented on the same electro-optical delay-coupled architecture used for computation with only minor changes to the original design. We find that, compared to when the backpropagation algorithm is not used, the error rate of the resulting computing device, evaluated on three benchmark tasks, decreases considerably. This demonstrates that electro-optical analog computers can embody a large part of their own training process, allowing them to be applied to new, more difficult tasks.

Fully analogue photonic reservoir computer.

Introduced a decade ago, reservoir computing is an efficient approach for signal processing. State of the art capabilities have already been demonstrated with both computer simulations and physical implementations. If photonic reservoir computing appears to be promising a solution for ultrafast nontrivial computing, all the implementations presented up to now require digital pre or post processing, which prevents them from exploiting their full potential, in particular in terms of processing speed. We address here the possibility to get rid simultaneously of both digital pre and post processing. The standalone fully analogue reservoir computer resulting from our endeavour is compared to previous experiments and only exhibits rather limited degradation of performances. Our experiment constitutes a proof of concept for standalone physical reservoir computers.

All-optical reservoir computer based on saturation of absorption.

Reservoir computing is a new bio-inspired computation paradigm. It exploits a dynamical system driven by a time-dependent input to carry out computation. For efficient information processing, only a few parameters of the reservoir needs to be tuned, which makes it a promising framework for hardware implementation. Recently, electronic, opto-electronic and all-optical experimental reservoir computers were reported. In those implementations, the nonlinear response of the reservoir is provided by active devices such as optoelectronic modulators or optical amplifiers. By contrast, we propose here the first reservoir computer based on a fully passive nonlinearity, namely the saturable absorption of a semiconductor mirror. Our experimental setup constitutes an important step towards the development of ultrafast low-consumption analog computers.

Dynamics of one-dimensional Kerr cavity solitons.

We present an experimental observation of an oscillating Kerr cavity soliton, i.e., a time-periodic oscillating one-dimensional temporally localized structure excited in a driven nonlinear fiber cavity with a Kerr-type nonlinearity. More generally, these oscillations result from a Hopf bifurcation of a (spatially or temporally) localized state in the generic class of driven dissipative systems close to the 1 : 1 resonance tongue. Furthermore, we theoretically analyze dynamical instabilities of the one-dimensional cavity soliton, revealing oscillations and different chaotic states in previously unexplored regions of parameter space. As cavity solitons are closely related to Kerr frequency combs, we expect these dynamical regimes to be highly relevant for the field of microresonator-based frequency combs.

Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities.

We study analytically, numerically, and experimentally the nonlinear symmetry breaking induced by broken reflection symmetry in an optical fiber system. In particular, we investigate the modulation instability regime and reveal the key role of the third-order dispersion on the asymmetry in the spectrum of the dissipative structures. Our theory explains early observations, and the predictions are in excellent agreement with our experimental findings.

Neck instability of bright solitons in normally dispersive Kerr media.

The neck instability of bright solitons of the hyperbolic nonlinear Shrödinger equation is investigated. It is shown that this instability originates from a four-wave mixing interaction that links on-axis to off-axis radiation at opposite frequency bands. Our experiment supports this interpretation.

All-optical reservoir computing.

Reservoir Computing is a novel computing paradigm that uses a nonlinear recurrent dynamical system to carry out information processing. Recent electronic and optoelectronic Reservoir Computers based on an architecture with a single nonlinear node and a delay loop have shown performance on standardized tasks comparable to state-of-the-art digital implementations. Here we report an all-optical implementation of a Reservoir Computer, made of off-the-shelf components for optical telecommunications. It uses the saturation of a semiconductor optical amplifier as nonlinearity. The present work shows that, within the Reservoir Computing paradigm, all-optical computing with state-of-the-art performance is possible.

Countering spatial soliton breakdown in nematic liquid crystals.

Spatial optical soliton propagation in any material is limited by the losses of the optical beam, which results in beam broadening. In nematic liquid crystals it is possible to tune the magnitude of the nonlinearity by means of a bias voltage. In this work we present the idea of increasing the nonlinearity along the propagation distance by changing the bias voltage. Next to a theoretical analysis, we present experimental proof of the validity of our method. The use of this technique offers a major advantage for optical interconnects because the beam broadening can be reduced over much longer propagation distances.

Photon pair source based on parametric fluorescence in periodically poled twin-hole silica fiber.

We present observations of quasi-phase matched parametric fluorescence in a periodically poled twin-hole silica fiber. The phase matching condition in the fiber enables the generation of a degenerate signal field in the fiber-optic communication band centered on 1556 nm. We performed coincidence measurements and a Hong-Ou-Mandel experiment to validate that the signal arises from photon pairs. A coincidence peak with a signal to noise ratio (SNR) of 4 using 43 mW of pump power and a Hong-Ou-Mandel dip showing 40% net visibility were measured. Moreover, the experiments were performed with standard single mode fibers spliced at both ends of the poled section, which makes this source easy to integrate in fiber-optic quantum communication applications.

Fast self-pulsing through nonlinear incoherent feedback.

We consider a double-pass ring cavity with nonlinear incoherent optical feedback and analyze its response when it is driven by a continuous laser beam. This particular cavity is equivalent, in the temporal domain, to a simple spatial-pattern-generating system made from a Kerr slice and a feedback mirror. After formulating the evolution equations, we investigate the behavior of small-amplitude solutions and obtain an expression for the round-trip gains. We then explore the important effect of dispersion in the nonlinear medium. Finally, we show that stable modes are possible by solving numerically the full nonlinear equations.

Switching through symmetry breaking in coupled nonlinear micro-cavities.

We describe stable symmetry-breaking states in systems with two coupled nonlinear cavities, using coupled-mode theory and rigorous simulations. Above a threshold input level the symmetric state of the passive Kerr system becomes unstable, and we show how this phenomenon can be employed for switching and flip-flop purposes, using positive pulses only. A device with compact photonic crystal microcavities is proposed by which we numerically demonstrate the principle.

Experimental observation of the elliptically polarized fundamental vector soliton of isotropic Kerr media.

We report the experimental observation of the elliptically polarized fundamental vector soliton of isotropic Kerr media and its unique polarization evolution. This was achieved in the spatial domain in a nonbirefringent CS2 planar waveguide.

Condensation in Hamiltonian parametric wave interaction.

In the generic Hamiltonian problem of parametric wave interaction, we show theoretically the existence of a sudden transition leading the wave system from completely incoherent states towards highly coherent states. This self-organization process is characterized by a reduction of the nonequilibrium entropy, in contrast with the H theorem of entropy growth inherent to the random phase approximation approach. The mechanism underlying this intriguing condensation process is in essence a reversible nonlinear damping. As a result, the lower the coherence of the initial state, the higher the coherence of the final state.

Incoherent solitons in instantaneous response nonlinear media.

We show theoretically and experimentally in an optical fiber system that solitons can be spontaneously generated from incoherent light in an instantaneous response nonlinear Kerr medium. The theory reveals that the unexpected existence of these incoherent solitons relies on a phase-locking mechanism, which leads to the emergence of a mutual coherence between the incoherent waves that constitute the soliton.

Simulations and experiments on self-focusing conditions in nematic liquid-crystal planar cells.

Owing to the nonlinear effect of optical field-induced director reorientation, self-focusing of an optical beam can occur in nematic liquid crystals and an almost diffraction-compensated propagation can be observed with milliwatts of light power and propagation lengths of several millimeters. This opens the way for applications in all-optical signal handling and reconfigurable optical interconnections. Self-focusing of an optical beam in nematic liquid-crystal cells has been studied experimentally and by means of numerical simulation. The relationships between bias voltage, cell thickness and required optical power have been examined, thus allowing the determination of the most favorable conditions for soliton-like beam propagation.

Hidden coherence along space-time trajectories in parametric wave mixing.

We show theoretically that the waves generated through the generic parametric three- or four-wave-mixing processes exhibit, as a general rule, a hidden coherence characterized by skewed coherence lines along specific space-time trajectories. Our study generalizes the concept of coherence in the sense that these previously unrecognized coherent states cannot be described through the standard definitions of spatial and temporal coherence.