Resource-constrained narrowband optoelectronic oscillator-based reservoir computing for classification of modulated signals.

We experimentally investigate the performance of narrowband optoelectronic oscillator (OEO) reservoir computers using the standard 10th-order nonlinear autoregressive-moving-average (NARMA10) task. Because comparing results from differently parameterized photonic time-delay systems can be difficult, we introduce a new, to the best of our knowledge, metric that accounts for system size, computational accuracy, and training effort overhead in order to provide an "at-a-glance" method to holistically determine a reservoir computer's performance. We then demonstrate the first experimental effort of narrowband OEO-based reservoir computing for the RADIOML dataset, which consists of recognizing and classifying IQ-modulated radio signals including analog and digital modulations.

Multistability, relaxation oscillations, and chaos in time-delayed optoelectronic oscillators with direct laser modulation.

We investigate the nonlinear dynamics of an optoelectronic oscillator that is implemented with a laser diode (LD) with time-delayed feedback. In this system, electrical-to-optical conversion is directly implemented using the direct modulation of the laser diode itself, instead of an electrooptical modulator as in conventional architectures. Moreover, we consider the cubic nonlinear saturation of the characteristic laser power-intensity (P-I) transfer function far above threshold, instead of its simplified piecewise linear counterpart.

Subharmonic instabilities in Kerr microcombs.

We report experimental observation of subharmonic mode excitation in primary Kerr optical frequency combs generated using crystalline whispering-gallery mode resonators. We show that the subcombs can be controlled and span a single or multiple free spectral ranges around the primary comb modes. In the spatial domain, the resulting multiscale combs correspond to an amplitude modulation of intracavity roll patterns.

Ultra-broadband Kerr microcomb through soliton spectral translation.

Broadband and low-noise microresonator frequency combs (microcombs) are critical for deployable optical frequency measurements. Here we expand the bandwidth of a microcomb far beyond its anomalous dispersion region on both sides of its spectrum through spectral translation mediated by mixing of a dissipative Kerr soliton and a secondary pump. We introduce the concept of synthetic dispersion to qualitatively capture the system's key physical behavior, in which the second pump enables spectral translation through four-wave mixing Bragg scattering.

Nonlinear dynamics of continuously tunable optoelectronic oscillators based on stimulated Brillouin amplification.

We present a theoretical analysis for tunable optoelectronic oscillators (OEOs) based on stimulated Brillouin scattering (SBS). A pump laser is used to generate a Brillouin gain which selectively amplifies a phase-modulated and contra-propagating laser signal. The radiofrequency beatnote generated after photodetection is filtered, amplified and fed back to the phase modulator to close the optoelectronic loop.

Nonlinear dynamics in an optoelectronic feedback delay oscillator with piecewise linear transfer functions from the laser diode and photodiode.

We investigate the nonlinear dynamics of a recent architecture of an optoelectronic oscillator, where the emitting laser and the receiving diode are connected in a head-to-tail configuration via an optical fiber delay line. The resulting nonlinear transfer function is a piecewise linear profile, and its interplay with the delay leads to many complex behaviors such as relaxation oscillations and deterministic chaos. This system belongs to a recent class of optoelectronic oscillators where the nonlinearity does not originate from the sinusoidal transfer function of an imbalanced interferometer, and, in particular, it is a simple optoelectronic oscillator configuration that is capable of displaying a chaotic behavior.

Nonlinear dynamics of miniature optoelectronic oscillators based on whispering-gallery mode electrooptical modulators.

We propose a time-domain model to analyze the dynamical behavior of miniature optoelectronic oscillators (OEOs) based on whispering-gallery mode resonators. In these systems, the whispering-gallery mode resonator features a quadratic nonlinearity and operates as an electrooptical modulator, thereby eliminating the need for an integrated Mach-Zehnder modulator. The narrow optical resonances also eliminate the need for both an optical fiber delay line and an electric bandpass filter in the optoelectronic feedback loop.

Fluctuations and correlations in Kerr optical frequency combs with additive Gaussian noise.

We investigate the effects of environmental stochastic fluctuations on Kerr optical frequency combs. This spatially extended dynamical system can be accurately studied using the Lugiato-Lefever equation, and we show that when additive noise is accounted for, the correlations of the modal field fluctuations can be determined theoretically. We propose a general theory for the computation of these field fluctuations and correlations, which is successfully compared to numerical simulations.

Machine learning based on reservoir computing with time-delayed optoelectronic and photonic systems.

The concept of reservoir computing emerged from a specific machine learning paradigm characterized by a three-layered architecture (input, reservoir, and output), where only the output layer is trained and optimized for a particular task. In recent years, this approach has been successfully implemented using various hardware platforms based on optoelectronic and photonic systems with time-delayed feedback. In this review, we provide a survey of the latest advances in this field, with some perspectives related to the relationship between reservoir computing, nonlinear dynamics, and network theory.

On the transition to secondary Kerr combs in whispering-gallery mode resonators.

We demonstrate that extended dissipative structures in Kerr-nonlinear whispering-gallery mode resonators undergo a spatiotemporal instability, as the pumping parameters are varied. We show that the dynamics of the patterns beyond this bifurcation yield specific Kerr comb and sub-comb spectra that can be subjected to a phase of frequency-locking when optimal conditions are met. Our numerical results are found to be in agreement with experimental measurements.

A normal form method for the determination of oscillations characteristics near the primary Hopf bifurcation in bandpass optoelectronic oscillators: Theory and experiment.

We propose a framework for the analysis of the integro-differential delay Ikeda equations ruling the dynamics of bandpass optoelectronic oscillators (OEOs). Our framework is based on the normal form reduction of OEOs and helps in the determination of the amplitude and the frequency of the primary Hopf limit-cycles as a function of the time delay and other parameters. The study is carried for both the negative and the positive slopes of the sinusoidal transfer function, and our analytical results are confirmed by the numerical and experimental data.

Spontaneous generation of orbital angular momentum crystals using a monolithic Nd:YAG nonplanar ring laser.

We report the emission of localized orbital angular momentum (OAM) crystals in a millimeter-size monolithic Nd:YAG nonplanar ring laser. Narrow-linewidth single-frequency lasing in the kilohertz level featuring crystal-like vortices is obtained via phase locking of Laguerre-Gaussian modes in the cavity. It is found that the spatially degenerate OAM of high-order LG modes can be easily broken by superimposing a low-order mode, leading to crystal-like vortices.

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.

Effect of crystalline family and orientation on stimulated Brillouin scattering in whispering-gallery mode resonators.

Ultra-high Q whispering-gallery mode resonators pumped by a continuous-wave laser are known to enhance stimulated Brillouin scattering when optimal resonance and phase-matching conditions are met. In crystalline resonators, this process depends critically on the crystal orientation and family, which impose the elastic constants defining the velocity of the acoustic waves. In this article, we investigate the effect of crystalline orientation and family on this velocity which is proportional to the Brillouin frequency down-shift.

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.

Laser-based optoelectronic generation of narrowband microwave chaos for radars and radio-communication scrambling.

This Letter proposes an optoelectronic oscillator architecture for narrowband microwave chaos generation. In the time domain, the microwave signal features a slowly varying envelope with amplitude and phase chaos while, in the frequency domain, it is quasi-indistinguishable from a band-limited white noise. A full theoretical analysis is performed to investigate the stability properties and route to chaos for the microwave oscillations.

Optimization of primary Kerr optical frequency combs for tunable microwave generation.

We analyze the condition under which Kerr combs generate the highest microwave output power after photodetection. These optimal comb states correspond to configurations in which the sidemode-to-pump ratio is the highest possible. For the case of primary combs, we show how the interplay between the power and frequency of the pump laser critically influences this ratio, which has a direct influence on the phase noise performance of the generated microwaves.

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.

On the phase noise performance of microwave and millimeter-wave signals generated with versatile Kerr optical frequency combs.

We investigate the phase noise performance of micro- and millimeter-wave signals generated using a ultra-high Q whispering gallery mode disk-resonator with Kerr nonlinearity. Our study focuses on the stability of the optical spectra and on the performances of the corresponding microwave and millimeter-wave beat notes in terms of power and phase noise. The blue slope of an optical mode of the resonator, allowing for the generation of optical frequency combs, is accurately explored in order to identify various comb patterns.

Phase-locking transition in Raman combs generated with whispering gallery mode resonators.

We investigate the mechanisms leading to phase locking in Raman optical frequency combs generated with ultrahigh Q crystalline whispering gallery mode disk resonators. We show that several regimes can be triggered depending on the pumping conditions, such as single-frequency Raman lasing, multimode operation involving more than one family of cavity eigenmodes, and Kerr-assisted Raman frequency comb generation. The phase locking and coherence of the combs are experimentally monitored through the measurement of beat signal spectra.

Universal nonlinear scattering in ultra-high Q whispering gallery-mode resonators.

Universal nonlinear scattering processes such as Brillouin, Raman, and Kerr effects are fundamental light-matter interactions of particular theoretical and experimental importance. They originate from the interaction of a laser field with an optical medium at the lattice, molecular, and electronic scale, respectively. These nonlinear effects are generally observed and analyzed separately, because they do not often occur concomitantly.

Giant thermo-optical relaxation oscillations in millimeter-size whispering gallery mode disk resonators.

In this Letter, we show that giant thermo-optical oscillations can be triggered in millimeter (mm)-size whispering gallery mode (WGM) disk resonators when they are pumped by a resonant continuous-wave laser. Our resonator is an ultrahigh-Q barium fluoride cavity that features a positive thermo-optic coefficient and a negative thermo-elastic coefficient. We demonstrate for the first time, to our knowledge, that the complex interplay between these two thermic coefficients and the intrinsic Kerr nonlinearity yields very sharp slow-fast relaxation oscillations with a slow timescale that can be exceptionally large, typically of the order of 1 s.

Spectro-temporal dynamics of Kerr combs with parametric seeding.

We report a joint theoretical and experimental investigation of the parametric seeding of a primary Kerr optical frequency comb. Electro-optic modulation sidebands matching multiple free-spectral ranges of an ultrahigh-Q millimeter-size magnesium fluoride disk resonator are used as seed signals. These seed signals interact through four-wave mixing with the spectral components of a stable primary comb and give rise to complex spectro-temporal patterns.