Phase shaping of dual-pumped Brillouin-Kerr frequency combs.

We investigate the spectral phase characteristics of dual-pumped Kerr frequency combs generated in a bichromatic Brillouin fiber laser architecture with normal dispersion, producing square-like pulse profiles. Using a pulse shaper, we measure the relative phase between the pump Stokes and adjacent lines, revealing a symmetric phase relationship. Our results highlight good phase coherence of the comb. By manipulating spectral amplitudes and phases, we demonstrate the transformation into various optical waveforms. The stability of our low-noise frequency comb ensures reliable performance in practical settings.

Analysis of interaction dynamics and rogue wave localization in modulation instability using data-driven dominant balance.

We analyze the dynamics of modulation instability in optical fiber (or any other nonlinear Schrödinger equation system) using the machine-learning technique of data-driven dominant balance. We aim to automate the identification of which particular physical processes drive propagation in different regimes, a task usually performed using intuition and comparison with asymptotic limits. We first apply the method to interpret known analytic results describing Akhmediev breather, Kuznetsov-Ma, and Peregrine soliton (rogue wave) structures, and show how we can automatically distinguish regions of dominant nonlinear propagation from regions where nonlinearity and dispersion combine to drive the observed spatio-temporal localization. Using numerical simulations, we then apply the technique to the more complex case of noise-driven spontaneous modulation instability, and show that we can readily isolate different regimes of dominant physical interactions, even within the dynamics of chaotic propagation.

Analysis of the dispersive Fourier transform dataset using dynamic mode decomposition: evidence of multiple vibrational modes and their interplay in a three-soliton molecule.

We demonstrate that the dynamic mode decomposition technique can effectively reduce the amount of noise in the dispersive Fourier transform dataset and allow for finer quantitative analysis of the experimental data. We therefore show that the oscillation pattern of a soliton molecule actually results from the interplay of several elementary vibration modes.

Genetic algorithm optimization of broadband operation in a noise-like pulse fiber laser.

The noise-like pulse regime of optical fiber lasers is highly complex, and associated with multiscale emission of random sub-picosecond pulses underneath a much longer envelope. With the addition of highly nonlinear fiber in the cavity, noise-like pulse lasers can also exhibit supercontinuum broadening and the generation of output spectra spanning 100's of nm. Achieving these broadest bandwidths, however, requires careful optimization of the nonlinear polarization rotation based saturable absorber, which involves a very large potential parameter space. Here we study the spectral characteristics of a broadband noise-like pulse laser by scanning the laser operation over a random sample of 50,000 polarization settings, and we quantify that these broadest bandwidths are generated in only [Formula: see text] 0.5% of cases. We also show that a genetic algorithm can replace trial and error optimization to align the cavity for these broadband operating states.

Synchronization, Desynchronization, and Intermediate Regime of Breathing Solitons and Soliton Molecules in a Laser Cavity.

We report on the experimental and numerical observations of synchronization and desynchronization of bound states of multiple breathing solitons (breathing soliton molecules) in an ultrafast fiber laser. In the desynchronization regime, although the breather molecules as wholes are not synchronized to the cavity, the individual breathers within a molecule are synchronized to each other with a delay (lag synchronization). An intermediate regime between the synchronization and desynchronization phases is also observed, featuring self-modulation of the synchronized state. This regime may also occur in other systems displaying synchronization. Breathing soliton molecules in a laser cavity open new avenues for the study of nonlinear synchronization dynamics.

Phase space topology of four-wave mixing reconstructed by a neural network.

The dynamics of ideal four-wave mixing in optical fiber is reconstructed by taking advantage of the combination of experimental measurements together with supervised machine learning strategies. The training data consist of power-dependent spectral phase and amplitude recorded at the output of a short fiber segment. The neural network is shown to be able to accurately predict the nonlinear dynamics over tens of kilometers, and to retrieve the main features of the phase space topology including multiple Fermi-Pasta-Ulam recurrence cycles and the system separatrix boundary.

Farey tree and devil's staircase of frequency-locked breathers in ultrafast lasers.

Nonlinear systems with two competing frequencies show locking or resonances. In lasers, the two interacting frequencies can be the cavity repetition rate and a frequency externally applied to the system. Conversely, the excitation of breather oscillations in lasers naturally triggers a second characteristic frequency in the system, therefore showing competition between the cavity repetition rate and the breathing frequency. Yet, the link between breathing solitons and frequency locking is missing. Here we demonstrate frequency locking at Farey fractions of a breather laser. The winding numbers exhibit the hierarchy of the Farey tree and the structure of a devil's staircase. Numerical simulations of a discrete laser model confirm the experimental findings. The breather laser may therefore serve as a simple test bed to explore ubiquitous synchronization dynamics of nonlinear systems. The locked breathing frequencies feature a high signal-to-noise ratio and can give rise to dense radio-frequency combs, which are attractive for applications.

Data-driven model discovery of ideal four-wave mixing in nonlinear fibre optics.

We show using numerical simulations that data driven discovery using sparse regression can be used to extract the governing differential equation model of ideal four-wave mixing in a nonlinear Schrödinger equation optical fibre system. Specifically, we consider the evolution of a strong single frequency pump interacting with two frequency detuned sidebands where the dynamics are governed by a reduced Hamiltonian system describing pump-sideband coupling. Based only on generated dynamical data from this system, sparse regression successfully recovers the underlying physical model, fully capturing the dynamical landscape on both sides of the system separatrix. We also discuss how analysing an ensemble over different initial conditions allows us to reliably identify the governing model in the presence of noise. These results extend the use of data driven discovery to ideal four-wave mixing in nonlinear Schrödinger equation systems.

Machine learning analysis of instabilities in noise-like pulse lasers.

Neural networks have been recently shown to be highly effective in predicting time-domain properties of optical fiber instabilities based only on analyzing spectral intensity profiles. Specifically, from only spectral intensity data, a suitably trained neural network can predict temporal soliton characteristics in supercontinuum generation, as well as the presence of temporal peaks in modulation instability satisfying rogue wave criteria. Here, we extend these previous studies of machine learning prediction for single-pass fiber propagation instabilities to the more complex case of noise-like pulse dynamics in a dissipative soliton laser. Using numerical simulations of highly chaotic behaviour in a noise-like pulse laser operating around 1550 nm, we generate large ensembles of spectral and temporal data for different regimes of operation, from relatively narrowband laser spectra of 70 nm bandwidth at the -20 dB level, to broadband supercontinuum spectra spanning 200 nm at the -20 dB level and with dispersive wave and long wavelength Raman extension spanning from 1150-1700 nm. Using supervised learning techniques, a trained neural network is shown to be able to accurately correlate spectral intensity profiles with time-domain intensity peaks and to reproduce the associated temporal intensity probability distributions.

Intracavity incoherent supercontinuum dynamics and rogue waves in a broadband dissipative soliton laser.

Understanding dynamical complexity is one of the most important challenges in science. Significant progress has recently been made in optics through the study of dissipative soliton laser systems, where dynamics are governed by a complex balance between nonlinearity, dispersion, and energy exchange. A particularly complex regime of such systems is associated with noise-like pulse multiscale instabilities, where sub-picosecond pulses with random characteristics evolve chaotically underneath a much longer envelope. However, although observed for decades in experiments, the physics of this regime remains poorly understood, especially for highly-nonlinear cavities generating broadband spectra. Here, we address this question directly with a combined numerical and experimental study that reveals the physical origin of instability as nonlinear soliton dynamics and supercontinuum turbulence. Real-time characterisation reveals intracavity extreme events satisfying statistical rogue wave criteria, and both real-time and time-averaged measurements are in quantitative agreement with modelling.

Real-time characterization of spectral instabilities in a mode-locked fibre laser exhibiting soliton-similariton dynamics.

The study of dissipative solitons in mode-locked lasers reveals a rich landscape of interaction dynamics resulting from the interplay of nonlinearity, dispersion and dissipation. Here, we characterize a range of instabilities in a dissipative soliton fibre laser in a regime where both conventional soliton and similariton propagation play significant roles in the intracavity pulse shaping. Specifically, we use the Dispersive Fourier Transform technique to perform real-time spectral measurements of buildup dynamics from noise to the generation of stable single pulses, phase evolution dynamics of bound state "similariton molecules", and several examples of intermittent instability and explosion dynamics. These results show that the instabilities previously seen in other classes of passively mode-locked fibre lasers are also observed in the presence of strong nonlinear attraction of similariton evolution in an optical fibre amplifier.

Si-rich Si nitride waveguides for optical transmissions and toward wavelength conversion around 2 µm.

We show that subwavelength Si-rich nitride waveguides efficiently sustain high-speed transmissions at 2 µm. We report the transmission of a 10 Gbit/s signal over 3.5 cm with negligible power penalty. Parametric conversion in the pulsed pump regime is also demonstrated using the same waveguide structure with an efficiency as high as -18 dB.

Phase evolution of Peregrine-like breathers in optics and hydrodynamics.

We present a simultaneous study of the phase properties of rational breather waves generated in a water wave tank and in an optical fiber platform, namely, the Peregrine soliton and related second-order solution. Our analysis of experimental wave measurements makes use of standard demodulation and filtering techniques in hydrodynamics and more complex phase retrieval techniques in optics to quantitatively confirm analytical and numerical predictions. We clearly highlight a characteristic phase shift that is a multiple of π between the central pulsed part and the continuous background of rational breathers at their maximum compression. Moreover, we reveal a large longitudinal phase shift across the point of maximum compression.

Experimental observation of the emergence of Peregrine-like events in focusing dam break flows.

Simple photonic fiber-based workbenches have been able to emulate well-known nonlinear wave dynamics occurring in deep or shallow water conditions. Here, by investigating the nonlinear reshaping of a flat-top pulse upon propagation in an anomalous dispersive optical fiber, we observe that typical signatures of focusing dam break flows and Peregrine-like breather events can locally coexist in spontaneous pattern formations. The experimental measurements are in good agreement with our numerical predictions.

Nonlinear spectrum broadening cancellation by sinusoidal phase modulation.

We propose and experimentally demonstrate a new approach to dramatically reduce the spectral broadening induced by self-phase modulation occurring in a Kerr medium. By using a temporal sinusoidal phase modulation, we efficiently cancel to a large extent the chirp induced by the nonlinear effect. Experimental validation carried out in a passive or amplifying fiber confirms the interest of the technique for the mitigation of the spectral expansion of long pulses.

Broadband etching-free metal grating couplers embedded in titanium dioxide waveguides.

Metal grating couplers embedded into a titanium dioxide layer are proposed. A coupling efficiency better than 20% is experimentally demonstrated with a 3 dB bandwidth of 86 nm which is in agreement with simulation results. This allowed us to perform error-free transmissions of 10 Gbit/s wavelength multiplexed signals in the C-band.

40 GHz pulse source based on cross-phase modulation-induced focusing in normally dispersive optical fibers.

We theoretically and experimentally investigate the design of a high-repetition rate source delivering well-separated optical pulses due to the nonlinear compression of a dual-frequency beat signal within a cavity-less normally dispersive fiber-based setup. This system is well described by a set of two coupled nonlinear Schrödinger equations for which the traditional normally dispersive defocusing regime is turned in a focusing temporal lens through a degenerated cross-phase modulation process (XPM). More precisely, the temporal compression of the initial beating is performed by the combined effects of normal dispersion and XPM-induced nonlinear phase shift provided by an intense beat signal on its weak out-of-phase replica co-propagating with orthogonal polarizations. This adiabatic reshaping process allows us to experimentally demonstrate the generation of a 40 GHz well-separated 3.3 ps pulse train at 1550 nm in a 5 km long normally dispersive fiber.

40-GHz photonic waveform generator by linear shaping of four spectral sidebands.

We show that the amplitude and phase shaping of only four sidebands of the optical spectrum is sufficient to synthesize parabolic, triangular, or flat-top pulse trains at high repetition rates. Selection of the symmetric carrier-suppressed waveform is easily achieved by changing the phase difference between the inner and outer spectral lines. Experiments carried out at a repetition rate of 40 GHz confirm the high quality of the intensity profiles that are obtained.

Experimental demonstration of spectral sideband splitting in strongly dispersion oscillating fibers.

By using a highly nonlinear, dispersion oscillating optical fiber operating in the telecom C band, we experimentally demonstrate the splitting experienced by quasi-phase matched gain sidebands in the strongly dispersion managed regime of a dispersion oscillating fiber as the power of a continuous-wave pump laser is increased over a certain threshold value. Very good agreement is found between the theoretical predictions and our experimental measurements.