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In this paper we experimentally show parametric amplification and wavelength conversion in a custom manufactured dual-core highly nonlinear fiber. On-off gain > 10 dB and conversion efficiencies between −1 and −8.5 dB were measured for both cores. The estimated effective nonlinear parameter for the cores of the fiber are 6.6 W−1.km−1 and 6.3 W−1.km−1, while the zero-dispersion wavelength for the individual cores is shown to be relatively close from each other. Furthermore, complementary analytical and numerical results show that coupled cores fiber optical parametric amplifier offer the potential of wide-band gain even when they have significantly distinct zero-dispersion wavelengths.

We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD). We consider Gaussian and dichotomous colored stochastic processes. We resort to different analytical methods (namely, the cumulant expansion and the functional approach) and assess their reliability in estimating the MI gain of stochastic origin. If the power spectral density (PSD) of the GVD fluctuations is centered at null wavenumber, we obtain low-frequency MI sidelobes which converge to those given by a white noise perturbation when the correlation length tends to 0. If instead the stochastic processes are modulated in space, one or more MI sidelobe pairs corresponding to the well-known parametric resonance (PR) condition can be found. A transition from small and broad sidelobes to peaks nearly indistinguishable from PR-MI is predicted, in the limit of large perturbation amplitudes and correlation lengths of the random process. We find that the cumulant expansion provides good analytical estimates for small PSD values and small correlation lengths, when the MI gain is very small. The functional approach is rigorous only for the dichotomous processes, but allows us to model a wider range of parameters and to predict the existence of MI sidelobes comparable to those observed in homogeneous fibers of anomalous GVD, 12 pages, 6 figures submitted

We report the observation of the thermalization of the Fermi-Pasta-Ulam-Tsingou recurrence process in optical fibers. We show the transition from a reversible regime to an irreversible one, revealing a spectrally thermalized state. To do so, we actively compensate the fiber loss to make the observation of several recurrences possible. We inject into the fiber a combination of three coherent continuous waves, which we call Fourier modes, and a random noise. We enhance the noise-driven modulation instability process against the coherent one by boosting the input noise power level to speed up the evolution to the thermalization. The distributions of the Fourier modes power along the fiber length are recorded thanks to a multi-heterodyne time-domain reflectometer. At low input noise levels, we observe up to four recurrences. Whereas, at higher noise levels, the Fourier modes fade into the noise-driven modulation instability spectrum revealing that the process reached an irreversible thermalized state., Comment: 7 pages, 5 figures

International audience; We report the experimental observation of a modulation instability induced Kerr frequency comb in an all fiber Fabry–Pérot resonator. We fully characterized, in intensity and phase, the frequency comb using a commercial 10 MHz resolution heterodyne detection system to reveal more than 125 comb teeth within each of the modulation instability sidelobes. Moreover, we were able to reveal the fine temporal structure in phase and intensity of the output Turing patterns. The experimental results are generally in good agreement with numerical simulations.

International audience; We show that geometric parametric instability (GPI) in graded-index multimode fibers is strongly influenced by higher-order dispersion. By measuring the output spectrum for different core radii, we distinguish peaks generated by GPI from other coexisting parametric processes using phase-matching arguments and numerical simulations. We highlight for the first time a non-degenerate GPI process involving two pumps at different wavelengths.

L’avènement des fibres à cristal photonique dans les années 90 a été une révolution sur les plans tant scientifique qu’applicatif. Leur structuration transverse complexe leur confère en effet des propriétés de guidage inédites. Les fibres optiques topographiques introduites dans les années 2010 offrent, quant à elles, un degré de liberté supplémentaire grâce à leur structuration longitudinale contrôlée. Bien que leur potentiel applicatif soit loin d’être totalement exploré, elles ont déjà été largement exploitées en optique guidée.

Machine learning algorithms have opened a breach in the fortress of the prediction of high-dimensional chaotic systems. Their ability to find hidden correlations in data can be exploited to perform model-free forecasting of spatiotemporal chaos and extreme events. However, the extensive feature of these evolutions constitutes a critical limitation for full-size forecasting processes. Hence, the main challenge for forecasting relevant events is to establish the set of pertinent information. Here, we identify precursors from the transfer entropy of the system and a deep Long Short-Term Memory network to forecast the complex dynamics of a system evolving in a high-dimensional spatiotemporal chaotic regime. Performances of this triggerable model-free prediction protocol based on the information flowing map are tested from experimental data originating from a passive resonator operating in such a complex nonlinear regime. We have been able to predict the occurrence of extreme events up to 9 round trips after the detection of precursor, i.e., 3 times the horizon provided by Lyapunov exponents, with 92 % of true positive predictions leading to 60 % of accuracy.

Pulsed pumping configurations are becoming an interesting scheme for triggering optical frequency combs (OFC) in passive resonators due to their high peak power and to their low induced thermal loading [1] . A careful change of the repetition rate of these pumps compared to the repetition rate of the resonators is required to get an efficient OFC generation. Small mismatches, cumulated over many round trips, can lead to significant drifts leading to crucial modifications of the dynamics of the processes. A deep investigation of the impact of the synchronization mismatch on the complex building-up of OFC has never been reported yet. Here, for simplicity, we first restricted our study to the impact of the synchronization mismatch on modulation instability, because MI is the first and simplest nonlinear phenomenon appearing in a passive resonator and involved in the formation of OFCs. In its basic formulation, MI phenomenon depends only on the even terms of the dispersion [1] . However, in the real world experimentation, it has been reported that under synchronous pumping, and in the weak dispersion regime, the slope of the dispersion leads the system to become convectively unstable inducing a power asymmetry between the side-bands [2] , [3] . Here we worked in a strong dispersion regime where these effects can be neglected. The cavity is pumped with square shape pulses with 560 ps duration, just above the MI threshold, (other parameters are listed in the figure’s caption). We recorded the output spectra with an optical spectrum analyzer and the round-trip to round-trip temporal evolution with a commercial time lens system (Picoluz). The evolution of the output spectra as a function of the synchronization mismatch is depicted in Fig. 1(a) . For perfect synchronization (ΔT=0), narrow MI sidebands are generated at 28.21 GHz (see inset), in pretty good agreement with theoretical predictions (40 GHz). Perfect synchronization operation is confirmed through the stable evolution of the pulse train round-trips over round -trips ( fig. 1(c) ). By slightly changing the synchronization mismatch of only a few tens of fs, the position of the sideband is shifted by more than 12 GHz. For large mismatch values (Mismatch> 0.01 ps/m), the positions of the sidebands are unchanged and they experience an important spectral broadening. This significant modification of the dynamics of the process is directly related to convective instabilities [2] , [3] associated with the synchronization mismatch as can be seen in Fig. 1(b) and (d) . Theoretically, it means that, the first order dispersion term (β 1 ) must be considered in the phase matching relation [2] , [3] .

International audience; Fermi Pasta Ulam (FPU) recurrence process describes the ability of a nonlinear system to excite multiple modes and then to return to its initial state. In fiber optics, such process has been investigated within the framework of modulation instability (MI) [1], corresponding to growth of weak perturbations at the expense of a strong pump. Nonlinear stage of MI and FPU recurrences in optical fibers have been widely investigated and many results have been obtained with an efficient compensation of the losses [2]. Investigations on water waves [3] demonstrated that dissipation of their water tank forces the system to operate in a single regime. Here, we provide a deeper and complete study on the impact of dissipation of the FPU dynamics. Thanks to a fiber optics system, we have been able to control the loss coefficient, allowing us to trigger the different corresponding FPU regimes. Using a setup similar to the one in [2] and based on a multiple HOTDR system, we managed to record FPU recurrences in power and phase along the fiber length as a function of the loss, Fig. 1. The dissipation is controlled thanks to a counter-propagating Raman pump whose power is tuned to get an effective loss coefficient. A direct relation between the Raman pump power and effective loss coefficient is obtained, allowing a direct comparison between experiments (left panel) and simulations (right panel). Three different regions are discernible. In the 3 rd

With the development of high-speed optical telecommunications, also appeared optical amplifiers such as Ra-man amplifiers [1] , [2] . Allowing a distributed amplification and offering a wider gain bandwidth than other amplification techniques, there are preferably used in their counter-pumped regime (relative intensity noise transfer reduced). In the case of a pulsed signal to amplify, it is important to understand the transient effects of such an amplifier [3] . In this paper, the influence of short pulses width on transient and saturation effects of a counter-pumped Raman amplifier is thus experimentally reported.

International audience; We report recent results obtained with a novel optical fiber experimental setup based on a heterodyne optical time-domain reflectometer in the context of FPU recurrence process. Moreover, we actively compensate the dissipation of the system. We show that we can observe several FPU recurrences by monitoring the power and relative phase evolutions of the main discrete frequency components involved in the process.

The classical theory of modulation instability (MI) attributed to Bespalov-Talanov in optics and Benjamin-Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both, optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here., 9 pages, 10 figures

International audience; We present the theory of modulation instability induced by spectrally dependent losses (optical filters) in passive driven nonlinear fiber ring resonators. Starting from an Ikeda map description of the propagation equation and boundary conditions, we derive a mean-field model-a generalized Lugiato-Lefever equation-which reproduces with great accuracy the predictions of the map. The effects on instability gain and comb generation of the different control parameters such as dispersion, cavity detuning, filter spectral position, and bandwidth are discussed.

International audience; We report an experimental study on the backward-pumped Raman amplification of short pulses into a 20.3 km long optical fiber. We demonstrate that the gain and the pump saturation depend on the pulse duration. We also reveal that for short enough pulses, the amplification process remains linear, and very high peak powers, even larger than the Raman pump, are achievable. Numerical simulations reproduce the experimental results with excellent agreement.

International audience; We study modulational instability (MI) in optical fibers with random group velocity dispersion (GVD) generated by sharply localized perturbations of a normal GVD fiber that are either randomly or periodically placed along the fiber and that have random strength. This perturbation leads to the appearance of low frequency MI side lobes that grow with the strength of the perturbations, whereas they are faded by randomness in their position. If the random perturbations exhibit a finite average value, they can be compared with periodically perturbed fibers, where Arnold tongues appear. In that case, increased randomness in the strengths of the variations tends to affect the Arnold tongues less than increased randomness in their positions.

International audience; We report the experimental observation of more than four Fermi-Pasta-Ulam-Tsingou recurrences in an optical fiber thanks to an ultra-low loss optical fiber and to an active loss compensation system. We observe both regular (in-phase) and symmetry-broken (phase-shifted) recurrences, triggered by the input phase. Experimental results are confirmed by numerical simulations.

We report the first, to the best of our knowledge, experimental observation of doubly periodic first-order solutions of the nonlinear Schrödinger equation in optical fibers. We confirm, experimentally, the existence of A -type and B -type solutions. This is done by using the initial conditions that consist of a strong pump and two weak sidebands. The evolution of power and phase of the main spectral components is recorded using heterodyne time-domain reflectometry. Another important part of our experiment is active loss compensation. We reach a good agreement between theory and experiment.

International audience; We examine the steady state and dynamic behavior of an optical resonator comprised of two interlinked fiber loops sharing a common pump. A coupled Ikeda map models with great accuracy the field evolution within and exchange between both fibers over a single round trip. We find this supports a range of rich multidimensional bistability in the continuous wave regime, as well as previously unseen cavity soliton states. Floquet analysis reveals that modulation and parametric instabilities occur over wider domains than in single-fiber resonators, which can be tailored by controlling the relative dispersion and resonance frequencies of the two fiber loops. Parametric instability gives birth to a train of pulses with a peculiar period-doubling behavior.

In optical fibres, weak modulations can grow at the expense of a strong pump to form a triangular comb of sideband pairs, until the process is reversed. Repeated cycles of such conversion and back-conversion constitute a manifestation of the universal nonlinear phenomenon known as Fermi–Pasta–Ulam recurrence. However, it remains a major challenge to observe the coexistence of different types of recurrences owing to the spontaneous symmetry-breaking nature of such a phenomenon. Here, we implement a novel non-destructive technique that allows the evolution in amplitude and phase of frequency modes to be reconstructed via post-processing of the fibre backscattered light. We clearly observe how control of the input modulation seed results in different recursive behaviours emerging from the phase-space structure dictated by the spontaneously broken symmetry. The proposed technique is an important tool to characterize other mixing processes and new regimes of rogue-wave formation and wave turbulence in fibre optics.

International audience; We experimentally investigate two cycles of Fermi-Pasta-Ulam-Tsingou recurrence in optical fibers. Using three waves input we characterize the distance of maximum compression points against sideband amplitude and relative phase, outlining the qualitative changes of the dynamics due to separatrix crossing. Experimental results are in good agreement with numerical simulations and analytical predictions.

International audience; Modulational instability in passive optical resonators, the triggering mechanism of frequency comb and pulse train generation, is shown to exhibit transitions between regimes involving period-one (P1) versus period-two (P2) dynamical evolutions. The latter is a signature of parametric resonance occurring in the system, which can arise either from intrinsic cavity periodicity or from spatial modulation of the cavity parameters. We characterize the P1-P2 transition for both cases employing a fiber resonator where the intra-cavity fiber can be either uniform or dispersion modulated. The key element of our setup is a time lens which we exploit to resolve the temporal dynamics over successive round-trips, allowing crystal clear evidence of the existence of P1-P2 transitions for suitable changes of cavity parameters, as well as for the successful characterization of the relative temporal patterns. Our findings reveal new regimes where the averaged model known as Lugiato-Lefever equation turns out to be inadequate to explain the dynamics, whereas the results are correctly predicted and described on the basis of the full Ikeda map.

Optical frequency combs (OFCs), consisting of a set of phase-locked, equally spaced laser frequency lines, have enabled a great leap in precision spectroscopy and metrology since seminal works of Hänsch et al. Nowadays, OFCs are cornerstones of a wealth of further applications ranging from chemistry and biology to astrophysics and including molecular fingerprinting and light detection and ranging (LIDAR) systems, among others. Driven passive optical resonators constitute the ideal platform for OFC generation in terms of compactness and low energy footprint. We propose here a technique for the generation of OFCs with a tuneable repetition rate in externally driven optical resonators based on the gain-through-filtering process, a simple and elegant method, due to asymmetric spectral filtering on one side of the pump wave. We demonstrate a proof-of-concept experimental result in a fibre resonator, pioneering a new technique that does not require specific engineering of the resonator dispersion to generate frequency-agile OFCs., In normal dispersion, modulation instability, which is a precursor of Kerr combs, is forbidden due to phase mismatch. Here, the authors show the compensation of such phase mismatch by introducing frequency-dependent loss using a notch filter, hence leading to effective parametric gain and comb formation.

The piston problem, i.e. the dynamics of a uniform gas at rest under the action of a moving piston, is fundamental in shock wave physics [1,2]. In conservative systems, shock waves are regularized by the formation, owing to dispersion, of rapidly oscillating non-stationary structures, called dispersive shock waves (DSWs) [3–6].

Full experimental characterization of short pulses (with discrete line spectra) of the electric field (phase+intensity) in optical fibers is of high interest to get a detailed description of a large variety of nonlinear phenomena governed by the general nonlinear Schrodinger equation such as rogue wave formation or frequency comb generation. Recently, new techniques allowing real-time full-field characterization has been shown in the context of rogue waves [1] and laser dynamics [2]. However, experimental methods were limited so far to localized characterization of the field.

Optical frequency combs consist in a set of equally spaced mutually coherent laser frequency lines with a wealth of applications in the most diverse fields of photonics technology including metrology, astrophysics and molecular spectroscopy. Mode-locked lasers and passive driven resonators are the most relevant platforms for their generation. In Kerr resonators, in general frequency combs are generated through four wave mixing triggered by modulation instability (MI) in the anomalous dispersion regime [1]. In this case however the comb repetition rate is not tuneable but it is simply determined by the cavity free spectral range. We present here experimental results about a new method for frequency combs, with tuneable repetition rate, generation in normal dispersion externally driven passive optical resonators with Kerr (cubic) nonlinearity. We exploit the gain-through-losses (GTL) process to excite a modulation instability (MI) which initiates the comb formation. GTL enables energy transfer from a powerful pump field to sidebands frequencies thanks to frequency asymmetric spectral losses for signal and idler waves. The lossy modes themselves are counterintuitively amplified in virtue of the losses presence [2]. We performed an experiment considering a ring fibre resonator of 104 m length, made with a normal dispersion fiber with group velocity dispersion coefficient β 2 =0.5 ps2/km. The resonator was pumped at 1545 nm by a continuous wave laser. A fiber Bragg grating (FBG) with reflection peak located at 400 GHz frequency shift from the pump was used in reflection as a filter with spectral asymmetry with respect to the pump, inducing losses only to the signal (the filter causes no losses to the idler). The GTL MI causes first amplification of frequencies located close to the maximum losses (signal) and to their symmetric with respect to the pump wavelength (idler), which in turn generate higher order harmonics through a cascaded four-wave mixing process hence generating the comb (See Fig. 1(a)). The presence of the unavoidable filter phase contribution is responsible for the shift of the first sideband from the frequency corresponding to the maximum attenuation of the filter. The number of comb lines is limited by the low finesse of our resonator, but could be potentially improved in the future. In the time domain, the waveform corresponds to a train of pulses on the finite background (See Fig. 1(b)). The pulses have a repetition rate related to the inverse of the frequency shift between the first GTL sideband and the pump. Due to the fact that the GTL MI induces amplification of sidebands located close to the filter maximum losses frequency, by changing the detuning between pump and filter it is possible to tune the comb repetition rate. We have indeed verified a tuneability of the comb repetition rate by approximately 100 GHz.

The dynamical Casimir effect is the generation of pairs of real particles or photons from the vacuum as a result of a non-adiabatic change of a system parameter or boundary condition. As opposed to standard parametric amplification where the modulation occurs both in space and in time, this fundamental process requires a pure modulation in time, which makes its detection particularly challenging at optical frequencies. In this paper we experimentally demonstrate a realisation of the optical analogue of the mechanical dynamical Casimir effect in the near-infrared optical regime in a dispersion-oscillating photonic crystal fibre. The experiments are based on the equivalence of the spatial modulation of the fibre core diameter to a pure temporal modulation when this is considered in the co-moving frame of the travelling pump pulse. We provide evidence of optical dynamical Casimir effect by measuring quantum correlations between the spectrally resolved photon pairs. The non-classical nature of the measured light is supported by evidence of anti-bunching photon statistics.

Full-field longitudinal characterization of picosecond pulse train formation in optical fibers is reported. The spatio-temporal evolution is obtained via fast and non-invasive distributed measurements in phase and intensity of the main spectral components of the pulses. To illustrate the performance of the setup, we report, to the best of our knowledge, the first time-domain experimental observation of the symmetry breaking of Fermi-Pasta-Ulam recurrences. The experimental results are in good agreement with numerical simulations.

International audience; We experimentally demonstrate a novel method based on the gain-through-losses modulation instability process to generate frequency combs with tunable repetition rate in a normal dispersion externally driven passive fibre resonator.

We demonstrate, numerically, the generation of supercontinuum using a high-power ultrafast source at 1.06-μm wavelength and a nonlinear hollow-core fiber. We yield a system that is less sensitive to noise by pumping in the normal-dispersion regime, yet still achieves enhanced spectral broadening by exciting an optical soliton in the midinfrared region. The pump pulse goes through a series of nonlinear effects leading to a supercontinuum output that spans across the midinfrared, 0.5–4.2 μm Published version

Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence process describes the ability of a multimodal system experiencing complex nonlinear dynamics to come back to its initial state, instead of reaching thermalization. In optics, it has particularly been investigated in the context of modulation instability (MI) [1], which plays a key role in many nonlinear phenomena such as rogue wave formation or supercontinuum generation. Recently, we reported a novel experimental setup [2] consisting in a heterodyne time-domain detection system which allows to perform along an optical fiber distributed measurement in phase and intensity of a pump wave and its modulation sidebands. Thanks to an active compensation of the losses, it enabled the observation of two FPUT recurrences cycle for the first time (Fig. 1(b,c)). Moreover, Grinevich and Santini recently reported [3] an advanced theoretical model to predict the characteristics of these recurrences which have been verified experimentally in a 3D photorefractive crystal [4]. Based on the setup described in [2], we report here its verification in an optical fiber.

A new method of seeding X2 optical parametric converters with X3 fiber optical parametric sources is introduced. We demonstrate a tunable mid-infrared source operating at around 3 µm with the technique and discuss the potential of this architecture.

International audience; We report on a mode-locked erbium-doped fiber laser delivering highly-chirped pulses with several tens of nanojoules of energy around 1560 nm and its exploitation to efficiently pump a fiber optical parametric oscillator (FOPO), thus enabling picosecond pulse generation around 1700 nm. The laser cavity features a high normal dispersion and mode-locking is sustained using tailored spectral filtering combined with nonlinear polarization evolution and a semiconductor saturable absorber. Numerical simulations show that the laser dynamics is governed by a strong mode-locking mechanism compensating for the large spectral and temporal pulse evolution along the cavity. In the frame of high energy picosecond pulse generation around 1700 nm, we then demonstrate that using highly-chirped pulses as pump pulses allows for the efficient tuning of the FOPO idler wavelength between 1620 and 1870 nm. In addition, satisfying noise characteristics have been achieved both for the Er-laser and the FOPO, with respective relative intensity noises (RIN) of −154 and −140 dBc/Hz, thus paving the way for the use of such sources in ultrafast instrumentation.

International audience; We report the experimental observation of dispersive wave emission from gray solitons in an optical fiber. We also observed the nonlinear wave mixing occurring during the collision of a dark soliton and a linear wave.

International audience; We develop an effective 1+1D model describing nonlinear propagation in multimode graded-index fibers. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission.

International audience; We show that a periodic modulation of the diameter of a graded-index multimode fiber modifies the intrinsic self-imaging pattern, generating new spectral components in the geometric parametric instability gain spectrum.

We present a theoretical and numerical study of light propagation in graded-index (GRIN) multimode fibers where the core diameter has been periodically modulated along the propagation direction. The additional degree of freedom represented by the modulation permits us to modify the intrinsic spatiotemporal dynamics which appears in multimode fibers. More precisely, we show that modulating the core diameter at a periodicity close to the self-imaging distance allows us to induce a moir\'e-like pattern, whereas a longer periodicity induces an adiabatic modulation or the self-imaging pattern. This complex dynamics modifies the geometric parametric instability gain observed in homogeneous GRIN fibers by generating new spectral peaks.

International audience; We provide a direct observation of a period-doubling phenomenon associated to the modulation instability in both uniform and dispersion oscillating passive fiber ring cavities. This has been done by performing roundtrip-to-roundtrip measurements of the temporal pattern generated through the instability.