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International audience; We present first fiber Bragg grating (FBG) inscribed in polarization maintaining (PM) optical fiber with artificially anisotropic core achieved by an appropriate distribution of discrete germanium-doped areas in nanoscale. We proved that this FBG reveals unique properties. Its single-resonance spectral shape, strain and temperature sensitivities are similar to that for grating written in cylindrically symmetrical optical fiber, which indicates that it behaves as the grating fabricated in a non-PM fiber, whereas it is written in the fiber that preserves the orthogonal polarization components of the mode. Moreover, due to the relatively low birefringence of the fiber, the FBG is insensitive to the excited polarization state and twist, and only a negligible shift of the spectrum is noticeable with no changes in its shape. Thus, FBG inscribed in ZEBRA fiber is a kind of hybrid structure that can be used for all-fiber lasers that generate polarized wave, as well as for polarization fiber sensors and components with spectral insensitivity to random or intentional twist.

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.

International audience; We experimentally and numerical investigate the coexistence of Gain through Filtering and parametric instability in a fiber ring cavity, and their dependency from input power and cavity phase detuning.

International audience; Fiber-based supercontinuum (SC) generation has been a subject of intense interest over the last decade, with a significant impact on both basic science and industry. New uses for SC fiber sources are constantly emerging due to their unique properties that combine high brightness, visible to mid-infrared (MIR) wavelength coverage, fiber delivery, and single-mode output. Recent years have seen significant progress in overcoming the current shortcomings of SC sources in terms of wavelength coverage towards the 2 to 20 mu molecular fingerprint mid-infrared (MIR) region and in the ultraviolet (UV) down to 100 nm, while also improving stability, noise, coherence, power density, and robustness. In this talk, we will review all the recent advances in supercontinuum generation in a range of specialty optical fibers including: fluoride, chalcogenide, telluride, and silicon-core fibers for the MIR; UV-grade silica fibers and gas-filled hollow-core fibers for the UV range; and all-normal dispersion fibers for ultra-low noise coherent SC generation. Significant developments have been made in reaching target UV and MIR wavelength ranges, and the fiber SC has matured considerably to become a truly disruptive technology able to meet a range of societal and industrial challenges.

We report the development of a silica glass single-mode polarization-maintaining fiber with birefringence induced by artificial anisotropic glass in the circular core without any external stress zones or structured cladding. The fiber core is composed of silica and germanium-doped silica nanorods ordered in submicrometer interleaved layers. The fiber has a measured cut-off wavelength at 1113 nm, phase birefringence of 0.3×10−4, and an effective mode diameter of 10.5 µm at the wavelength of 1550 nm. The polarization extinction ratio in the fiber is 20 dB at 1550 nm. The fiber is compatible with the standard SMF-28 fiber and can be easily integrated using standard fusion splicing with losses of 0.1 dB.

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 a stable, robust, and compact passively mode-locked thulium-doped fiber laser that can be wavelength-stabilized between 1958 and 2008 nm using the appropriate chirped fiber Bragg grating as a wavelength-selective element.

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

We demonstrate a new, to the best of our knowledge, method of generating mid-infrared pulses by difference frequency mixing the Stokes pulse generated by four-wave mixing in a photonic crystal fiber with the remaining pump pulse. The Stokes pulses generated by four-wave mixing are inherently overlapped temporally and spatially with the pump pulse at the output of the fiber. Focusing this output into a nonlinear crystal phase matched for difference frequency generation between the pump and Stokes pulses results in a simple method of generating mid-infrared pulses. With a pump source at 1.064 µm, and a photonic crystal fiber engineered to generate Stokes pulses at approximately 1.65 µm, we generate 160 mW of mid-infrared light at approximately 3 µm through difference frequency generation.

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.

Predicting complex nonlinear dynamical systems has been even more urgent because of the emergence of extreme events such as earthquakes, volcanic eruptions, extreme weather events (lightning, hurricanes/cyclones, blizzards, tornadoes), and giant oceanic rogue waves, to mention a few. The recent milestones in the machine learning framework offer a new prospect in this area [1] , [2] . For a high dimensional chaotic system, increasing the system’s size causes an augmentation of the complexity and, finally, more nodes in the network. Here, we propose a new supervised machine learning strategy to forecast bursts occurring in the turbulent regime of a fiber ring cavity. Indeed, we have recently demonstrated [3] that this system can continuously transform a stable periodic pattern with a well-defined frequency comb into a turbulent state via a spatiotemporal intermittency mechanism. Figure 1a ) shows an illustration of this transition. Even though a turbulent evolutions, an interesting feature is the persistent long-range correlation in the dynamics [3] . The system can then be seen as adjacent subdomains. Owing to this feature, instead of predicting the whole system, we use appropriate tools of chaos theory to identify recurrent picture in the past at the same location of the bursts. Figure 1b ) shows the statistics on the bursts (red) and the profiles detected at a previously computed time lag (blue). We have taken advantage of the apparent causality to make an association precursors-pulses. Knowing when and where the bursts may emerge, a fair question is " What is coming? ". On the other hand, as shown in Figure 1c ), no correlation can be found between the profile (amplitude and size) of the precursors of the corresponding pulse. However, using the pulses/precursors pairs to perform supervised learning with a recurrent neural network, we have obtained a high correlated map between the actual observation and the prediction, as can be seen in Figure 1d ). As our strategy deals with intrinsic characteristic quantities of the dynamical behavior, the pre-trained network can trigger the forecasting even for a more extensive system, provided that all the other parameters are the same.

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.

All-optical wavelength conversion of dual-polarization signals over 9.6 nm in C+L-band is demonstrated in a twin-core highly nonlinear fibre for the first time. Conversion efficiencies between -1 dB and -8.5 dB for both cores are obtained simultaneously.

We experimentally investigate the influence of optical fiber loss on the dynamics of the FPU process. We show that the symmetry of the FPU process can be broken several times by tuning the fiber loss value.

We propose a new counterintuitive mechanism of modulation instability: asymmetric, with respect to pump, losses can induce gain of sideband modes in absence of phase matching. The mechanism is experimentally demonstrated to generate frequency combs with tunable frequencies.

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.

We report the first experimental observation of four Fermi-Pasta-Ulam-Tsingou recurrences along an optical fiber thanks to an active compensation of the losses.

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.