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We report the generation of a stable, broadband frequency comb, covering more than 10 THz, using a normal dispersion fiber Fabry-Perot resonator with a high quality factor of 69 millions. This platform ensures robust and easy integration into photonic devices via FC/PC connectors, and feature quality factors comparable to those of microresonators. We demonstrate a passive mode-locking phenomenon induced by the coherent interaction of the Kerr effect and Brillouin scattering, which generates a frequency comb with a repetition rate exceeding the free spectral range of the cavity. This parametric process modulates the continuous wave (CW) pump and can then be transformed into a train of almost square-wave pulses thanks to the generation of switching waves. Our results are supported by advanced numerical simulations, and theoretical derivations that include the Brillouin effect in the Fabry-Perot configuration. The very high stable feature of this optical frequency comb lying in the GHz range is critical to several applications ranging from telecommunication, spectroscopy and advanced microwave generation.

This paper focuses on a Vision-based Landing task and presents the design and the validation of a dataset that would comply with the Operational Design Domain (ODD) of a Machine-Learning (ML) system. Relying on emerging certification standards, we describe the process for establishing ODDs at both the system and image levels. In the process, we present the translation of high-level system constraints into actionable image-level properties, allowing for the definition of verifiable Data Quality Requirements (DQRs). To illustrate this approach, we use the Landing Approach Runway Detection (LARD) dataset which combines synthetic imagery and real footage, and we focus on the steps required to verify the DQRs. The replicable framework presented in this paper addresses the challenges of designing a dataset compliant with the stringent needs of ML-based systems certification in safety-critical applications., Comment: 12th European Congress on Embedded Real Time Software and Systems, Jun 2024, Toulouse, France. arXiv admin note: text overlap with arXiv:2304.09938

We report a theoretical and experimental investigation of fiber Fabry-Perot cavities aimed at enhancing Kerr frequency comb generation. The modulation instability (MI) power threshold is derived from the linear stability analysis of a generalized Lugiato-Lefever equation. By combining this analysis with the concepts of power enhancement factor (PEF) and optimal coupling, we predict the ideal manufacturing parameters of fiber Fabry-Perot (FFP) cavities for the MI Kerr frequency comb generation. Our findings reveal a distinction between the optimal coupling for modulation instability and that of the cold cavity. Consequently, mirror reflectivity must be adjusted to suit the specific application. We verified the predictions of our theory by measuring the MI power threshold as a function of detuning for three different cavities.

We show how the recurrence phenomenon characteristic of the nonlinear stage of induced modulational instability in a passive fiber is affected by forcing. An additional linear amplification, even if extremely weak, induces separatrix crossing in correspondence of critical values of the gain around which the recurrence process considerably slows down, switching between dynamical orbits of different kind. We present evidence for such phenomenon in a fiber optics experiment where the gain is finely tuned by means of Raman amplification. A theoretical explanation is also provided that matches almost perfectly with our experimental results., Comment: 8 pages; 4 figures

We report the generation of broadband frequency combs in fiber Fabry-Perot resonators in the normal dispersion regime enabled by the excitation of switching waves. We theoretically characterise the process by means of a transverse linear stability analysis of the Lugiato-Lefever equation, enabling precise prediction of the switching waves' frequencies. Experimentally, we employed a pulsed-pump fiber Fabry-Perot resonator operating in the normal dispersion regime, integrated into an all-fiber experimental setup. The synchronisation mismatch and the influence of dispersion is thoroughly discussed, unveiling the potential to generate a frequency comb spanning over 15 THz bandwidth, specifically leveraging a flattened low dispersion cavity.

We report the generation of an optical frequency comb featuring 28 THz bandwidth, sustained by a single 80 fs cavity soliton recirculating in a fiber Fabry-Perot resonator. This large spectrum is comparable to frequency combs obtained with microresonators operating in the anomalous dispersion regime. Thanks to the compact design and the easy coupling of the resonator, cavity solitons can be generated in an all-fiber experimental setup with a continuous wave pumping scheme. We also observe the generation of a dispersive wave at higher frequencies which is supported by higher-order dispersion. These observations align remarkably well with both numerical simulations and the established theory of cavity solitons., Comment: 6 pages, 6 figures

We analyse the nonlinear dynamics of Fabry-Perot cavities of arbitrary finesse filled by a dispersive Kerr medium, pumped by a continuous wave laser or a synchronous train of flat-top pulses. The combined action of feedback, group velocity dispersion and Kerr nonlinearity leads to temporal instability with respect to perturbations at specified frequencies. We characterise the generation of new spectral bands by deriving the exact dispersion relation and we find approximate analytical expressions for the instabilities threshold and gain spectrum of modulation instability (MI). We show that, in contrast to ring-resonators, both the stationary solutions and the gain spectrum are dramatically affected by the duration of the pump pulse. We derive the extended Lugiato-Lefever equation for the Fabry-Perot resonator (FP-LLE) starting from coupled nonlinear Schr\"odinger equations (rather than Maxwell-Bloch equations) and we compare the outcome of the stability analysis of the two models. While FP-LLE gives overall good results, we show regimes that are not captured by the mean-field limit, namely the period-two modulation instability, which may appear in highly detuned or nonlinear regimes. We report numerical simulations of the generation of MI-induced Kerr combs by solving FP-LLE and the coupled Schr\"odinger equations.

As the interest in autonomous systems continues to grow, one of the major challenges is collecting sufficient and representative real-world data. Despite the strong practical and commercial interest in autonomous landing systems in the aerospace field, there is a lack of open-source datasets of aerial images. To address this issue, we present a dataset-lard-of high-quality aerial images for the task of runway detection during approach and landing phases. Most of the dataset is composed of synthetic images but we also provide manually labelled images from real landing footages, to extend the detection task to a more realistic setting. In addition, we offer the generator which can produce such synthetic front-view images and enables automatic annotation of the runway corners through geometric transformations. This dataset paves the way for further research such as the analysis of dataset quality or the development of models to cope with the detection tasks. Find data, code and more up-to-date information at https://github.com/deel-ai/LARD

We study modulational instability in a dispersion-managed system where the sign of the group-velocity dispersion is changed at uniformly distributed random distances around a reference length. An analytical technique is presented to estimate the instability gain from the linearized nonlinear Schr{\"o}dinger equation, which is also solved numerically. The comparison of numerical and analytical results confirms the validity of our approach. Modulational instability of purely stochastic origin appears. A competition between instability bands of periodic and stochastic origin is also discussed. We find an instability gain comparable to the conventional values found in a homogeneous anomalous dispersion fiber., Comment: 4 pages, 4 figure

We show that even small dissipation can strongly affect the Fermi-Pasta-Ulam-Tsingou recurrence phenomenon. Taking the fully nonlinear stage of modulational instability as an experimentally accessible example, we show that the linear attenuation induces the symmetry of the recurrence to be broken through separatrix crossing occurring at multiple critical values of the attenuation. We provide experimental evidence for this phenomenon in a fiber optics experiment designed in such a way that the effective losses can be carefully tailored by techniques based on Raman amplification.

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

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.

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, Comment: 12 pages, 6 figures submitted

The physics and applications of fiber-based supercontinuum (SC) sources have been a subject of intense interest over the last decade, with significant impact on both basic science and industry. New uses for SC sources are also constantly emerging due to their unique properties that combine high brightness, multi-octave frequency bandwidth, fiber delivery, and single-mode output. The last few years have seen significant research efforts focused on extending the wavelength coverage of SC sources towards the 2 to 20 $\mu$m molecular fingerprint mid-infrared (MIR) region and in the ultraviolet (UV) down to 100 nm, while also improving stability, noise and coherence, output power, and polarization properties. Here we review a selection of recent advances in SC 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 ultralow-noise coherent SC generation., Comment: Copyright 2021 Optica Publishing Group. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited

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.

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 generalised 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.

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., Comment: 9 pages, 10 figures

The piston problem, i.e. the dynamics in a uniform gas at rest under the action of a moving piston is fundamental problem of physics and a canonical case study in shock wave physics. We investigate theoretically and experimentally the analogous problem for a photon fluid, which turns out to be strongly influenced by the dispersive character of the problem. The experiment makes use of a fiber optics setup where an all-optically controlled quasi instantaneous change of frequency of the input light mimics the piston action. We show that the flow exhibits phase transitions which involve cross-over from regimes characterized by 2-shocks (pushing piston) to 2-rarefaction waves (retracting piston), with the appearance of cavitating states at critical amplitudes of the jump. Importantly, the appearance of vacuum points into the 2-shock marks the transition to a regime which is unique to the photon fluid. Our observations allow for the extensive and quantitative test of the state of the art description of the dispersive Riemann problem, i.e. Whitham modulation theory, applied to the universal defocusing nonlinear Schr\"odinger equation.

We examine the steady state and dynamic behaviour of an optical resonator comprised of two interlinked fibre loops sharing a common pump. A coupled Ikeda map models with great accuracy the field evolution within and exchange between both fibres over a single roundtrip. We find this supports a range of rich multi-dimensional 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-fibre resonators, which can be tailored by controlling the relative dispersion and resonance frequencies of the two fibre loops. Parametric instability gives birth to train of pulses with a peculiar period-doubling behavior.

We propose a new approach for modelling the functional behaviour of an Earth observation satellite. We leverage this approach in order to develop a safety critical software, a "telecommand verifier", that is in charge of checking onboard whether a sequence of instructions is safe for execution. This new service is needed in order to add more autonomy to satellites. To do so, we propose a new Domain Specific Modelling Language and the toolchain required for integration into an embedded software. This framework is based on the composition of deterministic finite state machines with safety conditions , timeouts, and transitions that accept durations as a parameter. It is able to generate code in the synchronous programming language Lustre from a high-level specification of the satellite. This gives a formal way to derive an event-based algorithm simulating the execution of telecommand sequence and, thereupon, a provably correct onboard verifier.

We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement techniques, whilst in oceanography we consider insights obtained from analysis of real-world ocean wave data and controlled experiments in wave tanks. Although significant progress in understanding rogue waves has been made based on an analogy between wave dynamics in optics and hydrodynamics, these comparisons have predominantly focused on one-dimensional nonlinear propagation scenarios. As a result, there remains significant debate about the dominant physical mechanisms driving the generation of ocean rogue waves in the complex environment of the open sea. Here, we review state-of-the-art of rogue wave studies in optics and hydrodynamics, aiming to clearly identify similarities and differences between the results obtained in the two fields. In hydrodynamics, we take care to review results that support both nonlinear and linear interpretations of ocean rogue wave formation, and in optics, we also summarise results from an emerging area of research applying the measurement techniques developed for the study of rogue waves to dissipative soliton systems. We conclude with a discussion of important future research directions.

Solitons on a finite a background, also called breathers, are solutions of the focusing nonlinear Schr\"odinger equation, which play a pivotal role in the description of rogue waves and modulation instability. The breather family includes Akhmediev breathers (AB), Kuznetsov-Ma (KM), and Peregrine solitons (PS), which have been successfully exploited to describe several physical effects. These families of solutions are actually only particular cases of a more general three-parameter class of solutions originally derived by Akhmediev, Eleonskii and Kulagin [Theor. Math. Phys. {\bf 72}, 809--818 (1987)]. Having more parameters to vary, this significantly wider family has a potential to describe many more physical effects of practical interest than its subsets mentioned above. The complexity of this class of solutions prevented researchers to study them deeply. In this paper, we overcome this difficulty and report several new effects that follow from more detailed analysis. Namely, we present the doubly periodic solutions and their Fourier expansions. In particular, we outline some striking properties of these solutions. Among the new effects, we mention (a) regular and shifted recurrence, (b) period doubling and (c) amplification of small periodic perturbations with frequencies outside the conventional modulation instability gain band.

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 H\"ansch et al. . Nowadays, OFCs are cornerstones of a wealth of further applications ranging from chemistry and biology to astrophysics and including molecular fingerprinting and LIDARs among others. Driven passive optical resonators constitute the ideal platform for OFCs generation in terms of compactness and low energy footprint. We propose here a new technique for generation of OFCs with tuneable repetition rate in externally driven optical resonators based on the gain-through-filtering process, a simple and elegant method, due to an 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.

Due to the difficulty to grow high quality semiconductors on ferromagnetic metals, the study of spin diffusion transport in Si was only limited to lateral geometry devices. In this work, by using ultra-high vacuum wafer-bonding technique, we have successfully fabricated metal semiconductor metal CoFeB/MgO/Si/Pt vertical structures. We hereby demonstrate pure spin-current injection and transport in the perpendicular current flow geometry over a distance larger than 2\mu m in n-type Si at room temperature. In those experiments, a pure propagating spin-current is generated via ferromagnetic resonance spin-pumping and converted into a measurable voltage by using the inverse spin-Hall effect occurring in the top Pt layer. A systematic study by varying both Si and MgO thicknesses reveals the important role played by the localized states at the MgO/Si interface for the spin-current generation. Proximity effects involving indirect exchange interactions between the ferromagnet and the MgO/Si interface states appears to be a prerequisite to establish the necessary out-of-equilibrium spin-population in Si under the spin-pumping action.

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.

We report an experimental observation of the collision between a linear wave propagating in the anomalous dispersion region of an optical fiber and a dark soliton located in the normal dispersion region. This interaction results in the emission of a new frequency component whose wavelength can be predicted using phase-matching arguments. The measured efficiency of this process shows a strong dependency with the soliton grayness and the linear wave wavelength, and is in a good agreement with theory and numerical simulations., Comment: 10 pages, 6 figures, 1 annexe

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 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 to induce a Moir\'{e}-like pattern, which modifies the geometric parametric instability gain observed in homogeneous GRIN fibers.

The possibility of tailoring the guidance properties of optical fibers along the same direction as the evolution of the optical field allows to explore new directions in nonlinear fiber optics. The new degree of freedom offered by axially-varying optical fibers enables to revisit well-established nonlinear phenomena, and even to discover novel short pulse nonlinear dynamics. Here we study the impact of meter-scale longitudinal variations of group velocity dispersion on the propagation of bright solitons and on their associated dispersive waves. We show that the longitudinal tailoring of fiber properties allows to observe experimentally unique dispersive waves dynamics, such as the emission of cascaded, multiple or polychromatic dispersive waves., Comment: Book Chapter in Handbook of Optical Fibers, Section: Solitons and Nonlinear waves in Optical Fibers

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists in a 1+1D generalized nonlinear Schr\"odinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.

We investigate the temporal photonic analogue of the dam-break phenomenon for shallow water by exploiting a fiber optics setup. We clearly observe the decay of the step-like input (photonic dam) into a pair of oppositely propagating rarefaction wave and dispersive shock wave. Our results show evidence for a critical transition of the dispersive shock into a self-cavitating state. The detailed observation of the cavitating state dynamics allows for a fully quantitative test of the Whitham modulation theory applied to the universal defocusing nonlinear Schroedinger equation.

A checkers-like model game with a simplified set of rules is studied through extensive simulations of agents with different expertise and strategies. The introduction of complementary strategies, in a quite general way, provides a tool to mimic the basic ingredients of a wide scope of real games. We find that only for the player having the higher offensive expertise (the dominant player ), maximizing the offensive always increases the probability to win. For the non-dominant player, interestingly, a complete minimization of the offensive becomes the best way to win in many situations, depending on the relative values of the defense expertise. Further simulations on the interplay of defense expertise were done separately, in the context of a fully-offensive scenario, offering a starting point for analytical treatments. In particular, we established that in this scenario the total number of moves is defined only by the player with the lower defensive expertise. We believe that these results stand for a first step towards a new way to improve decisions-making in a large number of zero-sum real games., Comment: 12 pages, 12 figures

We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schr\"odinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearised Floquet analysis.

We report the experimental observation of multiple dispersive waves emitted in the anomalous dispersion region of an optical fiber from a train of dark solitons. Each individual dispersive wave can be associated to one particular dark soliton of the train, using phase-matching arguments involving higher-order dispersion and soliton velocity. For a large number of dark solitons (>10), we observe the formation of a continuum associated with the efficient emission of dispersive waves., Comment: 5 pages, 4 figures