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We report on numerical predictions and experimental observations of a novel type of temporal localized dissipative structures that manifest themselves in the self-defocusing regime of driven nonlinear optical resonators with two polarization modes. These chiral dissipative solitons, which we term polarization faticons, break both temporal and polarization symmetry and consist of two bright lobes of opposite polarization handedness, interlocked by a domain wall. Our study reveals that faticons are connected to a vectorial modulational instability, from which they can be excited through a collapsing dynamic. Faticons could offer a novel pathway for frequency comb generation in normal dispersion resonators. More generally, they offer new fundamental insights into vectorial localized dissipative structures and could be relevant to other multi-component dissipative systems., Comment: 8 pages

We report on the theoretical analysis as well as the numerical simulations about the nonlinear dynamics of cavity solitons in a passive Kerr resonator operating in the multistable regime under the condition of a sufficiently strong pump. In this regime, the adjacent tilted cavity resonances might overlap, thus leading to the co-existence of combinatory states of temporal cavity solitons and the extended modulation instability patterns. Very interestingly, the cavity in the regime of multistablity may sustain distinct families of cavity solitons, vividly termed as super cavity solitons with much higher intensity and broader spectra if compared with those in the conventional bi-stable regime. The description of such complex cavity dynamics in the multstable regime requires either the infinite-dimensional Ikeda map, or the derived mean-field coupled Lugiato-Lefever equations by involving the contributing cavity resonances. With the latter model, for the first time, we revealed the existence of different orders of super cavity solitons, whose stationary solutions were obtained by using the Newton-Raphson algorithm. Along this line, with the continuation calculation, we have plotted the Hopf / saddle-node bifurcation curves, thus identifying the existing map of the stable and breathing (super) cavity solitons. With this defined parameter space, we have proposed an efficient method to excite and switch the super cavity solitons by adding an appropriate intensity (or phase) perturbation on the pump. Such deterministic cavity soliton manipulation technique is demonstrated to underpin the multi-level coding, which may enable the large capacity all-optical buffering based on the passive fiber ring cavities., Comment: 11 pages,5 figures

Simultaneously increasing the spectral bandwidth and average output power of mid-infrared supercontinuum sources remains a major challenge for their practical application. We address this issue through experimental developments of short tapered rods made from distinct glasses (silica, tellurite and chalcogenide families) for covering distinct spectral regions by means of supercontinuum generation in the femtosecond regime. We demonstrate that ultra-broadband spectral broadenings over the entire glass transmission window can be achieved in few-cm-long segments of tapered rods by a fine adjustment of input modal excitation. As the most significant example, our simple post-processing of glass rods unlocks the high-power regime for fiber-based supercontinuum sources beyond the 10 micron waveband. By using a 5-cm-long tapered Ge-Se-Te rod pumped at 6 micron, a supercontinuum spanning from 2 to 15 micron (3 to 14 micron) with an average output power of 93 mW (170 mW) is obtained for 500-kHz (1-MHz) repetition rate. Spectral coverages from the visible to 5 micron, and from the visible to 2.7 micron, are also reported with tapered rods made of tellurite and silica glasses, respectively. Numerical simulations are used to confirm the main contribution of the fundamental mode in the ultrafast nonlinear dynamics, as well as the possible preservation of coherence features. Our study opens a new route towards the power scaling of high-repetition-rate fiber supercontinuum sources over the full molecular fingerprint region.

The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in a from of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive media, such as hydrodynamics, optics, plasma, mechanical systems, electric transmission lines, and Bose-Einstein condensates, while its impact on applied sciences is steadily growing. Following the linear stability analysis of weakly nonlinear waves, the classical MI dynamics, can be triggered when a pair of small-amplitude sidebands are excited within a particular frequency range around the main peak frequency. That is, a three-wave system is usually required to initiate the wave focusing process. Breather solutions of the nonlinear Schr\"odinger equation (NLSE) revealed that MI can generate much more complex localized structures, beyond the three-wave system initialization approach or by means of a continuous spectrum. In this work, we report an experimental study for deep-water surface gravity waves asserting that a MI process can be triggered by a single unstable sideband only, and thus, from a two-wave process when including the contribution of the peak frequency. The experimental data are validated against fully nonlinear hydrodynamic numerical wave tank simulations and show very good agreement. The long-term evolution of such unstable wave trains shows a distinct shift in the recurrent Fermi-Pasta-Ulam-Tsingou focusing cycles, which are captured by the NLSE and fully nonlinear hydrodynamic simulations with minor distinctions.

We present theoretical and experimental evidence of high-gain far-detuned nonlinear frequency conversion, extending towards both the visible and the mid-infrared, in a few-mode graded-index silica fiber pumped at 1.064 $\mu$m, and more specifically achieving gains of hundreds of dB per meter below 0.65 $\mu$m and beyond 3.5 $\mu$m. Our findings highlight the potential of graded-index fibers in terms of strong modal confinement over an ultrabroad spectral range for enabling high-gain wavelength conversion. Such advancements require an accurate interpretation of intramodal and intermodal four-wave mixing processes., Comment: 8 pages, 4 figures

We numerically investigate azimuthal modulation instability in an optical fiber supporting orbital angular momentum modes only, i.e. a vortex fiber, by means of the scalar multimode unidirectional pulse propagation equation. We demonstrate that the nonlinear stage of azimuthal modulation instability taking place in such a ring-core fiber, with anomalous rotation group-velocity dispersion, can be simply described by analytical breather solutions of the corresponding nonlinear Schr\"odinger equation. Azimuthal soliton dynamics and nonlinear compression are also unveiled as well as specific spatial rotating features as a function of the topological charge involved. Our results open a new route for studying transverse nonlinear waves in optical fibers and for manipulating orbital angular momentum states.

We study a re-configurable nonreciprocal fiber ring cavity setup to generate tunable optical frequency combs. Coherent combs can be obtained by finely exploiting bi-chromatic Brillouin lasing and cascaded four-wave mixing in the nonlinear fiber cavity. We introduce a numerical model of the cavity system, which is validated by comparisons with experiments. Our work shows the importance of the mode pulling effect, controlled by the pump laser detuning, in setting the dynamics of the comb. This effect along with the impact of multimode lasing had been overlooked in previous fiber experiments. We discuss these limitations and devise several scaling laws for these system.

We provide a complete analysis, from theory to experiment, of the spontaneous emergence of a discretized conical wave of X-type (i.e., a localized 2D+1 space-time wavepacket) when an intense ultrashort pulse nonlinearly propagates in a multimode fiber. In particular, we reveal that this spatiotemporal phenomenon corresponds to broadband intermodal dispersive wave emission from an unsteady localized wave structure formed during nonlinear propagation. Theoretical phase-matching predictions are experimentally and numerically confirmed in a commercially-available step-index multimode fiber. Our results provide a general understanding of phase-matched radiations emitted by nonlinear waves in multidimensional dispersive optical system., Comment: 6 pages, 4 figures

Near-ideal four wave mixing dynamics are observed in a nonlinear Schr{\"o}dinger equation system using a new experimental technique associated with iterated sequential initial conditions in optical fiber. This novel approach mitigates against unwanted sideband generation and optical loss, extending the effective propagation distance by two orders of magnitude, allowing Kerr-driven coupling dynamics to be seen over 50 km of optical fiber using only one short fiber segment of 500 m. Our experiments reveal the full dynamical phase space topology in amplitude and phase, showing characteristic features of multiple Fermi-Pasta-Ulam recurrence cycles, stationary wave existence, and the system separatrix boundary. Experiments are shown to be in excellent quantitative agreement with numerical solutions of the canonical differential equation system describing the wave evolution.

Space-time light structuring has emerged as a very powerful tool for controlling the propagation dynamics of pulsed beam. The ability to manipulate and generate space-time distributions of light has been remarkably enhanced in past few years, letting envision applications across the entire spectrum of optics. Space-time optical wavepackets manipulated up to now are usually two-dimensional objects (one space dimension and time) whose mode-resolved spectra lie in a conical section. Using simple symmetry and invariance principles, we show that such wavepackets are particular cases of more general three-dimensional structures whose space-time frequencies lie on quadric surfaces. Our proposed framework allows here classifying space-time wavepackets localized in all dimensions, in any group-velocity dispersion regime, both in bulk and waveguides. Particular emphasis is placed on orbital angular momentum-carrying space-time wavepackets. This unprecedented theoretical approach opens the way for versatile synthesizing of space-time optics., Comment: 7 pages, 3 figures

Propagation-invariant or non-diffracting optical beams have received considerable attention during the last two decades. However, the pulsed nature of light waves and the structured property of optical media like waveguides are often overlooked. We here present a four-dimensional spatiotemporal approach that extends and unifies both concepts of conical waves and helicon beams, mainly studied in bulk media. By taking advantage of tight correlations between the spatial modes, the topological charges, and the frequencies embedded in an optical field, we reveal propagation-invariant (dispersion- and diffraction-free) space-time wavepackets carrying orbital angular momentum (OAM) that evolve on spiraling trajectories in both time and space in bulk media or multimode fibers. Besides their intrinsic linear nature, we show that such wave structures can spontaneously emerge when a rather intense ultrashort pulse propagates nonlinearly in OAM modes. With emerging technologies of pulse/beam shaping, multimode fibers and modal multiplexing, our proposed scheme to create OAM-carrying helicon wavepackets could find a plethora of applications.

Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schr\"odinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics.

Mutual interaction of localized nonlinear waves, e.g. solitons and modulation instability patterns, is a fascinating and intensively-studied topic of nonlinear science. In this research report, we report on the observation of a novel type of breather interaction in telecommunication optical fibers, in which two identical breathers propagate with opposite group velocities. Under certain conditions, neither amplification nor annihilation occur at the collision point and most interestingly, its amplitude is almost equal to another maximum of either oscillating breather. This ghost-like breather interaction dynamics can be fully described by the N-breather solution of the nonlinear Schr\"odinger equation.

We report on the experimental and numerical observation of polarization modulation instability (PMI) in a nonlinear fiber Kerr resonator. This phenomenon is phased-matched through the relative phase detuning between the intracavity fields associated with the two principal polarization modes of the cavity. Our experimental investigation is based on a 12-m long fiber ring resonator in which a polarization controller is inserted to finely control the level of intra-cavity birefringence. Depending on the amount of birefringence, the temporal patterns generated via PMI are found to be either stationary or to exhibit a period-doubled dynamics. Experimental results are in good agreement with numerical simulations based on an Ikeda map for the two orthogonally polarized modes. Our study provides new insights into the control of modulation instability in multimode Kerr resonators. Modulation instability (MI) is a nonlinear phenomenon characterized by the exponential growth and evolution of periodic perturbations on top of an intense continuous-wave (cw) laser beam [1, 2]. Underpinned by a nonlinearly phase-matched parametric process, it is associated with a transfer of energy from a narrow pump frequency component to a pair of sidebands arranged symmetrically around the pump. In single-pass optical fiber propagation, MI can be naturally phase-matched through a balance between anomalous group-velocity dispersion and Kerr nonlinearity [1, 2]. In contrast, more general phase-matching conditions are possible in the context of passive Kerr resonators, such as fiber ring cavities, because of the crucial role played by the systems' boundary conditions [3-5]. Various configurations of MI have been investigated in that context, including MI in the normal dispersion regime, MI via bichromatic or incoherent driving, as well as competition between MI and Faraday or period-doubled (P2) instabilities [6--12]. Moreover, at variance with single-pass propagation, MI in Kerr resonators can lead to the emergence of stationary periodic (Turing) patterns; such patterns are now understood to be intimately related to temporal cavity solitons and microresonator optical frequency combs [13--16]. Birefringence, and nonlinear coupling between the polarization components of light, is also known to contribute to the phase-matching of parametric processes. This leads to polarization MI (PMI) and the emergence of vector temporal patterns [17-19]. In driven resonators, PMI has only been investigated theoretically so far [20-22], but recent demonstrations of orthogonally-polarized dual comb generation in microresonators are sparking a renewed interest in this process [23]. In this Letter, we report on the direct experimental observation of PMI in a passive Kerr resonator. Our experimental test-bed is based on a normally dispersive fiber ring cavity that incorporates a polarization controller for adjustment of the intra-cavity birefringence. This localized birefringence gives rise to a relative phase detuning between the two orthogonal polarization modes of the cavity, which in turn affects the frequency shift of the PMI sidebands. We also find that birefringence can lead to period-doubled (P2) dynamics, characterized by a two round-trip cycle. Our experimental results are in good agreement with theoretical predictions and numerical simulations based on an iterative two-component Ikeda map. The experimental setup is displayed in Fig. 1(a). It consists of a L = 12-m long passive fiber ring cavity with a finesse F of about 27, mainly built out of spun fiber. To avoid competition with scalar MI [2], we have built a cavity with normal group-velocity dispersion estimated to 2 = 47 ps 2 /km, a value large enough to neglect third-order dispersion. Also, the use of a spun fiber (nearly isotropic) avoids group-velocity mismatch between the polarization components. Additionally, to prevent any additional source of bending-induced birefringence, the fiber was carefully off-spooled and wound directly on our experimental board with a large 50-cm diameter. We estimate that this causes a birefringence $\Delta$n no greater than 10 --8 [24], which can be neglected in our study.

Multimode optical fibers has emerged as the platform that will bridge the gap between nonlinear optics in bulk media and in single-mode fibers. However, the understanding of the transition between these two research fields still remains incomplete despite numerous investigations of intermodal nonlinear phenomena and spatiotemporal coupling. Some of the striking phenomena observed in bulk media with ultrashort and ultra-intense pulses (i.e., conical emission, harmonic generation and light bullets) require a deeper insight to be possibly unveiled in multimode fibers. Here we generalize the concept of conical waves described in bulk media towards structured media, such as multimode optical fibers, in which only a discrete and finite number of modes can propagate. The modal distribution of optical fibers provides a quantization of conical emission (e.g., quantized X-waves) through phase-matched resonant radiations (i.e., dispersive waves) seeded by optical shocks or ultrashort wave structures during spatiotemporal compression stages. Such quantized dispersion- and diffraction-free waves are generated when a rather intense short pulse propagates nonlinearly in a multimode waveguide, whatever the dispersion regime and waveguide geometry. Future nonlinear experiments in commercially-available multimode fibers could reveal different forms of conical emission and an easy control of supercontinuum light bullets., Comment: 6 pages, 3 figures

We present both theoretical description and experimental observation of the modulation instability process and related rogue breathers in the case of stationary periodic background waves, namely cnoidal and dnoidal envelopes. Despite being well-known solutions of the nonlinear Schrodinger equation, the stability of such background waves has remained unexplored experimentally until now, unlike the fundamental plane wave. By means of two experimental setups, namely, in nonlinear optics and hydrodynamics, we report on quantitative measurements of spontaneous modulation instability gain seeded by input random noise, as well as the formation of rogue breather solutions induced by a coherent perturbation. Our results confirm the generalization of modulation instability when more complex background waves are involved.

We analyse the temporal properties of the optical pulse wave that is obtained by applying a set of spectral $\pi/2$ phase shifts to continuous-wave light that is phase-modulated by a temporal sinusoidal wave. We develop an analytical model to describe this new optical waveform that we name 'besselon'. We also discuss the reduction of sidelobes in the wave intensity profile by means of an additional spectral $\pi$ phase shift, and show that the resulting pulses can be efficiently time-interleaved. The various predicted properties of the besselon are confirmed by experiments demonstrating the generation of low-duty cycle, high-quality pulses at repetition rates up to 28 GHz.

Material characteristics and input-field specifics limit the controllability of nonlinear electromagnetic-field interactions. As these nonlinear interactions could be exploited to create strongly localized bright and dark waves, such as nonlinear surface polaritons, ameliorating this limitation is important. We present our approach to amelioration, which is based on a surface-polaritonic waveguide reconfiguration that enables excitation, propagation and coherent control of coupled dark rogue waves having orthogonal polarizations. Our control mechanism is achieved by finely tuning laser-field intensities and their respective detuning at the interface between the atomic medium and the metamaterial layer. In particular, we utilize controllable electromagnetically induced transparency (EIT) windows commensurate with surface-polaritonic polarization-modulation instability to create symmetric and asymmetric polaritonic frequency combs associated with dark localized waves. Our method takes advantage of an atomic self-defocusing nonlinearity and dark rogue-wave propagation to obtain a sufficient condition for generating phase singularities. Underpinning this method is our theory which incorporates dissipation and dispersion due to the atomic medium being coupled to nonlinear surface-polaritonic waves~(SPWs). Consequently, our waveguide configuration acts as a bimodal polaritonic frequency-comb generator and a high-speed phase rotator, thereby opening prospects for phase singularities in nanophotonic and quantum communication devices.

We investigate in detail the qualitative similarities between the pulse localization characteristics observed using sinusoidal phase modulation during linear propagation and those seen during the evolution of Akhmediev breathers during propagation in a system governed by the nonlinear Schr{\"o}dinger equation. The profiles obtained at the point of maximum focusing indeed present very close temporal and spectral features. If the respective linear and nonlinear longitudinal evolutions of those profiles are similar in the vicinity of the point of maximum focusing, they may diverge significantly for longer propagation distance. Our analysis and numerical simulations are confirmed by experiments performed in optical fiber.

We theoretically and experimentally demonstrate a new electro-optic linear approach to generate high repetition-rate picosecond pulse trains. This simple cavity-free method is based on a temporal sinusoidal phase modulation combined with a triangular spectral phase processing. Experimental results validate the concept at repetition rates ranging from 10 GHz up to 40 GHz with the generation of background-free pulse trains made of nearly Gaussian Fourier-transform limited pulses.

Spontaneous emergence of self-organized patterns and their bifurcations towards a regime of complex dynamics in non-equilibrium dissipative systems is a paradigm of phase transition. Indeed, the behavior of these patterns in the highly nonlinear regime remains less explored, even in recent high-quality-factor resonators such as Kerr-nonlinear optical ones. Here, we investigate theoretically and experimentally the alteration of the resulting Kerr frequency combs from the weakly to the highly nonlinear regime, in the frameworks of spatiotemporal chaos, and dissipative phase transitions. We reveal the existence of a striking and easily accessible scenario of spatiotemporal chaos, free of cavity solitons, in a monostable operating regime, wherein a transition to amplitude turbulence via spatiotemporal intermittency is evidenced. Moreover, statistics of the light bursts in the resulting turbulent regime unveils the existence of rogue waves as extreme events characterized by long-tail statistics.

We present a detailed study of the phase properties of rational breather waves observed in the hydrodynamic and optical domains, namely the Peregrine soliton and related second-order solution. At the point of maximum compression, our experimental results recorded in a wave tank or using an optical fiber platform reveal a characteristic phase shift that is multiple of $\pi$ between the central part of the pulse and the continuous background, in agreement with analytical and numerical predictions. We also stress the existence of a large longitudinal phase shift across the point of maximum compression.

The data recorded in optical fiber [1] and in hydrodynamic [2] experiments reported the pioneering observation of nonlinear waves with spatiotemporal localization similar to the Peregrine soliton are examined by using nonlinear spectral analysis. Our approach is based on the integrable nature of the one-dimensional focusing nonlinear Schrodinger equation (1D-NLSE) that governs at leading order the propagation of the optical and hydrodynamic waves in the two experiments. Nonlinear spectral analysis provides certain spectral portraits of the analyzed structures that are composed of bands lying in the complex plane. The spectral portraits can be interpreted within the framework of the so-called finite gap theory (or periodic inverse scattering transform). In particular, the number N of bands composing the nonlinear spectrum determines the genus g = N - 1 of the solution that can be viewed as a measure of complexity of the space-time evolution of the considered solution. Within this setting the ideal, rational Peregrine soliton represents a special, degenerate genus 2 solution. While the fitting procedures employed in [1] and [2] show that the experimentally observed structures are quite well approximated by the Peregrine solitons, nonlinear spectral analysis of the breathers observed both in the optical fiber and in the water tank experiments reveals that they exhibit spectral portraits associated with more general, genus 4 finite-gap NLSE solutions. Moreover, the nonlinear spectral analysis shows that the nonlinear spectrum of the breathers observed in the experiments slowly changes with the propagation distance, thus confirming the influence of unavoidable perturbative higher order effects or dissipation in the experiments.

We theoretically and experimentally investigate the design of a high-repetition rate source delivering well-separated picosecond pulses thanks 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 NLS equations for which the usual normally dispersive defocusing regime is turned in a focusing temporal lens through a degenerated cross-phase modulation effect. More precisely, the temporal compression of the initial beating is performed by the combined effects of normal GVD and XPM-induced nonlinear phase shift yield by an intense beat-signal on its weak out-of-phase replica copropagating with orthogonal polarizations. This adiabatic reshaping process allows us to generate a 40GHz well-separated 3.3ps pulse train at 1550nm in a 5km long normally dispersive fiber.