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The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in the form 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. It is well-known that 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, consisting of the carrier wave together with a pair of unstable sidebands, is usually adopted to initiate the wave focusing process in a numerical or laboratory experiment. Breather solutions of the nonlinear Schrödinger 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, initialized 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 some distinctions. [ABSTRACT FROM AUTHOR]

Highly coherent frequency combs are of crucial importance for optical synthesis and metrology, spectroscopy, laser ranging, and optical communications. Kerr combs, generated via cascaded nonlinear frequency conversion in a passive optical cavity, typically offer high repetition rates, which is essential for some of these applications. Recently, new ways of generating Kerr combs combining Kerr and Brillouin effects have emerged with the aim of improving some performances, especially in the fiber cavity platform. Direct coherent pumping is replaced by lasing on specific cavity modes, offering easily adjustable repetition rates, and enhanced coherence by Brillouin purification. In this study, such a scheme is implemented and investigated in a non‐reciprocal cavity. Highly coherent combs are demonstrated by finely controlling bi‐chromatic Brillouin lasing and the Kerr comb parameters. A suitable numerical model is introduced to account for the interplay between Brillouin scattering, Kerr effect, and cavity resonant feedback. Quantitative agreements with experiments reveal the importance of the pump lasers detuning in setting the comb's properties, through the mode pulling effect. This phenomenon, along with multi‐mode lasing that impedes the coherence, is not studied in previous fiber‐based demonstrations. These limitations are discussed, and several scaling laws are devised. [ABSTRACT FROM AUTHOR]

Abstract: This paper is aimed at providing an overview on recent theoretical and experimental works in which a thermodynamic description of the incoherent regime of supercontinuum generation has been formulated. On the basis of the wave turbulence theory, we show that this highly nonlinear and quasi-continuous-wave regime of supercontinuum generation is characterized by two different phenomena. (i) A process of optical wave thermalization ruled by the four-wave mixing effects: The spectral broadening inherent to supercontinuum generation is shown to result from the natural tendency of the optical field to reach its thermodynamic equilibrium state, i.e., the state of maximum nonequilibrium entropy. This approach also reveals the existence of a thermodynamic phase-matching. (ii) The generation of spectral incoherent solitons induced by the Raman effect in the low frequency part of the supercontinuum spectrum. Contrary to conventional solitons, spectral incoherent solitons do not exhibit a confinement in the space–time domain, but solely in the frequency domain. They owe their existence to the causality property underlying the Raman response function. Both phenomena of optical wave thermalization and spectral incoherent solitons are described in detail by the wave turbulence theory. In this way, we provide a unified nonequilibrium thermodynamic description of the incoherent regime of supercontinuum generation. [Copyright &y& Elsevier]

Abstract: We provide an overview of our recent work on the shaping and stability of optical continua in the long pulse regime. Fibers with normal group-velocity dispersion at all-wavelengths are shown to allow for highly coherent continua that can be nonlinearly shaped using appropriate initial conditions. In contrast, supercontinua generated in the anomalous dispersion regime are shown to exhibit large fluctuations in the temporal and spectral domains that can be controlled using a carefully chosen seed. A particular example of this is the first experimental observation of the Peregrine soliton which constitutes a prototype of optical rogue-waves. [Copyright &y& Elsevier]

Abstract: Considering a simple one-dimensional nonlinear Schrödinger optical model, we study the existence of rogue wave events in the highly incoherent state of the system and compare them with the recently identified hierarchy of rational soliton solutions. We show that rogue waves can emerge in the genuine turbulent regime and that their coherent deterministic description provided by the rational soliton solutions is compatible with an accurate statistical description of the random wave provided by the wave turbulence theory. Furthermore, the simulations reveal that even in the weakly nonlinear regime, the nonlinearity can play a key role in the emergence of an individual rogue wave event in a turbulent environment. [Copyright &y& Elsevier]

The purpose of this paper is to demonstrate the quasi-phase-matching of third harmonic generation process in optical fibers using refractive-index gratings. We compare conversion efficiency calculated with analytical coupled-modes theory and numerical approach employing a system of coupled generalized nonlinear Schrödinger equation. Moreover, we show that introducing the phase matching condition that takes into account the nonlinear contribution to propagation constants significantly increases the conversion efficiency by several orders of magnitude. Finally, we optimize the grating constant to maximize conversion efficiency. [ABSTRACT FROM PUBLISHER]

Abstract: We provide some general physical insights into the emergence of rogue wave events from optical turbulence by analyzing the long term evolution of the field. Depending on the amount of incoherence in the system (i.e., Hamiltonian), we identify three turbulent regimes that lead to the emergence of specific rogue wave events: (i) persistent and coherent rogue quasi-solitons, (ii) intermittent-like rogue quasi-solitons that appear and disappear erratically, and (iii) sporadic rogue waves events that emerge from turbulent fluctuations as bursts of light or intense flashes. [ABSTRACT FROM AUTHOR]

Multimode optical fibers are essential in bridging the gap between nonlinear optics in bulk media and single-mode fibers. The understanding of the transition between the two fields remains complex due to intermodal nonlinear processes and spatiotemporal couplings, e.g., some striking phenomena observed in bulk media with ultrashort pulses have not yet been unveiled in such waveguides. 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. Such propagation-invariant optical wave packets can be linearly generated, in the limit of superposed monochromatic fields, by shaping their spatiotemporal spectrum, whatever the dispersion regime and waveguide geometry. Moreover, they can also spontaneously emerge when a rather intense short pulse propagates nonlinearly in a multimode waveguide, their finite energy is also associated with temporal dispersion. The modal distribution of optical fibers then provides a discretization of conical emission (e.g., discretized X waves). Future experiments in multimode fibers could reveal different forms of dispersion-engineered conical emission and supercontinuum light bullets. [ABSTRACT FROM AUTHOR]

Material characteristics and input-field specifics limit 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 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. Consequently, our waveguide configuration acts as a bimodal polaritonic frequency-comb generator and high-speed phase rotator, thereby opening prospects for phase singularities in nanophotonic and quantum communication devices. [ABSTRACT FROM AUTHOR]

In this study, we report the generation of multi-wavelength light sources through enhanced four-wave-mixing processes using a straightforward and adaptable dual-frequency Brillouin fiber laser. This passive optical and nonreciprocal cavity is first tested and analyzed with long fiber lengths up to 1 km in the 1.55 μm telecommunication C band and then in the 2-μm waveband. In the latter case, we demonstrate that our fiber cavity enables efficient multiple four-wave mixings, in the continuous-wave regime, which are commonly inaccessible in long silica-fibers due to increased losses. We also report on the tunable repetition rate from tens of GHz to hundreds of GHz, by simply changing the frequency spacing between the two continuous-wave pumps. The coherence limitations of our all-fiber system are discussed, along with the impact of the dispersion regime of the nonlinear fiber that forms the cavity. [ABSTRACT FROM AUTHOR]

We report on the experimental demonstration of temporal manipulations of dissipative polarization domain wall solitons in a Kerr nonlinear resonator operated in a period-doubled configuration. Our experiments are performed in a coherently driven normally dispersive fiber ring cavity, in which polarization domains emerge in virtue of a spontaneous symmetry breaking phenomenon. The addition of a lumped birefringent defect into the cavity forces their polarization components to swap on a two-round-trip cycle, thus protecting them from the deleterious impact of the system's asymmetries. We exploit these symbiotic dynamics in proof-of-concept buffering experiments, in which these dissipative structures are addressed individually and temporally manipulated through phase-encoded perturbations imprinted onto the driving beam. Our results provide new insights into the practical exploitation of spontaneous symmetry breaking mechanisms and the use of two-component dissipative structures for all-optical data storage applications. • Exploitation of the spontaneous polarization symmetry breaking phenomenon in a normally dispersive fiber Kerr resonator. • Generation of highly robust polarization domain wall solitons operated in a period-doubled configuration (P2-PDWs). • Temporal manipulations of these dissipative polarization domain walls in a proof-of concept buffering experiment. [ABSTRACT FROM AUTHOR]

We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear super-position of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. [ABSTRACT FROM AUTHOR]

Parabolic pulses in optical fibers have stimulated an increasing number of applications. We review here the physics underlying the generation of such pulses as well as the results obtained in a wide range of experimental configurations. [ABSTRACT FROM AUTHOR]

We reviewed the tellurite glass purification studies performed over the last 20 years, in particular dealing with the mid‐infrared (mid‐IR) transmission performances. Best results are obtained under rich O2 atmosphere with platinum crucibles although Gibbs energy calculations show that other crucibles material are possible such as gold or alumina. From the point of view of the thermodynamics of involved oxidation reactions only, we identified the suitable conditions based on Gibbs energy calculations to be a synthesis temperature set above 900 K and a O2 pressure around 105 Pa. The performances of the different purification techniques were also compared. Finally, we analyzed the tellurite fibers recently optimized for mid‐IR which present low attenuation up to 4 µm allowing supercontinuum generation up to 5 µm. [ABSTRACT FROM AUTHOR]

Highlights: [•] Fabrication of low-OH content and low-loss tellurite optical fibers. [•] Incorporation of fluoride ions makes tellurite fibers transparent up to 4μm. [•] 2000nm bandwidth supercontinuum in suspended core microstructured tellurite fiber. [Copyright &y& Elsevier]

We present both a theoretical description and experimental observation of the nonlinear mutual interactions between a pair of copropagative breathers in the framework of the focusing one-dimensional nonlinear Schrödinger equation. As a general case, we show that the resulting bound state of breathers exhibits moleculelike behavior with quasiperiodic oscillatory dynamics (i.e., internal coherent interactions and pulsations), while for commensurate conditions the molecule oscillations become exactly periodic. Our theoretical model is confirmed by an experimental observation of shaped moleculelike breather light waves propagating in a nearly conservative optical fiber system. Our work sheds new light on the existence of localized wave structures and recurrence dynamics beyond the multisoliton complexes. [ABSTRACT FROM AUTHOR]

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

The data recorded in optical fiber and in hydrodynamic 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 Schrödinger 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 previously employed 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. [ABSTRACT FROM AUTHOR]