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Stable light bullets and clusters of them are presented in the monostable regime using the mean-field Lugiato–Lefever equation [Gopalakrishnan, Panajotov, Taki, and Tlidi, Phys. Rev. Lett. 126, 153902 (2021)]. It is shown that three-dimensional (3D) dissipative structures occur in a strongly nonlinear regime where modulational instability is subcritical. We provide a detailed analysis on the formation of optical 3D crystals in both the super- and sub-critical modulational instability regimes, and we highlight their link to the formation of light bullets in diffractive and dispersive Kerr resonators. We construct bifurcation diagrams associated with the formation of optical crystals in both monostable and bistable regimes. An analytical study has predicted the predominance of body-centered-cubic (bcc) crystals in the intracavity field over a large variety of other 3D solutions with less symmetry. These results have been obtained using a weakly nonlinear analysis but have never been checked numerically. We show numerically that indeed the most robust structures over other self-organized crystals are the bcc crystals. Finally, we show that light-bullets and clusters of them can occur also in a bistable regime., SCOPUS: ar.j, info:eu-repo/semantics/published

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We investigate the spatio-temporal dynamics of a ring cavity filled with a non-instantaneous Kerr medium and driven by a coherent injected beam. We show the existence of a stable mixed-mode solution that can be either extended or localized in space. The mixed-mode solutions are obtained in a regime where Turing instability (often called modulational instability) interacts with self-pulsing phenomenon (Andronov-Hopf bifurcation). We numerically describe the transition from stationary inhomogeneous solutions to a branch of mixed-mode solutions. We characterize this transition by constructing the bifurcation diagram associated with these solutions. Finally, we show stable localized mixed-mode solutions, which consist of time-periodic oscillations that are localized in space., SCOPUS: ar.j, info:eu-repo/semantics/published

The pioneering paper 'Optical rogue waves' by Solli et al (2007 Nature 450 1054) started the new subfield in optics. This work launched a great deal of activity on this novel subject. As a result, the initial concept has expanded and has been enriched by new ideas. Various approaches have been suggested since then. A fresh look at the older results and new discoveries has been undertaken, stimulated by the concept of 'optical rogue waves'. Presently, there may not by a unique view on how this new scientific term should be used and developed. There is nothing surprising when the opinion of the experts diverge in any new field of research. After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation. We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems. Theorists, in turn, have suggested many other situations when rogue waves may be observed. The strict definition of a rogue wave is still an open question. For example, it has been suggested that it is defined as 'an optical pulse whose amplitude or intensity is much higher than that of the surrounding pulses'. This definition (as suggested by a peer reviewer) is clear at the intuitive level and can be easily extended to the case of spatial beams although additional clarifications are still needed. An extended definition has been presented earlier by N Akhmediev and E Pelinovsky (2010 Eur. Phys. J. Spec. Top. 185 1-4). Discussions along these lines are always useful and all new approaches stimulate research and encourage discoveries of new phenomena. Despite the potentially existing disagreements, the scientific terms 'optical rogue waves' and 'extreme events' do exist. Therefore coordination of our efforts in either unifying the concept or in introducing alternative definitions must be continued. From this point of view, a n, SCOPUS: ar.j, info:eu-repo/semantics/published

The dynamical evolution of the modulational instability is studied in a coherently driven passive optical fiber cavity.We showthat periodic pattern generated close to the threshold experience convective and absolute Eckhaus instabilities. In addition to this splitting of the secondary instabilities into convective and absolute instabilities we have observed that the onset of the absolute regime is accompanied by the emergence of spatio-temporal chaos. © Springer International Publishing Switzerland 2016., info:eu-repo/semantics/published, 3rd Dynamics Days South America Conference, 2014; Valparaiso; Chile; 3 November 2014 through 7 November 2014

It is analytically shown that symmetry breaking, in dissipative systems, affects the nature of the bifurcation at onset of instability resulting in transitions from super to subcritical bifurcations. In the case of a nonlinear fiber cavity, we have derived an amplitude equation to describe the nonlinear dynamics above threshold. An analytical expression of the critical transition curve is obtained and the predictions are in excellent agreement with the numerical solutions of the full dynamical model., SCOPUS: ar.j, info:eu-repo/semantics/published

We study secondary instabilities in a coherently driven passive optical fiber cavity. We show that time-modulated solutions which are generated at the onset of instability experience convective and absolute Eckhaus instabilities. The splitting of the secondary instabilities into convective and absolute instabilities drastically impacts the instability boundaries. As a consequence, the stability range of time-modulated waves is enlarged. More importantly, the threshold of absolute instability determines the transition from time-periodic wave trains to a chaotic regime. In the latter the wave trains are composed of irregular oscillations embedded in regular ones. The predictions are in excellent agreement with numerical simulations., SCOPUS: ar.j, info:eu-repo/semantics/published

We consider a bistable system consisting of all fiber cavity driven by an external injected continuous wave. We report on front propagation in a high finesse cavity. We study the asymptotic behavior of the front velocity. We show that the front velocity is affected by the distance from the critical point associated with bistability. We provide a scaling low governing its evolution near the up-switching point of the bistable curve. We show also that the velocity of front propagation obeys a generic power law when the front velocity approaches asymptotically its linear growing value. © 2014 Optical Society of America., SCOPUS: ar.j, info:eu-repo/semantics/published

The frequency spectrum asymmetry observed in fiber systems is shown to originate from a nonlinear symmetry breaking. Analytical and experimental results are in excellent agreement. Rogue waves formation in strongly nonlinear regimes is presented. © 2014 OSA., info:eu-repo/semantics/published

We study analytically, numerically, and experimentally the nonlinear symmetry breaking induced by broken reflection symmetry in an optical fiber system. In particular, we investigate the modulation instability regime and reveal the key role of the third-order dispersion on the asymmetry in the spectrum of the dissipative structures. Our theory explains early observations, and the predictions are in excellent agreement with our experimental findings., Journal Article, info:eu-repo/semantics/published

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In spatially extended convective systems, the reflection symmetry breaking induced by drift effects leads to a striking nonlinear effect that drastically affects the formation and stability of dissipative solitons in optical parametric oscillators. The phenomenon of nonlinear-induced convection dynamics is revealed using a model of the complex quintic Ginzburg-Landau equation with nonlinear gradient terms in it. Mechanisms leading to stabilization of dissipative solitons by convection are singled out. The predictions are in very good agreement with numerical solutions found from the governing equations of the optical parametric oscillators.

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Experimental observation of the 1D Kerr-Type cavity solitonTemporal cavity solitons constitute a remarkable family of light pulses. They don’t spread nor suffer losses and circulate indefinitely, round-trips after round-trips, along the closed path of a nonlinear cavity. To maintain their shape and power, they simply draw some energy from a continuous-wave external beam. Being robust attracting states, they can be easily written by an external pulse and naturally provide reshaping and wavelength conversion functionalities. We experimentally demonstrated the generation of such solitons. We were able to provide precise temporal and spectral characterization along with long-term observation. We also wrote the solitons in pairs and in data streams, showing that our fiber cavity could potentially be used as an all- optical buffer capable of storing 45,000 bits at 25G bits/s. These results have been recently published in Nature PhotonicsHigh repetition-rate pulse train generation through dissipative modulation instability in a passive fiber resonatorIn the early 90’s, a cavity configuration which allows for the generation of stable pulse trains through dis- sipative modulational instability was proposed. The experimental implementation of the so-called MI laser was demonstrated a few years later. Although the ideal parameters for the generation of a pulse train with a repetition rate in the THz range are easily deduced from the theory, no realization in that frequency range has been reported due to practical issues. Thanks to the tuning of the overall cavity dispersion based on the use of special fibers, we recently demonstrated the generation of a 1.6 THz repetition-rate optical pulse-train.Theoretical and experimental study of nonlinear symmetry breaking induced by the order dispersion in a passive fiber resonatorIn the regime of dissipative modulational instability, the repetition-rates of the generated pulse train can be tuned by changing, Doctorat en Sciences de l'ingénieur, info:eu-repo/semantics/nonPublished

We analyze the beating between intrinsic frequencies that are simultaneously generated by a modulation (Turing) instability in a nonlinear extended system. The model studied is that of a coherently driven photonic crystal fiber cavity. Beating in the form of a slow modulation of fast intensity oscillations is found to be stable for a wide range of parameters. We find that such beating can also be localized and contain only a finite number of slow modulations. These structures consist of dips in the amplitude of the fast intensity oscillations, which can either be isolated or regularly spaced. An asymptotic analysis close to the modulation instability threshold allows us to explain this phenomenon as a manifestation of homoclinic snaking for dissipative localized structures. © 2009 The American Physical Society., info:eu-repo/semantics/published

The title (WANDT) can be applied to two objects: rogue waves in the ocean and rational solutions of the nonlinear Schrödinger equation (NLSE). There is a hierarchy of rational solutions of 'focussing' NLSE with increasing order and with progressively inc

We study the dynamics of bound solitons of the complex cubic-quintic Ginzburg– Landau equation under the influence of external modulation. We consider periods of modulation being either smaller or larger than the soliton separation and the amplitude of modulation being either real or imaginary. For each case, we observe bifurcation and hysteresis phenomena in the parameters of the pair when changing the amplitude of modulation. Namely, soliton separation and phase difference between the solitons may take two or more values for the same modulation amplitude. In the case of gain-loss modulation, two solitons may split and be positioned in the two equilibrium states of the periodic potential. The complicated dynamics of this process is illustrated with numerical examples.

Using an optical fiber ring cavity with a GVD coefficient as low as ¡0.02 ps2/km, we experimentally generated pulse-trains with a repetition-rate in the THz range. We achieved the spectral and temporal characterization of this train. © 2009 Optical Society of America., SCOPUS: cp.p, info:eu-repo/semantics/published

We use the modulational instability regime of a passive optical fiber cavity to generate trains of pulses. The repetition rate of such trains is inversely proportional to the group velocity dispersion (GVD) of the fiber cavity. Using a dispersion shifted fiber (DSF), it was possible to work with a GVD coefficient as low as -0.02ps2/km. This allowed for the measurement of a pulse train with a 1.5THz repetition rate. The characterization of this train was performed in the spectral and in the temporal domains. This clearly demonstrates that optical passive fiber cavities can be used as sources of pulse-trains at a repetition rate above 1THz., info:eu-repo/semantics/published

We theoretically and experimentally evidence that fiber systems are convective systems since their nonlocal inherent properties, such as the dispersion and Raman effects, break the reflection symmetry. Theoretical analysis and numerical simulations carried out for a fiber ring cavity demonstrate that the third-order dispersion term leads to the appearance of convective and absolute instabilities. Their signature is an asymmetry in the output power spectrum. Using this criterion, experimental evidence of convective instabilities is given in a fiber cavity pumped by a pulsed laser.

We propose a one-dimensional model governing the propagation of heat waves in an optical fiber (the >fiber fuse>). The model has solutions in the form of high temperature localized waves moving towards the input end of the fiber, fueled by the laser power. These waves can be ignited by local heating at any point along the fiber. The effect of such a wave is irreversible damage to the fiber core. The phenomenon was observed earlier by Hand and Russell, when locally heating a fiber through which CW light of modest intensity was propagating. This induced self-destruction of the optical fiber core. © 2007 Elsevier B.V. All rights reserved.