From rogue waves to random walks:nonlinear instabilities in supercontinuum generation

The noise properties of supercontinuum generation continue to be a subject of wide interest within both pure and applied physics. Aside from immediate applications in supercontinuum source development, detailed studies of supercontinuum noise mechanisms have attracted interdisciplinary attention because of links with extreme instabilities in other physical systems, especially the infamous and destructive oceanic rogue waves. But the instabilities inherent in supercontinuum generation can also be interpreted in terms of natural links with the general field of random processes, and this raises new possibilities for applications in areas such as random number generation. In this contribution we will describe recent work where we interpret supercontinuum intensity and phase fluctuations in this way.

Optical rogue waves in telecommunication data streams

Large broadening of short optical pulses due to fiber dispersion leads to a strong overlap in information data streams resulting in statistical deviations of the local power from its average. We present a theoretical analysis of rare events of high-intensity fluctuations-optical freak waves-that occur in fiber communication links using bit-overlapping transmission. Although the nature of the large fluctuations examined here is completely linear, as compared to commonly studied freak waves generated by nonlinear effects, the considered deviations inherit from rogue waves the key features of practical interest-random appearance of localized high-intensity pulses. We use the term "rogue wave" in an unusual context mostly to attract attention to both the possibility of purely linear statistical generation of huge amplitude waves and to the fact that in optics the occurrence of such pulses might be observable even with the standard Gaussian or even rarer-than-Gaussian statistics, without imposing the condition of an increased probability of extreme value events. © 2011 American Physical Society.

Reply to "comment on 'Optical rogue waves in telecommunication data streams'"

We feel that the main claim made in the abstract of the preceding Comment is wrong. Using results obtained in our paper, we prove that rogue waves with amplitudes much larger than the average level can be observed during a short period of time in purely linear propagation regimes in optical fiber systems. © 2011 American Physical Society.

Dynamics of vector rogue waves in a fiber laser with a ring cavity

A pulse–pulse interaction that leads to rogue wave (RW) generation in lasers was previously attributed either to soliton–soliton or soliton–dispersive-wave interaction. The beating between polarization modes in the absence of a saturable absorber causes similar effects. Accounting for these polarization modes in a laser resonator is the purpose of the distributed vector model of laser resonators. Furthermore, high pump power, high amplitude, and short pulse duration are not necessary conditions to observe pulse attraction, repulsion, and collisions and the resonance exchange of energy between among them. The regimes of interest can be tuned just by changing the birefringence in the cavity with the pump power slightly higher than the laser threshold. This allows the observation of a wide range of RW patterns in the same experiment, as well as to classify them. The dynamics of the interaction between pulses leads us to the conclusion that all of these effects occur due to nonlinearity induced by the inverse population in the active fiber as well as an intrinsic nonlinearity in the passive part of the cavity. Most of the mechanisms of pulse–pulse interaction were found to be mutually exclusive. This means that all the observed RW patterns, namely, the “lonely,” “twins,” “three sisters,” and “cross,” are probably different cases of the same process.

Slow deterministic vector rogue waves

For an erbium-doped fiber laser mode-locked by carbon nanotubes, we demonstrate experimentally and theoretically a new type of the vector rogue waves emerging as a result of the chaotic evolution of the trajectories between two orthogonal states of polarization on the Poincare sphere. In terms of fluctuation induced phenomena, by tuning polarization controller for the pump wave and in-cavity polarization controller, we are able to control the Kramers time, i.e. the residence time of the trajectory in vicinity of each orthogonal state of polarization, and so can cause the rare events satisfying rogue wave criteria and having the form of transitions from the state with the long residence time to the state with a short residence time.

Temporal scaling of optical rogue waves in unidirectional ring fiber laser

A fiber mode-lock laser allows generation of the optical rogue wave (ORW) at different time scales. The criteria for distinguishing between them is a comparison of the event lifetime with the main characteristic time of the system. The characteristic time can be estimated from the decay of an autocorrelation function (AF). Thus, in comparison with AF characteristic time, fast optical rogue wave (FORW) events have duration less than the AF decay time and it appeared due to pulse-pulse interaction and nonlinear pulses dynamics. While slow optical rogue wave (SORW) have a duration much more longer than the decay time of the AF which it papered due to hopping between different attractors. Switching between regimes can be managed by change the artificial birefringence that induced in a laser cavity. For understanding the role playing by the periodical amplification and the resonator, we have performed an unidirectional fiber laser experiments without a saturable absorber. This laser experiment allowed to generate of most of the RW patterns which were either observed experimentally or predicted theoretically. In this way, we have observed the generation of an FORW along with SORW under similar conditions. Most of the patterns were found to be mutually exclusive which means that only one RW mechanism was realized in each regime of generation.

Bright and dark vector rogue waves

For an Erbium-doped mode locked fibre laser, we demonstrate experimentally a new type of vector rogue waves (RWs) emergence of which is caused by the coherent coupling of the orthogonal states of polarisation (SOPs). Unlike weak interaction between neighbouring dissipative solitons for the soliton rain, this creates a new type of the energy landscape where the interaction of the orthogonal SOPs leads to polarisation trapping or escapes from the trapping triggered by polarisation instabilities and so results in the pulse dynamics satisfying criteria of the 'dark' and 'bright' RWs. The obtained results, apart from the fundamental interest, can provide a base for development of the rogue waves mitigation techniques in the context of the applications in photonics and beyond.

Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser

We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.

Nonlinear spectral shaping and optical rogue events in fiber-based systems

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.

Nonlinear spectral shaping and optical rogue events in fiber-based systems

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. © 2012 Elsevier Inc. All rights reserved.

Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion

One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrödinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.

Ginzburg-Landau turbulence in quasi-CW Raman fiber lasers

Fiber lasers operating via Raman gain or based on rare-earth-doped active fibers are widely used as sources of CW radiation. However, these lasers are only quasi-CW: their intensity fluctuates strongly on short time scales. Here the framework of the complex Ginzburg-Landau equations, which are well known as an efficient model of mode-locked fiber lasers, is applied for the description of quasi-CW fiber lasers. The vector Ginzburg-Landau model of a Raman fiber laser describes the experimentally observed turbulent-like intensity dynamics, as well as polarization rogue waves. Our results open debates about the common underlying physics of operation of very different laser types - quasi-CW lasers and passively mode-locked lasers. Fiber lasers operating via Raman gain or based on rare-earth-doped active fibers are widely used as sources of CW radiation. However, these lasers are only quasi-CW: their intensity fluctuates strongly on short time scales. Here the framework of the complex Ginzburg-Landau equations, which are well known as an efficient model of mode-locked fiber lasers, is applied for the description of quasi-CW fiber lasers. The vector Ginzburg-Landau model of a Raman fiber laser describes the experimentally observed turbulent-like intensity dynamics, as well as polarization rogue waves. Our results open debates about the common underlying physics of operation of very different laser types - quasi-CW lasers and passively mode-locked lasers.