This Review explains the concept of dissipative solitons and their application to high-energy mode-locked fibre laser cavities. Dynamics and effects such as dissipative soliton ‘explosions’ and ‘rain’ are summarized, and an outlook of the field is also provided.

/pdf/dissipative-solitons-for-mode-locked-lasers-1fudg0a89g.pdf

Dissipative solitons for mode-locked lasers

http://personalpages.to.infn.it/~onorato/publications_files/2013_Onorato_etal_PhysRep.pdf

Rogue waves and their generating mechanisms in different physical contexts

Wave collapse in physics: principles and applications to light and plasma waves

We report results of numerical simulations on multiple-soliton generation and soliton energy quantization in a soliton fiber ring laser passively mode locked by using the nonlinear polarization rotation technique. We found numerically that the formation of multiple solitons in the laser is caused by a peak-power-limiting effect of the laser cavity. It is also the same effect that suppresses the soliton pulse collapse, an intrinsic feature of solitons propagating in gain media, and makes the solitons stable in the laser. Furthermore, we show that the soliton energy quantization observed in the lasers is a natural consequence of the gain competition between the multiple solitons. Enlightened by the numerical result we speculate that multisoliton formation and soliton energy quantization observed in other types of soliton fiber lasers could have a similar mechanism.

https://nocweba.ntu.edu.sg/laq_mems/journal%20papers/2005/Mechanism%20of%20multisoliton%20formation%20and%20soliton%20energy%20quantization%20in%20passively%20mode-locked%20fiber%20lasers.pdf

Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers

Cascading is the process by which the exchange of energy between optical beams interacting via second order nonlinearities (χ(2)) leads to various effects such as nonlinear phase shifts, the generation of new beams, all-optical transistor action, the formation of soliton-like (solitary) waves, etc. Here we review the fundamentals of the processes and discuss experimental verification of the effects and various related applications.

χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons

Turbulence in dynamical systems is one of the most intriguing phenomena of modern science. Integrable systems offer the possibility to understand, to some extent, turbulence. Recent numerical and experimental data suggest that the probability of the appearance of rogue waves in a chaotic wave state in such systems increases when the initial state is a random function of sufficiently high amplitude. We provide explanations for this effect.

/pdf/integrable-turbulence-and-rogue-waves-breathers-or-solitons-1hu66w556n.pdf

Integrable Turbulence and Rogue Waves: Breathers or Solitons?

We observe polarization-locked vector solitons in a mode-locked ﬁber laser. Temporal vectorsolitons have components along both birefringent axes. Despite different phase velocities due to linearbirefringence, the relative phase of the components is locked at 6py2. The value of 6py2 andcomponent magnitudes agree with a simple analysis of the Kerr nonlinearity. These fragile phase-locked vector solitons have been the subject of much theoretical conjecture, but have previously eludedexperimental observation. [S0031-9007(99)09109-7]

Observation of polarization-locked vector solitions in optical fiber

Optical-fiber transmission of pulses can be modeled with the complex Ginzburg–Landau equation. We find novel stable soliton pairs and trains, which are relevant in this case, and analyze them. We suggest that the distance between the pulses and the phase difference between them is defined by energy and momentum balance equations, rather than by equations of standard perturbation theory. We present a two-dimensional phase plane (interaction plane) for analyzing the stability properties and general dynamics of two-soliton solutions of the Complex Ginzburg–Landau equation.

/pdf/stable-soliton-pairs-in-optical-transmission-lines-and-fiber-rqxbisig4w.pdf

Stable soliton pairs in optical transmission lines and fiber lasers

We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrodinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which includes, as particular cases, both the discrete Ablowitz-Ladik equation and the discrete modified Korteweg-de Vries (mKdV) equation.

/pdf/discrete-rogue-waves-of-the-ablowitz-ladik-and-hirota-23lnkdtlic.pdf

Discrete rogue waves of the Ablowitz-Ladik and Hirota equations

We have numerically calculated the resonance curve and the region of existence of high-energy dissipative solitons in systems governed by the complex cubic-quintic Ginzburg-Landau equation. The calculations are carried out for negative reactive quintic nonlinearity. This choice allows the resonance curve to be continued into the region of positive net dispersion, thus showing that high-energy pulses can also be generated by lasers operating in the anomalous dispersion regime.

/pdf/dissipative-soliton-resonances-in-the-anomalous-dispersion-2xj8z3739f.pdf

J.M. Soto-Crespo

Papers

Integrable Turbulence and Rogue Waves: Breathers or Solitons?

Observation of polarization-locked vector solitions in optical fiber

Stable soliton pairs in optical transmission lines and fiber lasers

Discrete rogue waves of the Ablowitz-Ladik and Hirota equations

Dissipative soliton resonances in the anomalous dispersion regime