## Abstract

Dissipative solitons (DSs) in a nonlinear medium are localised coherent structures

that result from the composite balance between conservative effects (nonlinearity

and dispersion/diffraction) and dissipative ones (gain and loss). In addition

to parameter-invariant stationary DSs, numerous nonlinear systems support breathing

(pulsating) DSs, the energy of which is localised in space but oscillates in time, or

vice versa. Such nonlinear waves are attracting considerable research interest in

optics owing to their strong connection with the Fermi-Pasta-Ulam paradox, formation

of rogue waves, turbulence and modulation instability phenomena. Apart from

their fundamental importance in nonlinear science, breathing solitons are also attractive

because of their potential for practical applications, such as in spectroscopy. Yet,

the observation of these breathers has been mainly restricted to optical microresonator platforms.

In this talk, I will report on the generation and study of breathing DSs in passively

mode-locked fibre lasers. Breathing solitons feature periodic spectral and temporal

evolutions over cavity round trips. Experimentally, we capture such fast dynamics

spectrally and temporally in real time using time-stretch dispersive Fourier transform

based single-shot spectral measurements and spatio-temporal intensity measurements.

Remarkably, in the normal-dispersion regime of the laser cavity, breathers

are excited in the laser under the pump threshold for stationary DS mode locking.

For the first time in experiments with mode-locked fibre lasers, breathing soliton pair

molecules are also generated in the cavity, which represent double-breather bound

states with a close intra-pulse separation. The universal nature of the breather formation is indicated by our observation in a varying-length cavity, and further confirmed by numerical simulations of the laser model described by the complex cubic-quintic Ginzburg-Landau equation (CQGLE). When the laser has an average anomalous

cavity dispersion, we observe a regime of operation where the laser oscillator generates

multiple pulsating solitons with extreme ratios of maximal to minimal intensities

in each period of pulsations. The soliton spectra also experience large periodic broadening

and compression. These observations are, to the best of our knowledge, the first

of their kind in a laser system.

Breathers introduce a new regime of mode locking into ultrafast lasers. These

findings not only carry importance from an application perspective, but also contribute

more broadly to the fundamental understanding of dissipative soliton physics. Our

observations further demonstrate that mode-locked fibre lasers are an ideal test bed for

the study of complex nonlinear wave dynamics relevant to a large variety of physical

systems. More generally, the complex CQGLE is the most common mathematical

implementation of a dissipative system, describing many different nonlinear effects

in physics, such as nonlinear waves, superconductivity, superfluidity, Bose-Einstein

condensates, liquid crystals, plasmas, and numerous other phenomena. Therefore, it is

reasonable to assume that the breathing DS dynamics found in this work are not limited

to optical systems and will also be discovered in various other physical systems.

that result from the composite balance between conservative effects (nonlinearity

and dispersion/diffraction) and dissipative ones (gain and loss). In addition

to parameter-invariant stationary DSs, numerous nonlinear systems support breathing

(pulsating) DSs, the energy of which is localised in space but oscillates in time, or

vice versa. Such nonlinear waves are attracting considerable research interest in

optics owing to their strong connection with the Fermi-Pasta-Ulam paradox, formation

of rogue waves, turbulence and modulation instability phenomena. Apart from

their fundamental importance in nonlinear science, breathing solitons are also attractive

because of their potential for practical applications, such as in spectroscopy. Yet,

the observation of these breathers has been mainly restricted to optical microresonator platforms.

In this talk, I will report on the generation and study of breathing DSs in passively

mode-locked fibre lasers. Breathing solitons feature periodic spectral and temporal

evolutions over cavity round trips. Experimentally, we capture such fast dynamics

spectrally and temporally in real time using time-stretch dispersive Fourier transform

based single-shot spectral measurements and spatio-temporal intensity measurements.

Remarkably, in the normal-dispersion regime of the laser cavity, breathers

are excited in the laser under the pump threshold for stationary DS mode locking.

For the first time in experiments with mode-locked fibre lasers, breathing soliton pair

molecules are also generated in the cavity, which represent double-breather bound

states with a close intra-pulse separation. The universal nature of the breather formation is indicated by our observation in a varying-length cavity, and further confirmed by numerical simulations of the laser model described by the complex cubic-quintic Ginzburg-Landau equation (CQGLE). When the laser has an average anomalous

cavity dispersion, we observe a regime of operation where the laser oscillator generates

multiple pulsating solitons with extreme ratios of maximal to minimal intensities

in each period of pulsations. The soliton spectra also experience large periodic broadening

and compression. These observations are, to the best of our knowledge, the first

of their kind in a laser system.

Breathers introduce a new regime of mode locking into ultrafast lasers. These

findings not only carry importance from an application perspective, but also contribute

more broadly to the fundamental understanding of dissipative soliton physics. Our

observations further demonstrate that mode-locked fibre lasers are an ideal test bed for

the study of complex nonlinear wave dynamics relevant to a large variety of physical

systems. More generally, the complex CQGLE is the most common mathematical

implementation of a dissipative system, describing many different nonlinear effects

in physics, such as nonlinear waves, superconductivity, superfluidity, Bose-Einstein

condensates, liquid crystals, plasmas, and numerous other phenomena. Therefore, it is

reasonable to assume that the breathing DS dynamics found in this work are not limited

to optical systems and will also be discovered in various other physical systems.

Original language | English |
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Title of host publication | Book of Abstracts of Partial Differential Equations in Analysis and Mathematical Physics |

Place of Publication | Cagliari, Sardinia (Italy) |

Pages | 27-28 |

Number of pages | 2 |

Publication status | Published - 30 May 2019 |

Event | Partial Differential Equations in Analysis and Mathematical Physics - Santa Margherita di Pula (Hotel Flamingo), Cagliari, Italy Duration: 30 May 2019 → 1 Jun 2019 http://sites.unica.it/pdeamp/ |

### Conference

Conference | Partial Differential Equations in Analysis and Mathematical Physics |
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Abbreviated title | PDEAMP |

Country | Italy |

City | Cagliari |

Period | 30/05/19 → 1/06/19 |

Internet address |