It should be noted that dissipative solitons are considered to be self-localized coherent structures issuing from the balance between energy supply and dissipation. Breathing dissipative solitons find their applications both in nonlinear science and practical applications, for instance, in spectroscopy. Herewith, the main application is in a mode-locked fiber laser system.
The thing is that these solitons prevail in the laser system cavity under the pump threshold of stationary mode-locking. The fiber laser systems allow performing fast detection resulting in the observation of the breather and breathing soliton molecules’ temporal and spectral evolutions in real-time. Therefore, breathers offer a new mode-locking regime into ultrafast fiber lasers.
The researches of dissipative solitons may promote the design of advanced laser beam sources and discover new opportunities for generating breathers in different dissipative systems. The breathing dissipative solitons in fiber laser systems are regarded as highly attractive in optics due to such features as “their strong connection with the Fermi-Pasta-Ulam paradox, formation of rogue waves, turbulence, and modulation instability phenomena”.
Additionally, dissipative solitons in laser systems play an important role in practical applications, for instance, breathers enable to increase the resolution of microresonator-based dual-comb sources. Herewith, mode-locked fiber lasers propose an ideal platform for the fundamental exploration of complex dissipative nonlinear dynamics.
Also, mode-locked fiber laser systems have allowed different notable nonlinear phenomena (rogue waves, soliton molecules and molecular complexes, pulsations of soliton bunches, and soliton explosions) to be observed. The thing is that several operating regimes are distinguished in which laser beam oscillators may produce breathing solitons with large ratios of maximal to minimal energies in each period of pulsation.
Nevertheless, the observation and characterization of the laser system regimes remain challenging because of the fast evolutionary breather behavior and relatively slow speed of conventional measurement devices. The use of breather fiber lasers is highly promising and may find their applications as direct sources of supercontinuum light, while the periodic variation in output pulse parameters offered by these fiber laser systems can be employed as well.
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