Femtosecond Optical Superregular Breathers

Abstract: Superregular (SR) breathers are nonlinear wave structures formed by a unique nonlinear superposition of pairs of quasi-Akhmediev breathers. They describe a complete scenario of modulation instability that develops from localized small perturbations as well as an unusual quasiannihilation of breather collision. Here, we demonstrate that femtosecond optical SR breathers in optical fibers exhibit intriguing half-transition and full-suppression states, which are absent in the picosecond regime governed by the standard nonlinear Schr\"{o}dinger equation. In particular, the full-suppression mode, which is strictly associated with the regime of vanishing growth rate of modulation instability, reveals a crucial \textit{non-amplifying} nonlinear dynamics of localized small perturbations. We numerically confirm the robustness of such different SR modes excited from ideal and nonideal initial states in both integrable and nonintegrable cases.