  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.
