Revealing breathing dynamics of pulsating Nyquist solitons from an Er-doped mode-locked fiber oscillator

Nyquist solitons are highly attractive for high-capacity optical communications due to their rectangular spectra and sinc-shaped temporal profiles, which enable high spectral efficiency and zero inter-symbol interference. However, their pulsating behavior from mode-locked fiber oscillators has not yet been reported. In this work, the generation and breathing dynamics of pulsating Nyquist solitons from an Er-doped fiber oscillator are numerically demonstrated. By constructing a mode-locking state diagram associated with the gain saturation energy (Esat), flexible transitions among unstable emission, stable Nyquist solitons, and pulsating Nyquist solitons are revealed. Analysis of the pulsating evolution over a complete breathing period indicates that the temporal structure is characterized by a main peak with nearly clamped intensity, accompanied by sidelobes whose energy oscillates under the interplay of intracavity gain and filtering loss. Correspondingly, the spectral center profile undergoes a periodic convex-concave-convex modulation. Notably, despite the pronounced breathing behavior, the temporal profile maintains a fitting coefficient exceeding 99% with respect to the ideal Nyquist pulse, confirming the intrinsic Nyquist characteristics in the time domain. Furthermore, the average pulse duration exhibits a non-monotonic dependent on Esat, remaining nearly unchanged within a certain range and reaching a minimum at an optimal Esat. These results provide deep physical insights into the nonlinear pulsating dynamics of Nyquist solitons and establish a theoretical foundation for dynamically controlling their properties.