Soliton macromolecule dynamics in fiber lasers with sinusoidal filtered nonlinear optical loop mirror

We numerically investigated the pulse dynamics of soliton macromolecules (SMs) in erbium-doped fiber lasers mode-locked using a nonlinear optical loop mirror (NOLM) with a sinusoidal spectral filter (SSF). SM regimes with various pulse intervals were proposed by modulating the saturation energy and filter period, distributed discretely owing to the restriction of the cavity length and pulse-to-pulse interaction. Several SM properties were discovered in stable SM states with filter periods of 1.3 and 1.95 nm, including the $\ensuremath{\pi}\text{\ensuremath{-}}\mathrm{phase}$ difference between adjacent pulses, Kelly sidebands in optical spectra, and the alternating change of phases against round trips. The laser worked in transition regimes, such as pulse splitting and pulsating to a stable SM, by increasing the saturation energy with certain filter periods. In pulsating SM regimes, soliton collisions and periodic variations of pulse intervals and peak powers occurred, accompanied by energy transfer between different spectrum components or spectrum shifts. This study reveals that the SSF-based NOLM enables SM generation and provides a method for controlling the SM dynamics in fiber lasers.