Real-time observation of pulsating period-doubled vector solitons in a passively mode-locked fiber laser

Dissipative solitons (DSs) are self-organized localized structures in non-conservative systems, which require a continuous energy exchange with external sources. In addition to parameter-invariant stationary DSs, there exists a variety of dynamical ones manifesting breathing behaviors. Such intriguing phenomena, termed as soliton pulsations, have been widely studied in recent years under the impetus of advances in real-time spectroscopy. Here, we experimentally investigate various pulsating period-doubled solitons (PDSs) in a fiber laser mode-locked by single-wall carbon nanotubes. Both single- and double-periodic PDS pulsations are found in the cavity. Thanks to the emerging dispersive Fourier transform technique, the polarization-resolved transient spectra of these pulsating PDSs are measured. It is shown that their polarization ellipses rotate with a period of two cavity roundtrips. Moreover, the intensity-modulation behaviors of the two orthogonal polarization components in the odd (even) roundtrips are always asynchronous, which confirms additional slower polarization modulations. Especially, we demonstrate that three combined intensity-modulation periods are involved in the double-periodic PDS pulsation process for the first time, to the best of our knowledge. Our results would stimulate further research on the vector features of multiple-period pulsating solitons in mode-locked fiber lasers.