Breathing solitons, i.e., dynamic dissipative solitons with oscillating pulse shape and energy caused by different mechanisms of spatiotemporal instabilities, have received considerable interest from the aspects of nonlinear science and potential applications. However, by far, the study of breathing solitons is still limited within the time scale of hundreds of cavity round trips, which ignores the slow dynamics. To fill this lacuna, we theoretically investigate a new type of vector dissipative soliton breathing regime and experimentally demonstrate this concept using mode-locked fiber lasers, which arise from the desynchronization of orthogonal states of polarization (SOPs) in the form of complex oscillations of the phase difference between the states. The dynamic evolution of polarization states of the vector breathings solitons takes the form of a trajectory connecting two quasi-equilibrium orthogonal SOPs on the surface of the Poincaré sphere. The dwelling time near each state is on the scale of a tenth of a thousand cavity round trip times that equals the breathing period, which is up to 2 orders of magnitude longer than that for common breathers. The obtained results can reveal concepts in nonlinear science and may unlock approaches to the flexible manipulation of laser waveforms toward various applications in spectroscopy and metrology.

Dissipative solitons have been realized in mode-locked fiber lasers in the theoretical framework of the Ginzburg–Landau equation and have significantly improved the pulse energy and peak power levels of such lasers. It is interesting to explore whether dissipative solitons exist in optical parametric oscillators in the framework of three-wave coupling equations in order to substantially increase the performance of optical parametric oscillators. Here, we demonstrate a temporal-filtering dissipative soliton in a synchronously pumped optical parametric oscillator. The temporal-gain filtering of the pump pulse combined with strong cascading nonlinearity and dispersion in the optical parametric oscillator enables the generation of a broad spectrum with a nearly linear chirp; consequently, a significantly compressed pulse and high peak power can be realized after dechirping outside the cavity. Furthermore, we realized, for the first time, dissipative solitons in an optical system with a negative nonlinear phase shift and anomalous dispersion, extending the parameter region of dissipative solitons. The findings may open a new research block for dissipative solitons and provide new opportunities for mid-infrared ultrafast science.