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Dissipative solitons emerge as stable pulse solutions of nonintegrable and nonconservative nonlinear physical systems, owing to a balance of nonlinearity, dispersion, and loss/gain. A considerable research effort has been dedicated to characterizing amplitude and phase evolutions in the spatiotemporal dynamics of dissipative solitons emerging from fiber lasers. Yet, the picture of the buildup process of dissipative solitons in fiber lasers is incomplete in the absence of corresponding information about the polarization evolution. Here, we characterize probabilistic polarization distributions in the buildup of dissipative solitons in a net-normal dispersion fiber laser system, mode-locked by single-wall carbon nanotubes. The output optical spectra under different pump powers are filtered by a tunable filter, and are detected by a polarization state analyzer. The laser system operates from random amplified spontaneous emission into a stable dissipative soliton state as the cavity gain is progressively increased. Correspondingly, the state of polarization of each spectral wavelength converges towards a fixed point. To reveal the invariant polarization relationship among the various wavelength components of the laser output field, the phase diagram of the ellipticity angle and the spherical orientation angle is introduced. We find that, within the central spectral region of the dissipative soliton, the state of polarization evolves with frequency by tracing a uniform arc on the Poincaré sphere, whereas in the edges of the dissipative soliton spectrum, the state of polarization abruptly changes its path. Increasing cavity gain leads to spectral broadening, accompanied by a random scattering of the state of polarization of newly generated frequencies. Further increases of pump power result in dissipative soliton explosions, accompanied by the emergence of a new type of optical polarization rogue waves. These experimental results provide a deeper insight into the transient dynamics of dissipative soliton fiber lasers.

The buildup process of coherent structures and patterns from the composite balance between conservative and dissipative effects is a universal phenomenon that occurs in various areas of physics, ranging from quantum mechanics to astrophysics. Dissipative solitons are highly coherent solutions of nonlinear wave equations, and provide an excellent research platform for ultrafast transient phenomena. Here, by taking advantage of the fast detection technique provided by the dispersive Fourier transform, we experimentally observe the spectral broadening and breathing behavior of transient dissipative structures produced asynchronously during the buildup process of dissipative solitons. These observations unveil a novel dynamics of dissipative soliton generation, which is accompanied by energy quantization, self-phase modulation induced spectral broadening, structural dissipative soliton formation, and Raman soliton self-frequency shifting, thus providing a new insight in transient ultrafast laser dynamics.

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