  Dissipative solitons are localized solutions in non-integrable and
non-conservative nonlinear system, due to a balance of nonlinearity,
dispersion, filtering, and loss/gain. Different from conventional soliton, they
exhibit extremely complex and striking dynamics, and are more universal in the
far-from-equilibrium natural system. Taking advantage of dispersive Fourier
transform and time lens, the spatio-temporal transient dynamics of dissipative
solitons have been characterized with both amplitude and phase. Yet, a full
avenue of the buildup process of dissipative soliton is full of debris for the
lack of the polarization evolution information. Here, we characterize the
probabilistic polarization distributions in the buildup of dissipative soliton
in a net-normal dispersion fiber laser system mode-locked by single-wall carbon
nanotubes. The lasing system operates from random amplified spontaneous
emission to stable dissipative soliton when the cavity gain is increasing, and
state of polarization of each wavelength convergence exponentially towards a
fixed point. To reveal the invariant polarization relationship among various
wavelengths, the phase diagram of the ellipticity angle and spherical
orientation angle is introduced. We find that the polarization of each filtered
wavelength in the central region of the dissipative soliton is linearly spaced,
while those in the two fronts are spatially varying. Increasing cavity gain
leads to spectrum broadening, meanwhile, the polarizations of the new generated
frequencies are extending to scatter. Further increasing pump power results
into dissipative soliton explosion, during which a kind of polarization optical
rogue waves is identified. Those experimental results provide more information
for deeper insights into the transient dynamics of dissipative soliton fiber
laser.
