  Optical solitons-stable waves balancing delicately between nonlinearities and
dispersive effects-have advanced the field of ultrafast optics and dynamics,
with contributions spanning supercontinuum generation and soliton fission, to
optical event horizon, Hawking radiation, and optical rogue waves, amongst
others. Here we investigate picojoule soliton dynamics in silicon slow-light
photonic-bandgap waveguides under the influence of Drude-modeled free-carrier
induced nonlinear effects. Using real-time and single shot amplified dispersive
Fourier transform spectroscopy simultaneously with high-fidelity
cross-correlation frequency-resolved optical gating at femtojoule sensitivity
and femtosecond resolution, we examine the soliton stability limits, the
soliton dynamics including free-carrier quartic slow-light scaling and
acceleration, and the Drude electron-hole-plasma induced perturbations on
Cherenkov radiation and modulation instability. Our real-time single shot and
time-averaged cross-correlation measurements are matched with our detailed
theoretical modeling, examining the reduced group velocity free-carrier
kinetics on solitons at picojoule.
