  Both positive- and negative-polarity Gaussian monocycle and doublet pulses,
for which the pulse shapes are the first and second derivatives of Gaussian
functions respectively, are generated in a ring-cavity erbium-doped fiber laser
from polarization-locked vector solitons by using passive optical technology.
The pulse states are switchable and are found to be the superposition of bright
and dark solitons with different widths, amplitudes, time delays,
polarizations, and wavelengths. Qualitative analysis of the properties of
vector solitons are performed by solving coupled complex Ginzburg-Landau
equations. By theoretical representing the envelopes of bright soliton by sech
and dark soliton by tanh functions, the incoherent superposition of these two
soliton components have simulated the experimental observations, and the
underlying mechanisms on the formation for monocycle and doublet pulses are
attributed to the polarization locking of bright and dark solitons. The results
of tunable optical vectos solitons are compared with atomic solitons in the
system of Bose-Einstein condensation. Since governing equations for soliton
generation in fiber lasers and Bose-Einstein condensation have many properties
in common and thus the simulation and propagation of pulsating waves may open a
new route to explore the classical solitary dynamics in nonlinear optics and
its quantum analogy in ultralcold fields.
