  We study the interplay between coherent light-matter interactions and
non-resonant pulse propagation effects when ultra-short pulses propagate in
room-temperature quantum-dot (QD) semiconductor optical amplifiers (SOAs). The
signatures observed on a pulse envelope after propagating in a transparent SOA,
when coherent Rabi-oscillations are absent, highlight the contribution of
two-photon absorption (TPA), and its accompanying Kerr-like effect, as well as
of linear dispersion, to the modification of the pulse complex electric field
profile. These effects are incorporated into our previously developed
finite-difference time-domain comprehensive model that describes the
interaction between the pulses and the QD SOA. The present, generalized, model
is used to investigate the combined effect of coherent and non-resonant
phenomena in the gain and absorption regimes of the QD SOA. It confirms that in
the QD SOA we examined, linear dispersion in the presence of the Kerr-like
effect causes pulse compression, which counteracts the pulse peak suppression
due to TPA, and also modifies the patterns which the coherent Rabi-oscillations
imprint on the pulse envelope under both gain and absorption conditions. The
inclusion of these effects leads to a better fit with experiments and to a
better understanding of the interplay among the various mechanisms so as to be
able to better analyze more complex future experiments of coherent light-matter
interaction induced by short pulses propagating along an SOA.
