  The multiple scattering of an ultrashort laser pulse by a turbid dispersive
medium (namely a cloud of bubbles in water) is investigated by means of Monte
Carlo simulations. The theory of Gouesbet and Gr\'ehan [Part. Part. Syst.
Charact. 17 213-224 (2000)] is used to derive an energetic model of the
scattering transient. The spreading and extinction of the pulse is decoupled
from the transient of scattering to describe each phenomenon individually. The
transient of scattering is modeled with the Lorenz-Mie Theory, thus also valid
for a relative refractive index lower than one, contrary to the Debye series
expansion which does not converge close to the critical angle. To this aim, the
Scattering Impulse Response Function (SIRF) allows to detect the different
modes of scattering transient in time and direction. The present approach is
more generic and can simulate clouds of air bubbles in water. Two Monte-Carlo
approaches are proposed. The first is a pure Monte Carlo approach where the
delay due to the scattering is randomly drawn at each event, while the second
is based on the transport of the whole scattering signal. They are both
embedded in the Monte Carlo code Scatter3D [JOSA A 24, 2206-2219 (2007)]. Both
models produce equivalent trends and are validated against published numerical
results. They are applied to the multiple scattering of ultra short pulse by a
cloud of bubble in water in the forward direction. The pulse spread due to the
propagation in water is computed for a wide range of traveled distances and
pulse durations, and the optimal pulse duration is given to minimize the pulse
spread at a given distance. The main result is that the scattered photons exit
the turbid medium earlier than the ballistic photons and produce a double peak
related to the refraction in the bubble. This demonstrates the possibility to
develop new diagnostics to characterize dynamic bubbly flows.
