  We present detailed theoretical calculations of two color, time-resolved
pump-probe differential reflectivity measurements. The experiments modeled were
performed on InMnAs/GaSb heterostructures and showed pronounced oscillations in
the differential reflectivity as well as a time-dependent background signal.
Previously, we showed that the oscillations resulted from generation of
coherent acoustic phonon wavepackets in the epilayer and were not associated
with the ferromagnetism. Now we take into account not only the oscillations,
but also the background signal which arises from photoexcited carrier effects.
The two color pump-probe reflectivity experiments are modeled using a Boltzmann
equation formalism. We include photogeneration of hot carriers in the InMnAs
quantum well by a pump laser and their subsequent cooling and relaxation by
emission of confined LO phonons. Recombination of electron-hole pairs via the
Schockley-Read carrier trapping mechanism is included in a simple relaxation
time approximation. The time resolved differential reflectivity in the
heterostructure is obtained by solving Maxwell's equations and compared with
experiment. Phase space filling, carrier capture and trapping, band-gap
renormalization and induced absorption are all shown to influence the spectra.
