  The effect of the pulse-shape on pump-probe spectroscopies is examined for
the simplest model of noninteracting fermions on an infinite-dimensional
hypercubic lattice. The probe-modified density of states follows the time
evolution of the pump and displays narrowing and Floquet-like sidebands at the
pump maximum, whereas the photoelectron spectra are also strongly affected by
the nonequilibrium occupation of the single-particle states due to the
excitation from the pump. The nonequilibrium Raman cross section is derived,
and the nonresonant one in both the $A_{1\mathrm{g}}$ and $B_{1\mathrm{g}}$
symmetries contains a number of peaks at the pump maximum, which can be
attributed to an interference effect or Brillouin scattering off the time
variations of the stress tensor. Both the "measured" occupation of
single-particle states and the ratio of Stokes to anti-Stokes peaks are
strongly modified by the probe-pulse width, which must be included in the
interpretation of experimental results.
