  Light propagation through multimode fibers suffers from spatial distortions
that lead to a scrambled intensity profile. In previous work, the correction of
such distortions using various wavefront control methods has been demonstrated
in the continuous wave case. However, in the ultra-fast pulse regime, modal
dispersion temporally broadens a pulse after propagation. Here, we present a
method that compensates for spatial distortions and mitigates temporal
broadening due to modal dispersion by a selective phase conjugation process in
which only modes of similar group velocities are excited. The selectively
excited modes are forced to follow certain paths through the multimode fiber
and interfere constructively at the distal tip to form a focused spot with
minimal temporal broadening. We demonstrate the delivery of focused 500 fs
pulses through a 30 cm long step-index multimode fiber. The achieved pulse
duration corresponds to approximately 1/30th of the duration obtained if modal
dispersion was not controlled. Moreover, we measured a detailed two-dimensional
map of the pulse duration at the output of the fiber and confirmed that the
focused spot produces a two-photon absorption effect. This work opens new
possibilities for ultra-thin multiphoton imaging through multimode fibers.
