  Multimode optical fibers have seen increasing applications in communication,
imaging, high-power lasers and amplifiers. However, inherent imperfections and
environmental perturbations cause random polarization and mode mixing, making
the output polarization states very different from the input one. This poses a
serious issue for employing polarization sensitive techniques to control
light-matter interactions or nonlinear optical processes at the distal end of a
fiber probe. Here we demonstrate a complete control of polarization states for
all output channels by only manipulating the spatial wavefront of a laser beam
into the fiber. Arbitrary polarization states for individual output channels
are generated by wavefront shaping without constraint on input polarizations.
The strong coupling between spatial and polarization degrees of freedom in a
multimode fiber enables full polarization control with spatial degrees of
freedom alone, transforming a multimode fiber to a highly-efficient
reconfigurable matrix of waveplates.
