  We demonstrate an optomechanical platform where optical mode conversion
mediated by mechanical motion enables arbitrary tailoring of polarization
states of propagating light fields. Optomechanical interactions are realized in
a Fabry-Per\'ot resonator, which naturally supports two polarization-degenerate
states while an optical control field induces rotational symmetry breaking.
Applying such principles, the entire Poincar\'e sphere is spanned by just
optical control of the driving field, realizing reciprocal and non-reciprocal
optomechanically-induced birefringence for linearly polarized and circularly
polarized control driving. A straightforward extension of this setup also
enables all-optical tunable isolation and circulation. Our findings open new
avenues to exploit optomechanics for arbitrary manipulation of light
polarization.
