  Kerr-effect-induced changes of the polarization state of light are well known
in pulsed laser systems. An example is nonlinearpolarization rotation, which is
critical to the operation of many types of mode-locked lasers. Here, we
demonstrate that the Kerreffect in a high-finesse Fabry-P\'erot resonator can
be utilized to control the polarization of a continuous wave laser. It is
shownthat a linearly-polarized input field is converted into a left- or
right-circularly-polarized field, controlled via the optical power.The
observations are explained by Kerr-nonlinearity induced symmetry breaking,
which splits the resonance frequencies ofdegenerate modes with opposite
polarization handedness in an otherwise symmetric resonator. The all-optical
polarizationcontrol is demonstrated at threshold powers down to 7 mW. The
physical principle of such Kerr effect-based polarizationcontrollers is generic
to high-Q Kerr-nonlinear resonators and could also be implemented in photonic
integrated circuits. Beyondpolarization control, the spontaneous symmetry
breaking of polarization states could be used for polarization filters or
highlysensitive polarization sensors when operated close to the
symmetry-breaking poin
