  We theoretically study quadrature and polarization squeezing in dispersive
optical bistability through a vectorial Kerr cavity model describing a
nonlinear cavity filled with an isotropic chi(3) medium in which self-phase and
cross-phase modulation, as well as four--wave mixing, occur. We derive
expressions for the quantum fluctuations of the output field quadratures as a
function of which we express the spectrum of fluctuations of the output field
Stokes parameters. We pay particular attention to study how the bifurcations
affecting the non-null linearly polarized output mode squeezes the orthogonally
polarized vacuum mode, and show how this produces polarization squeezing.
