  Vector polarization induced by a change in scalar phase has been far beyond
our understanding of the relationship between polarization and phase in
classical optics due to the entanglement of inherent polarized modes of light
beams. To overcome this limitation, we establish this miraculous relationship
by the principle of phase vectorization, which can transform three particular
phases into linear, circular and elliptical polarizations. A polarized-spatial
light modulator based on the principle of phase vectorization can be achieved
using a phase-only spatial light modulator, which not only enables pixel-level
polarization manipulation of light beams in a real-time dynamic way but also
simultaneously retains complete phase control. This work demonstrates the
phase-to-polarization link and reports the creation of polarized-spatial light
modulator, which will transform our view of the natural properties of light
beam and pave the way for the era of vector optics.
