Establishment of the fundamental phase-to-polarization link in classical optics

Vector polarization induced by a change in the scalar phase is far beyond our understanding of the relationship between polarization and phase in classical optics due to the entanglement of the 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 a polarized-spatial light modulator, which will transform our view of the natural properties of light beams and pave the way for the era of vector optics.