Controlling phase of arbitrary polarizations using both the geometric phase and the propagation phase

Subwavelength spatial control of phase using metasurfaces is attractive for practical applications such as flat lens, vector beam generator, ultrathin wave-plate and high-resolution holography. All-dielectric metasurfaces provide two phase modulation mechanisms, which are propagation phase dependent on the dimension of meta-atoms and geometric phase dependent on the orientation of meta-atoms. Recently, it was proposed that by combining geometric phase and propagation phase, arbitrary and independent phase profiles can be imposed on a pair of orthogonal polarizations. However, a succinct expression of phase change introduced during an arbitrary polarization conversion process has not been presented. Here, we derive the geometric phase for the general case of nonorthogonal polarization conversions. Through the numerical simulations of a metasurface orbital angular momentum generator under both circular and elliptical polarization illuminations, we verify our theoretical analyses. This work presents the mechanism of controlling polarization and phase of arbitrary polarizations using both geometric phase and propagation phase, which exhibits the potential to enrich the capacity of polarization multiplexed metasurfaces.