Abstract

Besides the path-length dependent phase (dynamic phase) that light accumulate during its propagation, a polarized optical wave can experience a phase-shift that is path-independent, also known as geometric phase. The latter emerges under cyclic transformation of degrees of freedom of light such as: propagation direction, Rytov-Vladimirskii-Berry phase; and polarization, Pancharatnam-Berry (PB) phase [1]. To obtain the PB phase, the polarization is modulated using wave plates with spatially varying optical axis. For half-wave plates with optical axis at angle θ, and incident circular polarized light of handedness σ, the phase is known to be 2σθ [2,3]. These spatially varying wave plates can be realized using sub-wavelength gratings [2] or liquid crystals [3]. After the seminal paper of Marrucci et al. [3], a wide range of Pancharatnam-Berry optical elements (PBOEs) with advanced phase shaping functionalities were demonstrated using statically structured liquid crystalline media [3,4]. Dynamical PBOEs device have also been developed using electro-optical liquid crystals valves [5,6], and were used to generate singular optical beams. In the above cases of PB phase, light still need to traverse the bulk of the medium.

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