Reflective geometrie phase in liquid crystal photonics

Summary form only given. 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.By using twisted Bragg reflectors such as cholesteric liquid crystals (CLCs), we demonstrate a novel type of geometric phase where the interaction light and matter is limited to the surface of reflection and the polarization state is unchanged. Even though planar CLC layers reflect circular polarized light with the same handedness as the helix without changing the polarization state, we demonstrated that reflected light exhibit a geometric phase ΦB 8 = 2σ8, where 8 is the angle of the optical axis at the input face and σ the handedness of the polarization. This result has been validated numerically (Fig. 1 (a)), and experimentally with planar CLC reflector with piecewise uniform optical axis at the input interface (Fig. (b-d)).