Transmissive active metasurfaces for dynamic wavefront shaping based on the geometric phase. (a) Graphene nanocross metasurface with space-variant orientation for deflection of the circularly-polarized beam. (b) The transmitted circularly-polarized beam with the opposite handedness of the excitation gains the geometric phase as twice the rotation angle while keeping the transmission amplitude of 0.4 at the optimum frequency. (c) Deflection efficiency spectrum when the graphene nanocrosses have different Fermi levels. The large deflection efficiency is well maintained over a wide bandwidth and a large range of the Fermi level. Reproduced with permission from [51], Copyright WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2015. (d) Schematic of the active metasurface composed of a single layer of graphene deposited on a U-shaped metallic aperture where the spatial phase function is defined by the orientation of the U-shaped aperture. (e) Variation of the efficiency of anomalous refraction with biasing voltage and frequency. (f) Electric field distribution at two different gate voltages when the metasurface is designed for anomalous refraction. The metasurface works best at the CNP and shows reduced intensity with additional biasing due to increased loss in graphene. Reproduced with permission from [52], Copyright WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2017. (g) Monolayer graphene attached to gold aperture antennas with different orientations for geometric phase response and different lengths for resonance phase response. The resonance phase is tunable by voltage to carefully compensate the variation of the phase function at different frequencies. (h,i) The phase profile is dynamically tuned to satisfy two parabolic functions at two Fermi levels, leading to different focal lengths with comparable focusing efficiency. Reproduced with permission from [53], Copyright Chinese Laser Press, 2018.