Graphene has attracted widespread attention in dynamic optoelectronic devices due to its tunable electrical and optical properties. But different modulation capabilities of the graphene-based designs at different frequencies are less studied.We study the electrical tunability of transmissive metalenses based on graphene when working at three frequencies 0.3, 1.25, and 2 THz, respectively. The constitutive meta-atoms are composed of graphene patches and metallic gratings for efficient phase shift in the orthogonal polarization. Although the conductivity of graphene is tunable at all the frequencies, responses of meta-atoms show weak and strong dependence on the Fermi level at the low and high frequencies, respectively. Therefore, the focal length of the metalens is not electrically tunable at 0.3 THz. In contrast, the metalenses designed at 1.25 and 2 THz show electrically adjustable focal lengths, and the tuning range of the focal length increases with frequency. The research here provides clear guidance for the design of graphene metalenses with different electrical tunabilities for a variety of application scenarios.
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