| Summary: | Electromagnetic vortex carries the orbital angular momentum, one of the most fundamental properties of waves. The order of such vortex can be unbounded in principle, thus facilitating high-capability wave technologies for optical communications, photonic integrated circuits and others. However, it remains a key challenge to generate the high-order vortex beams in a reconfigurable, broadband and cost-effective manner. Here, inspired by the balanced-ternary concept, we demonstrate the reconfigurable generation of order-controllable vortices via cascaded N-layer metasurfaces. We theoretically showed that 3N−1${3}^{N}-1$ different vortex modes can be generated by cascading N metasurfaces, each one serving as an individual vortex beam generator for the order of 3k${3}^{k}$ (k = 0,1,2 …, N−1$N-1$). As a proof-of-concept demonstration, a reconfigurable generation of 26 different vortex beams, with orders from 1 to 13 and from −1 to −13, is showcased in a broad millimeter-wave region by a cascade of 3 metasurfaces. Our method can be easily extended to vortex beam generator of arbitrary orders in a reconfigurable and easily implementable manner, paving a new avenue towards tremendous practical applications.
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