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 3 N − 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 3 k ${3}^{k}$ (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.

中文翻译：

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使用级联超表面的平衡三元启发可重构涡旋光束

电磁涡旋携带轨道角动量，这是波最基本的特性之一。这种涡旋的阶数原则上可以是无界的，从而促进了用于光通信、光子集成电路等的高性能波技术。然而，以可重构、宽带和具有成本效益的方式生成高阶涡旋光束仍然是一个关键挑战。在这里，受平衡三元概念的启发，我们展示了通过级联生成可重构的有序可控涡旋。ñ层超表面。我们从理论上证明了 3 ñ - 1 ${3}^{N}-1$ 级联可以产生不同的涡流模式ñ超表面，每个都用作单独的涡流束发生器，数量级为 3 ķ ${3}^{k}$ (ķ= 0,1,2 …, ñ - 1 $N-1$ ）。作为概念验证演示，通过级联的 3 个超表面在宽毫米波区域展示了 26 个不同涡旋光束的可重构代，其阶数从 1 到 13 和从 -1 到 -13。我们的方法可以很容易地以可重新配置和易于实现的方式扩展到任意阶的涡流束发生器，为巨大的实际应用铺平了新的道路。