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Recently, spatiotemporally modulated metamaterial has been theoretically demonstrated for the design of Doppler cloak, a technique used to cloak the motion of moving objects from the observer by compensating for the Doppler shift. Linear Doppler effect has an angular counterpart, i.e., the rotational Doppler effect, which can be observed by the orbital angular momentum (OAM) of light scattered from a spinning object. In this work, we predict that the spatiotemporally modulated metamaterial has its angular equivalent phenomenon. We therefore propose a technique to observe the rotational Doppler effect by cylindrical spatiotemporally modulated metamaterial. Conversely, such a metamaterial is able to cloak the Doppler shift associated with linear motion by generating an opposite rotational Doppler shift. This novel concept is theoretically analyzed, and a conceptual design by spatiotemporally modulating the permittivity of a voltage-controlled OAM ferroelectric reflector is demonstrated by theoretical calculation and numerical simulation. Finally, a Doppler cloak is experimentally demonstrated by a spinning OAM metasurface in radar system, which the spatiotemporal reflection phase are mechanically modulated. Our work presented in this paper may pave the way for new directions of OAM carrying beams and science of cloaking, and also explore the potential applications of tunable materials and metasurfaces.

Design and experimental demonstration of Doppler cloak from spatiotemporally modulated metamaterials based on rotational Doppler effect