There recently has been increasing interest in the research and application of the rotational Doppler effect (RDE), which paves a promising way to detect rotating objects remotely. In order to obtain more information about the rotating object from the rotational Doppler signal, composite vortex beams by coaxial superposition of orbital angular momentum (OAM) modes are often used as the probe beam. However, to the best of our knowledge, the RDE of composite vortex beams with arbitrary OAM spectra has not yet been comprehensively studied. In this paper, the correspondence between the OAM spectrum of a probe beam and the frequency spectrum of a rotational Doppler signal is theoretically analyzed. It is explicitly revealed that the RDE frequency spectrum of scattered light is related to the product of two autocorrelation functions: one from the OAM spectrum of probe beam and the other from the spiral spectrum of rotating object. On the basis of this relation, one can regulate the RDE frequency spectrum on demand via tailoring the OAM spectrum of the probe beam. As a proof of concept we design a special composite vortex beam to eliminate the broadening of the RDE spectrum induced by misalignment. These findings are of practical value in applications such as remote sensing and optical metrology.

中文翻译：

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具有定制 OAM 谱的复合涡旋光束的旋转多普勒效应


最近，人们对旋转多普勒效应（RDE）的研究和应用越来越感兴趣，它为远程检测旋转物体开辟了一条有前景的方法。为了从旋转多普勒信号中获得更多有关旋转物体的信息，通常采用轨道角动量（OAM）模式同轴叠加的复合涡旋光束作为探测光束。然而，据我们所知，具有任意OAM谱的复合涡旋光束的RDE尚未得到全面研究。本文从理论上分析了探测光束的OAM频谱与旋转多普勒信号的频谱之间的对应关系。明确揭示了散射光的RDE频谱与两个自相关函数的乘积有关：一个来自探测光束的OAM频谱，另一个来自旋转物体的螺旋频谱。基于这一关系，可以通过定制探测波束的OAM频谱来按需调节RDE频谱。作为概念验证，我们设计了一种特殊的复合涡旋光束，以消除因未对准引起的 RDE 光谱展宽。这些发现在遥感和光学计量等应用中具有实用价值。