在旋转和线性多普勒效应之间共享共同的起源
Sharing a common origin between the rotational and linear Doppler effects
摘要：
众所周知的线性多普勒效应来自于源和观察者之间的线性运动，而不太为人所知的旋转多普勒效应来自于旋转运动。在这里，我们提出的理论和实验说明旋转和线性多普勒效应之间的关系。螺旋相位板用于产生携带轨道角动量的光束，并且测量由其旋转和/或线性运动引起的频移。通过考虑运动引起的时间演化相位或光-物质相互作用中的动量和能量守恒，我们导出了与旋转和线性运动相关的旋转多普勒频移、线性多普勒频移和整体多普勒频移。我们证明了旋转和线性多普勒频移之间的关系，其中任何一个可以从其他效果，从而说明他们的共同起源。此外，对于更一般的运动粗糙表面，还推导出旋转和线性多普勒效应之间的密切关系。
英文摘要：
The well-known linear Doppler effect arises from the linear motion between source and observer, while the less well-known rotational Doppler effect arises from the rotational motion. Here, we present both theories and experiments illustrating the relationship between the rotational and linear Doppler effects. A spiral phaseplate is used to generate a light beam carrying orbital angular momentum and the frequency shift is measured arising from its rotational and/or linear motion. By considering either the motion-induced time-evolving phase or the momentum and energy conservation in light-matter interactions, we derive the rotational Doppler shift, linear Doppler shift, and overall Doppler shift associated with rotational and linear motions. We demonstrate the relationship between rotational and linear Doppler shifts, either of which can be derived from the other effect, thereby illustrating their shared origin. Moreover, the close relationship between rotational and linear Doppler effects is also deduced for a more general moving rough surface.
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