Rotational Doppler effect

A frequency change associated with rotation and exchange of angular momentum. If an optical element rotates at angular velocity $\Omega$ about a chosen axis and gains angular momentum $\Delta L$ from a photon, its mechanical energy gain is $\Omega \Delta L$ in the prescribed slow-rotation model. Energy conservation then gives photon frequency change $\Delta \omega =-\Omega \Delta L/\hslash$. The rotating half-wave plate frequency shift is a spin-polarization example.