Analysis on rotational Doppler Effect based on modal expansion method

We theoretically investigate the optical rotational Doppler Effect using modal expansion method. We find that the frequency shift content is only determined by the surface of spinning object and the reduced Doppler shift is linear to the change of mode index. The theoretical model makes us better understand the physical processes of rotational Doppler Effect. It can provide theoretical guidance for many related applications, such as detection of rotating bodies, detection of OAM and frequency shift.