Spatial dependence of the frequency spectrum of a rotating optical beam

A rotating optical beam displaced relative to the rotational axis becomes polychromatic due to the rotational Doppler effect. The case where the initial beam has the form of a superposition of two Laguerre-Gauss modes and carries an elementary image in the form of an asymmetric intensity distribution is considered. The spatial distribution of the monochromatic components in the beam cross section is determined.