The mechanism for energy transfer in the rotational frequency shift of a light beam

It is well known that when a light beam containing angular momentum is rotated about the propagation axis it is shifted in frequency. The magnitude of the shift is equal to the angular momentum per photon, in units of h, multiplied by the rotation frequency of the beam. Here it is shown that the associated energy transfer can be understood in terms of ray optics and the torque acting on the optical component inducing the rotation.