Angular momentum of rotating paraxial light beams

We investigate the total angular momentum (AM) of paraxial light beams that slowly rotate around the propagation axis. The correction of the first order in angular velocity is obtained to Berry's formula giving the ratio of the total AM in the cross-section to the linear energy density for an arbitrarily polarized paraxial beam (Berry 1998 Proc. SPIE 3487 6). It is demonstrated that rotation gives rise to entanglement of the spin and the orbital AM operators in the expression for the total AM, a property not found for non-rotating beams. A particular case of rotating linear and circular optical vortices is studied, as well as rotating Hermite–Gaussian beams (Bekshaev et al 2005 Opt. Commun. 249 367). A connection with the rotational Doppler effect is made.