Transverse linear and orbital angular momenta of beam waves and propagation in random media

For paraxial propagation of scalar waves, the classic electromagnetic theory definition of transverse linear (TLM) and orbital angular (OAM) momenta of the beam wave are represented in terms of the coherence function. We show in examples that neither is the presence of optical vortices necessary for the intrinsic OAM, nor does the presence of optical vortices warrant the non-zero intrinsic OAM. The OAM is analyzed for homogeneously coherent and twisted partially coherent beam waves. A twisted Gaussian beam has an intrinsic OAM with a per-unit power value that can be continuously changed by varying the twist parameters. Using the parabolic propagation equation for the coherence function, we show that both the total TLM and OAM are conserved for the free-space propagation, but not for propagation in an inhomogeneous medium. In the presence of the random inhomogeneous medium, the total TLM and OAM are conserved in average, but the OAM fluctuations grow with the propagation path. This growth is slower for beams with rotation-symmetric irradiance.