For paraxial propagation of scalar waves classic electromagnetic theory definitions of transverse linear (TLM) and orbital angular (OAM) momenta of beam waves are simply related to the wave coherence function in the coherent wave case. This allows the extension of the TLM and OAM density concepts to the case of partially coherent waves when phase is indeterminate. We introduce a general class of Radial Irradiance-Angular Phase (RI-AP) waves that includes the Laguerre-Gaussian (LG) beams, and similar to LG beams have discrete OAM to power ratio, but have more complex phase shape than simple helices of LG beans. We show on several examples that there no direct connection between the intrinsic OAM and optical vorticity. Namely, neither the presence of the optical vortices is necessary for the intrinsic OAM, nor the presence of the optical vortices warrants the non-zero intrinsic OAM. We examine OAM for two classes of partially-coherent beam waves and show that the common, Schell-type coherence, does not add variety to the TLM and OAM in comparison to coherent waves. However, Twisted Gaussian beam has an intrinsic OAM with per unit power value that can be continuously changed by varying the twist parameters. This analysis suggests an intrinsic OAM creation method based on rotation of tilted Gaussian beam. Using the parabolic propagation equation for the coherence function, we show that both total TLM and OAM are conserved for the free space propagation. We discuss the application of the Shack-Hartman wave front sensor for the OAM measurements.
Mikhail Charnotskii, "Propagation of transverse linear and orbital angular momenta of beam waves," Proc. SPIE 10347, Optical Trapping and Optical Micromanipulation XIV, 103470Z (Presented at SPIE Nanoscience + Engineering: August 06, 2017; Published: 25 August 2017); https://doi.org/10.1117/12.2273093.
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