Alieva Krasheninnikova, TatianaBastiaans, Martin J.2023-06-202023-06-202004-07-150146-959210.1364/OL.29.001587https://hdl.handle.net/20.500.14352/51280© 2004 Optical Society of America. T. Alieva thanks the Spanish Ministry of Science and Technology for financial support of this research (Ramon y Cajal grant and project TIC 2002-01846). M. J. Bastiaan’s e-mail address is m.j.bastiaans@tue.nl. T. Alieva’s e-mail address is talieva@fis.ucm.es.We analyze the evolution of the vortex and the asymmetrical parts of orbital angular momentum during its propagation through separable first-order optical systems. We find that the evolution of the vortex part depends on only parameters a(x), a(y), b(x), and b(y) of the ray transformation matrix and that isotropic systems with the same ratio b/a produce the same change of the vortex part of the orbital angular momentum. Finally, it is shown that, when light propagates through an optical fiber with a quadratic refractive-index profile, the vortex part of the orbital angular momentum cannot change its sign more than four times per period.engjournal articlehttp://dx.doi.org/10.1364/OL.29.001587http://www.opticsinfobase.org/open access535Wigner distribution functionPartially coherent-lightBeamsÓptica (Física)2209.19 Óptica Física