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<sub>x</sub>, a<sub>y</sub>, b<sub>x</sub>, and b<sub>y</sub> 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.
© 2004 Optical Society of America
(030.5630) Coherence and statistical optics : Radiometry
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.4690) Fourier optics and signal processing : Morphological transformations
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(140.3300) Lasers and laser optics : Laser beam shaping
Tatiana Alieva and Martin J. Bastiaans, "Evolution of the vortex and the asymmetrical parts of orbital angular momentum in separable first-order optical systems," Opt. Lett. 29, 1587-1589 (2004)