The entire range of transformations that a Laguerre-Gaussian (LG) beam with astigmatism can go through in free space is clarified. The transformations are governed by the relative phase between the astigmatic Hermite-Gaussian components. Formulas describing the behavior of this relative phase are obtained and used to classify and map the transformation patterns to initial beam parameters. The difference between an LG beam and a phase singular beam generated by a hologram under astigmatic conditions is also investigated.
© 2005 Optical Society of America
(080.1010) Geometric optics : Aberrations (global)
(140.3300) Lasers and laser optics : Laser beam shaping
(220.1010) Optical design and fabrication : Aberrations (global)
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation
Atsushi Wada, Takumi Ohtani, Yoko Miyamoto, and Mitsuo Takeda, "Propagation analysis of the Laguerre-Gaussian beam with astigmatism," J. Opt. Soc. Am. A 22, 2746-2755 (2005)