We studied a novel family of paraxial laser beams forming an overcomplete yet nonorthogonal set of modes. These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. The intensity profile is characterized by a single brilliant ring with the singularity at its center, where the field amplitude vanishes. The complex amplitude is proportional to the degenerate (confluent) hypergeometric function, and therefore we term such beams hypergeometric-Gaussian (HyGG) modes. Unlike the recently introduced hypergeometric modes [ Opt. Lett. 32, 742 (2007) ], the HyGG modes carry a finite power and have been generated in this work with a liquid-crystal spatial light modulator. We briefly consider some subfamilies of the HyGG modes as the modified Bessel Gaussian modes, the modified exponential Gaussian modes, and the modified Laguerre–Gaussian modes.
© 2007 Optical Society of America
Original Manuscript: August 6, 2007
Manuscript Accepted: September 11, 2007
Published: October 15, 2007
Ebrahim Karimi, Gianluigi Zito, Bruno Piccirillo, Lorenzo Marrucci, and Enrico Santamato, "Hypergeometric-Gaussian modes," Opt. Lett. 32, 3053-3055 (2007)