OSA's Digital Library

Optics Letters

Optics Letters


  • Editor: Anthony J. Campillo
  • Vol. 32, Iss. 21 — Nov. 1, 2007
  • pp: 3053–3055

Hypergeometric-Gaussian modes

Ebrahim Karimi, Gianluigi Zito, Bruno Piccirillo, Lorenzo Marrucci, and Enrico Santamato  »View Author Affiliations

Optics Letters, Vol. 32, Issue 21, pp. 3053-3055 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (145 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(230.6120) Optical devices : Spatial light modulators

ToC Category:
Optical Devices

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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995). [CrossRef]
  2. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987). [CrossRef] [PubMed]
  3. J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. Lett. 83, 1171 (1999). [CrossRef]
  4. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987). [CrossRef]
  5. J. A. Davis, D. E. McNamara, D. M. Cottrell, and J. Campos, Opt. Lett. 25, 99 (2000). [CrossRef]
  6. G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002). [CrossRef] [PubMed]
  7. G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007). [CrossRef]
  8. W. Miller, Jr., Symmetry and Separation of Variables (Addison-Wesley, 1977).
  9. V. V. Kotlyar, R. V. Skidanov, S. N. Khonina, and V. A. Soifer, Opt. Lett. 32, 742 (2007). [CrossRef] [PubMed]
  10. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1970).
  11. The Hilbert inner product is defined according to ⟨u∣v⟩=∫u*vρdρdphiv.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited