## Family of hypergeometric laser beams

JOSA A, Vol. 25, Issue 1, pp. 262-270 (2008)

http://dx.doi.org/10.1364/JOSAA.25.000262

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### Abstract

We discuss a three-parameter family of paraxial coherent light fields that originate from a complex amplitude composed of the following four cofactors: the Gaussian beam, a logarithmic axicon, a spiral phase plate (angular harmonic), and an amplitude power function with a possible singularity at the origin of coordinates. For such types of beams, the near-field complex amplitude is proportional to the degenerate hypergeometric function, prompting the beams’ name—hypergeometric (HyG) beams. When the Gaussian beam is replaced by a plane wave, the above beams change to generalized HyG modes that preserve their structure up to scale upon propagation. The intensity profile of the HyG beams is similar to that of the Bessel modes, forming a set of alternating bright and dark rings. However, the thickness of the rings of the HyG beams decreases with increasing ring number.

© 2008 Optical Society of America

**OCIS Codes**

(030.4070) Coherence and statistical optics : Modes

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(050.4865) Diffraction and gratings : Optical vortices

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: September 21, 2007

Manuscript Accepted: November 9, 2007

Published: December 21, 2007

**Citation**

Victor V. Kotlyar and Alexey A. Kovalev, "Family of hypergeometric laser beams," J. Opt. Soc. Am. A **25**, 262-270 (2008)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-1-262

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### References

- M. Gao, C. Gao, and Z. Lin, "Generation and application of the twisted beam with orbital angular momentum," Chin. Opt. Lett. 5, 89-92 (2007).
- K. Duan and B. Lu, "Application of the Wiener distribution function to complex-argument Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation," Opt. Laser Technol. 39, 110-115 (2007). [CrossRef]
- S. R. Seshardi, "Self-interaction and mutual interaction of complex-argument Laguerre-Gauss beams," Opt. Lett. 31, 619-621 (2006). [CrossRef]
- A. Kostenbauder, Y. Sun, and A. E. Siegman, "Eigenmode expansions using biorthogonal functions: complex-valued Hermite-Gaussians: reply to comment," J. Opt. Soc. Am. A 23, 1528-1529 (2006). [CrossRef]
- V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, "Elliptic Laguerre-Gaussian beams," J. Opt. Soc. Am. A 23, 43-56 (2006). [CrossRef]
- Z. Mei, J. Gu, and D. Zhao, "The elliptical Laguerre-Gaussian beam and its propagation," Optik (Stuttgart) 118, 9-12 (2007).
- A. Burvall, K. Kolacz, A. V. Goncharov, Z. Jaroszewicz, and C. Dainty, "Lens axicons in oblique illumination," Appl. Opt. 46, 312-318 (2007). [CrossRef] [PubMed]
- V. V. Kotlyar, S. N. Khonina, R. V. Skidanov, and V. A. Soifer, "Rotation of laser beams with zero of the orbital angular momentum," Opt. Commun. 274, 8-14 (2007). [CrossRef]
- V. Kotlyar, A. Kovalev, V. Soifer, C. Tuvey, and J. Devis, "Sidelobes contrast reduction for optical vortex beams using a helical axicon," Opt. Lett. 32, 921-923 (2007). [CrossRef] [PubMed]
- R. K. Singh, P. Senthilkumaran, and K. Singh, "Effect of coma on the focusing of an apertured singular beam," Opt. Lasers Eng. 45, 488-494 (2007). [CrossRef]
- R. K. Singh, P. Senthilkumaran, and K. Singh, "Focusing of a vortex carrying beam with Gaussian background by a lens in the presence of spherical aberration and defocusing," Opt. Lasers Eng. 45, 773-782 (2007). [CrossRef]
- R. K. Singh, P. Senthilkumaran, and K. Singh, "Influence of astigmatism and defocusing on the focusing of a singular beam," Opt. Commun. 270, 128-138 (2007). [CrossRef]
- R. K. Singh, P. Senthilkumaran, and K. Singh, "The effect of astigmatism on the diffraction of a vortex carrying beam with a Gaussian background," J. Opt. A, Pure Appl. Opt. 9, 543-554 (2007). [CrossRef]
- V. V. Kotlyar, R. V. Skidanov, S. N. Khonina, and V. A. Soifer, "Hypergeometric modes," Opt. Lett. 32, 742-744 (2007). [CrossRef] [PubMed]
- V. V. Kotlyar, R. V. Skidanov, S. N. Khonina, and S. A. Balalayev, "Hyper-geometric modes," Comput. Opt. 30, 16-22 (2006) (in Russian).
- J. Durnin, J. J. Miceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1-1501 (1987). [CrossRef]
- S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, "Rotation of microparticles with Bessel beams generated by diffractive elements," J. Mod. Opt. 51, 2167-2184 (2004). [CrossRef]
- Z. Jaroszewicz, J. Sochacki, A. Kolodziejczyk, and L. R. Staronski, "Apodized annular-aperture logarithmic axicon: smoothness and uniformity of intensity distributions," Opt. Lett. 18, 1893-1895 (1993). [CrossRef] [PubMed]
- J. Sochacki, Z. Jaroszewicz, L. R. Staronski, and A. Kolodziejczyk, "Annular-aperture logarithmic axicon," J. Opt. Soc. Am. A 10, 1765-1768 (1993). [CrossRef]
- A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marychev, Integrals and Series. Special Functions (Nauka, 1983) (in Russian).
- M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions, Applied Mathematics Series (National Bureau of Standards, 1965).
- V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, "Diffraction of conic and Gaussian beams by a spiral phase plate," Appl. Opt. 45, 2656-2665 (2006). [CrossRef] [PubMed]
- A. E. Siegman, Lasers (University Science, 1986).
- E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato, "Hypergeometric-Gaussian modes," Opt. Lett. 32, 3053-3055 (2007). [CrossRef] [PubMed]
- S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Pääkkönen, J. Simonen, and J. Turunen, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001). [CrossRef]
- V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, "Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate," J. Opt. Soc. Am. A 22, 849-861 (2005). [CrossRef]

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