OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 9 — Apr. 23, 2012
  • pp: 9682–9691

Hollow sinh-Gaussian beams and their paraxial properties

Qiongge Sun, Keya Zhou, Guangyu Fang, Guoqiang Zhang, Zhengjun Liu, and Shutian Liu  »View Author Affiliations

Optics Express, Vol. 20, Issue 9, pp. 9682-9691 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1477 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A new mathematical model of dark-hollow beams, described as hollow sinh-Gaussian (HsG) beams, has been introduced. The intensity distributions of HsG beams are characterized by a single bright ring along the propagation whose size is determined by the order of beams; the shape of the ring can be controlled by beam width and this leads to the elliptical HsG beams. Propagation characteristics of HsG beams through an ABCD optical system have been researched, they can be regarded as superposition of a series of Hypergeometric-Gaussian (HyGG) beams. As a numerical example, the propagation characteristics of HsG beams in free space have been demonstrated graphically.

© 2012 OSA

OCIS Codes
(140.3300) Lasers and laser optics : Laser beam shaping
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

Original Manuscript: February 28, 2012
Revised Manuscript: April 3, 2012
Manuscript Accepted: April 3, 2012
Published: April 12, 2012

Qiongge Sun, Keya Zhou, Guangyu Fang, Guoqiang Zhang, Zhengjun Liu, and Shutian Liu, "Hollow sinh-Gaussian beams and their paraxial properties," Opt. Express 20, 9682-9691 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett.78(25), 4713–4716 (1997). [CrossRef]
  2. M. Yan, J. Yin, and Y. Zhu, “Dark-hollow-beam guiding and splitting of a low-velocity atomic beam,” J. Opt. Soc. Am. B17(11), 1817–1820 (2000). [CrossRef]
  3. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987). [CrossRef] [PubMed]
  4. R. M. Herman and T. A. Wiggins, “Production and uses of diffraction less beams,” J. Opt. Soc. Am. A8(6), 932–942 (1991). [CrossRef]
  5. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun.177(1-6), 297–301 (2000). [CrossRef]
  6. S. Topuzoski and Lj. Janicijevic, “Conversion of high-order Laguerre-Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun.282(17), 3426–3432 (2009). [CrossRef]
  7. C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express17(15), 12891–12899 (2009). [CrossRef] [PubMed]
  8. I. A. Litvin, N. A. Khilo, A. Forbes, and V. N. Belyi, “Intra-cavity generation of Bessel-like beams with longitudinally dependent cone angles,” Opt. Express18(5), 4701–4708 (2010). [CrossRef] [PubMed]
  9. A. Carbajal-Dominguez, J. Bernal, A. Martin-Ruiz, and G. M. Niconoff, “Generation of J(0) Bessel beams with controlled spatial coherence featuresJ0,” Opt. Express18(8), 8400–8405 (2010). [CrossRef] [PubMed]
  10. Q. Sun, K. Zhou, G. Fang, Z. Liu, and S. Liu, “Generation of spiraling high-order Bessel beams,” Appl. Phys. B104(1), 215–221 (2011). [CrossRef]
  11. V. Belyi, A. Forbes, N. Kazak, N. Khilo, and P. Ropot, “Bessel-like beams with z-dependent cone angles,” Opt. Express18(3), 1966–1973 (2010). [CrossRef] [PubMed]
  12. Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett.28(13), 1084–1086 (2003). [CrossRef] [PubMed]
  13. Y. Cai and Q. Lin, “Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems,” J. Opt. Soc. Am. A21(6), 1058–1065 (2004). [CrossRef] [PubMed]
  14. Y. Cai and S. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express14(4), 1353–1367 (2006). [CrossRef] [PubMed]
  15. V. V. Kotlyar, R. V. Skidanov, S. N. Khonina, and V. A. Soifer, “Hypergeometric modes,” Opt. Lett.32(7), 742–744 (2007). [CrossRef] [PubMed]
  16. E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato, “Hypergeometric-Gaussian modes,” Opt. Lett.32(21), 3053–3055 (2007). [CrossRef] [PubMed]
  17. V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, S. N. Khonina, and J. Turunen, “Generating hypergeometric laser beams with a diffractive optical element,” Appl. Opt.47(32), 6124–6133 (2008). [CrossRef] [PubMed]
  18. B. Piccirillo, L. Marrucci, E. Karimi, and E. Santamato, “Improved focusing with Hypergeometric-Gaussian type-II optical modes,” Opt. Express16, 21070–21075 (2008).
  19. V. V. Kotlyar and A. A. Kovalev, “Family of hypergeometric laser beams,” J. Opt. Soc. Am. A25(1), 262–270 (2008). [CrossRef] [PubMed]
  20. V. V. Kotlyar, A. A. Kovalev, and V. A. Soifer, “Lensless focusing of hypergeometric laser beams,” J. Opt.13(7), 075703 (2011). [CrossRef]
  21. Z. Mei and D. Zhao, “Controllable dark-hollow beams and their propagation characteristics,” J. Opt. Soc. Am. A22(9), 1898–1902 (2005). [CrossRef] [PubMed]
  22. Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett.32(15), 2076–2078 (2007). [CrossRef] [PubMed]
  23. G. Zeng-Hui and L. Bai-Da, “Nonparaxial dark-hollow Gaussian beams,” Chin. Phys. Lett.23(1), 106–109 (2006). [CrossRef]
  24. Z. Mei and D. Zhao, “Nonparaxial propagation of controllable dark-hollow beams,” J. Opt. Soc. Am. A25(3), 537–542 (2008). [CrossRef] [PubMed]
  25. G. Schweiger, R. Nett, B. Özel, and T. Weigel, “Generation of hollow beams by spiral rays in multimode light guides,” Opt. Express18(5), 4510–4517 (2010). [CrossRef] [PubMed]
  26. D. Kuang and Z. Fang, “Microaxicave: inverted microaxicon to generate a hollow beam,” Opt. Lett.35(13), 2158–2160 (2010). [CrossRef] [PubMed]
  27. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A27(9), 2072–2077 (2010). [CrossRef] [PubMed]
  28. Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express18(26), 26946–26958 (2010). [CrossRef] [PubMed]
  29. L. W. Casperson, D. G. Hall, and A. A. Tovar, “Sinusoidal-Gaussian beams in complex optical systems,” J. Opt. Soc. Am. A14(12), 3341–3348 (1997). [CrossRef]
  30. L. W. Casperson and A. A. Tovar, “Hermite–sinusoidal-Gaussian beams in complex optical systems,” J. Opt. Soc. Am. A15(4), 954–961 (1998). [CrossRef]
  31. A. A. Tovar and L. W. Casperson, “Production and propagation of Hermite-sinusoidal-Gaussian laser beams,” J. Opt. Soc. Am. A15(9), 2425–2432 (1998). [CrossRef] [PubMed]
  32. Y. Baykal, “Correlation and structure functions of Hermite-sinusoidal-Gaussian laser beams in a turbulent atmosphere,” J. Opt. Soc. Am. A21(7), 1290–1299 (2004). [CrossRef] [PubMed]
  33. S. Konar and S. Jana, “Linear and nonlinear propagation of sinh-Gaussian pulses in dispersive media possessing Kerr nonlinearity,” Opt. Commun.236(1-3), 7–20 (2004). [CrossRef]
  34. R. P. Chen, H. P. Zheng, and X. X. Chu, “Propagation properties of a sinh-Gaussian beam in a Kerr medium,” Appl. Phys. B102(3), 695–698 (2011). [CrossRef]
  35. A. Erdelyi, W. Magnus, and F. Oberhettinger, Tables of Integral Transforms (McGraw-Hill, 1954).

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.

Supplementary Material

» Media 1: MOV (91 KB)     
» Media 2: MOV (112 KB)     
» Media 3: MOV (91 KB)     
» Media 4: MOV (110 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited