OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 19 — Sep. 15, 2008
  • pp: 15254–15267

An alternative theoretical model for an anomalous hollow beam

Yangjian Cai, Zhaoying Wang, and Qiang Lin  »View Author Affiliations

Optics Express, Vol. 16, Issue 19, pp. 15254-15267 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (759 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An alternative and convenient theoretical model is proposed to describe a flexible anomalous hollow beam of elliptical symmetry with an elliptical solid core, which was observed in experiment recently (Phys. Rev. Lett, 94 (2005) 134802). In this model, the electric field of anomalous hollow beam is expressed as a finite sum of elliptical Gaussian modes. Flat-topped beams, dark hollow beams and Gaussian beams are special cases of our model. Analytical propagation formulae for coherent and partially coherent anomalous hollow beams passing through astigmatic ABCD optical systems are derived. Some numerical examples are calculated to show the propagation and focusing properties of coherent and partially coherent anomalous hollow beams.

© 2008 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(140.3430) Lasers and laser optics : Laser theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

Original Manuscript: June 17, 2008
Revised Manuscript: September 2, 2008
Manuscript Accepted: September 7, 2008
Published: September 12, 2008

Yangjian Cai, Zhaoying Wang, and Qiang Lin, "An alternative theoretical model for an anomalous hollow beam," Opt. Express 16, 15254-15267 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. Palma, "Decentered Gaussian beams, ray bundles and Bessel-Gaussian beams," Appl. Opt. 36, 1116-1120 (1997). [CrossRef] [PubMed]
  2. J. D. Strohschein, H. J. J. Seguin, and C. E. Capjack, "Beam propagation constans for a radial laser array," Appl. Opt. 37, 1045-1048 (1998). [CrossRef]
  3. N. Nishi, T. Jitsuno, K. Tsubakimoto, S. Matsuoka, N. Miyanaga, and M. Nakatsuka, "Two-dimensional multi-lens array with circular aperture spherical lens for flat-top irradiation of inertial confinement fusion target," Opt. Rev. 7, 216-220 (2000). [CrossRef]
  4. Y. Li, "Light beam with flat-topped profiles," Opt. Lett. 27, 1007-1009 (2002). [CrossRef]
  5. Y. Cai and Q. Lin, "Light beams with elliptical flat-topped profile," J. Opt. A: Pure Appl. Opt. 6, 390-395 (2004). [CrossRef]
  6. Y. Cai and L. Zhang, "Coherent and partially coherent dark hollow beams with rectangular symmetry and paraxial propagation properties," J. Opt. Soc. Am. B 23, 1398-1407 (2006). [CrossRef]
  7. Y. Cai and S. He, "Propagation of various dark hollow beams in a turbulent atmosphere," Opt. Express 14, 1353-1367 (2006). [CrossRef] [PubMed]
  8. Z. Mei and D. Zhao, "Controllable elliptical dark-hollow beams," J. Opt. Soc. Am. A 23, 919-925 (2006). [CrossRef]
  9. H. T. Eyyuboðlu, "Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence," Opt. Laser Technol. 40, 156-166 (2008). [CrossRef]
  10. Y. Baykal, "Formulation of correlations for general-type beams in atmospheric turbulence," J. Opt. Soc. Am. A 23, 889-893 (2006). [CrossRef]
  11. C. Arpali, C. Yazicioglu, H. T. Eyyuboglu, S. A. Arpali, and Y. Baykal, "Simulator for general-type beam propagation in turbulent atmosphere," Opt. Express 14, 8918-8928 (2006). [CrossRef] [PubMed]
  12. J. Yin, W. Gao, and Y. Zhu, "Generation of dark hollow beams and their applications," in Progress in Optics, Vol. 44, E. Wolf, ed., (North-Holland, Amsterdam, 2003), pp.119-204.
  13. 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, 4713-4716 (1997). [CrossRef]
  14. J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297-301 (2000). [CrossRef]
  15. Y. Cai, X. Lu, and Q. Lin, "Hollow Gaussian beam and its propagation," Opt. Lett. 28, 1084-1086 (2003). [CrossRef] [PubMed]
  16. Y. Cai and Q. Lin, "Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems," J. Opt. Soc. Am. A 21, 1058-1065 (2004). [CrossRef]
  17. D. Deng, X. Fu, C. Wei, J. Shao, and Z. Fan, "Far-field intensity distribution and M2 factor of hollow Gaussian beams," Appl. Opt. 44, 7187-7190 (2005). [CrossRef] [PubMed]
  18. D. Deng, H. Yu, S. Xu, J. Shao, and Z. Fan, "Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals," Opt. Commun. 281, 202-202 (2008). [CrossRef]
  19. D. Deng, H. Yu, S. Xu, G. Tian, and Z. Fan, "Nonparaxial propagation of vectorial hollow Gaussian beams," J. Opt. Soc. Am. B 25, 83-87 (2008). [CrossRef]
  20. 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, 2076-2078 (2007). [CrossRef] [PubMed]
  21. Y. Zhang, "Generation of thin and hollow beams by the axicon with a large open angle," Opt. Commun. 281, 508-514 (2008). [CrossRef]
  22. R. K. Singh, P. Senthilkumaran, and K. Singh, "Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma," Opt. Commun. 281, 923-934 (2008). [CrossRef]
  23. G. Wu, Q. Lou, and J. Zhou, "Analytical vectorial structure of hollow Gaussian beams in the far field," Opt. Express 16, 6417-6424 (2008). [CrossRef] [PubMed]
  24. T. Wang, J. Pu, and Z. Chen, "Propagation of partially coherent vortex beams in a turbulent atmosphere," Opt. Eng. 47, 036002 (2008). [CrossRef]
  25. Y. Cai, H. T. Eyyuboðlu, and Y. Baykal, "Scintillation of astigmatic dark hollow beams in a weak turbulent atmosphere," J. Opt. Soc. Am. A 25, 1497-1503 (2008). [CrossRef]
  26. Y. K. Wu, J. Li, and J. Wu, "Anomalous hollow electron beams in a storage ring," Phys. Rev. Lett. 94, 134802 (2005). [CrossRef] [PubMed]
  27. Y. Cai, "Model for an anomalous hollow beam and its paraxial propagation," Opt. Lett. 32, 3179-3181 (2007). [CrossRef] [PubMed]
  28. Y. Cai and F. Wang, "Partially coherent anomalous hollow beam and its paraxial propagation," Phys. Lett. A 372, 4654-4660 (2008).
  29. J. A. Arnaud, "Hamiltonian theory of beam mode propagation," in Progress in Optics, Vol. XI, E. Wolf, ed. (North-Holland, 1973), pp. 247-304.
  30. Q. Lin, S. Wang, J. Alda, and E. Bernabeu, "Transformation of non-symmetric Gaussian beam into symmetric one by means of tensor ABCD law," Optik 85, 67 (1990).
  31. S. A. Collins, "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Am. 60, 1168-1177 (1970). [CrossRef]
  32. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, 1964).
  33. S. Wang and L. Ronchi, "Principles and design of optical arrays," in Progress in Optics, Vol. XXV, E. Wolf, ed. (North-Holland, 1988), pp. 279.
  34. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  35. Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, "Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression," Phys. Rev. Lett. 53, 1057-1060 (1984). [CrossRef]
  36. J. C. Ricklin and F. M. Davidson, "Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication," J. Opt. Soc. Am. A 19, 1794-1802 (2002). [CrossRef]
  37. Q. Lin and Y. Cai, "Tensor ABCD law for partially coherent twisted anisotropic Gaussian Schell-model beams," Opt. Lett. 27, 216-218 (2002). [CrossRef]
  38. Y. Cai and S. Zhu, "Ghost imaging with incoherent and partially coherent light radiation," Phys. Rev. E 71, 056607 (2005). [CrossRef]
  39. Y. Cai and S. Zhu, "Ghost interference with partially coherent radiation," Opt. Lett. 29, 2716-2718 (2004). [CrossRef] [PubMed]
  40. Y. Cai, Q. Lin, and S. Zhu, "Coincidence fractional Fourier transform with entangled photon pairs and incoherent light," Appl. Phy. Lett. 86, 021112 (2005). [CrossRef]
  41. Y. Cai and S. Zhu, "Coincidence fractional Fourier transform with partially coherent light radiation," J. Opt. Soc. Am. A 22, 1798-1804 (2005). [CrossRef]
  42. F. Wang, Y. Cai, and S. He, "Experimental observation of coincidence fractional Fourier transform with a partially coherent beam," Opt. Express 14, 6999-7004 (2006). [CrossRef] [PubMed]
  43. Y. Cai and S. He, "Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere," Appl. Phys. Lett. 89, 041117 (2006). [CrossRef]
  44. Y. Cai and L. Hu, "Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system," Opt. Lett. 31, 685-687 (2006). [CrossRef] [PubMed]
  45. Y. Cai and U. Peschel, "Second-harmonic generation by an astigmatic partially coherent beam," Opt. Express 15, 15480-15492 (2007). [CrossRef] [PubMed]
  46. F. Wang and Y. Cai, "Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics," J. Opt. Soc. Am. A 24, 1937-1944 (2007). [CrossRef]
  47. X. Lü and Y. Cai, "Partially coherent circular and elliptical dark hollow beams and their paraxial propagations," Phys. Lett. A 369, 157-166 (2007). [CrossRef]
  48. C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, "Generation of a high-quality partially coherent dark hollow beam with a multimode fiber," Opt. Lett. 33, 1389-1391(2008). [CrossRef] [PubMed]
  49. F. V. Dijk, G. Gbur, and T. D. Visser, "Shaping the focal intensity distribution using spatial coherence," J. Opt. Soc. Am. A 25, 575-581 (2008). [CrossRef]
  50. F. Wang and Y. Cai, "Experimental generation of a partially coherent flat-topped beam," Opt. Lett. 33, 1795-1797 (2008). [CrossRef] [PubMed]

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited