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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 6 — Jun. 1, 2004
  • pp: 1058–1065

Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems

Yangjian Cai and Qiang Lin  »View Author Affiliations

JOSA A, Vol. 21, Issue 6, pp. 1058-1065 (2004)

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A new mathematical model called hollow elliptical Gaussian beam (HEGB) is proposed to describe a dark-hollow laser beam with noncircular symmetry in terms of a tensor method. The HEGB can be expressed as a superposition of a series of elliptical Hermite–Gaussian modes. By using the generalized diffraction integral formulas for light passing through paraxial optical systems, analytical propagation formulas for HEGBs passing through paraxial aligned and misaligned optical systems are obtained through vector integration. As examples of applications, evolution properties of the intensity distribution of HEGBs in free-space propagation were studied. Propagation properties of HEGBs through a misaligned thin lens were also studied. The HEGB provides a convenient way to describe elliptical dark-hollow laser beams and can be used conveniently to study the motion of atoms in a dark-hollow laser beam.

© 2004 Optical Society of America

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

Original Manuscript: August 28, 2003
Revised Manuscript: November 24, 2003
Manuscript Accepted: November 24, 2003
Published: June 1, 2004

Yangjian Cai and Qiang Lin, "Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems," J. Opt. Soc. Am. A 21, 1058-1065 (2004)

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  1. S. Marksteiner, C. M. Savage, P. Zoller, S. Rolston, “Coherent atomic waveguides from hollow optical fibers: quantized atomic motion,” Phys. Rev. A 50, 2680–2690 (1994). [CrossRef] [PubMed]
  2. W. Jhe, M. Ohtsu, H. Hori, S. R. Friberg, “Atomic waveguide using evanescent waves near optical fibers,” Jpn. J. Appl. Phys. 33, L1680–L1682 (1994). [CrossRef]
  3. M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253–3256 (1995). [CrossRef] [PubMed]
  4. H. Ito, K. Sakaki, W. Jhe, M. Ohtsu, “Evanescent-light induced atom-guidance using a hollow optical fiber with light coupled sideways,” Opt. Commun. 141, 43–47 (1997). [CrossRef]
  5. M. J. Renn, E. A. Donley, E. A. Cornell, C. E. Wieman, D. Z. Anderson, “Evanescent-wave guiding of atoms in hollow optical fibers,” Phys. Rev. A 53, R648–R651 (1996). [CrossRef] [PubMed]
  6. H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee, W. Jhe, “Laser spectroscopy of atoms guiding by evanescent waves in micro-sized hollow optical fibers,” Phys. Rev. Lett. 76, 4500–4503 (1996). [CrossRef] [PubMed]
  7. M. J. Renn, A. Z. Zozulya, E. A. Donley, E. A. Cornell, D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3697 (1997). [CrossRef]
  8. H. Ito, K. Sakaki, M. Ohtsu, W. Jhe, “Evanescent-light guiding of atoms through hollow optical fiber for optically controlled atomic deposition,” Appl. Phys. Lett. 70, 2496–2498 (1997). [CrossRef]
  9. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997). [CrossRef]
  10. Yu. B. Ovchinnikov, I. Manek, R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997). [CrossRef]
  11. J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138, 287–292 (1997). [CrossRef]
  12. S. Kuppens, M. Rauner, M. Schiffer, K. Sengstock, W. Ertmer, “Polarization-gradient cooling in a strong doughnut-mode dipole potential,” Phys. Rev. A 58, 3068–3079 (1998). [CrossRef]
  13. X. Y. Xu, V. G. Minogin, K. Lee, Y. Z. Wang, W. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999). [CrossRef]
  14. O. Morsch, D. R. Meacher, “Proposal for an optical funnel trap,” Opt. Commun. 148, 49–53 (1998). [CrossRef]
  15. J. Yin, Y. Zhu, W. Jhe, Y. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58, 509–513 (1998). [CrossRef]
  16. J. Yin, Y. Zhu, W. Wang, Y. Wang, W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998). [CrossRef]
  17. J. Yin, W. Gao, H. Wang, Q. Long, Y. Wang, “Generations of dark hollow beams and their applications in laser cooling of atoms and all-optical-type Bose–Einstein condensation,” Chin. Phys. 11, 1157–1169 (2002). [CrossRef]
  18. R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991). [CrossRef]
  19. X. Wang, M. G. Littman, “Laser cavity for generation of variable-radius rings of light,” Opt. Lett. 18, 767–770 (1993). [CrossRef] [PubMed]
  20. C. Paterson, R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996). [CrossRef]
  21. V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996). [CrossRef]
  22. J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000). [CrossRef]
  23. V. I. Balykin, V. S. Letokhov, “The possibility of deep laser focusing of an atomic beam into the AA-region,” Opt. Commun. 64, 151–156 (1987). [CrossRef]
  24. A. A. Tovar, “Propagation of flat-topped multi-Gaussian laser beams,” J. Opt. Soc. Am. A 18, 1897–1904 (2001). [CrossRef]
  25. K. Zhu, H. Tang, X. Sun, X. Wang, T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002). [CrossRef]
  26. K. Zhu, H. Tang, X. Wang, T. Liu, “Flattened light beams with an axial shadow generated through superposing cosh-Gaussian beams,” Optik 113, 222–226 (2002). [CrossRef]
  27. Y. Cai, X. Lu, Q. Lin, “Hollow Gaussian beam and its propagation,” Opt. Lett. 28, 1084–1086 (2003). [CrossRef] [PubMed]
  28. F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994). [CrossRef]
  29. J. Alda, S. Wang, E. Bernabeu, “Analytical expression for the complex radius of curvature tensor Q for generalized Gaussian beams,” Opt. Commun. 80, 350–352 (1991). [CrossRef]
  30. Y. Cai, Q. Lin, “The elliptical Hermite–Gaussian beam and its propagation through paraxial systems,” Opt. Commun. 207, 139–147 (2002). [CrossRef]
  31. S. Wang, L. Ronchi, “Principles and design of optical arrays,” in Progress in Optics, Vol. XXV, E. Wolf, ed. (Elsevier Science, Amsterdam, 1988), p. 279.

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