OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 5, Iss. 6 — Jun. 1, 1988
  • pp: 1323–1334

Dispersive self-focusing in atomic media

A. W. McCord, R. J. Ballagh, and J. Cooper  »View Author Affiliations

JOSA B, Vol. 5, Issue 6, pp. 1323-1334 (1988)

View Full Text Article

Enhanced HTML    Acrobat PDF (1381 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An analytic model based on a single encoding–diffraction sequence is developed to describe the first main region of focusing that occurs when a cw off-resonant monochromatic Gaussian beam enters a medium of two-state atoms. A quantitative definition of the dispersive regime for self-focusing is given, and an explicit form is obtained for the field encoding produced by the initial propagation. The phase profile of this encoded field incorporates the effects of both the medium and diffraction, and we find a simple expression for the fundamental length scale, which determines where diffractive effects become dominant. An analytic expression is obtained for the on-axis field, which results once the encoded field begins to diffract freely, and simple expressions for the position and size of the main enhancement are given. We give a simple interpretation of the focusing and the two parameters required for its characterization. The model gives excellent agreement to the full numeric solution over a wide parameter range and, in particular, explains the rapid on-axis oscillations at the outset of focusing.

© 1988 Optical Society of America

Original Manuscript: September 10, 1987
Manuscript Accepted: October 30, 1987
Published: June 1, 1988

A. W. McCord, R. J. Ballagh, and J. Cooper, "Dispersive self-focusing in atomic media," J. Opt. Soc. Am. B 5, 1323-1334 (1988)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975). [CrossRef]
  2. See, in particular, Secs. 5 and 8 of Ref. 1 and references therein.
  3. W. G. Wagner, H. A. Haus, J. H. Marburger, “Large-scale self-trapping of optical beams in the paraxial ray approximation,” Phys. Rev. 175, 256–266 (1968). [CrossRef]
  4. M. LeBerre, E. Ressayre, A. Tallet, F. P. Mattar, “Qausi-trapping of Gaussian beams in two-level systems,” J. Opt. Soc. Am. B 2, 956–967 (1985). [CrossRef]
  5. M. LeBerre, E. Ressayre, A. Tallet, “Self-focusing and spatial ringing of intense cw light propagating through a strong absorbing medium,” Phys. Rev. A 25, 1604–1618 (1982). [CrossRef]
  6. M. LeBerre, E. Ressayre, A. Tallet, “Resonant self-focusing of a cw intense light beam,” Phys. Rev. A 29, 2669–2676 (1984). [CrossRef]
  7. M. G. Boshier, W. J. Sandle, “Self-focusing in a vapour of two-state atoms,” Opt. Commun. 42, 371–376 (1982). [CrossRef]
  8. D. E. McClelland, R. J. Ballagh, W. J. Sandle, “Simple analytic approximation to continuous-wave on-resonance beam reshaping,” J. Opt. Soc. Am. B 3, 212–218 (1986). [CrossRef]
  9. M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, N. Peyghambarian, “Continuous-wave off-resonance rings and continuous-wave on-resonance enhancement,” J. Opt. Soc. Am. B 1, 591–605 (1984). [CrossRef]
  10. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), p. 112.
  11. N. Wright, M. C. Newstein, “Self-focusing of coherent pulses,” Opt. Commun 9, 8–13 (1973). [CrossRef]
  12. A. Icsevgi, W. E. Lamb, “Propagation of light pulses in a laser amplifier,” Phys. Rev. 185, 517–545 (1969). [CrossRef]
  13. This is not a simple frequency scan since both I and F are scaled in units of (1 + Δ2).
  14. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), p. 31.
  15. E. T. Copson, Asymptotic Expansions, Vol. 55 of Cambridge Tracts in Mathematics and Mathematical Physics (Cambridge U. Press, Cambridge, 1965), pp. 91–98. [CrossRef]
  16. G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers, 2nd ed. (McGraw-Hill, New York, 1968), p. 720.
  17. R. J. Ballagh, J. Cooper, W. J. Sandle, “Effective two-state behavior of collisionally perturbed Zeeman degenerate atomic transition and its application to optical bistability,” J. Phys. B 14, 3881–3890 (1981). [CrossRef]

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