OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 16, Iss. 6 — Jun. 1, 1999
  • pp: 952–960

Degenerate four-wave mixing for arbitrary pump and probe intensities

R. T. Bratfalean, G. M. Lloyd, and P. Ewart  »View Author Affiliations

JOSA B, Vol. 16, Issue 6, pp. 952-960 (1999)

View Full Text Article

Enhanced HTML    Acrobat PDF (324 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An analytical expression for the degenerate four-wave mixing signal produced in a medium composed of two-level atoms by pump and probe lasers of arbitrary intensities and parallel linear polarization, suffering negligible absorption and depletion, has been derived. The Abrams–Lind approach [Opt. Lett. 2, 94 and 3, 205 (1978)] for deriving the phase-matched polarization has been extended to find all the other higher-order polarization terms contributing to the signal. The signal field amplitude is expressed as an infinite series whose convergence rate depends on the intensity of the input fields and their detuning from resonance. The solution is successfully verified by comparison with a full numerical nonperturbative calculation and is found to be equivalent to the Abrams–Lind result in the limit of weak probe intensity. The result is used to calculate the saturation effects on spectral line shape that are relevant to simulation of molecular spectra obtained by degenerate four-wave mixing with saturating pump and probe fields. The result is extended to treat atomic motion in the case of forward geometry of the input beams.

© 1999 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.1900) Nonlinear optics : Diagnostic applications of nonlinear optics
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(300.6290) Spectroscopy : Spectroscopy, four-wave mixing
(300.6420) Spectroscopy : Spectroscopy, nonlinear

R. T. Bratfalean, G. M. Lloyd, and P. Ewart, "Degenerate four-wave mixing for arbitrary pump and probe intensities," J. Opt. Soc. Am. B 16, 952-960 (1999)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
  2. R. L. Abrams and R. C. Lind, Opt. Lett. 2, 94–96 and 3, 205 (1978).
  3. D. Bloch and M. Ducloy, J. Opt. Soc. Am. 73, 635–646 (1983) and 73, 1844–1845 (1983). [CrossRef]
  4. G. Grynberg, M. Pinard, and P. Verkerk, Opt. Commun. 50, 261–264 (1984). [CrossRef]
  5. R. P. Lucht, R. L. Farrow, and D. J. Rakestraw, J. Opt. Soc. Am. B 10, 1508–1520 (1993). [CrossRef]
  6. R. G. Caro and M. C. Gower, IEEE J. Quantum Electron. QE-18, 1376–1380 (1982). [CrossRef]
  7. W. P. Brown, J. Opt. Soc. Am. 73, 629–634 (1983). [CrossRef]
  8. P. Ewart and S. V. O’Leary, J. Phys. B 17, 4595–4608 (1984). [CrossRef]
  9. M. T. Gruneisen, A. L. Gaeta, and R. W. Boyd, J. Opt. Soc. Am. 2, 1117–1121 (1985). [CrossRef]
  10. J. Cooper, A. Charlton, D. Meacher, P. Ewart, and G. Alber, Phys. Rev. A 40, 5705–5715 (1989). [CrossRef] [PubMed]
  11. D. R. Meacher, P. G. R. Smith, P. Ewart, and J. Cooper, Phys. Rev. A 46, 2718–2725 (1992). [CrossRef] [PubMed]
  12. M. Ducloy, F. A. M. de Oliveira, and D. Bloch, Phys. Rev. A 32, 1614–1623 (1985). [CrossRef] [PubMed]
  13. P. Verkerk, P. Pinard, and G. Grynberg, Phys. Rev. A 35, 4679–4695 (1987). [CrossRef]
  14. S. Williams, R. N. Zare, and L. A. Rahn, J. Chem. Phys. 101, 1093–1107 (1994). [CrossRef]
  15. D. G. Steel, R. C. Lind, and J. F. Lam, Phys. Rev. A 23, 2513–2524 (1981). [CrossRef]
  16. P. M. Danehy, E. J. Friedmanhill, R. P. Lucht, and R. L. Farrow, Appl. Phys. B: Photophys. Laser Chem. 57, 243–248 (1993). [CrossRef]
  17. S. M. Wandzura, Opt. Lett. 4, 208–210 (1979). [CrossRef] [PubMed]
  18. B. Attal-Tretout, H. Bervas, J. P. Taran, S. Le Boiteux, P. Kelley, and T. K. Gustafson, J. Phys. B 30, 497–522 (1997). [CrossRef]
  19. R. J. Knize, Opt. Lett. 18, 1606–1608 (1993). [CrossRef] [PubMed]
  20. B. Ai and R. J. Knize, J. Opt. Soc. Am. B 13, 2408–2419 (1996). [CrossRef]
  21. R. W. Boyd, Nonlinear Optics (Academic, New York, 1995), p. 59.
  22. Ref. 21, p. 201.
  23. I. S. Gradstein and I. M. Ryzik, Table of Integrals, Series and Products, 4th ed. (Academic, New York, 1965).

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