OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 37, Iss. 33 — Nov. 20, 1998
  • pp: 7821–7826

Spatial shifts of the conjugate beam generated by a nondegenerate photorefractive phase-conjugate mirror

Abdul-Azeez R. Al-Rashed, Bradley M. Jost, and Bahaa E. A. Saleh  »View Author Affiliations

Applied Optics, Vol. 37, Issue 33, pp. 7821-7826 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (174 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We demonstrate that the phase conjugation of a beam during nondegenerate four-wave mixing is accompanied by a spatial shift relative to the degenerate conjugate-beam location. Experiments with a photorefractive phase-conjugate mirror reveal that the phase-conjugate beam shifts have a nonmonotonic dependence on the probe’s detuning frequency and comprise both lateral displacements of up to 218 μm and angular tilts of up to 34 arc sec. An approximate theory based on spatial dispersion coefficients is in partial agreement with the experimental results.

© 1998 Optical Society of America

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(190.5040) Nonlinear optics : Phase conjugation
(190.5330) Nonlinear optics : Photorefractive optics

Original Manuscript: March 31, 1998
Revised Manuscript: August 14, 1998
Published: November 20, 1998

Abdul-Azeez R. Al-Rashed, Bradley M. Jost, and Bahaa E. A. Saleh, "Spatial shifts of the conjugate beam generated by a nondegenerate photorefractive phase-conjugate mirror," Appl. Opt. 37, 7821-7826 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. C. Papen, B. E. A. Saleh, “Lateral and focal shifts of phase-conjugated beams in photorefractive materials,” Opt. Lett. 14, 745–747 (1989). [CrossRef] [PubMed]
  2. F. Goos, H. Hänchen, “A new and fundamental experiment on total reflection,” Ann. Phys. (Leipzig) 6(1), 333–346 (1947); “A new measurement of the displacement of the beam at total reflection,” Ann. Phys. (Leipzig) 6(5), 251–252 (1949).
  3. K. Artmann, “Calculation of the displacement of a totally reflected ray,” Ann. Phys. (Leipzig) 6(2), 87–102 (1948).
  4. I. Newton, Opticks (Dover, New York, 1952).
  5. H. M. Lai, F. C. Cheng, W. K. Tang, “Goos–Hänchen effect around and off the critical angle,” J. Opt. Soc. Am. A 3, 550–557 (1986). [CrossRef]
  6. N. H. Tran, L. Dutriaux, Ph. Balcou, A. Le Floch, F. Bretenaker, “Angular Goos–Hänchen effect in curved dielectric microstructures,” Opt. Lett. 20, 1233–1235 (1995). [CrossRef] [PubMed]
  7. W. J. Tomlinson, J. P. Gordon, P. W. Smith, A. E. Kaplan, “Reflection of a Gaussian beam at a nonlinear interface,” Appl. Opt. 21, 2041–2051 (1982). [CrossRef] [PubMed]
  8. O. Emile, T. Galstyan, A. Le Floch, F. Bretenaker, “Measurement of the nonlinear Goos–Hänchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75, 1511–1513 (1995). [CrossRef] [PubMed]
  9. For a review, see A. Puri, J. L. Birman, “Goos–Hänchen beam shift at total internal reflection with application to spatially dispersive media,” J. Opt. Soc. Am. A 3, 543–549 (1986).
  10. See, for example, M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, New York, 1980), Chap. 1, p. 49; M. Young, Optics and Lasers, 3rd ed. (Springer-Verlag, New York, 1986), Chap. 8, pp. 178–180.
  11. A.-A. R. Al-Rashed, B. E. A. Saleh, “Modes of resonators with dispersive phase-conjugate mirrors,” Appl. Opt. 36, 3400–3412 (1997). [CrossRef] [PubMed]
  12. Preliminary reports of this research were presented at the 1997 Annual Meeting of the Optical Society of America in Long Beach, California; B. M. Jost, A.-A. R. Al-Rashed, B. E. A. Saleh, “Observation of the Goos–Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81, 2233–2235 (1998).
  13. J.-P. Huignard, J. P. Herriau, G. Rivet, P. N. Günter, “Phase-conjugation and spatial frequency dependence of wave-front reflectivity in Bi12SiO20 crystals,” Opt. Lett. 5, 102–104 (1980). [CrossRef] [PubMed]
  14. J. Feinberg, R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519–521 (1980). [CrossRef] [PubMed]
  15. K. R. MacDonald, J. Feinberg, “Enhanced four-wave mixing by use of frequency-shifted optical waves in photorefractive BaTiO3,” Phys. Rev. Lett. 55, 821–824 (1985). [CrossRef] [PubMed]
  16. B. Fischer, “Theory of self-frequency detuning of oscillations by wave mixing in photorefractive crystals,” Opt. Lett. 11, 236–238 (1986). [CrossRef] [PubMed]
  17. R. A. Fisher, ed., Optical Phase Conjugation (Academic, San Diego, Calif., 1983).
  18. B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985). [CrossRef]
  19. M. Gower, D. Proch, eds., Optical Phase Conjugation (Springer-Verlag, New York, 1994).
  20. P. Xie, J.-L. Wu, J.-H. Dai, P.-Y. Wang, H.-J. Zhang, “Observation of transverse spatial modulation in probe-pump configurations in BaTiO3:Ce,” Opt. Commun. 126, 255–259 (1996). [CrossRef]
  21. A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994);“Spatial and temporal fidelity of photorefractive image correlators,” J. Opt. Soc. Am. B 11, 1848 (1994); “Measurement of the spatio-temporal response of photorefractive conjugation,” Opt. Commun. 115, 121 (1995). [CrossRef]
  22. D. Magerefteh, J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990). [CrossRef]
  23. B. M. Jost, A.-A. R. Al-Rashed, J. A. Tataronis, B. E. A. Saleh, “Enhancement of phase-conjugate reflectivity with linear absorption in four-wave mixing systems,” Opt. Commun. 144, 222–226 (1997). [CrossRef]
  24. G. C. Papen, B. E. A. Saleh, J. A. Tataronis, “Analysis of transient phase conjugation in photorefractive media,” J. Opt. Soc. Am. B 5, 1763–1774 (1988). [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