OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 3 — Mar. 1, 2002
  • pp: 405–411

Second-order optical phase transition in a semilinear photorefractive oscillator with two counterpropagating pump waves

Pierre Mathey, Pierre Jullien, Serguey G. Odoulov, and Oksana A. Shinkarenko  »View Author Affiliations

JOSA B, Vol. 19, Issue 3, pp. 405-411 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (154 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Soft-mode onset of coherent oscillation is revealed in a semilinear cavity with two counterpropagating pump waves. From the dynamics of the oscillation intensity and the dynamics of the grating decay with the feedback applied, critical behavior is detected: Both the characteristic time of oscillation onset and grating decay time go to infinity exactly at the threshold coupling strength. A conclusion is made about the similarity of this type of oscillator to the second-order phase transition.

© 2002 Optical Society of America

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.5040) Nonlinear optics : Phase conjugation
(190.5330) Nonlinear optics : Photorefractive optics
(230.4910) Optical devices : Oscillators

Pierre Mathey, Pierre Jullien, Serguey G. Odoulov, and Oksana A. Shinkarenko, "Second-order optical phase transition in a semilinear photorefractive oscillator with two counterpropagating pump waves," J. Opt. Soc. Am. B 19, 405-411 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984). [CrossRef]
  2. B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550–569 (1989). [CrossRef]
  3. S. Odoulov, M. Soskin, and A. Khizhiak, Optical Oscillators with Degenerate Four-Wave Mixing Dynamic Grating Lasers (Harwood Academic, Chur, Switzerland, 1991), pp. 37–39.
  4. M. Goul’kov, S. Odoulov, and R. Troth, “Temporal threshold of oscillation in a ring-loop photorefractive oscillator,” Ukr. Phys. J. 36, 1007–1010 (1991).
  5. D. Engin, S. Orlov, M. Segev, G. Valley, and A. Yariv, “Order-disorder phase transition and critical slowing down in photorefractive self-oscillators,” Phys. Rev. Lett. 74, 1743–1746 (1995). [CrossRef] [PubMed]
  6. S. Odoulov, M. Goul’kov, and O. Shinkarenko, “Threshold behavior in formation of optical hexagons and first order optical phase transition,” Phys. Rev. Lett. 83, 3637–3640 (1999). [CrossRef]
  7. D. A. Fish, T. J. Hall, and A. K. Powell, “Four-wave mixing critical slowing down,” Opt. Commun. 84, 85–89 (1991). [CrossRef]
  8. Siuying R. Liu and G. Indebetouw, “Periodic and chaotic spatiotemporal states in a phase-conjugate resonator using a photorefractive BaTiO3 phase-conjugate mirror,” J. Opt. Soc. Am. B 9, 1507–1520 (1992). [CrossRef]
  9. F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics,” Phys. Rev. Lett. 65, 2531–2534 (1990). [CrossRef] [PubMed]
  10. F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Vortices and defect statistics in two-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991). [CrossRef] [PubMed]
  11. P. L. Ramazza, S. Residori, G. Giacomelli, and F. T. Arecchi, “Statistics of topological defects in linear and nonlinear optics,” Europhys. Lett. 19, 475–480 (1992). [CrossRef]
  12. H. Haken, Synergetics (Springer-Verlag, Berlin, 1978).
  13. M. Harris, R. Loudon, G. Mander, and J. M. Vaughan, “Above-threshold laser amplifier,” Phys. Rev. Lett. 67, 1743–1746 (1991). [CrossRef] [PubMed]
  14. R. Loudon, M. Harris, T. Shepherd, and J. M. Vaughan, “Laser-amplifier gain and noise,” Phys. Rev. A 48, 681–701 (1993). [CrossRef] [PubMed]
  15. S. Odoulov, M. Goul’kov, O. Shinkarenko, E. Kraetzig, and R. Pankrath, “Threshold of oscillation in a ring-loop phase conjugator as a second order optical phase transition,” Appl. Phys. B 72, 187–190 (2000).
  16. A. Yariv and D. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16–18 (1977). [CrossRef] [PubMed]
  17. J. Feinberg and R. Hellwarth, “Phase conjugate mirror with continuous wave gain,” Opt. Lett. 5, 519–521 (1980). [CrossRef]
  18. A. A. Bagan, V. B. Gerasimov, A. V. Golyanov, V. E. Ogluzdin, V. A. Sugrobov, I. L. Rubtsova, and A. I. Khyzhnjak, “Conditions for the stimulated emission from a laser with cavities coupled via a dynamic hologram,” Sov. J. Quantum Electron. 17, 49–51 (1990).
  19. M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993). [CrossRef]
  20. R. L. Abrams and R. C. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978). [CrossRef] [PubMed]
  21. D. Engin, M. Segev, S. Orlov, and A. Yariv, “Double phase conjugation,” J. Opt. Soc. Am. 11, 1708–1717 (1994). [CrossRef]
  22. D. Pohl and V. Irniger, “Observation of second sound in NaF by means of light scattering,” Phys. Rev. Lett. 36, 480–483 (1976). [CrossRef]
  23. F. Rondelez, H. Hervet, and W. Urbach, “Origin of thermal conductivity anisotropy in liquid crystalline phases,” Phys. Rev. Lett. 41, 1058–1062 (1978). [CrossRef]
  24. H. J. Eichler, P. Guenter, and D. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
  25. S. Odoulov, U. van Olfen, and E. Kraetzig, “Mirrorless parametric oscillation in BaTiO3,” Appl. Phys. B 54, 313–317 (1992). [CrossRef]
  26. B. Sturman, S. Odoulov, and M. Goul’kov, “Parametric four-wave processes in photorefractive crystals,” Phys. Rep. 275, 197–254 (1996). [CrossRef]
  27. P. Jullien, P. Mathey, S. Odoulov, and O. Shinkarenko, “Critical slowing-down in photorefractive scattering below the self-oscillation threshold,” in International Quantum Electronics Conference, 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), paper QTuE27.
  28. A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993). [CrossRef]
  29. R. Kubo, Statistical Mechanics (North-Holland, Amsterdam, 1965).
  30. F. Iona and G. Shirane, Ferroelectric Crystals (Pergamon, London, 1962).
  31. E. Garmire, J. H. Marburger, S. D. Allen, and H. G. Winful, “Transient response of hybrid bistable optical devices,” Appl. Phys. Lett. 34, 374–376 (1979). [CrossRef]
  32. H. A. Al-Attar, H. A. McKenzie, and W. J. Firth, “Critical slowing-down phenomena in an InSb optically bistable étalon,” J. Opt. Soc. Am. B 3, 1157–1163 (1986). [CrossRef]
  33. Sze-Keung Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumped phase-conjugate mirror,” Appl. Phys. Lett. 45, 1016–1018 (1984). [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