OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 12, Iss. 9 — Sep. 1, 1995
  • pp: 1602–1616

Spatiotemporal effects in double phase conjugation

M. R. Belić, J. Leonardy, D. Timotijević, and F. Kaiser  »View Author Affiliations

JOSA B, Vol. 12, Issue 9, pp. 1602-1616 (1995)

View Full Text Article

Enhanced HTML    Acrobat PDF (3645 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Spatial and temporal effects arising in photorefractive crystals during the process of double phase conjugation are analyzed numerically with a novel beam-propagation method. Slowly varying envelope wave equations in the paraxial approximation are solved under the appropriate boundary conditions. Our analysis includes dynamical effects caused by the buildup of diffraction gratings in the crystal and the turn-on of phase-conjugate beams as well as spatial effects caused by the finite transverse spread of beams and by the propagation directions of the beams. Various phenomena are observed, such as self-bending of phase-conjugate beams, convective flow of energy out of the interaction region, mode oscillations, critical slowing down at the oscillation threshold, and irregular spatial pattern formation. For a real beam-coupling constant and constructive interaction of interference fringes in the crystal we find steady or periodic behavior. For a complex coupling constant and/or induced phase mismatch in the grating a transition to spatiotemporal chaos is observed. We believe that under stable operating conditions the transverse double phase-conjugate mirror in the paraxial approximation is a convective oscillator, rather than an amplifier. Improved agreement with experimental results is obtained.

© 1995 Optical Society of America

M. R. Belić, J. Leonardy, D. Timotijević, and F. Kaiser, "Spatiotemporal effects in double phase conjugation," J. Opt. Soc. Am. B 12, 1602-1616 (1995)

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); S. Sternklar, S. Weiss, M. Segev, and B. Fischer, "Beam coupling and locking of lasers using photorefractive four-wave mixing," Opt. Lett. 11, 528–530 (1986); S. Weiss, S. Sternklar, and B. Fischer, "Double phase-conjugation: analysis, demonstration, and applications," Opt. Lett. 12, 114–116 (1987). [CrossRef] [PubMed]
  3. A. A. Zozulya, "Double phase-conjugate mirror is not an oscillator," Opt. Lett. 16, 545–547 (1991); V. V. Eliseev, V. T. Tikhonchuk, and A. A. Zozulya, "Double phase-conjugate mirror: two-dimensional analysis," J. Opt. Soc. Am. B 8, 2497–2504 (1991). [CrossRef] [PubMed]
  4. N. V. Bogodaev, V. V. Eliseev, L. I. Ivleva, A. S. Korshunov, S. S. Orlov, N. M. Polozkov, and A. A. Zozulya, "Double phase-conjugate mirror: experimental investigation and comparison with theory," J. Opt. Soc. Am. B 9, 1493–1498 (1992). [CrossRef]
  5. A. A. Zozulya, M. Saffman, and D. Z. Anderson, "Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries," Phys. Rev. Lett. 73, 818–821 (1994); "Double phase-conjugate mirror: convection and diffraction," J. Opt. Soc. Am. B 12, 255–264 (1995). [CrossRef] [PubMed]
  6. M. Segev, D. Engin, A. Yariv, and G. C. Valley, "Temporal evolution of photorefractive double phase-conjugate mirrors," Opt. Lett. 18, 1828–1830 (1993); S. Orlov, M. Segev, A. Yariv, and G. C. Valley, "Conjugation fidelity and reflectivity in photorefractive double phase-conjugate mirrors," Opt. Lett. 19, 578–580 (1994); D. Engin, M. Segev, S. Orlov, and A. Yariv, "Double phase conjugation," J. Opt. Soc. Am. B 11, 1708–1717 (1994). [CrossRef] [PubMed]
  7. K. D. Shaw, "The double phase conjugate mirror is an oscillator," Opt. Commun. 90, 133–138 (1992). [CrossRef]
  8. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York), Chap. 6, p. 112.
  9. The situation has changed considerably since this paper was submitted for publication. A number of treatments have appeared and are listed in Refs. 5, 6, and 10.
  10. M. Cronin-Golomb, "Whole beam method for photorefractive nonlinear optics," Opt. Commun. 89, 276–282 (1992); K. Ratnam and P. P. Banerjee, "Nonlinear theory of two-beam coupling in a photorefractive material," Opt. Commun. 107, 522–530 (1994). [CrossRef]
  11. S. R. Liu and G. Indebetouw, "Spatiotemporal patterns and vortices dynamics in phase conjugate resonators," Opt. Commun. 101, 442–455 (1993). [CrossRef]
  12. W. Krolikowski, M. R. Belić, M. Cronin-Golomb, and A. Bledowski, "Chaos in photorefractive four-wave mixing with a single interaction region," J. Opt. Soc. Am. B 7, 1204–1209 (1990). [CrossRef]
  13. J. V. Moloney, M. R. Belić, and H. M. Gibbs, "Calculation of transverse effects in optical bistability using fast Fourier transform techniques," Opt. Commun. 41, 379–382 (1982); M. Lax, G. P. Agrawal, M. R. Belić, B. J. Coffey, and W. L. Louisell, "Electromagnetic field distribution in loaded unstable resonators," J. Opt. Soc. Am. A 2, 731–742 (1985). [CrossRef]
  14. M. R. Belić and M. Petrović, "Unified method for solution of wave equations in photorefractive media," J. Opt. Soc. Am. B 11, 481–485 (1994). [CrossRef]
  15. M. R. Belić, J. Leonardy, D. Timotijević, and F. Kaiser, "Transverse effects in double phase conjugation," Opt. Commun. 111, 99–104 (1994). [CrossRef]
  16. N. Wolffer, P. Gravey, J. V. Moisan, C. Laulan, and J. C. Launay, "Analysis of double phase conjugate mirror interaction in absorbing photorefractive crystals: application to BGO:Cu," Opt. Commun. 73, 351–356 (1989); N. Wolffer and P. Gravey, "High quality phase conjugation in adouble phase conjugate mirror using InP:Fe at 1.3 μm," Opt. Commun. 107, 115–119 (1994). [CrossRef]
  17. F. T. Arecchi, "Space-time complexity in nonlinear optics," Physica D 51, 450–464 (1991); F. T. Arecchi, S. Boccaletti, G. Giacomelli, G. P. Puccioni, P. L. Ramazza, and S. Residori, "Space–time chaos and topological defects in nonlinear optics," Physica D 61, 25–39 (1992). [CrossRef]
  18. W. Krolikowski and B. Luther-Davies, "The effect of a high external electric field on a photorefractive ring phase conjugator," Appl. Phys. B 55, 180–182 (1992). [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