Abstract

The transition of the single-frequency oscillation of a semilinear photorefractive coherent oscillator for sufficiently large coupling strengths into two-frequency oscillation is predicted and is observed experimentally. The critical value of coupling strength at which the bifurcation occurs is a function of pump-intensity ratio and cavity losses. For certain combinations of these parameters, the critical coupling strength for spectrum bifurcation becomes smaller than the threshold coupling strength: in these cases double-frequency oscillation appears at the threshold. The supercritical bifurcation in the oscillation spectrum is analogous to the second-order phase transition.

© 2002 Optical Society of America

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  1. A. Yariv and D. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16–18 (1977).
    [CrossRef] [PubMed]
  2. J. Feinberg and R. Hellwarth, “Phase conjugate mirror with continuous wave gain,” Opt. Lett. 5, 519–521 (1980).
    [CrossRef]
  3. 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]
  4. 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).
  5. G. C. Valley and G. J. Dunning, “Observation of optical chaos in a phase conjugate resonator,” Opt. Lett. 9, 513–515 (1984).
    [CrossRef] [PubMed]
  6. 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]
  7. P. Mathey, P. Jullien, S. Odoulov, and O. Shinkarenko, “Manifestation of optical Curie–Weiss law for optical phase transition,” Appl. Phys. B 73, 711–715 (2001).
    [CrossRef]
  8. P. Mathey, P. Jullien, S. Odoulov, and O. 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).
    [CrossRef]
  9. M. G. Reznikov and A. I. Khizhnyak, “Properties of a resonator with a wavefront reversing mirror,” Sov. J. Quantum Electron. 10, 533–634 (1979).
  10. P. A. Belanger, A. Hardy, and A. Siegman, “Resonant modes of optical cavities with phase-conjugate mirrors,” Appl. Opt. 19, 602–609 (1980).
    [CrossRef] [PubMed]
  11. G. Nicolis, Introduction to Nonlinear Science (Cambridge University, New York, 1995).
  12. M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
    [CrossRef]
  13. K. R. McDonald and J. Feinberg, “Enhanced four-wave mixing by use of frequency shifted waves in photorefractive BaTiO3,” Phys. Rev. Lett. 55, 821–824 (1985).
    [CrossRef]
  14. S. Odoulov, M. Soskin, and A. Khyzhnyak, Optical Coherent Oscillators with Degenerate Four-Wave Mixing (Dynamic Grating Lasers) (Harwood Academic, Chur, Switzerland, 1991), pp. 37–39.
  15. J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486–488 (1982).
    [CrossRef] [PubMed]
  16. Y. Feinman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
  17. 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]
  18. M. Goul’kov, O. Shinkarenko, S. Odoulov, 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 (2001).
    [CrossRef]
  19. D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
    [CrossRef] [PubMed]
  20. P. Mathey, B. Mazué, P. Jullien, and D. Rytz, “Dynamics of optical filtering and edge enhancement in cobalt-doped barium titanate,” J. Opt. Soc. Am. B 15, 1353–1361 (1998).
    [CrossRef]
  21. J. P. Jiang and J. Feinberg, “Dancing modes and frequency shifts in a phase conjugator,” Opt. Lett. 12, 266–268 (1987).
    [CrossRef] [PubMed]
  22. A. Mazur and S. Odoulov, “Ring photorefractive oscillator with linear cavity distortion,” IEEE J. Quantum Electron. 26, 963–966 (1990).
    [CrossRef]
  23. S. Odoulov, U. van Olfen, and E. Kraetzig, “Mirrorless parametric oscillation in BaTiO3,” Appl. Phys. B 54, 313–317 (1992).
    [CrossRef]
  24. B. Sturman, S. Odoulov, and M. Goul’kov, “Parametric four-wave processes in photorefractive crystals,” Phys. Rep. 275, 197–254 (1996).
    [CrossRef]
  25. R. Grousson, S. Mallick, and S. Odoulov, “Amplified backward scattering in LiNbO3:Fe,” Opt. Commun. 51, 342–346 (1984).
    [CrossRef]
  26. D. Dolfi, A. Delboulbe, and J.-P. Huignard, “Forward mixing of two mutually incoherent beams in a photorefractive crystal,” Electron. Lett. 29, 450–451 (1993).
    [CrossRef]
  27. A. Yariv, Quantum Electronics (Wiley, New York, 1989).
  28. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  29. V. S. Mashkievich, “Theory of laser kinetics for systems with inhomogeneously broadened luminescence spectra,” Ukr. Phys. J. 12, 1731–1736 (1967).
  30. A. D. Manuilskii, S. G. Odoulov, and M. S. Soskin, “Homogeneous linewidth determination for disordered active media from stimulated emission spectra of internal modes,” Phys. Status Solidi 35, k111–k113 (1969).
    [CrossRef]
  31. O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, “Vectorial excess noise factor in common lasers,” Europhys. Lett. 43, 153–157 (1998).
    [CrossRef]
  32. A. Shumelyuk, S. Odoulov, and G. Brost, “Multiline coherent oscillation in photorefractive crystals with two species of movable carriers,” Appl. Phys. B 68, 959–966 (1999).
    [CrossRef]

2002

2001

P. Mathey, P. Jullien, S. Odoulov, and O. Shinkarenko, “Manifestation of optical Curie–Weiss law for optical phase transition,” Appl. Phys. B 73, 711–715 (2001).
[CrossRef]

M. Goul’kov, O. Shinkarenko, S. Odoulov, 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 (2001).
[CrossRef]

1999

A. Shumelyuk, S. Odoulov, and G. Brost, “Multiline coherent oscillation in photorefractive crystals with two species of movable carriers,” Appl. Phys. B 68, 959–966 (1999).
[CrossRef]

1998

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, “Vectorial excess noise factor in common lasers,” Europhys. Lett. 43, 153–157 (1998).
[CrossRef]

P. Mathey, B. Mazué, P. Jullien, and D. Rytz, “Dynamics of optical filtering and edge enhancement in cobalt-doped barium titanate,” J. Opt. Soc. Am. B 15, 1353–1361 (1998).
[CrossRef]

1996

B. Sturman, S. Odoulov, and M. Goul’kov, “Parametric four-wave processes in photorefractive crystals,” Phys. Rep. 275, 197–254 (1996).
[CrossRef]

1995

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]

1993

M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

D. Dolfi, A. Delboulbe, and J.-P. Huignard, “Forward mixing of two mutually incoherent beams in a photorefractive crystal,” Electron. Lett. 29, 450–451 (1993).
[CrossRef]

1992

1990

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).

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef] [PubMed]

A. Mazur and S. Odoulov, “Ring photorefractive oscillator with linear cavity distortion,” IEEE J. Quantum Electron. 26, 963–966 (1990).
[CrossRef]

1987

1986

Y. Feinman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).

1985

K. R. McDonald and J. Feinberg, “Enhanced four-wave mixing by use of frequency shifted waves in photorefractive BaTiO3,” Phys. Rev. Lett. 55, 821–824 (1985).
[CrossRef]

1984

G. C. Valley and G. J. Dunning, “Observation of optical chaos in a phase conjugate resonator,” Opt. Lett. 9, 513–515 (1984).
[CrossRef] [PubMed]

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]

R. Grousson, S. Mallick, and S. Odoulov, “Amplified backward scattering in LiNbO3:Fe,” Opt. Commun. 51, 342–346 (1984).
[CrossRef]

1982

1980

1979

M. G. Reznikov and A. I. Khizhnyak, “Properties of a resonator with a wavefront reversing mirror,” Sov. J. Quantum Electron. 10, 533–634 (1979).

1977

1969

A. D. Manuilskii, S. G. Odoulov, and M. S. Soskin, “Homogeneous linewidth determination for disordered active media from stimulated emission spectra of internal modes,” Phys. Status Solidi 35, k111–k113 (1969).
[CrossRef]

1967

V. S. Mashkievich, “Theory of laser kinetics for systems with inhomogeneously broadened luminescence spectra,” Ukr. Phys. J. 12, 1731–1736 (1967).

Bagan, A. A.

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).

Belanger, P. A.

Bretenaker, F.

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, “Vectorial excess noise factor in common lasers,” Europhys. Lett. 43, 153–157 (1998).
[CrossRef]

Brost, G.

A. Shumelyuk, S. Odoulov, and G. Brost, “Multiline coherent oscillation in photorefractive crystals with two species of movable carriers,” Appl. Phys. B 68, 959–966 (1999).
[CrossRef]

Brunel, M.

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, “Vectorial excess noise factor in common lasers,” Europhys. Lett. 43, 153–157 (1998).
[CrossRef]

Cronin-Golomb, M.

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]

Cross, M. C.

M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

Delboulbe, A.

D. Dolfi, A. Delboulbe, and J.-P. Huignard, “Forward mixing of two mutually incoherent beams in a photorefractive crystal,” Electron. Lett. 29, 450–451 (1993).
[CrossRef]

Dolfi, D.

D. Dolfi, A. Delboulbe, and J.-P. Huignard, “Forward mixing of two mutually incoherent beams in a photorefractive crystal,” Electron. Lett. 29, 450–451 (1993).
[CrossRef]

Dunning, G. J.

Emile, O.

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, “Vectorial excess noise factor in common lasers,” Europhys. Lett. 43, 153–157 (1998).
[CrossRef]

Engin, D.

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]

Feinberg, J.

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef] [PubMed]

J. P. Jiang and J. Feinberg, “Dancing modes and frequency shifts in a phase conjugator,” Opt. Lett. 12, 266–268 (1987).
[CrossRef] [PubMed]

K. R. McDonald and J. Feinberg, “Enhanced four-wave mixing by use of frequency shifted waves in photorefractive BaTiO3,” Phys. Rev. Lett. 55, 821–824 (1985).
[CrossRef]

J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486–488 (1982).
[CrossRef] [PubMed]

J. Feinberg and R. Hellwarth, “Phase conjugate mirror with continuous wave gain,” Opt. Lett. 5, 519–521 (1980).
[CrossRef]

Feinman, Y.

Y. Feinman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).

Fischer, B.

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]

Gerasimov, V. B.

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).

Golyanov, A. V.

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).

Goul’kov, M.

M. Goul’kov, O. Shinkarenko, S. Odoulov, 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 (2001).
[CrossRef]

B. Sturman, S. Odoulov, and M. Goul’kov, “Parametric four-wave processes in photorefractive crystals,” Phys. Rep. 275, 197–254 (1996).
[CrossRef]

Grousson, R.

R. Grousson, S. Mallick, and S. Odoulov, “Amplified backward scattering in LiNbO3:Fe,” Opt. Commun. 51, 342–346 (1984).
[CrossRef]

Hardy, A.

Hellwarth, R.

Hohenberg, P. C.

M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

Huignard, J.-P.

D. Dolfi, A. Delboulbe, and J.-P. Huignard, “Forward mixing of two mutually incoherent beams in a photorefractive crystal,” Electron. Lett. 29, 450–451 (1993).
[CrossRef]

Indebetouw, G.

Jiang, J. P.

Jullien, P.

Khizhnyak, A. I.

M. G. Reznikov and A. I. Khizhnyak, “Properties of a resonator with a wavefront reversing mirror,” Sov. J. Quantum Electron. 10, 533–634 (1979).

Khyzhnjak, A. I.

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).

Klancnik, E.

Y. Feinman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).

Kraetzig, E.

M. Goul’kov, O. Shinkarenko, S. Odoulov, 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 (2001).
[CrossRef]

S. Odoulov, U. van Olfen, and E. Kraetzig, “Mirrorless parametric oscillation in BaTiO3,” Appl. Phys. B 54, 313–317 (1992).
[CrossRef]

Le Floch, A.

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, “Vectorial excess noise factor in common lasers,” Europhys. Lett. 43, 153–157 (1998).
[CrossRef]

Lee, S. H.

Y. Feinman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).

Liu, Siuying R.

Mahgerefteh, D.

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef] [PubMed]

Mallick, S.

R. Grousson, S. Mallick, and S. Odoulov, “Amplified backward scattering in LiNbO3:Fe,” Opt. Commun. 51, 342–346 (1984).
[CrossRef]

Manuilskii, A. D.

A. D. Manuilskii, S. G. Odoulov, and M. S. Soskin, “Homogeneous linewidth determination for disordered active media from stimulated emission spectra of internal modes,” Phys. Status Solidi 35, k111–k113 (1969).
[CrossRef]

Mashkievich, V. S.

V. S. Mashkievich, “Theory of laser kinetics for systems with inhomogeneously broadened luminescence spectra,” Ukr. Phys. J. 12, 1731–1736 (1967).

Mathey, P.

Mazué, B.

Mazur, A.

A. Mazur and S. Odoulov, “Ring photorefractive oscillator with linear cavity distortion,” IEEE J. Quantum Electron. 26, 963–966 (1990).
[CrossRef]

McDonald, K. R.

K. R. McDonald and J. Feinberg, “Enhanced four-wave mixing by use of frequency shifted waves in photorefractive BaTiO3,” Phys. Rev. Lett. 55, 821–824 (1985).
[CrossRef]

Odoulov, S.

P. Mathey, P. Jullien, S. Odoulov, and O. 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).
[CrossRef]

P. Mathey, P. Jullien, S. Odoulov, and O. Shinkarenko, “Manifestation of optical Curie–Weiss law for optical phase transition,” Appl. Phys. B 73, 711–715 (2001).
[CrossRef]

M. Goul’kov, O. Shinkarenko, S. Odoulov, 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 (2001).
[CrossRef]

A. Shumelyuk, S. Odoulov, and G. Brost, “Multiline coherent oscillation in photorefractive crystals with two species of movable carriers,” Appl. Phys. B 68, 959–966 (1999).
[CrossRef]

B. Sturman, S. Odoulov, and M. Goul’kov, “Parametric four-wave processes in photorefractive crystals,” Phys. Rep. 275, 197–254 (1996).
[CrossRef]

S. Odoulov, U. van Olfen, and E. Kraetzig, “Mirrorless parametric oscillation in BaTiO3,” Appl. Phys. B 54, 313–317 (1992).
[CrossRef]

A. Mazur and S. Odoulov, “Ring photorefractive oscillator with linear cavity distortion,” IEEE J. Quantum Electron. 26, 963–966 (1990).
[CrossRef]

R. Grousson, S. Mallick, and S. Odoulov, “Amplified backward scattering in LiNbO3:Fe,” Opt. Commun. 51, 342–346 (1984).
[CrossRef]

Odoulov, S. G.

A. D. Manuilskii, S. G. Odoulov, and M. S. Soskin, “Homogeneous linewidth determination for disordered active media from stimulated emission spectra of internal modes,” Phys. Status Solidi 35, k111–k113 (1969).
[CrossRef]

Ogluzdin, V. E.

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).

Orlov, S.

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]

Pankrath, R.

M. Goul’kov, O. Shinkarenko, S. Odoulov, 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 (2001).
[CrossRef]

Pepper, D.

Reznikov, M. G.

M. G. Reznikov and A. I. Khizhnyak, “Properties of a resonator with a wavefront reversing mirror,” Sov. J. Quantum Electron. 10, 533–634 (1979).

Rubtsova, I. L.

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).

Rytz, D.

Segev, M.

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]

Shinkarenko, O.

P. Mathey, P. Jullien, S. Odoulov, and O. 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).
[CrossRef]

P. Mathey, P. Jullien, S. Odoulov, and O. Shinkarenko, “Manifestation of optical Curie–Weiss law for optical phase transition,” Appl. Phys. B 73, 711–715 (2001).
[CrossRef]

M. Goul’kov, O. Shinkarenko, S. Odoulov, 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 (2001).
[CrossRef]

Shumelyuk, A.

A. Shumelyuk, S. Odoulov, and G. Brost, “Multiline coherent oscillation in photorefractive crystals with two species of movable carriers,” Appl. Phys. B 68, 959–966 (1999).
[CrossRef]

Siegman, A.

Soskin, M. S.

A. D. Manuilskii, S. G. Odoulov, and M. S. Soskin, “Homogeneous linewidth determination for disordered active media from stimulated emission spectra of internal modes,” Phys. Status Solidi 35, k111–k113 (1969).
[CrossRef]

Sturman, B.

B. Sturman, S. Odoulov, and M. Goul’kov, “Parametric four-wave processes in photorefractive crystals,” Phys. Rep. 275, 197–254 (1996).
[CrossRef]

Sugrobov, V. A.

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).

Valley, G.

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]

Valley, G. C.

van Olfen, U.

S. Odoulov, U. van Olfen, and E. Kraetzig, “Mirrorless parametric oscillation in BaTiO3,” Appl. Phys. B 54, 313–317 (1992).
[CrossRef]

White, J. O.

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]

Yariv, A.

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]

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]

A. Yariv and D. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16–18 (1977).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. B

P. Mathey, P. Jullien, S. Odoulov, and O. Shinkarenko, “Manifestation of optical Curie–Weiss law for optical phase transition,” Appl. Phys. B 73, 711–715 (2001).
[CrossRef]

M. Goul’kov, O. Shinkarenko, S. Odoulov, 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 (2001).
[CrossRef]

S. Odoulov, U. van Olfen, and E. Kraetzig, “Mirrorless parametric oscillation in BaTiO3,” Appl. Phys. B 54, 313–317 (1992).
[CrossRef]

A. Shumelyuk, S. Odoulov, and G. Brost, “Multiline coherent oscillation in photorefractive crystals with two species of movable carriers,” Appl. Phys. B 68, 959–966 (1999).
[CrossRef]

Electron. Lett.

D. Dolfi, A. Delboulbe, and J.-P. Huignard, “Forward mixing of two mutually incoherent beams in a photorefractive crystal,” Electron. Lett. 29, 450–451 (1993).
[CrossRef]

Europhys. Lett.

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, “Vectorial excess noise factor in common lasers,” Europhys. Lett. 43, 153–157 (1998).
[CrossRef]

IEEE J. Quantum Electron.

A. Mazur and S. Odoulov, “Ring photorefractive oscillator with linear cavity distortion,” IEEE J. Quantum Electron. 26, 963–966 (1990).
[CrossRef]

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]

J. Opt. Soc. Am. B

Opt. Commun.

R. Grousson, S. Mallick, and S. Odoulov, “Amplified backward scattering in LiNbO3:Fe,” Opt. Commun. 51, 342–346 (1984).
[CrossRef]

Opt. Eng.

Y. Feinman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).

Opt. Lett.

Phys. Rep.

B. Sturman, S. Odoulov, and M. Goul’kov, “Parametric four-wave processes in photorefractive crystals,” Phys. Rep. 275, 197–254 (1996).
[CrossRef]

Phys. Rev. Lett.

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef] [PubMed]

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]

K. R. McDonald and J. Feinberg, “Enhanced four-wave mixing by use of frequency shifted waves in photorefractive BaTiO3,” Phys. Rev. Lett. 55, 821–824 (1985).
[CrossRef]

Phys. Status Solidi

A. D. Manuilskii, S. G. Odoulov, and M. S. Soskin, “Homogeneous linewidth determination for disordered active media from stimulated emission spectra of internal modes,” Phys. Status Solidi 35, k111–k113 (1969).
[CrossRef]

Rev. Mod. Phys.

M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

Sov. J. Quantum Electron.

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).

M. G. Reznikov and A. I. Khizhnyak, “Properties of a resonator with a wavefront reversing mirror,” Sov. J. Quantum Electron. 10, 533–634 (1979).

Ukr. Phys. J.

V. S. Mashkievich, “Theory of laser kinetics for systems with inhomogeneously broadened luminescence spectra,” Ukr. Phys. J. 12, 1731–1736 (1967).

Other

A. Yariv, Quantum Electronics (Wiley, New York, 1989).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

S. Odoulov, M. Soskin, and A. Khyzhnyak, Optical Coherent Oscillators with Degenerate Four-Wave Mixing (Dynamic Grating Lasers) (Harwood Academic, Chur, Switzerland, 1991), pp. 37–39.

G. Nicolis, Introduction to Nonlinear Science (Cambridge University, New York, 1995).

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Figures (17)

Fig. 1
Fig. 1

Schematic representation of the considered oscillator. The oscillator consists of a four-wave mixing phase-conjugate mirror, PCM, and a conventional mirror, M; the aperture D is placed inside the cavity to reduce its Fresnel number to be NF1. Pump waves are labeled 1 and 2, and 3 and 4 define the oscillation wave.

Fig. 2
Fig. 2

Spectra of phase-conjugate reflectivity (black dashed and solid curves) and cavity losses (horizontal gray lines) that show the threshold condition of oscillation. Coupling strength is equal to -1 (curve 1), -2.1 (curve 2), -3 (curve 3), -5 (curve 4), and -π (curve 5). Pump ratio r is equal to 2 for all dashed curves and 1 for the black solid curve. The mirror reflectivities are indicated near the horizontal lines, depicting loss levels.

Fig. 3
Fig. 3

Calculated pump-ratio dependences of the threshold-coupling strength (solid curve) and threshold frequency detuning (dashed curve) for the mirrorless coherent oscillation.

Fig. 4
Fig. 4

Calculated pump-ratio dependences of (A) the threshold coupling strength and (B) the threshold frequency detuning for the coherent oscillation in a semilinear cavity. Cavity mirror reflectivity R=1 for filled dots, 0.5 for diamonds, 0.25 for slanted crosses, 0.1 for straight crosses, 0.01 for triangles, 0 for the dotted curve (mirrorless oscillation), and 5 for the dashed curve (oscillation with amplifier inside the cavity). Solid curves in (A) represent an analytical solution for single-frequency oscillation.

Fig. 5
Fig. 5

Calculated pump-ratio dependence of the threshold frequency detuning for coherent oscillation with a high-reflecting (R=1) cavity mirror in the vicinity of the bifurcation point. The curve shows the fit to a square-root dependence of Eq. (16).

Fig. 6
Fig. 6

Two-dimensional diagram of coherent oscillation existence. Light-gray color defines the area where only single-frequency oscillation is possible, and deep-gray color marks areas where both single-frequency and double-frequency oscillation may occur, depending on cavity losses. For pump ratios smaller than that indicated by a white straight line, only double-frequency oscillation can be excited. Diamonds show the pump-ratio dependence of the smallest threshold coupling strength for different cavity mirror reflectivities. The tilted straight line represents the coupling strength that optimizes the phase-conjugate reflectivity for a frequency-degenerate oscillation.

Fig. 7
Fig. 7

Experimental arrangement for the study of coherent oscillation in a semilinear cavity. Beam splitter BS and mirrors M1 and M2 form two counterpropagating pump beams that impinge upon the BaTiO3 sample (PRC). Mc is a highly reflecting conventional convex mirror, D is a diaphragm, and L2 is a lens that collects the oscillation light (reflected from the sample face closest to the beam splitter) and sends it to photodetector PD. The polarizer P and half-wave phase retarder λ/2 serve to control the intensity of pump wave 1. The Faraday optical isolator (not shown in this picture) is put between the argon laser and beam splitter.

Fig. 8
Fig. 8

Temporal evolution of the oscillation intensity for the semilinear cavity (A) with a large Fresnel number (no aperture inside the cavity) and (B,C) with a 0.5-mm aperture inside. The cavity mirror reflectivity is R=1, the pump ratio r=200 for (B), and r=20 for (C).

Fig. 9
Fig. 9

Beat frequency in the oscillation wave versus laser pump power. The dashed curve is the fit to Ix dependence.

Fig. 10
Fig. 10

Temporal intensity variations for the oscillation wave plus a coherent reference wave from the Ar+-laser and intensity variations of the oscillation wave only.

Fig. 11
Fig. 11

Pump-ratio dependences of (A) oscillation intensity and (B) modulation frequency.

Fig. 12
Fig. 12

Oscillation frequency versus pump-intensity ratio. The measured values are shown by filled dots. Solid gray curves represent the results of calculation (see text).

Fig. 13
Fig. 13

Far-field intensity distribution for double-frequency oscillation, recorded (A) at maximum and (B) minimum of periodic intensity variations.

Fig. 14
Fig. 14

Fringe pattern of far-field intensity distribution for two-frequency oscillation and Gaussian reference beam from an Ar+ laser. Consecutive frames A and B show clearly the switch of interlinks between the fringes in two bright areas, which is due to the fringe motion in opposite directions. Markers on the screen allow the detection of the fringe-motion directions.

Fig. 15
Fig. 15

Schematic representation of tilted rays in the cavity with the phase-conjugate mirror (see text).

Fig. 16
Fig. 16

Angular distribution of (A) light-induced scattering and (B) light-induced scattering with mirrorless oscillation.

Fig. 17
Fig. 17

(A) Temporal variations of the mirrorless oscillation intensity and (B) their corresponding Fourier spectrum.

Equations (22)

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RpcR=1.
Rpc=sinh2γ02cosh2γ02-ln r2,
r=exp(γ0),
exp(-γ0)4/R.
(-γ0)th=-ln(R)+ln 4.
E3(0)E2(0)A(γ0)-(γ0)th(γ0)th,
(γ0)th=ln rR-1r(R+r),
(γ)=γ01+τ2Ω2+iτΩ γ01+τ2Ω2=(γ)+i(γ),
Rpc=sinh2γ2+sin2γ2cosh2γ-ln r2-sin2γ2.
RpcR=1,
dRpcdΩ=0,
d(γ)dΩ -2 sin2γ2sinhγ-ln r2
+2 sinhγ2coshγ-ln r2
=-dγdΩ sin(γ)coshγ-ln r2.
2 sin2(γ/2)=1,
d(γ)dΩtanh(γ)=-d(γ)dΩtan(γ).
cosh2γ-ln r2=sin2(γ/2),
Ωthml=πln r,
(γ0)thml=-ln r1+πln r2,
ΩthBln rcr-ln rln rcr,
d2Rpcd2Ω=0,
r=γ0 exp(γ0)+2[1-exp(γ0)]-γ0 exp(-γ0)+2[1-exp(-γ0)].

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