Abstract

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

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2000 (1)

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).

1999 (1)

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]

1996 (1)

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

1995 (1)

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]

1994 (1)

D. Engin, M. Segev, S. Orlov, and A. Yariv, “Double phase conjugation,” J. Opt. Soc. Am. 11, 1708–1717 (1994).
[CrossRef]

1993 (3)

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

A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
[CrossRef]

R. Loudon, M. Harris, T. Shepherd, and J. M. Vaughan, “Laser-amplifier gain and noise,” Phys. Rev. A 48, 681–701 (1993).
[CrossRef] [PubMed]

1992 (3)

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]

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]

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

1991 (4)

D. A. Fish, T. J. Hall, and A. K. Powell, “Four-wave mixing critical slowing down,” Opt. Commun. 84, 85–89 (1991).
[CrossRef]

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).

M. Harris, R. Loudon, G. Mander, and J. M. Vaughan, “Above-threshold laser amplifier,” Phys. Rev. Lett. 67, 1743–1746 (1991).
[CrossRef] [PubMed]

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]

1990 (2)

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).

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]

1989 (1)

B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550–569 (1989).
[CrossRef]

1986 (1)

1984 (2)

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]

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]

1980 (1)

1979 (1)

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]

1978 (2)

F. Rondelez, H. Hervet, and W. Urbach, “Origin of thermal conductivity anisotropy in liquid crystalline phases,” Phys. Rev. Lett. 41, 1058–1062 (1978).
[CrossRef]

R. L. Abrams and R. C. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978).
[CrossRef] [PubMed]

1977 (1)

1976 (1)

D. Pohl and V. Irniger, “Observation of second sound in NaF by means of light scattering,” Phys. Rev. Lett. 36, 480–483 (1976).
[CrossRef]

Abrams, R. L.

Al-Attar, H. A.

Allen, S. D.

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]

Arecchi, F. T.

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]

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]

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]

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).

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]

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]

Cross, M. C.

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

D. Engin, M. Segev, S. Orlov, and A. Yariv, “Double phase conjugation,” J. Opt. Soc. Am. 11, 1708–1717 (1994).
[CrossRef]

Feinberg, J.

Firth, W. J.

Fischer, B.

B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550–569 (1989).
[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]

Fish, D. A.

D. A. Fish, T. J. Hall, and A. K. Powell, “Four-wave mixing critical slowing down,” Opt. Commun. 84, 85–89 (1991).
[CrossRef]

Garmire, E.

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]

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).

Giacomelli, G.

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]

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]

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]

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.

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).

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]

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

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).

Hall, T. J.

D. A. Fish, T. J. Hall, and A. K. Powell, “Four-wave mixing critical slowing down,” Opt. Commun. 84, 85–89 (1991).
[CrossRef]

Harris, M.

R. Loudon, M. Harris, T. Shepherd, and J. M. Vaughan, “Laser-amplifier gain and noise,” Phys. Rev. A 48, 681–701 (1993).
[CrossRef] [PubMed]

M. Harris, R. Loudon, G. Mander, and J. M. Vaughan, “Above-threshold laser amplifier,” Phys. Rev. Lett. 67, 1743–1746 (1991).
[CrossRef] [PubMed]

Hellwarth, R.

Hervet, H.

F. Rondelez, H. Hervet, and W. Urbach, “Origin of thermal conductivity anisotropy in liquid crystalline phases,” Phys. Rev. Lett. 41, 1058–1062 (1978).
[CrossRef]

Hohenberg, P. C.

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

Indebetouw, G.

Irniger, V.

D. Pohl and V. Irniger, “Observation of second sound in NaF by means of light scattering,” Phys. Rev. Lett. 36, 480–483 (1976).
[CrossRef]

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).

Kraetzig, E.

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).

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

Kwong, Sze-Keung

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]

Lind, R. C.

Liu, Siuying R.

Loudon, R.

R. Loudon, M. Harris, T. Shepherd, and J. M. Vaughan, “Laser-amplifier gain and noise,” Phys. Rev. A 48, 681–701 (1993).
[CrossRef] [PubMed]

M. Harris, R. Loudon, G. Mander, and J. M. Vaughan, “Above-threshold laser amplifier,” Phys. Rev. Lett. 67, 1743–1746 (1991).
[CrossRef] [PubMed]

Mander, G.

M. Harris, R. Loudon, G. Mander, and J. M. Vaughan, “Above-threshold laser amplifier,” Phys. Rev. Lett. 67, 1743–1746 (1991).
[CrossRef] [PubMed]

Marburger, J. H.

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]

McKenzie, H. A.

Odoulov, S.

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).

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]

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]

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).

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]

D. Engin, M. Segev, S. Orlov, and A. Yariv, “Double phase conjugation,” J. Opt. Soc. Am. 11, 1708–1717 (1994).
[CrossRef]

Pankrath, R.

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).

Pepper, D.

Pohl, D.

D. Pohl and V. Irniger, “Observation of second sound in NaF by means of light scattering,” Phys. Rev. Lett. 36, 480–483 (1976).
[CrossRef]

Powell, A. K.

D. A. Fish, T. J. Hall, and A. K. Powell, “Four-wave mixing critical slowing down,” Opt. Commun. 84, 85–89 (1991).
[CrossRef]

Ramazza, P. L.

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]

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]

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]

Residori, S.

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]

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]

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]

Rondelez, F.

F. Rondelez, H. Hervet, and W. Urbach, “Origin of thermal conductivity anisotropy in liquid crystalline phases,” Phys. Rev. Lett. 41, 1058–1062 (1978).
[CrossRef]

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).

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]

D. Engin, M. Segev, S. Orlov, and A. Yariv, “Double phase conjugation,” J. Opt. Soc. Am. 11, 1708–1717 (1994).
[CrossRef]

Shepherd, T.

R. Loudon, M. Harris, T. Shepherd, and J. M. Vaughan, “Laser-amplifier gain and noise,” Phys. Rev. A 48, 681–701 (1993).
[CrossRef] [PubMed]

Shinkarenko, O.

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).

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]

Sternklar, S.

B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550–569 (1989).
[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).

Troth, R.

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).

Urbach, W.

F. Rondelez, H. Hervet, and W. Urbach, “Origin of thermal conductivity anisotropy in liquid crystalline phases,” Phys. Rev. Lett. 41, 1058–1062 (1978).
[CrossRef]

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]

van Olfen, U.

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

Vaughan, J. M.

R. Loudon, M. Harris, T. Shepherd, and J. M. Vaughan, “Laser-amplifier gain and noise,” Phys. Rev. A 48, 681–701 (1993).
[CrossRef] [PubMed]

M. Harris, R. Loudon, G. Mander, and J. M. Vaughan, “Above-threshold laser amplifier,” Phys. Rev. Lett. 67, 1743–1746 (1991).
[CrossRef] [PubMed]

Weiss, S.

B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550–569 (1989).
[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]

Winful, H. G.

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]

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]

D. Engin, M. Segev, S. Orlov, and A. Yariv, “Double phase conjugation,” J. Opt. Soc. Am. 11, 1708–1717 (1994).
[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]

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]

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

Zozulya, A. A.

A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
[CrossRef]

Appl. Phys. B (2)

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).

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

Appl. Phys. Lett. (2)

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]

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]

Europhys. Lett. (1)

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]

IEEE J. Quantum Electron. (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]

B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550–569 (1989).
[CrossRef]

A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

D. Engin, M. Segev, S. Orlov, and A. Yariv, “Double phase conjugation,” J. Opt. Soc. Am. 11, 1708–1717 (1994).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

D. A. Fish, T. J. Hall, and A. K. Powell, “Four-wave mixing critical slowing down,” Opt. Commun. 84, 85–89 (1991).
[CrossRef]

Opt. Lett. (3)

Phys. Rep. (1)

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

Phys. Rev. A (1)

R. Loudon, M. Harris, T. Shepherd, and J. M. Vaughan, “Laser-amplifier gain and noise,” Phys. Rev. A 48, 681–701 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (7)

M. Harris, R. Loudon, G. Mander, and J. M. Vaughan, “Above-threshold laser amplifier,” Phys. Rev. Lett. 67, 1743–1746 (1991).
[CrossRef] [PubMed]

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]

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]

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]

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]

D. Pohl and V. Irniger, “Observation of second sound in NaF by means of light scattering,” Phys. Rev. Lett. 36, 480–483 (1976).
[CrossRef]

F. Rondelez, H. Hervet, and W. Urbach, “Origin of thermal conductivity anisotropy in liquid crystalline phases,” Phys. Rev. Lett. 41, 1058–1062 (1978).
[CrossRef]

Rev. Mod. Phys. (1)

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

Sov. J. Quantum Electron. (1)

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).

Ukr. Phys. J. (1)

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).

Other (6)

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.

H. Haken, Synergetics (Springer-Verlag, Berlin, 1978).

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.

H. J. Eichler, P. Guenter, and D. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).

R. Kubo, Statistical Mechanics (North-Holland, Amsterdam, 1965).

F. Iona and G. Shirane, Ferroelectric Crystals (Pergamon, London, 1962).

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Figures (6)

Fig. 1
Fig. 1

Geometry of the oscillator considered.

Fig. 2
Fig. 2

Calculated coupling-strength dependence of the oscillation-wave output intensity for geometries (a) with two independent counterpropagating waves and (b) for the transmitted pump wave retroreflected into the sample.

Fig. 3
Fig. 3

Schematic representation of experimental arrangement: PRC is the photorefractive crystal sample with the ferroelectric axis in the plane of drawing, M is the mirror, BS is the beam splitter, Det is the photodetector, and Sh is the shutter.

Fig. 4
Fig. 4

Temporal evolution of oscillation intensity. Curves 1, 2, 3, and 4 correspond to the decreasing coupling strength. The dashed curve in curve 2 shows how oscillation delay time Δtos is evaluated.

Fig. 5
Fig. 5

Temporal dependence of grating decay below oscillation threshold. (a) Grating decay with counterpropagating pump-wave present; (b) decay with the beam splitter BS blocked.

Fig. 6
Fig. 6

Coupling-strength dependence of (a) oscillation intensity, (b) characteristic relaxation time, and (c) inverse characteristic time.

Equations (11)

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RRpc=1,
Rpc=sinh2γl2cosh2γl2+ln r2,
γ=-2π2reff n3kBT sin θeλ2 cos θ,
(γl)th=2 ln1+1+RR.
γl=I0Δ2+4|c|2ln|c|2-I1(0)I2(l)+I3(0)I2(l)-I3(0)Δ2+4|c|2|c|2-I1(0)I2(l)+I3(0)I2(l)+I3(0)Δ2+|4|c2,
|c|2=[I1(0)I2(l)-RI1(0)I3(0)±I3(0)R]2,
Δ=I2(l)-I1(0)-RI3(0),
I0=I2(l)+I1(0)+RI3(0).
I1(0)=[I2(l)-I3(0)]Rp,
γl=(γl)01+(IE/I0),
1τ|γl-(γ)th|,

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