Abstract

Phase conjugation (PC) that is due to degenerate forward four-wave mixing is studied both theoretically and experimentally. Similarly to backward four-wave mixing, the limiting efficiency of this process corresponds to the total energy transfer from each pump wave into the signal and conjugate waves, although in this case the Yariv oscillations do not occur. The numerical solution of the nonstationary problem is presented, revealing the transient oscillations of the PC-beam intensity with maxima many times exceeding the saturation value. PC of Q-switched and free-oscillating solid-state laser radiation is obtained by using the thermal nonlinearity of absorbing solutions. PC of cw laser radiation is obtained in a LiNbO3 crystal, the PC-beam intensity being six times larger than the initial intensity of the signal beam. The self-compensation of nonlinear phase distortions of the recording medium is demonstrated.

© 1984 Optical Society of America

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  1. B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “Recording of two-dimensional and three-dimensional dynamic holograms in transparent substances,” Sov. Phys. Dokl. 16, 46–48 (1971).
  2. R. W. Hellwarth, “Generation of time-reversed wave fronts by nonlinear refraction,” J. Opt. Soc. Am. 67, 1–3 (1977).
    [Crossref]
  3. D. M. Pepper, “Nonlinear optical phase conjugation,” Opt. Eng. 21, 156–183 (1982).
    [Crossref]
  4. C. V. Heer, N. C. Griffen, “Generation of a phase conjugate wave in the forward direction with thin Na-vapor cell,” Opt. Lett. 4, 239–249 (1979).
    [Crossref] [PubMed]
  5. N. Kukhtarev, S. Odoulov, “Wavefront conjugation via anisotropic self-diffraction,” Pis’ma Zh. Tech. Fiz. 6, 1176–1180 (1980) [Sov. Tech. Phys. Lett. 6, 503–505 (1980)].
  6. Yu. Anan’ev, V. Soloviev, “Particular features of forward and backward schemes of four-wave mixing with mirror reflection of signal beam,” Opt. Spectrosc. 54, 136–143 (1983).
  7. R. Y. Chiao, E. Garmire, C. Townes, P. L. Kelley, “Self trapping of optical beams,” Phys. Rev. Lett. 43, 479–481 (1964); “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
    [Crossref]
  8. N. Blombergen, Nonlinear Optics (Benjamin, New York, 1965).
  9. V. I. Bespalov, V. I. Talanov, “On filamentary structure of the light beams in nonlinear liquids,” Sov. Phys. JETP Lett. 3, 307–310 (1966).
  10. H. J. Gerritsen, “Nonlinear effects in image formation,” Appl. Phys. Lett. 10, 234–241 (1967).
    [Crossref]
  11. H. J. Eichler, B. Kluzowski, “Lichinduzierte Amplitudengitter in Sattigungsabsorbern und ihr Nachweis durch Beugungser-scheinungen,” Z. Angew. Phys. 27, 4–5 (1969).
  12. J. P. Woerdman, B. Bolger, “Diffraction of light by laser induced grating in Si,” Phys. Lett. A 30, 164–166 (1969).
    [Crossref]
  13. D. L. Staebler, J. J. Amodei, “Coupled wave analisis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042–1049 (1972).
    [Crossref]
  14. K. Jarasiunas, Yu. Vaitkus, “Properties of a laser induced phase grating in CdS,” Phys. Status Solidi A 23, K19–K21 (1974).
    [Crossref]
  15. A. Yariv, “Phase conjugation optics and real time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
    [Crossref]
  16. J. Marburger, J. Lam, “Nonlinear theory of degenerate four-wave mixing,” Appl. Phys. Lett. 34, 381–391 (1979).
    [Crossref]
  17. M. Soskin, A. Khyzniak, “On an interaction of four counter-propagating plane waves in a medium with inertial cubic nonlinearity,” Kvantovaya Elektron. (Moscow) 7, 42–49 (1980).
  18. B. L. Stansfield, R. Nodwell, J. Meyer, “Enchanced scattering of laser light by optical mixing in a plasma,” Phys. Rev. Lett. 26, 1219–1221 (1971).
    [Crossref]
  19. A. R. Bogdan, Y. Prior, N. Bloembergen, “Pressure-induced degenerate frequency resonanse in four-wave light mixing,” Opt. Lett. 6, 82–84 (1981).
    [Crossref] [PubMed]
  20. A. R. Bogdan, M. W. Downer, N. Bloembergen, “Quantitative characteristics of pressure-induced degenerate frequency resonance in four-wave mixing with continuous-wave laser beams,” Opt. Lett. 6, 348–350 (1981).
    [Crossref] [PubMed]
  21. L. Bol’shov, D. Vlasov, R. Garaev, “On a spatial resonance under four-photon interaction between corunning waves in a cubic medium,” Kvantovaya Electron. 9, 83–91 (1982).
  22. A. Yariv, “Four-wave nonlinear optical mixing as real-time holography,” Opt. Commun. 25, 23–25 (1978).
    [Crossref]
  23. V. Vinetski, N. Kukhtarev, S. Odoulov, M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–760 (1979).
    [Crossref]
  24. S. A. Akhmanov, R. W. Khokhlov, Problems of Nonlinear Optics (Academy of Sciences of the USSR, Moscow, 1965) (in Russian).
  25. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  26. A. Khyzniak, “On efficiency of four-wave mixing in media with third order nonlinearity,” Izv. Akad. Nauk Ser. Fiz. 45, 640–649 (1981).
  27. A. Yariv, D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16–18 (1977).
    [Crossref] [PubMed]
  28. A. Khyzniak, V. Soloviev, “Forward four-wave mixing,” Opt. Spectrosc. 53, 723–727 (1982).
  29. V. Kremenitski, S. Odoulov, M. Soskin, “Wavefront reversion due to degenerate four-wave mixing CdTe crystals,” Izv. Akad. Nauk SSSR Ser. Fiz. 44, 2029–2034 (1980) [Bull. Acad. Sci. USSR Phys. Ser. 44,24–28 (1980)].
  30. This crystal has been successfully used for PC of a cw laser beam in a BFWM arrangement. See N. Kukhtarev, S. Odoulov, “Inversion of a wave front associated with a four-wave interaction in media with nonlocal nonlinearity,” Sov. Phys. JETP Lett. 30, 4–8 (1979); “Wavefront conjugation via degenerate four-wave mixing in electrooptic crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 213, 2–9 (1979).
  31. V. I. Belinitcher, B. I. Sturman, “Photovoltaic effect in non-centrosymmetric media,” Uspekhi Fiz. Nauk 130, 415–458 (1980).
  32. D. Fekete, J. A. Yeung, A. Yariv, “Phase conjugate reflection by degenerate four-wave mixing in a nematic liquid crystal in the isotropic phase,” Optics Lett. 5, 51–53 (1980).
    [Crossref]
  33. J. F. Kanaev, V. K. Malinouvski, B. I. Sturman, “Investigation of light induced scattering in LiNbO3,” Opt. Commun. 34, 95–100 (1980).
    [Crossref]

1983 (1)

Yu. Anan’ev, V. Soloviev, “Particular features of forward and backward schemes of four-wave mixing with mirror reflection of signal beam,” Opt. Spectrosc. 54, 136–143 (1983).

1982 (3)

D. M. Pepper, “Nonlinear optical phase conjugation,” Opt. Eng. 21, 156–183 (1982).
[Crossref]

L. Bol’shov, D. Vlasov, R. Garaev, “On a spatial resonance under four-photon interaction between corunning waves in a cubic medium,” Kvantovaya Electron. 9, 83–91 (1982).

A. Khyzniak, V. Soloviev, “Forward four-wave mixing,” Opt. Spectrosc. 53, 723–727 (1982).

1981 (3)

1980 (6)

V. Kremenitski, S. Odoulov, M. Soskin, “Wavefront reversion due to degenerate four-wave mixing CdTe crystals,” Izv. Akad. Nauk SSSR Ser. Fiz. 44, 2029–2034 (1980) [Bull. Acad. Sci. USSR Phys. Ser. 44,24–28 (1980)].

V. I. Belinitcher, B. I. Sturman, “Photovoltaic effect in non-centrosymmetric media,” Uspekhi Fiz. Nauk 130, 415–458 (1980).

D. Fekete, J. A. Yeung, A. Yariv, “Phase conjugate reflection by degenerate four-wave mixing in a nematic liquid crystal in the isotropic phase,” Optics Lett. 5, 51–53 (1980).
[Crossref]

J. F. Kanaev, V. K. Malinouvski, B. I. Sturman, “Investigation of light induced scattering in LiNbO3,” Opt. Commun. 34, 95–100 (1980).
[Crossref]

N. Kukhtarev, S. Odoulov, “Wavefront conjugation via anisotropic self-diffraction,” Pis’ma Zh. Tech. Fiz. 6, 1176–1180 (1980) [Sov. Tech. Phys. Lett. 6, 503–505 (1980)].

M. Soskin, A. Khyzniak, “On an interaction of four counter-propagating plane waves in a medium with inertial cubic nonlinearity,” Kvantovaya Elektron. (Moscow) 7, 42–49 (1980).

1979 (4)

C. V. Heer, N. C. Griffen, “Generation of a phase conjugate wave in the forward direction with thin Na-vapor cell,” Opt. Lett. 4, 239–249 (1979).
[Crossref] [PubMed]

This crystal has been successfully used for PC of a cw laser beam in a BFWM arrangement. See N. Kukhtarev, S. Odoulov, “Inversion of a wave front associated with a four-wave interaction in media with nonlocal nonlinearity,” Sov. Phys. JETP Lett. 30, 4–8 (1979); “Wavefront conjugation via degenerate four-wave mixing in electrooptic crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 213, 2–9 (1979).

J. Marburger, J. Lam, “Nonlinear theory of degenerate four-wave mixing,” Appl. Phys. Lett. 34, 381–391 (1979).
[Crossref]

V. Vinetski, N. Kukhtarev, S. Odoulov, M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–760 (1979).
[Crossref]

1978 (2)

A. Yariv, “Four-wave nonlinear optical mixing as real-time holography,” Opt. Commun. 25, 23–25 (1978).
[Crossref]

A. Yariv, “Phase conjugation optics and real time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
[Crossref]

1977 (2)

1974 (1)

K. Jarasiunas, Yu. Vaitkus, “Properties of a laser induced phase grating in CdS,” Phys. Status Solidi A 23, K19–K21 (1974).
[Crossref]

1972 (1)

D. L. Staebler, J. J. Amodei, “Coupled wave analisis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042–1049 (1972).
[Crossref]

1971 (2)

B. L. Stansfield, R. Nodwell, J. Meyer, “Enchanced scattering of laser light by optical mixing in a plasma,” Phys. Rev. Lett. 26, 1219–1221 (1971).
[Crossref]

B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “Recording of two-dimensional and three-dimensional dynamic holograms in transparent substances,” Sov. Phys. Dokl. 16, 46–48 (1971).

1969 (3)

H. J. Eichler, B. Kluzowski, “Lichinduzierte Amplitudengitter in Sattigungsabsorbern und ihr Nachweis durch Beugungser-scheinungen,” Z. Angew. Phys. 27, 4–5 (1969).

J. P. Woerdman, B. Bolger, “Diffraction of light by laser induced grating in Si,” Phys. Lett. A 30, 164–166 (1969).
[Crossref]

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1967 (1)

H. J. Gerritsen, “Nonlinear effects in image formation,” Appl. Phys. Lett. 10, 234–241 (1967).
[Crossref]

1966 (1)

V. I. Bespalov, V. I. Talanov, “On filamentary structure of the light beams in nonlinear liquids,” Sov. Phys. JETP Lett. 3, 307–310 (1966).

1964 (1)

R. Y. Chiao, E. Garmire, C. Townes, P. L. Kelley, “Self trapping of optical beams,” Phys. Rev. Lett. 43, 479–481 (1964); “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[Crossref]

Akhmanov, S. A.

S. A. Akhmanov, R. W. Khokhlov, Problems of Nonlinear Optics (Academy of Sciences of the USSR, Moscow, 1965) (in Russian).

Amodei, J. J.

D. L. Staebler, J. J. Amodei, “Coupled wave analisis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042–1049 (1972).
[Crossref]

Anan’ev, Yu.

Yu. Anan’ev, V. Soloviev, “Particular features of forward and backward schemes of four-wave mixing with mirror reflection of signal beam,” Opt. Spectrosc. 54, 136–143 (1983).

Belinitcher, V. I.

V. I. Belinitcher, B. I. Sturman, “Photovoltaic effect in non-centrosymmetric media,” Uspekhi Fiz. Nauk 130, 415–458 (1980).

Bespalov, V. I.

V. I. Bespalov, V. I. Talanov, “On filamentary structure of the light beams in nonlinear liquids,” Sov. Phys. JETP Lett. 3, 307–310 (1966).

Bloembergen, N.

Blombergen, N.

N. Blombergen, Nonlinear Optics (Benjamin, New York, 1965).

Bogdan, A. R.

Bol’shov, L.

L. Bol’shov, D. Vlasov, R. Garaev, “On a spatial resonance under four-photon interaction between corunning waves in a cubic medium,” Kvantovaya Electron. 9, 83–91 (1982).

Bolger, B.

J. P. Woerdman, B. Bolger, “Diffraction of light by laser induced grating in Si,” Phys. Lett. A 30, 164–166 (1969).
[Crossref]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, C. Townes, P. L. Kelley, “Self trapping of optical beams,” Phys. Rev. Lett. 43, 479–481 (1964); “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[Crossref]

Downer, M. W.

Eichler, H. J.

H. J. Eichler, B. Kluzowski, “Lichinduzierte Amplitudengitter in Sattigungsabsorbern und ihr Nachweis durch Beugungser-scheinungen,” Z. Angew. Phys. 27, 4–5 (1969).

Fekete, D.

D. Fekete, J. A. Yeung, A. Yariv, “Phase conjugate reflection by degenerate four-wave mixing in a nematic liquid crystal in the isotropic phase,” Optics Lett. 5, 51–53 (1980).
[Crossref]

Garaev, R.

L. Bol’shov, D. Vlasov, R. Garaev, “On a spatial resonance under four-photon interaction between corunning waves in a cubic medium,” Kvantovaya Electron. 9, 83–91 (1982).

Garmire, E.

R. Y. Chiao, E. Garmire, C. Townes, P. L. Kelley, “Self trapping of optical beams,” Phys. Rev. Lett. 43, 479–481 (1964); “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[Crossref]

Gerritsen, H. J.

H. J. Gerritsen, “Nonlinear effects in image formation,” Appl. Phys. Lett. 10, 234–241 (1967).
[Crossref]

Griffen, N. C.

Heer, C. V.

Hellwarth, R. W.

Ivakin, E. V.

B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “Recording of two-dimensional and three-dimensional dynamic holograms in transparent substances,” Sov. Phys. Dokl. 16, 46–48 (1971).

Jarasiunas, K.

K. Jarasiunas, Yu. Vaitkus, “Properties of a laser induced phase grating in CdS,” Phys. Status Solidi A 23, K19–K21 (1974).
[Crossref]

Kanaev, J. F.

J. F. Kanaev, V. K. Malinouvski, B. I. Sturman, “Investigation of light induced scattering in LiNbO3,” Opt. Commun. 34, 95–100 (1980).
[Crossref]

Kelley, P. L.

R. Y. Chiao, E. Garmire, C. Townes, P. L. Kelley, “Self trapping of optical beams,” Phys. Rev. Lett. 43, 479–481 (1964); “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[Crossref]

Khokhlov, R. W.

S. A. Akhmanov, R. W. Khokhlov, Problems of Nonlinear Optics (Academy of Sciences of the USSR, Moscow, 1965) (in Russian).

Khyzniak, A.

A. Khyzniak, V. Soloviev, “Forward four-wave mixing,” Opt. Spectrosc. 53, 723–727 (1982).

A. Khyzniak, “On efficiency of four-wave mixing in media with third order nonlinearity,” Izv. Akad. Nauk Ser. Fiz. 45, 640–649 (1981).

M. Soskin, A. Khyzniak, “On an interaction of four counter-propagating plane waves in a medium with inertial cubic nonlinearity,” Kvantovaya Elektron. (Moscow) 7, 42–49 (1980).

Kluzowski, B.

H. J. Eichler, B. Kluzowski, “Lichinduzierte Amplitudengitter in Sattigungsabsorbern und ihr Nachweis durch Beugungser-scheinungen,” Z. Angew. Phys. 27, 4–5 (1969).

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kremenitski, V.

V. Kremenitski, S. Odoulov, M. Soskin, “Wavefront reversion due to degenerate four-wave mixing CdTe crystals,” Izv. Akad. Nauk SSSR Ser. Fiz. 44, 2029–2034 (1980) [Bull. Acad. Sci. USSR Phys. Ser. 44,24–28 (1980)].

Kukhtarev, N.

N. Kukhtarev, S. Odoulov, “Wavefront conjugation via anisotropic self-diffraction,” Pis’ma Zh. Tech. Fiz. 6, 1176–1180 (1980) [Sov. Tech. Phys. Lett. 6, 503–505 (1980)].

V. Vinetski, N. Kukhtarev, S. Odoulov, M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–760 (1979).
[Crossref]

This crystal has been successfully used for PC of a cw laser beam in a BFWM arrangement. See N. Kukhtarev, S. Odoulov, “Inversion of a wave front associated with a four-wave interaction in media with nonlocal nonlinearity,” Sov. Phys. JETP Lett. 30, 4–8 (1979); “Wavefront conjugation via degenerate four-wave mixing in electrooptic crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 213, 2–9 (1979).

Lam, J.

J. Marburger, J. Lam, “Nonlinear theory of degenerate four-wave mixing,” Appl. Phys. Lett. 34, 381–391 (1979).
[Crossref]

Malinouvski, V. K.

J. F. Kanaev, V. K. Malinouvski, B. I. Sturman, “Investigation of light induced scattering in LiNbO3,” Opt. Commun. 34, 95–100 (1980).
[Crossref]

Marburger, J.

J. Marburger, J. Lam, “Nonlinear theory of degenerate four-wave mixing,” Appl. Phys. Lett. 34, 381–391 (1979).
[Crossref]

Meyer, J.

B. L. Stansfield, R. Nodwell, J. Meyer, “Enchanced scattering of laser light by optical mixing in a plasma,” Phys. Rev. Lett. 26, 1219–1221 (1971).
[Crossref]

Nodwell, R.

B. L. Stansfield, R. Nodwell, J. Meyer, “Enchanced scattering of laser light by optical mixing in a plasma,” Phys. Rev. Lett. 26, 1219–1221 (1971).
[Crossref]

Odoulov, S.

N. Kukhtarev, S. Odoulov, “Wavefront conjugation via anisotropic self-diffraction,” Pis’ma Zh. Tech. Fiz. 6, 1176–1180 (1980) [Sov. Tech. Phys. Lett. 6, 503–505 (1980)].

V. Kremenitski, S. Odoulov, M. Soskin, “Wavefront reversion due to degenerate four-wave mixing CdTe crystals,” Izv. Akad. Nauk SSSR Ser. Fiz. 44, 2029–2034 (1980) [Bull. Acad. Sci. USSR Phys. Ser. 44,24–28 (1980)].

This crystal has been successfully used for PC of a cw laser beam in a BFWM arrangement. See N. Kukhtarev, S. Odoulov, “Inversion of a wave front associated with a four-wave interaction in media with nonlocal nonlinearity,” Sov. Phys. JETP Lett. 30, 4–8 (1979); “Wavefront conjugation via degenerate four-wave mixing in electrooptic crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 213, 2–9 (1979).

V. Vinetski, N. Kukhtarev, S. Odoulov, M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–760 (1979).
[Crossref]

Pepper, D. M.

Prior, Y.

Rubanov, A. S.

B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “Recording of two-dimensional and three-dimensional dynamic holograms in transparent substances,” Sov. Phys. Dokl. 16, 46–48 (1971).

Soloviev, V.

Yu. Anan’ev, V. Soloviev, “Particular features of forward and backward schemes of four-wave mixing with mirror reflection of signal beam,” Opt. Spectrosc. 54, 136–143 (1983).

A. Khyzniak, V. Soloviev, “Forward four-wave mixing,” Opt. Spectrosc. 53, 723–727 (1982).

Soskin, M.

V. Kremenitski, S. Odoulov, M. Soskin, “Wavefront reversion due to degenerate four-wave mixing CdTe crystals,” Izv. Akad. Nauk SSSR Ser. Fiz. 44, 2029–2034 (1980) [Bull. Acad. Sci. USSR Phys. Ser. 44,24–28 (1980)].

M. Soskin, A. Khyzniak, “On an interaction of four counter-propagating plane waves in a medium with inertial cubic nonlinearity,” Kvantovaya Elektron. (Moscow) 7, 42–49 (1980).

V. Vinetski, N. Kukhtarev, S. Odoulov, M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–760 (1979).
[Crossref]

Staebler, D. L.

D. L. Staebler, J. J. Amodei, “Coupled wave analisis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042–1049 (1972).
[Crossref]

Stansfield, B. L.

B. L. Stansfield, R. Nodwell, J. Meyer, “Enchanced scattering of laser light by optical mixing in a plasma,” Phys. Rev. Lett. 26, 1219–1221 (1971).
[Crossref]

Stepanov, B. I.

B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “Recording of two-dimensional and three-dimensional dynamic holograms in transparent substances,” Sov. Phys. Dokl. 16, 46–48 (1971).

Sturman, B. I.

V. I. Belinitcher, B. I. Sturman, “Photovoltaic effect in non-centrosymmetric media,” Uspekhi Fiz. Nauk 130, 415–458 (1980).

J. F. Kanaev, V. K. Malinouvski, B. I. Sturman, “Investigation of light induced scattering in LiNbO3,” Opt. Commun. 34, 95–100 (1980).
[Crossref]

Talanov, V. I.

V. I. Bespalov, V. I. Talanov, “On filamentary structure of the light beams in nonlinear liquids,” Sov. Phys. JETP Lett. 3, 307–310 (1966).

Townes, C.

R. Y. Chiao, E. Garmire, C. Townes, P. L. Kelley, “Self trapping of optical beams,” Phys. Rev. Lett. 43, 479–481 (1964); “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[Crossref]

Vaitkus, Yu.

K. Jarasiunas, Yu. Vaitkus, “Properties of a laser induced phase grating in CdS,” Phys. Status Solidi A 23, K19–K21 (1974).
[Crossref]

Vinetski, V.

V. Vinetski, N. Kukhtarev, S. Odoulov, M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–760 (1979).
[Crossref]

Vlasov, D.

L. Bol’shov, D. Vlasov, R. Garaev, “On a spatial resonance under four-photon interaction between corunning waves in a cubic medium,” Kvantovaya Electron. 9, 83–91 (1982).

Woerdman, J. P.

J. P. Woerdman, B. Bolger, “Diffraction of light by laser induced grating in Si,” Phys. Lett. A 30, 164–166 (1969).
[Crossref]

Yariv, A.

D. Fekete, J. A. Yeung, A. Yariv, “Phase conjugate reflection by degenerate four-wave mixing in a nematic liquid crystal in the isotropic phase,” Optics Lett. 5, 51–53 (1980).
[Crossref]

A. Yariv, “Phase conjugation optics and real time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
[Crossref]

A. Yariv, “Four-wave nonlinear optical mixing as real-time holography,” Opt. Commun. 25, 23–25 (1978).
[Crossref]

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

Yeung, J. A.

D. Fekete, J. A. Yeung, A. Yariv, “Phase conjugate reflection by degenerate four-wave mixing in a nematic liquid crystal in the isotropic phase,” Optics Lett. 5, 51–53 (1980).
[Crossref]

Appl. Phys. Lett. (2)

H. J. Gerritsen, “Nonlinear effects in image formation,” Appl. Phys. Lett. 10, 234–241 (1967).
[Crossref]

J. Marburger, J. Lam, “Nonlinear theory of degenerate four-wave mixing,” Appl. Phys. Lett. 34, 381–391 (1979).
[Crossref]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

IEEE J. Quantum Electron. (1)

A. Yariv, “Phase conjugation optics and real time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
[Crossref]

Izv. Akad. Nauk Ser. Fiz. (1)

A. Khyzniak, “On efficiency of four-wave mixing in media with third order nonlinearity,” Izv. Akad. Nauk Ser. Fiz. 45, 640–649 (1981).

Izv. Akad. Nauk SSSR Ser. Fiz. (1)

V. Kremenitski, S. Odoulov, M. Soskin, “Wavefront reversion due to degenerate four-wave mixing CdTe crystals,” Izv. Akad. Nauk SSSR Ser. Fiz. 44, 2029–2034 (1980) [Bull. Acad. Sci. USSR Phys. Ser. 44,24–28 (1980)].

J. Appl. Phys. (1)

D. L. Staebler, J. J. Amodei, “Coupled wave analisis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042–1049 (1972).
[Crossref]

J. Opt. Soc. Am. (1)

Kvantovaya Electron. (1)

L. Bol’shov, D. Vlasov, R. Garaev, “On a spatial resonance under four-photon interaction between corunning waves in a cubic medium,” Kvantovaya Electron. 9, 83–91 (1982).

Kvantovaya Elektron. (Moscow) (1)

M. Soskin, A. Khyzniak, “On an interaction of four counter-propagating plane waves in a medium with inertial cubic nonlinearity,” Kvantovaya Elektron. (Moscow) 7, 42–49 (1980).

Opt. Commun. (2)

A. Yariv, “Four-wave nonlinear optical mixing as real-time holography,” Opt. Commun. 25, 23–25 (1978).
[Crossref]

J. F. Kanaev, V. K. Malinouvski, B. I. Sturman, “Investigation of light induced scattering in LiNbO3,” Opt. Commun. 34, 95–100 (1980).
[Crossref]

Opt. Eng. (1)

D. M. Pepper, “Nonlinear optical phase conjugation,” Opt. Eng. 21, 156–183 (1982).
[Crossref]

Opt. Lett. (4)

Opt. Spectrosc. (2)

A. Khyzniak, V. Soloviev, “Forward four-wave mixing,” Opt. Spectrosc. 53, 723–727 (1982).

Yu. Anan’ev, V. Soloviev, “Particular features of forward and backward schemes of four-wave mixing with mirror reflection of signal beam,” Opt. Spectrosc. 54, 136–143 (1983).

Optics Lett. (1)

D. Fekete, J. A. Yeung, A. Yariv, “Phase conjugate reflection by degenerate four-wave mixing in a nematic liquid crystal in the isotropic phase,” Optics Lett. 5, 51–53 (1980).
[Crossref]

Phys. Lett. A (1)

J. P. Woerdman, B. Bolger, “Diffraction of light by laser induced grating in Si,” Phys. Lett. A 30, 164–166 (1969).
[Crossref]

Phys. Rev. Lett. (2)

R. Y. Chiao, E. Garmire, C. Townes, P. L. Kelley, “Self trapping of optical beams,” Phys. Rev. Lett. 43, 479–481 (1964); “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[Crossref]

B. L. Stansfield, R. Nodwell, J. Meyer, “Enchanced scattering of laser light by optical mixing in a plasma,” Phys. Rev. Lett. 26, 1219–1221 (1971).
[Crossref]

Phys. Status Solidi A (1)

K. Jarasiunas, Yu. Vaitkus, “Properties of a laser induced phase grating in CdS,” Phys. Status Solidi A 23, K19–K21 (1974).
[Crossref]

Pis’ma Zh. Tech. Fiz. (1)

N. Kukhtarev, S. Odoulov, “Wavefront conjugation via anisotropic self-diffraction,” Pis’ma Zh. Tech. Fiz. 6, 1176–1180 (1980) [Sov. Tech. Phys. Lett. 6, 503–505 (1980)].

Sov. Phys. Dokl. (1)

B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “Recording of two-dimensional and three-dimensional dynamic holograms in transparent substances,” Sov. Phys. Dokl. 16, 46–48 (1971).

Sov. Phys. JETP Lett. (2)

V. I. Bespalov, V. I. Talanov, “On filamentary structure of the light beams in nonlinear liquids,” Sov. Phys. JETP Lett. 3, 307–310 (1966).

This crystal has been successfully used for PC of a cw laser beam in a BFWM arrangement. See N. Kukhtarev, S. Odoulov, “Inversion of a wave front associated with a four-wave interaction in media with nonlocal nonlinearity,” Sov. Phys. JETP Lett. 30, 4–8 (1979); “Wavefront conjugation via degenerate four-wave mixing in electrooptic crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 213, 2–9 (1979).

Sov. Phys. Usp. (1)

V. Vinetski, N. Kukhtarev, S. Odoulov, M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–760 (1979).
[Crossref]

Uspekhi Fiz. Nauk (1)

V. I. Belinitcher, B. I. Sturman, “Photovoltaic effect in non-centrosymmetric media,” Uspekhi Fiz. Nauk 130, 415–458 (1980).

Z. Angew. Phys. (1)

H. J. Eichler, B. Kluzowski, “Lichinduzierte Amplitudengitter in Sattigungsabsorbern und ihr Nachweis durch Beugungser-scheinungen,” Z. Angew. Phys. 27, 4–5 (1969).

Other (2)

N. Blombergen, Nonlinear Optics (Benjamin, New York, 1965).

S. A. Akhmanov, R. W. Khokhlov, Problems of Nonlinear Optics (Academy of Sciences of the USSR, Moscow, 1965) (in Russian).

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Figures (9)

Fig. 1
Fig. 1

Vector diagram of degenerate forward four-wave mixing. K1 and K2, pump waves; K3 and K4, signal and phase-conjugate waves.

Fig. 2
Fig. 2

Calculated temporal dependencies of interacting beam intensities for initial intensity ratios: A, I1:I2:I3 = 0.45:0.45:0.1 and B, I1 = I2 = I3. Input intensity of the fourth beam is zero for the both cases. Normalized thickness of the sample ξ = 3. Dashed line corresponds to the saturation value of the beam intensities.

Fig. 3
Fig. 3

Calculated dependence: A of relative phases (solid lines) of a holographic grating recorded by ith and jth beams and the fringe pattern (dashed lines) of the same beams, and B, of normalized beam intensities on the normalized thickness of the nonlinear layer.

Fig. 4
Fig. 4

Time traces: A, of intensities incident upon the dye-cell, and B, of the apparent phase-conjugate wave intensity. Time scale, 250 μsec/div.

Fig. 5
Fig. 5

Angular dependence of the fourth beam energy for the signal beam tilted in 1, the YZ plane and 2, the XZ plane.

Fig. 6
Fig. 6

A, transmittance of the cell with the saturating (solid line) and nonsaturating (dashed line) absorbers versus total energy of the incident beams. B, normalized energy of the fourth beam (curve 1); diffracted intensity of the testing beam for the saturating (curve 2) and nonsaturating (curve 3) absorbers versus total energy of incident beams.

Fig. 7
Fig. 7

Qualitative explanation of heat grating degradation with increasing pump energy (see text).

Fig. 8
Fig. 8

Schematic of FFWM with the reflection of the signal wave from the entrance edge of the crystal.

Fig. 9
Fig. 9

Time variation of the signal beam and the phase-conjugate beam divergence for FFWM in LiNbO3:Fe, 0.03 wt. %.

Equations (20)

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k 4 = k 1 + k 2 - k 3 ,
= 0 + Δ ( r , t ) .
( Δ ) / t = γ E 2 - Δ / T 0 + D 2 ( Δ ) ,
a 1 , 2 ξ = - i { a 2 , 1 - τ a 1 , 2 a 1 , 2 * exp ( - τ - τ τ 1 ) d τ + a 3 - τ [ a 3 * a 1 , 2 + a 4 a 2 , 1 * ] exp ( - τ - τ τ ) d τ + a 4 - τ [ a 4 * a 1 , 2 + a 3 a 2 , 1 * ] exp ( - τ - τ τ 3 ) } , a 3 , 4 ξ = - i { a 4 , 3 - τ a 3 , 4 a 4 , 3 * exp ( - τ - τ τ 1 ) d τ + a 1 - τ [ a 1 * a 3 , 4 + a 3 , 4 * a 2 ] exp ( - τ - τ τ 3 ) d τ + a 2 - τ [ a 2 * a 3 , 4 + a 4 , 3 * a 1 ] exp ( - τ - τ τ 2 ) d τ } ,
a i = { E i / ( k = 1 4 E k ( 0 ) 2 ) 1 / 2 ] exp i τ 0 ξ [ 1 - exp ( - τ / τ 0 ) ] × exp ( α 0 z / 2 ) , ξ = ( k 0 2 γ k = 1 4 E k ( 0 ) 2 / 2 k z α 0 ) T 1 [ 1 - exp ( - α 0 z ) ]
k = 1 4 a k 2 = 1.
β 1 , 2 d a 1 , 2 ξ ¯ = i a 1 , 2 2 a 1 , 2 - 2 i k = 1 4 a k 2 a 1 , 2 - 2 i a 3 a 4 a 2 , 1 * exp ( i δ ξ ¯ ) , β 3 , 4 d a 3 , 4 d ξ ¯ = i a 3 , 4 2 a 3 , 4 - 2 i k = 1 4 a k 2 a 3 , 4 - 2 i a 1 a 2 a 4 , 3 * exp ( - i δ ξ ¯ ) ,
I 1 = β 1 a 1 2 + β 4 a 4 2 , I 2 = β 2 a 2 2 + β 4 a 4 2 , I 3 = β 3 a 3 2 - β 4 a 4 2 .
d y d ξ = ± 4 [ ( I 1 - y ) ( I 2 - y ) ( I 3 - y ) y - ( η y 2 / 8 + σ y / 4 + Γ 0 ) 2 ] 1 / 2 ,
cos Φ [ ( I 1 - y ) ( I 2 - y ) ( I 3 + y ) y ] 1 / 2 = η y 2 / 8 + σ y / 4 + Γ 0 .
y = - α 2 α 4 sn 2 ( m / u ) / [ α 2 - α 4 - α 2 sn 2 ( m / u ) ] ,
y [ ( I 1 - y ) ( I 2 - y ) ( I 3 - y ) - y ( η y / 8 + σ / 4 ) 2 ] = 0 ,
α 4 - 16 q I 3 / [ 16 q - ( 1 + q ) 2 ] ,             m = 1 , α 1 , 2 I 1 ( 1 + q ) 2 { 1 ± 2 [ 1 - 4 q / ( 1 + q ) 2 ] : 1 / 2 / 3 } , μ = 8 / I 1 ( 1 + q ) [ 16 q / ( 1 + q ) 2 - 1 ] 1 / 2 ,
y = 16 q I 3 16 q - ( 1 + q ) 2 sinh 2 ( 4 ξ / M ) 1 + B ( I 3 , I 1 , ξ ) , B = 32 I 3 q cosh 2 ( 4 ξ / μ ) I 1 ( 1 + q ) [ 16 q - ( 1 + q ) 2 ] { 1 - 2 [ 1 - 4 q / ( 1 + q ) 2 ] 1 / 2 / 3 } .
y = I 1 ( 1 + q ) 2 P { 1 - 2 [ 1 - 4 q / ( 1 + q ) 2 ] 1 / 2 / 3 } .
u = K ( m ) ,
φ 4 ( D ) = - π / 2 - φ 3 ( 0 ) + φ 1 ( D ) + φ 2 ( 0 ) - [ 3 ( I 1 - I 2 ) + 5 I 3 ] D / 2 β 2 ,
φ 4 ( D ) = - π / 2 - φ s ( D ) + φ 1 ( 0 ) + φ 2 ( 0 ) + ( I 1 + I 2 - I 3 ) D / 2 β 2 .
L 2 d tan ( θ / 2 ) .
Δ θ Λ / d cos ( θ / 2 ) ,

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