Abstract

Spectral dependence of the third-order optical nonlinearity in a bulk crystal of GaSe is studied at room temperature. The experimental techniques involved are nonlinear transmission and laser-induced self-diffraction. A theory of self-diffraction, which for the first time takes into account the multiple-beam interferences, is developed. The measurements are carried out in the spectral range around the excitonic transition of GaSe. The refractive-index changes resulting from electron–hole plasma effect contribute to the generation of a phase grating below the band gap.

© 1997 Optical Society of America

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  1. M. Schlüter, “The electronic structure of GaSe,” Nuovo Cimento 13, 313–360 (1973).
    [CrossRef]
  2. E. Mooser and M. Schlüter, “The band-gap exciton in Gallium Selenide,” Nuovo Cimento 18, 164–208 (1973).
  3. P. Fielding, G. Fisher, and E. Mooser, “Semiconductors of the type AIIIBVI,” J. Phys. Chem. Solids 8, 434–437 (1959).
    [CrossRef]
  4. G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Sovel’ev, E. Yu. Solaev, and V. V. Smirnov, “GaSe, a new effective material for nonlinear optics,” JETP Lett. 16, 90–92 (1972).
  5. G. A. Akhundov, A. A. Agaeva, V. M. Salmanov, Yu. P. Sharonov, and I. D. Yaroshetskii, “Second harmonic generation in III-VI compounds,” Sov. Phys. Semicond. 7, 826–827 (1973).
  6. Ph. Kupecek, E. Batifol, and A. Khun, “Conversion de fréquences optiques dans le séléniure de gallium (GaSe),” Opt. Commun. 11, 291–295 (1974).
    [CrossRef]
  7. I. M. Catalano, A. Cingolani, A. Minafra, and C. Paorici, “Second harmonic generation in layered compounds,” Opt. Commun. 24, 105–108 (1979).
    [CrossRef]
  8. Yu. F. Solomonov and V. K. Subashiev, “The study of the third order nonlinear susceptibility in GaSe,” Phys. Status Solidi A 74, 75–78 (1982).
    [CrossRef]
  9. C. Hirlimann, J. F. Morhange, and A. Chevy, “Excitonic resonant second harmonic in GaSe,” Solid State Commun. 69, 1019–1022 (1989).
    [CrossRef]
  10. C. Hirlimann, J. F. Morhange, M. A. Kanehisa, A. Chevy, and C. H. Brito-Cruz, “Resonant excitonic optical Stark effect in GaSe,” Appl. Phys. Lett. 55, 2307–2309 (1989).
    [CrossRef]
  11. Yu. V. Vandyshev, V. S. Dneprovskii, V. I. Klimov, Z. D. Kovalyuk, M. G. Novikov, D. K. Okorokov, and A. I. Furtichev, “Exciton-exciton interaction and resonant nonlinearities in GaSe,” Sov. Phys. Solid State 31, 988–992 (1989).
  12. A. Bourdon, E. Bringuier, M. T. Portella, M. Vivières, and N. Piccioli, “Angular properties of second harmonic polarization due to high-order nonlinearities: Application to GaSe and InSe,” Phys. Rev. Lett. 65, 1925–1928 (1990).
    [CrossRef] [PubMed]
  13. K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Grigenyukov, R. K. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
    [CrossRef]
  14. E. Bringuier, A. Bourdon, N. Piccioli, and A. Chevy, “Optical second harmonic generation in lossy media: Application to GaSe and InSe,” Phys. Rev. B 49, 16971–16982 (1994).
    [CrossRef]
  15. J. Amzallag, H. Benisty, S. Debrus, M. May, M. Eddrief, A. Bourdon, A. Chevy, and N. Piccioli, “Second harmonic generation as a probe of antiphase domains in layered GaSe thin films on Si(111) substrates,” Appl. Phys. Lett. 66, 982–984 (1995).
    [CrossRef]
  16. B. Ratajska-Gadomska and W. Gadomski, “Intrinsic optical bistability in layered crystals,” Appl. Opt. 34, 4326–4330 (1995).
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  17. H. F. Eichleir, P. Günter, and D. W. Pohl, Laser Induced Dynamic Gratings, Vol. 50 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1986).
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  18. F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris) 5, 598–640 (1950).
  19. O. S. Heavens, Optical Properties of Thin Films (Butterworth, London, 1955; Dover, New York, 1965).
  20. R. Le Toullec, N. Piccioli, M. Mejatty, and M. Balkanski, “Optical constants of ε-GaSe,” Nuovo Cimento 38B, 159–167 (1977).
    [CrossRef]
  21. J. N. Ravn, “Laser-induced gratings in ZnO,” IEEE J. Quantum Electron. 28, 315–322 (1992).
    [CrossRef]

1995 (2)

J. Amzallag, H. Benisty, S. Debrus, M. May, M. Eddrief, A. Bourdon, A. Chevy, and N. Piccioli, “Second harmonic generation as a probe of antiphase domains in layered GaSe thin films on Si(111) substrates,” Appl. Phys. Lett. 66, 982–984 (1995).
[CrossRef]

B. Ratajska-Gadomska and W. Gadomski, “Intrinsic optical bistability in layered crystals,” Appl. Opt. 34, 4326–4330 (1995).
[CrossRef] [PubMed]

1994 (1)

E. Bringuier, A. Bourdon, N. Piccioli, and A. Chevy, “Optical second harmonic generation in lossy media: Application to GaSe and InSe,” Phys. Rev. B 49, 16971–16982 (1994).
[CrossRef]

1992 (1)

J. N. Ravn, “Laser-induced gratings in ZnO,” IEEE J. Quantum Electron. 28, 315–322 (1992).
[CrossRef]

1991 (1)

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Grigenyukov, R. K. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

1990 (1)

A. Bourdon, E. Bringuier, M. T. Portella, M. Vivières, and N. Piccioli, “Angular properties of second harmonic polarization due to high-order nonlinearities: Application to GaSe and InSe,” Phys. Rev. Lett. 65, 1925–1928 (1990).
[CrossRef] [PubMed]

1989 (3)

C. Hirlimann, J. F. Morhange, and A. Chevy, “Excitonic resonant second harmonic in GaSe,” Solid State Commun. 69, 1019–1022 (1989).
[CrossRef]

C. Hirlimann, J. F. Morhange, M. A. Kanehisa, A. Chevy, and C. H. Brito-Cruz, “Resonant excitonic optical Stark effect in GaSe,” Appl. Phys. Lett. 55, 2307–2309 (1989).
[CrossRef]

Yu. V. Vandyshev, V. S. Dneprovskii, V. I. Klimov, Z. D. Kovalyuk, M. G. Novikov, D. K. Okorokov, and A. I. Furtichev, “Exciton-exciton interaction and resonant nonlinearities in GaSe,” Sov. Phys. Solid State 31, 988–992 (1989).

1982 (1)

Yu. F. Solomonov and V. K. Subashiev, “The study of the third order nonlinear susceptibility in GaSe,” Phys. Status Solidi A 74, 75–78 (1982).
[CrossRef]

1979 (1)

I. M. Catalano, A. Cingolani, A. Minafra, and C. Paorici, “Second harmonic generation in layered compounds,” Opt. Commun. 24, 105–108 (1979).
[CrossRef]

1977 (1)

R. Le Toullec, N. Piccioli, M. Mejatty, and M. Balkanski, “Optical constants of ε-GaSe,” Nuovo Cimento 38B, 159–167 (1977).
[CrossRef]

1974 (1)

Ph. Kupecek, E. Batifol, and A. Khun, “Conversion de fréquences optiques dans le séléniure de gallium (GaSe),” Opt. Commun. 11, 291–295 (1974).
[CrossRef]

1973 (3)

M. Schlüter, “The electronic structure of GaSe,” Nuovo Cimento 13, 313–360 (1973).
[CrossRef]

E. Mooser and M. Schlüter, “The band-gap exciton in Gallium Selenide,” Nuovo Cimento 18, 164–208 (1973).

G. A. Akhundov, A. A. Agaeva, V. M. Salmanov, Yu. P. Sharonov, and I. D. Yaroshetskii, “Second harmonic generation in III-VI compounds,” Sov. Phys. Semicond. 7, 826–827 (1973).

1972 (1)

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Sovel’ev, E. Yu. Solaev, and V. V. Smirnov, “GaSe, a new effective material for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

1959 (1)

P. Fielding, G. Fisher, and E. Mooser, “Semiconductors of the type AIIIBVI,” J. Phys. Chem. Solids 8, 434–437 (1959).
[CrossRef]

1950 (1)

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris) 5, 598–640 (1950).

Abdullaev, G. B.

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Sovel’ev, E. Yu. Solaev, and V. V. Smirnov, “GaSe, a new effective material for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Abelès, F.

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris) 5, 598–640 (1950).

Agaeva, A. A.

G. A. Akhundov, A. A. Agaeva, V. M. Salmanov, Yu. P. Sharonov, and I. D. Yaroshetskii, “Second harmonic generation in III-VI compounds,” Sov. Phys. Semicond. 7, 826–827 (1973).

Akhundov, G. A.

G. A. Akhundov, A. A. Agaeva, V. M. Salmanov, Yu. P. Sharonov, and I. D. Yaroshetskii, “Second harmonic generation in III-VI compounds,” Sov. Phys. Semicond. 7, 826–827 (1973).

Allakhverdiev, R. K.

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Grigenyukov, R. K. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

Amzallag, J.

J. Amzallag, H. Benisty, S. Debrus, M. May, M. Eddrief, A. Bourdon, A. Chevy, and N. Piccioli, “Second harmonic generation as a probe of antiphase domains in layered GaSe thin films on Si(111) substrates,” Appl. Phys. Lett. 66, 982–984 (1995).
[CrossRef]

Balkanski, M.

R. Le Toullec, N. Piccioli, M. Mejatty, and M. Balkanski, “Optical constants of ε-GaSe,” Nuovo Cimento 38B, 159–167 (1977).
[CrossRef]

Batifol, E.

Ph. Kupecek, E. Batifol, and A. Khun, “Conversion de fréquences optiques dans le séléniure de gallium (GaSe),” Opt. Commun. 11, 291–295 (1974).
[CrossRef]

Benisty, H.

J. Amzallag, H. Benisty, S. Debrus, M. May, M. Eddrief, A. Bourdon, A. Chevy, and N. Piccioli, “Second harmonic generation as a probe of antiphase domains in layered GaSe thin films on Si(111) substrates,” Appl. Phys. Lett. 66, 982–984 (1995).
[CrossRef]

Bourdon, A.

J. Amzallag, H. Benisty, S. Debrus, M. May, M. Eddrief, A. Bourdon, A. Chevy, and N. Piccioli, “Second harmonic generation as a probe of antiphase domains in layered GaSe thin films on Si(111) substrates,” Appl. Phys. Lett. 66, 982–984 (1995).
[CrossRef]

E. Bringuier, A. Bourdon, N. Piccioli, and A. Chevy, “Optical second harmonic generation in lossy media: Application to GaSe and InSe,” Phys. Rev. B 49, 16971–16982 (1994).
[CrossRef]

A. Bourdon, E. Bringuier, M. T. Portella, M. Vivières, and N. Piccioli, “Angular properties of second harmonic polarization due to high-order nonlinearities: Application to GaSe and InSe,” Phys. Rev. Lett. 65, 1925–1928 (1990).
[CrossRef] [PubMed]

Bringuier, E.

E. Bringuier, A. Bourdon, N. Piccioli, and A. Chevy, “Optical second harmonic generation in lossy media: Application to GaSe and InSe,” Phys. Rev. B 49, 16971–16982 (1994).
[CrossRef]

A. Bourdon, E. Bringuier, M. T. Portella, M. Vivières, and N. Piccioli, “Angular properties of second harmonic polarization due to high-order nonlinearities: Application to GaSe and InSe,” Phys. Rev. Lett. 65, 1925–1928 (1990).
[CrossRef] [PubMed]

Brito-Cruz, C. H.

C. Hirlimann, J. F. Morhange, M. A. Kanehisa, A. Chevy, and C. H. Brito-Cruz, “Resonant excitonic optical Stark effect in GaSe,” Appl. Phys. Lett. 55, 2307–2309 (1989).
[CrossRef]

Catalano, I. M.

I. M. Catalano, A. Cingolani, A. Minafra, and C. Paorici, “Second harmonic generation in layered compounds,” Opt. Commun. 24, 105–108 (1979).
[CrossRef]

Chevy, A.

J. Amzallag, H. Benisty, S. Debrus, M. May, M. Eddrief, A. Bourdon, A. Chevy, and N. Piccioli, “Second harmonic generation as a probe of antiphase domains in layered GaSe thin films on Si(111) substrates,” Appl. Phys. Lett. 66, 982–984 (1995).
[CrossRef]

E. Bringuier, A. Bourdon, N. Piccioli, and A. Chevy, “Optical second harmonic generation in lossy media: Application to GaSe and InSe,” Phys. Rev. B 49, 16971–16982 (1994).
[CrossRef]

C. Hirlimann, J. F. Morhange, M. A. Kanehisa, A. Chevy, and C. H. Brito-Cruz, “Resonant excitonic optical Stark effect in GaSe,” Appl. Phys. Lett. 55, 2307–2309 (1989).
[CrossRef]

C. Hirlimann, J. F. Morhange, and A. Chevy, “Excitonic resonant second harmonic in GaSe,” Solid State Commun. 69, 1019–1022 (1989).
[CrossRef]

Cingolani, A.

I. M. Catalano, A. Cingolani, A. Minafra, and C. Paorici, “Second harmonic generation in layered compounds,” Opt. Commun. 24, 105–108 (1979).
[CrossRef]

Debrus, S.

J. Amzallag, H. Benisty, S. Debrus, M. May, M. Eddrief, A. Bourdon, A. Chevy, and N. Piccioli, “Second harmonic generation as a probe of antiphase domains in layered GaSe thin films on Si(111) substrates,” Appl. Phys. Lett. 66, 982–984 (1995).
[CrossRef]

Dneprovskii, V. S.

Yu. V. Vandyshev, V. S. Dneprovskii, V. I. Klimov, Z. D. Kovalyuk, M. G. Novikov, D. K. Okorokov, and A. I. Furtichev, “Exciton-exciton interaction and resonant nonlinearities in GaSe,” Sov. Phys. Solid State 31, 988–992 (1989).

Eddrief, M.

J. Amzallag, H. Benisty, S. Debrus, M. May, M. Eddrief, A. Bourdon, A. Chevy, and N. Piccioli, “Second harmonic generation as a probe of antiphase domains in layered GaSe thin films on Si(111) substrates,” Appl. Phys. Lett. 66, 982–984 (1995).
[CrossRef]

Fielding, P.

P. Fielding, G. Fisher, and E. Mooser, “Semiconductors of the type AIIIBVI,” J. Phys. Chem. Solids 8, 434–437 (1959).
[CrossRef]

Fisher, G.

P. Fielding, G. Fisher, and E. Mooser, “Semiconductors of the type AIIIBVI,” J. Phys. Chem. Solids 8, 434–437 (1959).
[CrossRef]

Furtichev, A. I.

Yu. V. Vandyshev, V. S. Dneprovskii, V. I. Klimov, Z. D. Kovalyuk, M. G. Novikov, D. K. Okorokov, and A. I. Furtichev, “Exciton-exciton interaction and resonant nonlinearities in GaSe,” Sov. Phys. Solid State 31, 988–992 (1989).

Gadomski, W.

Grigenyukov, A. I.

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Grigenyukov, R. K. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

Hirlimann, C.

C. Hirlimann, J. F. Morhange, and A. Chevy, “Excitonic resonant second harmonic in GaSe,” Solid State Commun. 69, 1019–1022 (1989).
[CrossRef]

C. Hirlimann, J. F. Morhange, M. A. Kanehisa, A. Chevy, and C. H. Brito-Cruz, “Resonant excitonic optical Stark effect in GaSe,” Appl. Phys. Lett. 55, 2307–2309 (1989).
[CrossRef]

Kanehisa, M. A.

C. Hirlimann, J. F. Morhange, M. A. Kanehisa, A. Chevy, and C. H. Brito-Cruz, “Resonant excitonic optical Stark effect in GaSe,” Appl. Phys. Lett. 55, 2307–2309 (1989).
[CrossRef]

Kerimov, T. A.

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Grigenyukov, R. K. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

Khun, A.

Ph. Kupecek, E. Batifol, and A. Khun, “Conversion de fréquences optiques dans le séléniure de gallium (GaSe),” Opt. Commun. 11, 291–295 (1974).
[CrossRef]

Klimov, V. I.

Yu. V. Vandyshev, V. S. Dneprovskii, V. I. Klimov, Z. D. Kovalyuk, M. G. Novikov, D. K. Okorokov, and A. I. Furtichev, “Exciton-exciton interaction and resonant nonlinearities in GaSe,” Sov. Phys. Solid State 31, 988–992 (1989).

Kovalyuk, Z. D.

Yu. V. Vandyshev, V. S. Dneprovskii, V. I. Klimov, Z. D. Kovalyuk, M. G. Novikov, D. K. Okorokov, and A. I. Furtichev, “Exciton-exciton interaction and resonant nonlinearities in GaSe,” Sov. Phys. Solid State 31, 988–992 (1989).

Kulevskii, L. A.

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Grigenyukov, R. K. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Sovel’ev, E. Yu. Solaev, and V. V. Smirnov, “GaSe, a new effective material for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Kupecek, Ph.

Ph. Kupecek, E. Batifol, and A. Khun, “Conversion de fréquences optiques dans le séléniure de gallium (GaSe),” Opt. Commun. 11, 291–295 (1974).
[CrossRef]

Le Toullec, R.

R. Le Toullec, N. Piccioli, M. Mejatty, and M. Balkanski, “Optical constants of ε-GaSe,” Nuovo Cimento 38B, 159–167 (1977).
[CrossRef]

May, M.

J. Amzallag, H. Benisty, S. Debrus, M. May, M. Eddrief, A. Bourdon, A. Chevy, and N. Piccioli, “Second harmonic generation as a probe of antiphase domains in layered GaSe thin films on Si(111) substrates,” Appl. Phys. Lett. 66, 982–984 (1995).
[CrossRef]

Mejatty, M.

R. Le Toullec, N. Piccioli, M. Mejatty, and M. Balkanski, “Optical constants of ε-GaSe,” Nuovo Cimento 38B, 159–167 (1977).
[CrossRef]

Minafra, A.

I. M. Catalano, A. Cingolani, A. Minafra, and C. Paorici, “Second harmonic generation in layered compounds,” Opt. Commun. 24, 105–108 (1979).
[CrossRef]

Mooser, E.

E. Mooser and M. Schlüter, “The band-gap exciton in Gallium Selenide,” Nuovo Cimento 18, 164–208 (1973).

P. Fielding, G. Fisher, and E. Mooser, “Semiconductors of the type AIIIBVI,” J. Phys. Chem. Solids 8, 434–437 (1959).
[CrossRef]

Morhange, J. F.

C. Hirlimann, J. F. Morhange, M. A. Kanehisa, A. Chevy, and C. H. Brito-Cruz, “Resonant excitonic optical Stark effect in GaSe,” Appl. Phys. Lett. 55, 2307–2309 (1989).
[CrossRef]

C. Hirlimann, J. F. Morhange, and A. Chevy, “Excitonic resonant second harmonic in GaSe,” Solid State Commun. 69, 1019–1022 (1989).
[CrossRef]

Novikov, M. G.

Yu. V. Vandyshev, V. S. Dneprovskii, V. I. Klimov, Z. D. Kovalyuk, M. G. Novikov, D. K. Okorokov, and A. I. Furtichev, “Exciton-exciton interaction and resonant nonlinearities in GaSe,” Sov. Phys. Solid State 31, 988–992 (1989).

Okorokov, D. K.

Yu. V. Vandyshev, V. S. Dneprovskii, V. I. Klimov, Z. D. Kovalyuk, M. G. Novikov, D. K. Okorokov, and A. I. Furtichev, “Exciton-exciton interaction and resonant nonlinearities in GaSe,” Sov. Phys. Solid State 31, 988–992 (1989).

Paorici, C.

I. M. Catalano, A. Cingolani, A. Minafra, and C. Paorici, “Second harmonic generation in layered compounds,” Opt. Commun. 24, 105–108 (1979).
[CrossRef]

Piccioli, N.

J. Amzallag, H. Benisty, S. Debrus, M. May, M. Eddrief, A. Bourdon, A. Chevy, and N. Piccioli, “Second harmonic generation as a probe of antiphase domains in layered GaSe thin films on Si(111) substrates,” Appl. Phys. Lett. 66, 982–984 (1995).
[CrossRef]

E. Bringuier, A. Bourdon, N. Piccioli, and A. Chevy, “Optical second harmonic generation in lossy media: Application to GaSe and InSe,” Phys. Rev. B 49, 16971–16982 (1994).
[CrossRef]

A. Bourdon, E. Bringuier, M. T. Portella, M. Vivières, and N. Piccioli, “Angular properties of second harmonic polarization due to high-order nonlinearities: Application to GaSe and InSe,” Phys. Rev. Lett. 65, 1925–1928 (1990).
[CrossRef] [PubMed]

R. Le Toullec, N. Piccioli, M. Mejatty, and M. Balkanski, “Optical constants of ε-GaSe,” Nuovo Cimento 38B, 159–167 (1977).
[CrossRef]

Portella, M. T.

A. Bourdon, E. Bringuier, M. T. Portella, M. Vivières, and N. Piccioli, “Angular properties of second harmonic polarization due to high-order nonlinearities: Application to GaSe and InSe,” Phys. Rev. Lett. 65, 1925–1928 (1990).
[CrossRef] [PubMed]

Prokhorov, A. M.

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Sovel’ev, E. Yu. Solaev, and V. V. Smirnov, “GaSe, a new effective material for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Ratajska-Gadomska, B.

Ravn, J. N.

J. N. Ravn, “Laser-induced gratings in ZnO,” IEEE J. Quantum Electron. 28, 315–322 (1992).
[CrossRef]

Salmanov, V. M.

G. A. Akhundov, A. A. Agaeva, V. M. Salmanov, Yu. P. Sharonov, and I. D. Yaroshetskii, “Second harmonic generation in III-VI compounds,” Sov. Phys. Semicond. 7, 826–827 (1973).

Schlüter, M.

E. Mooser and M. Schlüter, “The band-gap exciton in Gallium Selenide,” Nuovo Cimento 18, 164–208 (1973).

M. Schlüter, “The electronic structure of GaSe,” Nuovo Cimento 13, 313–360 (1973).
[CrossRef]

Sharonov, Yu. P.

G. A. Akhundov, A. A. Agaeva, V. M. Salmanov, Yu. P. Sharonov, and I. D. Yaroshetskii, “Second harmonic generation in III-VI compounds,” Sov. Phys. Semicond. 7, 826–827 (1973).

Smirnov, V. V.

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Sovel’ev, E. Yu. Solaev, and V. V. Smirnov, “GaSe, a new effective material for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Solaev, E. Yu.

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Sovel’ev, E. Yu. Solaev, and V. V. Smirnov, “GaSe, a new effective material for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Solomonov, Yu. F.

Yu. F. Solomonov and V. K. Subashiev, “The study of the third order nonlinear susceptibility in GaSe,” Phys. Status Solidi A 74, 75–78 (1982).
[CrossRef]

Sovel’ev, A. D.

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Sovel’ev, E. Yu. Solaev, and V. V. Smirnov, “GaSe, a new effective material for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Subashiev, V. K.

Yu. F. Solomonov and V. K. Subashiev, “The study of the third order nonlinear susceptibility in GaSe,” Phys. Status Solidi A 74, 75–78 (1982).
[CrossRef]

Vandyshev, Yu. V.

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Figures (8)

Fig. 1
Fig. 1

(a) Illumination of the crystal by two coherent pumping beams, perpendicularly polarized to the plane of incidence; (b) Configuration of the electromagnetic fields generated in successive media by one of the incident waves.

Fig. 2
Fig. 2

Transmitted far field of the photoinduced grating.

Fig. 3
Fig. 3

Experimental transmission spectra of GaSe for different pumping power densities: (a) 1 MW/cm2, (b) 4 MW/cm2, (c) 8 MW/cm2.

Fig. 4
Fig. 4

Experimental self-diffraction spectra for the same pumping power densities as in Fig. 3.

Fig. 5
Fig. 5

Nonlinear absorption coefficients of GaSe as a function of the wavelength for different pumping power densities: (b) 1 MW/cm2, (c) 4 MW/cm2, (d) 8 MW/cm2. (a), Linear absorption.

Fig. 6
Fig. 6

Variations of the mean absorbed intensity versus wavelength for different pumping power densities: (a) 1 MW/cm2, (b) 4 MW/cm2, (c) 8 MW/cm2.

Fig. 7
Fig. 7

Comparison between experimental self-diffraction spectra and theory: (a) 1 MW/cm2, (b) 4 MW/cm2, (c) 8 MW/cm2.

Fig. 8
Fig. 8

Self-diffracted intensity Id as a function of the incident power density Ioin at (a) 616 nm, (b) 630 nm.

Equations (45)

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Iax=0dαcos rIz, xdz=Im1+12expiK·OM+12exp-iK·OM,
Im=2Iointam21+R2 exp-2ad-2R exp-adcos Φ×1-exp-ad1+R exp-ad-2rmaad exp-adsin ΦΦ
a=αcos r,Φ=2knd cos r,
n=n0+ΔnMB+12ΔnMB exp(iK·OM)+12ΔnMB exp(-iK·OM),
α=α0+ΔαMB+12ΔαMB exp(iK·OM)+12ΔαMB exp(-iK·OM),
Mam=1tam1ramram1,Mma=1tma1rmarma1,
Ψ˜=expiψ˜00exp-iψ˜,
ψ˜=dkn cos r-iα2 cos r=ψ˜0+Δψ˜.
Ein,jEr,j=MamΨ˜MmaETj0,
ETj=TEin,jexp(iψ˜)-R exp(-iψ˜).
Q=λd2n0Λ2=2d sin2 iλn0.
It=T2Ioinexp(αd)+R2 exp(-αd)-2R cos(2knd).
α=α0+δα,
n=n0+δn,
ΔΦMB=2kdΔnMB cos r=2kdn2(λ)Im cos r,
n2(ω)=n201ω31{[ω-Ω(ω)]2+[Γ(ω)/2]2},
Id(λ)k2[n2(λ)]2[Im(λ)]2ItMB,
Id=Ioinexp(-AIoin)[J0(ξIoin)]2[|J2(ξIoin)|2+|J1(ξIoin)|2-2|J1(ξIoin)||J2(ξIoin)|sin θ],
Ein(x, z)=Ein,1 exp(-iβin,1·OM)+Ein,2 exp(-iβin,2·OM),
Er(x, z)=Er1 exp(-iβr1·OM]+Er2 exp[-iβr2·OM],
βin,1=k sin i0k cos i,βin,2=-k sin i0k cos i,
βr1=k sin i0-k cos i,βr2=-k sin i0-k cos i,
EC(x, z)=EF1(z) exp(-iβF1·OM)+EF2(z) exp(-iβF2·OM)+EB1(z) exp(-iβB1·OM)+EB2(z)exp(-iβB2·OM),
βF1=kn sin r0kn cos r,βF2=-kn sin r0kn cos r,
βB1=kn sin r0-kn cos r,βB2=-kn sin r0-kn cos r.
Et(x, z)=Et1 exp(-iβt1·OM)+Et2 exp(-iβt2·OM)
dEFj(z)dz,dEBj(z)dz,
EFj=Ein, jtma1-(rma)2 exp(-2iψ˜),
EBj=rma exp[-2iψ˜]EFj,
ECx, z=2tmaEin cosknx sin r1-R exp-2iψ˜exp-αz2 cos r×exp-iknz cos r+rma×expαz-2d2 cos rexpiknz-2dcos r,
I(x, z)=12ECEC*
Ix, z=2Iointam21+cosK·OM1+R2 exp-2αdcos r-2R exp-αdcos rcos2knd cos rexp-αzcos r+R expαz-2dcos r+2rma exp-αdcos rcos2knz-dcos r,
tam=cos in cos rtma=2 cos icos i+n cos r,
R=ram2=-rma2=cos i-n cos rcos i+n cos r2=1-tmatam=1-T.
ET(x, z)=TEin(x, z)exp(iψ˜)-R exp(-iψ˜),
ψ˜=ψ˜0+Δψ˜MB+Δψ˜MB cos(K·OM)=ψ˜1+Δψ˜MB cos(K·OM)=12[(Φ0-ia0d)+(ΔΦMB-iΔaMBd)+(ΔΦMB-iΔaMBd)cos(K·OM)]
ΔΦMB=2kdΔnMB cos r,ΔaMB=ΔαMBcos r.
D=exp(iψ˜1)exp[iΔψ˜MB cos(K·OM)]-R exp(-iψ˜1)exp[-iΔψ˜MB cos(K·OM)]
exp[±iΔψ˜MB cos(K·OM)]=J0(Δψ˜MB)+2p=1(-1)pJ2p(Δψ˜MB)×cos[2p(K·OM)]-(±2i)×p=1(-1)pJ2p-1(Δψ˜MB)×cos[(2p-1)(K·OM)]
ETx, z=TEinx, zJ0Δψ˜MB1expiψ˜1-R exp-iψ˜1×1-2J0Δψ˜MBp=1-1pJ2pΔψ˜MB×cos2pK·OM+2iJ0Δψ˜MBexpiψ˜1+R exp-iψ˜1expiψ˜1-R exp-iψ˜1×p=1-1pJ2p-1Δψ˜MB×cos2p-1K·OM.
Ed=TEinJ0Δψ˜MB21expiψ˜1-R exp-iψ˜1×J2Δψ˜MB-iexpiψ˜1+R exp-iψ˜1expiψ˜1-R exp-iψ˜1J1Δψ˜MB.
Ed=-i2TEinexp(iψ˜1)-R exp(-iψ˜1)×exp(iψ˜1)+R exp(-iψ˜1)exp(iψ˜1)-R exp(-iψ˜1)Δψ˜MB.
Idλ=14ΔΦMB22+dΔaMB22ItMB,
It=T2Ioinexp(ad)+R2 exp(-ad)-2R cos Φ
MB=exp(ad)+R2 exp(-ad)+2R cos Φexp(ad)+R2 exp(-ad)-2R cos Φ

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