Abstract

We introduce a temporal delay in one beam of the two-color Z-scan apparatus, which measures nondegenerate nonlinear absorption and nondegenerate nonlinear refraction. This technique allows us to time resolve separately the sign and the magnitude of the nonlinear absorption and refraction at frequency ωp that are due to the presence of a strong excitation at frequency ωe. For example, in semiconductors we specifically measure the bound electronic, nondegenerate nonlinear refraction and nondegenerate two-photon absorption, as well as the two-photon-generated free-carrier refraction and absorption as functions of time. We demonstrate this technique on ZnSe, ZnS, and CS2, using picosecond pulses at 1.06 and 0.532 μm.

© 1994 Optical Society of America

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  1. J. J. Wynne, “Optical third-order mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. 178, 1295 (1969); see also P. Roussignol, D. Ricard, and C. Flytzanis, “Nonlinear optical properties of commercial semiconductor doped glasses,” Appl. Phys. A 44, 285 (1987).
    [CrossRef]
  2. E. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, “Degenerate four wave mixing measurements of higher order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991).
    [CrossRef]
  3. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
    [CrossRef]
  4. H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurement of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666 (1991).
    [CrossRef]
  5. J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. 17, 260 (1992).
    [CrossRef]
  6. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2measurements,” Opt. Lett. 14, 955 (1989).
    [CrossRef] [PubMed]
  7. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  8. E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).
  9. D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, “Picosecond spectroscopy of the semiconductors,” Solid-State Electron. 21, 147 (1978).
    [CrossRef]
  10. E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, New York, 1982), p. 368.
    [CrossRef]
  11. M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon- absorption,” Phys. Rev. Lett. 65, 96 (1989).
    [CrossRef]
  12. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solid,” IEEE J. Quantum Electron. 27, 1296 (1991).
    [CrossRef]
  13. D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers–Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1 (1992).
    [CrossRef]
  14. F. Bassani and S. Scandolo, “Dispersion relations and sum rules in nonlinear optics,” Phys. Rev. B 44, 8446 (1991).
    [CrossRef]
  15. D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197 (1981).
    [CrossRef]
  16. A. G. Aronov, D. E. Pikus, and D. Sh. Shekhter, “Quantum theory of free-electron dielectric constant in semiconductors,” Sov. Phys. Solid State 10, 645 (1968).
  17. L. Banyai and S. W. Koch, “A simple theory for the effects of the plasma screening on the optical spectra of highly excited semiconductors,” Z. Phys. B 63, 283 (1986).
    [CrossRef]
  18. R. Luzzi and A. R. Vasconcellos, “Relaxation processes in nonequilibrium semiconductor plasma,” in Semiconductors Probed by Ultrafast Laser Spectroscopy, R. R. Alfano, ed. (Academic, New York, 1984), Vol. 1.
    [CrossRef]
  19. J. I. Pankove, Optical Processes in Semiconductors (Prentice-Hall, Englewood Cliffs, N.J., 1971).
  20. S. A. Akmanov, R. V. Khokhlov, and A. P. Sukhorukov, “Self-focusing, self-defocusing, and self-modulation of laser beams,” in Laser Handbook, F. T. Arecchi and E. O. Schultz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, p. 1151.
  21. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  22. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  23. J. Wang, “The dispersion and symmetry of optical nonlinearities in semiconductors,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 1993).
  24. B. Ray, II–VI Compounds (Pergamon, Edinburgh, 1969), Chap. 6.
  25. R. J. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  26. M. Sheik-Bahae, J. Wang, E. J. Canto-Said, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Two-photon coherence and symmetry of χ(3)in semiconductors,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), paper QTuK26.
  27. M. Sheik-Bahae, J. Wang, and E. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. (to be published).
  28. E. O. Kane, “Band structure of indium antimonide,” J. Chem. Phys. 1, 249 (1957).

1992 (4)

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. 17, 260 (1992).
[CrossRef]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers–Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

R. J. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

1991 (4)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solid,” IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

F. Bassani and S. Scandolo, “Dispersion relations and sum rules in nonlinear optics,” Phys. Rev. B 44, 8446 (1991).
[CrossRef]

H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurement of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666 (1991).
[CrossRef]

E. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, “Degenerate four wave mixing measurements of higher order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1989 (2)

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2measurements,” Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon- absorption,” Phys. Rev. Lett. 65, 96 (1989).
[CrossRef]

1986 (1)

L. Banyai and S. W. Koch, “A simple theory for the effects of the plasma screening on the optical spectra of highly excited semiconductors,” Z. Phys. B 63, 283 (1986).
[CrossRef]

1985 (1)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).

1981 (1)

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197 (1981).
[CrossRef]

1978 (1)

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, “Picosecond spectroscopy of the semiconductors,” Solid-State Electron. 21, 147 (1978).
[CrossRef]

1969 (1)

J. J. Wynne, “Optical third-order mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. 178, 1295 (1969); see also P. Roussignol, D. Ricard, and C. Flytzanis, “Nonlinear optical properties of commercial semiconductor doped glasses,” Appl. Phys. A 44, 285 (1987).
[CrossRef]

1968 (1)

A. G. Aronov, D. E. Pikus, and D. Sh. Shekhter, “Quantum theory of free-electron dielectric constant in semiconductors,” Sov. Phys. Solid State 10, 645 (1968).

1957 (1)

E. O. Kane, “Band structure of indium antimonide,” J. Chem. Phys. 1, 249 (1957).

Akmanov, S. A.

S. A. Akmanov, R. V. Khokhlov, and A. P. Sukhorukov, “Self-focusing, self-defocusing, and self-modulation of laser beams,” in Laser Handbook, F. T. Arecchi and E. O. Schultz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, p. 1151.

Aronov, A. G.

A. G. Aronov, D. E. Pikus, and D. Sh. Shekhter, “Quantum theory of free-electron dielectric constant in semiconductors,” Sov. Phys. Solid State 10, 645 (1968).

Auston, D. H.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, “Picosecond spectroscopy of the semiconductors,” Solid-State Electron. 21, 147 (1978).
[CrossRef]

Banyai, L.

L. Banyai and S. W. Koch, “A simple theory for the effects of the plasma screening on the optical spectra of highly excited semiconductors,” Z. Phys. B 63, 283 (1986).
[CrossRef]

Bassani, F.

F. Bassani and S. Scandolo, “Dispersion relations and sum rules in nonlinear optics,” Phys. Rev. B 44, 8446 (1991).
[CrossRef]

Boggess, T. F.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, New York, 1982), p. 368.
[CrossRef]

Canto-Said, E.

E. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, “Degenerate four wave mixing measurements of higher order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

Canto-Said, E. J.

M. Sheik-Bahae, J. Wang, E. J. Canto-Said, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Two-photon coherence and symmetry of χ(3)in semiconductors,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), paper QTuK26.

de Araujo, C. B.

H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurement of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666 (1991).
[CrossRef]

DeSalvo, R.

J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. 17, 260 (1992).
[CrossRef]

M. Sheik-Bahae, J. Wang, E. J. Canto-Said, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Two-photon coherence and symmetry of χ(3)in semiconductors,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), paper QTuK26.

DeSalvo, R. J.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Gomes, A. S. L.

H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurement of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666 (1991).
[CrossRef]

Guha, S.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).

Hagan, D. J.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers–Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. 17, 260 (1992).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

R. J. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

E. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, “Degenerate four wave mixing measurements of higher order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solid,” IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon- absorption,” Phys. Rev. Lett. 65, 96 (1989).
[CrossRef]

M. Sheik-Bahae, J. Wang, E. J. Canto-Said, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Two-photon coherence and symmetry of χ(3)in semiconductors,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), paper QTuK26.

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Hopf, F.

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, New York, 1982), p. 368.
[CrossRef]

Hutchings, D. C.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers–Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solid,” IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

Ippen, E. P.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, “Picosecond spectroscopy of the semiconductors,” Solid-State Electron. 21, 147 (1978).
[CrossRef]

Kane, E. O.

E. O. Kane, “Band structure of indium antimonide,” J. Chem. Phys. 1, 249 (1957).

Khokhlov, R. V.

S. A. Akmanov, R. V. Khokhlov, and A. P. Sukhorukov, “Self-focusing, self-defocusing, and self-modulation of laser beams,” in Laser Handbook, F. T. Arecchi and E. O. Schultz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, p. 1151.

Koch, S. W.

L. Banyai and S. W. Koch, “A simple theory for the effects of the plasma screening on the optical spectra of highly excited semiconductors,” Z. Phys. B 63, 283 (1986).
[CrossRef]

Luzzi, R.

R. Luzzi and A. R. Vasconcellos, “Relaxation processes in nonequilibrium semiconductor plasma,” in Semiconductors Probed by Ultrafast Laser Spectroscopy, R. R. Alfano, ed. (Academic, New York, 1984), Vol. 1.
[CrossRef]

Ma, H.

H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurement of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666 (1991).
[CrossRef]

McAffee, S.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, “Picosecond spectroscopy of the semiconductors,” Solid-State Electron. 21, 147 (1978).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197 (1981).
[CrossRef]

Pankove, J. I.

J. I. Pankove, Optical Processes in Semiconductors (Prentice-Hall, Englewood Cliffs, N.J., 1971).

Pikus, D. E.

A. G. Aronov, D. E. Pikus, and D. Sh. Shekhter, “Quantum theory of free-electron dielectric constant in semiconductors,” Sov. Phys. Solid State 10, 645 (1968).

Prise, M. E.

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197 (1981).
[CrossRef]

Ray, B.

B. Ray, II–VI Compounds (Pergamon, Edinburgh, 1969), Chap. 6.

Said, A. A.

Scandolo, S.

F. Bassani and S. Scandolo, “Dispersion relations and sum rules in nonlinear optics,” Phys. Rev. B 44, 8446 (1991).
[CrossRef]

Seaton, C. T.

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197 (1981).
[CrossRef]

Shank, C. V.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, “Picosecond spectroscopy of the semiconductors,” Solid-State Electron. 21, 147 (1978).
[CrossRef]

Sheik-Bahae, J.

J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. 17, 260 (1992).
[CrossRef]

Sheik-Bahae, M.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers–Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

R. J. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solid,” IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon- absorption,” Phys. Rev. Lett. 65, 96 (1989).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2measurements,” Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

M. Sheik-Bahae, J. Wang, and E. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. (to be published).

M. Sheik-Bahae, J. Wang, E. J. Canto-Said, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Two-photon coherence and symmetry of χ(3)in semiconductors,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), paper QTuK26.

Shekhter, D. Sh.

A. G. Aronov, D. E. Pikus, and D. Sh. Shekhter, “Quantum theory of free-electron dielectric constant in semiconductors,” Sov. Phys. Solid State 10, 645 (1968).

Smirl, A. L.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, New York, 1982), p. 368.
[CrossRef]

Smith, S. D.

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197 (1981).
[CrossRef]

Soileau, M. J.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, New York, 1982), p. 368.
[CrossRef]

Stegeman, G.

Sukhorukov, A. P.

S. A. Akmanov, R. V. Khokhlov, and A. P. Sukhorukov, “Self-focusing, self-defocusing, and self-modulation of laser beams,” in Laser Handbook, F. T. Arecchi and E. O. Schultz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, p. 1151.

Teschke, O.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, “Picosecond spectroscopy of the semiconductors,” Solid-State Electron. 21, 147 (1978).
[CrossRef]

Van Stryland, E.

M. Sheik-Bahae, J. Wang, and E. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. (to be published).

Van Stryland, E. W.

R. J. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers–Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. 17, 260 (1992).
[CrossRef]

E. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, “Degenerate four wave mixing measurements of higher order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solid,” IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon- absorption,” Phys. Rev. Lett. 65, 96 (1989).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2measurements,” Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, New York, 1982), p. 368.
[CrossRef]

M. Sheik-Bahae, J. Wang, E. J. Canto-Said, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Two-photon coherence and symmetry of χ(3)in semiconductors,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), paper QTuK26.

Vanherzeele, H.

R. J. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).

Vasconcellos, A. R.

R. Luzzi and A. R. Vasconcellos, “Relaxation processes in nonequilibrium semiconductor plasma,” in Semiconductors Probed by Ultrafast Laser Spectroscopy, R. R. Alfano, ed. (Academic, New York, 1984), Vol. 1.
[CrossRef]

Wang, J.

J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. 17, 260 (1992).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, J. Wang, and E. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. (to be published).

M. Sheik-Bahae, J. Wang, E. J. Canto-Said, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Two-photon coherence and symmetry of χ(3)in semiconductors,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), paper QTuK26.

J. Wang, “The dispersion and symmetry of optical nonlinearities in semiconductors,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 1993).

Wei, T. H.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wherrett, B. S.

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, New York, 1982), p. 368.
[CrossRef]

Woodall, M. A.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).

Wynne, J. J.

J. J. Wynne, “Optical third-order mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. 178, 1295 (1969); see also P. Roussignol, D. Ricard, and C. Flytzanis, “Nonlinear optical properties of commercial semiconductor doped glasses,” Appl. Phys. A 44, 285 (1987).
[CrossRef]

Young, J.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

E. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, “Degenerate four wave mixing measurements of higher order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

Appl. Phys. Lett. (1)

H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurement of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666 (1991).
[CrossRef]

IEEE J. Quantum Electron. (3)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solid,” IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

E. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, “Degenerate four wave mixing measurements of higher order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

J. Chem. Phys. (1)

E. O. Kane, “Band structure of indium antimonide,” J. Chem. Phys. 1, 249 (1957).

J. Opt. Soc. Am. B (1)

Opt. Eng. (1)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).

Opt. Lett. (3)

Opt. Quantum Electron. (1)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers–Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

Phys. Rev. (1)

J. J. Wynne, “Optical third-order mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. 178, 1295 (1969); see also P. Roussignol, D. Ricard, and C. Flytzanis, “Nonlinear optical properties of commercial semiconductor doped glasses,” Appl. Phys. A 44, 285 (1987).
[CrossRef]

Phys. Rev. B (1)

F. Bassani and S. Scandolo, “Dispersion relations and sum rules in nonlinear optics,” Phys. Rev. B 44, 8446 (1991).
[CrossRef]

Phys. Rev. Lett. (2)

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197 (1981).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon- absorption,” Phys. Rev. Lett. 65, 96 (1989).
[CrossRef]

Solid-State Electron. (1)

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, “Picosecond spectroscopy of the semiconductors,” Solid-State Electron. 21, 147 (1978).
[CrossRef]

Sov. Phys. Solid State (1)

A. G. Aronov, D. E. Pikus, and D. Sh. Shekhter, “Quantum theory of free-electron dielectric constant in semiconductors,” Sov. Phys. Solid State 10, 645 (1968).

Z. Phys. B (1)

L. Banyai and S. W. Koch, “A simple theory for the effects of the plasma screening on the optical spectra of highly excited semiconductors,” Z. Phys. B 63, 283 (1986).
[CrossRef]

Other (10)

R. Luzzi and A. R. Vasconcellos, “Relaxation processes in nonequilibrium semiconductor plasma,” in Semiconductors Probed by Ultrafast Laser Spectroscopy, R. R. Alfano, ed. (Academic, New York, 1984), Vol. 1.
[CrossRef]

J. I. Pankove, Optical Processes in Semiconductors (Prentice-Hall, Englewood Cliffs, N.J., 1971).

S. A. Akmanov, R. V. Khokhlov, and A. P. Sukhorukov, “Self-focusing, self-defocusing, and self-modulation of laser beams,” in Laser Handbook, F. T. Arecchi and E. O. Schultz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, p. 1151.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

J. Wang, “The dispersion and symmetry of optical nonlinearities in semiconductors,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 1993).

B. Ray, II–VI Compounds (Pergamon, Edinburgh, 1969), Chap. 6.

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, New York, 1982), p. 368.
[CrossRef]

M. Sheik-Bahae, J. Wang, E. J. Canto-Said, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Two-photon coherence and symmetry of χ(3)in semiconductors,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), paper QTuK26.

M. Sheik-Bahae, J. Wang, and E. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. (to be published).

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Figures (8)

Fig. 1
Fig. 1

Time-resolved excite–probe two-color Z-scan experimental apparatus. D1–D4, detectors. SHG, second-harmonic-generating crystal.

Fig. 2
Fig. 2

Time-resolved two-color Z scan of CS2 obtained with λ = 1.06 μm as the excitation and λ = 0.532 μm as the probe. This procedure gives the cross correlation of these two pulses and determines the zero-time-delay position.

Fig. 3
Fig. 3

Open-aperture data (filled circles) and closed-aperture data (open circles) for ZnSe obtained with perpendicularly polarized beams at zero time delay (excitation at 1.06 μm and probe at 0.532 μm). The squares show the division of the two data sets, and the curves represent theoretical fits.

Fig. 4
Fig. 4

Closed-aperture degenerate Z-scan data (filled circles) and closed-aperture nondegenerate data (open circles) obtained with excitation at 1.06 μm and probe at 0.532 μm for ZnS obtained with parallel-polarized beams at zero time delay. The curves represent theoretical fits.

Fig. 5
Fig. 5

(a) Nonlinear refraction as determined by ΔTpv(td) and (b) nonlinear absorption from the normalized transmittance Top(td) as a function of probe-beam time delay td for ZnSe measured at Ie = 1.2 GW/cm2 (open symbols) and Ie = 0.7 GW/cm2 (filled squares). τr = 1 ns. The curves are fits to the data obtained with the values given in Table 1.

Fig. 6
Fig. 6

Nondegenerate divided Z scans on ZnSe at time delays of 100 ps (circles) and 200 ps (squares) obtained with 0.53 μm as the excitation source and 1.06 μm as the probe. The curve shows the theoretical fit for the free-carrier refraction (and absorption).

Fig. 7
Fig. 7

(a) Nonlinear refraction as determined by ΔTpv and (b) nonlinear absorption from the normalized transmittance Top as a function of probe-beam time delay td for ZnS measured at Ie = 0.7 GW/cm2 (filled circles) and Ie = 1.45 GW/cm2 (open circles). The curves are fits to the data obtained with the values given in Table 1.

Fig. 8
Fig. 8

Free-carrier nonlinear refraction as a function of probe-beam photon energy (ħωp/Eg) for ZnS at 0.532 μm and for ZnSe at 1.06 and 0.532 μm.

Tables (1)

Tables Icon

Table 1 Nondegenerate Nonlinear Parameters Extracted from the Time-Resolved Two-Color Z-Scan Dataa

Equations (18)

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Δ n ( ω p ; ω e ) = Δ n b + Δ n f ,
Δ α ( ω p ; ω e ) = Δ α b + Δ α f .
Δ n b ( ω p ; ω e ) = 2 n 2 ( ω p ; ω e ) I e ,
Δ α b ( ω p ; ω e ) = 2 β ( ω p ; ω e ) I e ,
Δ n f ( ω p ; ω e ) = σ r ( ω p ) Δ N ( t ) ,
Δ α f ( ω p ; ω e ) = σ a ( ω p ) Δ N ( t ) ,
d Δ N d t = β ( ω e ; ω e ) 2 ω e I e 2 - Δ N τ r ,
2 E p z + α p E p = - 2 β ( ω p ; ω e ) E p I e - σ a ( ω p ) Δ N E p ,
ϕ p z = ω p c 2 n 2 ( ω p ; ω e ) I e + σ r ( ω p ) Δ N .
I e z + α e I e = - β ( ω e ; ω e ) I e 2 ,
E p ( z = 0 ) = E 0 p w 0 p w p exp [ - r 2 w p 2 ( 1 + i Z Z 0 p ) - t 2 2 τ p 2 ] × exp [ - i tan - 1 ( Z Z 0 p ) ] ,
I e ( z = 0 ) = I 0 e w 0 e 2 w e 2 exp [ - 2 r 2 w e 2 - ( t - t d ) 2 τ e 2 ] ,
E a ( r , t , Z ) = 2 π i λ p ( d - Z ) exp [ i π r 2 λ p ( d - Z ) ] × 0 r d r E p ( r , t , Z , z = L ) × exp [ i π r 2 λ p ( d - Z ) ] J 0 [ 2 π r r λ p ( d - Z ) ] ,
T ( t d , Z ) = - + d t 0 r a r d r E a 2 - + d t 0 r a r d r E a ( I e = 0 ) 2 ,
Δ T pv ( t d ) = ± [ T ( t d , Z p ) T op ( t d , Z p ) - T ( t d , Z v ) T op ( t d , Z v ) ] for S < 1 , T op ( t d ) = T ( t d , 0 ) with S = 1 ,
Δ n ( ω p ) = 2 π e 2 Δ N m e - h ( - 1 ω p 2 - 1 ω g 2 - ω p 2 ) ,
m e - h m 0 E g E p ,
Δ n ( ω p ) = A E p n 0 E g 3 H ( ω p E g ) Δ N ,

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