Abstract

We extend the application of the Z-scan experimental technique to determine free-carrier nonlinearities in the presence of bound electronic refraction and two-photon absorption. We employ this method, using picosecond pulses in CdTe, GaAs, and ZnTe at 1.06 μm and in ZnSe at 1.06 and 0.53 μm, to measure the refractive-index change induced by two-photon-excited free carriers (coefficient σr,), the two-photon absorption coefficient β, and the bound electronic nonlinear refractive index n2. The real and imaginary parts of the third-order susceptibility (i.e., n2 and β, respectively) are determined by Z scans with low inputs, and the refraction from carriers generated by two-photon absorption (an effecitve fifth-order nonlinearity) is determined from Z scans with higher input energies. We compare our experimental results with theoretical models and deduce that the three measured parameters are well predicted by simple two-band models. n2 changes from positive to negative as the photon energy approaches the band edge, in accordance with a recent theory of the dispersion of n2 in solids based on Kramers–Kronig transformations [ Phys. Rev. Lett. 65, 96 ( 1990); IEEE J. Quantum Electron. 27, 1296 ( 1991)]. We find that the values of σr are in agreement with simple band-filling models.

© 1992 Optical Society of America

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  1. D. A. B. Miller, S. D. Smith, A. M. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low power effects in InSb,” App. Phys. Lett. 35, 658 (1979).
    [CrossRef]
  2. H. M. Gibbs, S. L. McCall, T. N. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451 (1979).
    [CrossRef]
  3. A. Miller, D. Duncan, “Optical nonlinearities in narrow gap semiconductors,” in Optical Properties of Narrow-Gap Low-Dimensional Structures, C. M. Sotomayor Torres, J. C. Portal, J. C. Maan, R. A. Stradling, eds. (Plenum, New York, 1987).
    [CrossRef]
  4. E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1981 (1988).
  5. M. Sheik-Bahae, H. S. Kwok, “Picosecond CO2laser-induced self-focusing in InSb,” IEEE J. Quantum Electron. QE-23, 1974 (1987).
    [CrossRef]
  6. S. Guha, E. W. Van Stryland, M. J. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption,” Opt. Lett. 10, 285 (1985).
    [CrossRef] [PubMed]
  7. E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613 (1985).
  8. A. K. Kar, J. G. H. Mathew, S. D. Smith, B. Davis, W. Prettl, “Optical bistability in InSb at room temperature with two photon absorption,” Appl. Phys. Lett. 42, 334 (1983).
    [CrossRef]
  9. E. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, “Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991); D. J. Hagan, E. Canto, E. Meisak, M. J. Soileau, E. W. Van Stryland, “Picosecond degenerate four-wave mixing studies in ZnSe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 160.
    [CrossRef]
  10. A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. J. Canto-Said, Y. Y. Wu, J. Young, T. H. Wei, E. W. Van Stryland, “Nonlinearities in semiconductors for optical limiting,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soleau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 294 (1990).
    [CrossRef]
  11. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  12. M. Sheik-Bahae, D. J. Hagan, 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 (1990).
    [CrossRef] [PubMed]
  13. M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, “High-sensitivity, single-beam n2measurement,” Opt. Lett. 14, 955 (1989).
    [CrossRef] [PubMed]
  14. A. E. Kaplan, “External self-focusing of light by a nonlinear lens,” Radiophys. Quantum Electron. 12, 692 (1969).
    [CrossRef]
  15. S. A. Akhmanov, R. V. Khokhlov, A. P. Sukhorukov, “Self-focusing, self-defocusing, and self-modulation of laser beams,” in Laser Handbook, F. T. Arecchi, E. O. Shultz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, p. 1151.
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    [CrossRef]
  17. E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490 (1985).
    [CrossRef] [PubMed]
  18. T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488 (1985).
    [CrossRef]
  19. D. A. B. Miller, C. T. Seaton, M. E. Prise, S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197 (1981).
    [CrossRef]
  20. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics(Wiley, New York, 1978).
  21. The ZnSe sample was obtained from Heriot-Watt University, Edinburgh, UK; CdTe II–VI, from Saxonburgh, Pa.; GaAs from the Massachusetts Institute of Technology, Boston, Mass.; and ZnTe from Cleveland Crystals, Cleveland, Ohio.
  22. A. L. Smirl, T. F. Boggess, J. Dubard, A. G. Cui, “Single and multiple beam nonlinear absorption and refraction measurements in semiconductors,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 251 (1990).
    [CrossRef]
  23. M. Sheik-Bahae, D. Hutchings, D. J. Hagan, E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296 (1991).
    [CrossRef]
  24. M. Weiler, “Nonparabolicity and exciton effects in two photon absorption in zinc-blende semiconductors,” Solid State Commun. 39, 937 (1981).
    [CrossRef]
  25. B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1, 67 (1984).
    [CrossRef]
  26. C. C. Lee, H. Y. Fan, “Two photon absorption with exciton effects for degenerate valence bands,” Phys. Rev. B 9, 3502 (1974).
    [CrossRef]
  27. A. G. Aronov, D. E. Pikus, D. Sh. Shekhter, “Quantum theory of free-electron dielectric constant in semiconductors,” So. Phys. Solid State 10, 645 (1968).
  28. D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, O. Teschke, “Picosecond spectroscopy of semiconductors,” Solid State Electron. 21, 147 (1978).
    [CrossRef]
  29. B. S. Wherrett, A. C. Walker, F. A. P. Tooley, “Nonlinear refraction for cw optical bistability,” in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, New York, 1988), p. 239.
    [CrossRef]
  30. T. S. Moss, “Theory of intensity dependence of refractive index,” Phys. Status Solidi B 101, 555 (1980).
    [CrossRef]
  31. E. O. Kane, “Band structure of InSb,” J. Chem. Phys. Solids 1, 249 (1957).
    [CrossRef]
  32. K.-H. Hellwege, editor, Landolt–Börnstein Numerical Data and Functional Relationships in Science and Technology, Vol. 17, Semiconductors (Springer-Verlag, New York, 1982), Subvol. (b).
  33. R. K. Jain, M. B. Klein, “Degenerate four-wave mixing in semiconductors,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 335.
  34. L. Banyai, S. W. Koch, “A simple theory for the effects of plasma screening on the optical spectra of highly excited semiconductors,” Z. Phys. B 63, (1986).
    [CrossRef]
  35. S. W. Koch, Optical Sciences Center, University of Arizona, Tucson, Ariz. 85721 (personal communication).

1991 (2)

E. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, “Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991); D. J. Hagan, E. Canto, E. Meisak, M. J. Soileau, E. W. Van Stryland, “Picosecond degenerate four-wave mixing studies in ZnSe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 160.
[CrossRef]

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

1990 (2)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, 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, 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 (1990).
[CrossRef] [PubMed]

1989 (1)

1988 (1)

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1981 (1988).

1987 (1)

M. Sheik-Bahae, H. S. Kwok, “Picosecond CO2laser-induced self-focusing in InSb,” IEEE J. Quantum Electron. QE-23, 1974 (1987).
[CrossRef]

1986 (1)

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

1985 (4)

S. Guha, E. W. Van Stryland, M. J. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption,” Opt. Lett. 10, 285 (1985).
[CrossRef] [PubMed]

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490 (1985).
[CrossRef] [PubMed]

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

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

1984 (1)

1983 (1)

A. K. Kar, J. G. H. Mathew, S. D. Smith, B. Davis, W. Prettl, “Optical bistability in InSb at room temperature with two photon absorption,” Appl. Phys. Lett. 42, 334 (1983).
[CrossRef]

1981 (2)

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

M. Weiler, “Nonparabolicity and exciton effects in two photon absorption in zinc-blende semiconductors,” Solid State Commun. 39, 937 (1981).
[CrossRef]

1980 (1)

T. S. Moss, “Theory of intensity dependence of refractive index,” Phys. Status Solidi B 101, 555 (1980).
[CrossRef]

1979 (2)

D. A. B. Miller, S. D. Smith, A. M. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low power effects in InSb,” App. Phys. Lett. 35, 658 (1979).
[CrossRef]

H. M. Gibbs, S. L. McCall, T. N. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451 (1979).
[CrossRef]

1978 (1)

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

1976 (1)

J. H. Bechtel, W. L. Smith, “Two-photon absorption in semiconductors with picosecond pulses,” Phys. Rev. B 13, 3515 (1976).
[CrossRef]

1974 (1)

C. C. Lee, H. Y. Fan, “Two photon absorption with exciton effects for degenerate valence bands,” Phys. Rev. B 9, 3502 (1974).
[CrossRef]

1969 (1)

A. E. Kaplan, “External self-focusing of light by a nonlinear lens,” Radiophys. Quantum Electron. 12, 692 (1969).
[CrossRef]

1968 (1)

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

1957 (1)

E. O. Kane, “Band structure of InSb,” J. Chem. Phys. Solids 1, 249 (1957).
[CrossRef]

Akhmanov, S. A.

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

Aronov, A. G.

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

Auston, D. H.

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

Banyai, L.

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

Bechtel, J. H.

J. H. Bechtel, W. L. Smith, “Two-photon absorption in semiconductors with picosecond pulses,” Phys. Rev. B 13, 3515 (1976).
[CrossRef]

Boggess, T. F.

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

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

A. L. Smirl, T. F. Boggess, J. Dubard, A. G. Cui, “Single and multiple beam nonlinear absorption and refraction measurements in semiconductors,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 251 (1990).
[CrossRef]

Boyd, I. W.

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

Canto-Said, E.

E. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, “Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991); D. J. Hagan, E. Canto, E. Meisak, M. J. Soileau, E. W. Van Stryland, “Picosecond degenerate four-wave mixing studies in ZnSe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 160.
[CrossRef]

Canto-Said, E. J.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. J. Canto-Said, Y. Y. Wu, J. Young, T. H. Wei, E. W. Van Stryland, “Nonlinearities in semiconductors for optical limiting,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soleau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 294 (1990).
[CrossRef]

Cui, A. G.

A. L. Smirl, T. F. Boggess, J. Dubard, A. G. Cui, “Single and multiple beam nonlinear absorption and refraction measurements in semiconductors,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 251 (1990).
[CrossRef]

Davis, B.

A. K. Kar, J. G. H. Mathew, S. D. Smith, B. Davis, W. Prettl, “Optical bistability in InSb at room temperature with two photon absorption,” Appl. Phys. Lett. 42, 334 (1983).
[CrossRef]

Dubard, J.

A. L. Smirl, T. F. Boggess, J. Dubard, A. G. Cui, “Single and multiple beam nonlinear absorption and refraction measurements in semiconductors,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 251 (1990).
[CrossRef]

Duncan, D.

A. Miller, D. Duncan, “Optical nonlinearities in narrow gap semiconductors,” in Optical Properties of Narrow-Gap Low-Dimensional Structures, C. M. Sotomayor Torres, J. C. Portal, J. C. Maan, R. A. Stradling, eds. (Plenum, New York, 1987).
[CrossRef]

Fan, H. Y.

C. C. Lee, H. Y. Fan, “Two photon absorption with exciton effects for degenerate valence bands,” Phys. Rev. B 9, 3502 (1974).
[CrossRef]

Gaskill, J. D.

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

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, T. N. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451 (1979).
[CrossRef]

Gossard, A. C.

H. M. Gibbs, S. L. McCall, T. N. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451 (1979).
[CrossRef]

Guha, S.

S. Guha, E. W. Van Stryland, M. J. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption,” Opt. Lett. 10, 285 (1985).
[CrossRef] [PubMed]

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

Hagan, D. J.

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

E. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, “Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991); D. J. Hagan, E. Canto, E. Meisak, M. J. Soileau, E. W. Van Stryland, “Picosecond degenerate four-wave mixing studies in ZnSe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 160.
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, 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 (1990).
[CrossRef] [PubMed]

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

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1981 (1988).

A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. J. Canto-Said, Y. Y. Wu, J. Young, T. H. Wei, E. W. Van Stryland, “Nonlinearities in semiconductors for optical limiting,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soleau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 294 (1990).
[CrossRef]

Hutchings, D.

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

Ippen, E. P.

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

Jain, R. K.

R. K. Jain, M. B. Klein, “Degenerate four-wave mixing in semiconductors,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 335.

Johnston, A. M.

D. A. B. Miller, S. D. Smith, A. M. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low power effects in InSb,” App. Phys. Lett. 35, 658 (1979).
[CrossRef]

Kane, E. O.

E. O. Kane, “Band structure of InSb,” J. Chem. Phys. Solids 1, 249 (1957).
[CrossRef]

Kaplan, A. E.

A. E. Kaplan, “External self-focusing of light by a nonlinear lens,” Radiophys. Quantum Electron. 12, 692 (1969).
[CrossRef]

Kar, A. K.

A. K. Kar, J. G. H. Mathew, S. D. Smith, B. Davis, W. Prettl, “Optical bistability in InSb at room temperature with two photon absorption,” Appl. Phys. Lett. 42, 334 (1983).
[CrossRef]

Khokhlov, R. V.

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

Klein, M. B.

R. K. Jain, M. B. Klein, “Degenerate four-wave mixing in semiconductors,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 335.

Koch, S. W.

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

S. W. Koch, Optical Sciences Center, University of Arizona, Tucson, Ariz. 85721 (personal communication).

Kwok, H. S.

M. Sheik-Bahae, H. S. Kwok, “Picosecond CO2laser-induced self-focusing in InSb,” IEEE J. Quantum Electron. QE-23, 1974 (1987).
[CrossRef]

Lee, C. C.

C. C. Lee, H. Y. Fan, “Two photon absorption with exciton effects for degenerate valence bands,” Phys. Rev. B 9, 3502 (1974).
[CrossRef]

Mansour, K.

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1981 (1988).

Mathew, J. G. H.

A. K. Kar, J. G. H. Mathew, S. D. Smith, B. Davis, W. Prettl, “Optical bistability in InSb at room temperature with two photon absorption,” Appl. Phys. Lett. 42, 334 (1983).
[CrossRef]

McAffee, S.

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

McCall, S. L.

H. M. Gibbs, S. L. McCall, T. N. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451 (1979).
[CrossRef]

Miller, A.

A. Miller, D. Duncan, “Optical nonlinearities in narrow gap semiconductors,” in Optical Properties of Narrow-Gap Low-Dimensional Structures, C. M. Sotomayor Torres, J. C. Portal, J. C. Maan, R. A. Stradling, eds. (Plenum, New York, 1987).
[CrossRef]

Miller, D. A. B.

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

D. A. B. Miller, S. D. Smith, A. M. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low power effects in InSb,” App. Phys. Lett. 35, 658 (1979).
[CrossRef]

Moss, S. C.

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

Moss, T. S.

T. S. Moss, “Theory of intensity dependence of refractive index,” Phys. Status Solidi B 101, 555 (1980).
[CrossRef]

Passner, A.

H. M. Gibbs, S. L. McCall, T. N. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451 (1979).
[CrossRef]

Pikus, D. E.

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

Prettl, W.

A. K. Kar, J. G. H. Mathew, S. D. Smith, B. Davis, W. Prettl, “Optical bistability in InSb at room temperature with two photon absorption,” Appl. Phys. Lett. 42, 334 (1983).
[CrossRef]

Prise, M. E.

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

Said, A. A.

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

M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, “High-sensitivity, single-beam n2measurement,” Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. J. Canto-Said, Y. Y. Wu, J. Young, T. H. Wei, E. W. Van Stryland, “Nonlinearities in semiconductors for optical limiting,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soleau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 294 (1990).
[CrossRef]

Seaton, C. T.

D. A. B. Miller, C. T. Seaton, M. E. Prise, 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, O. Teschke, “Picosecond spectroscopy of semiconductors,” Solid State Electron. 21, 147 (1978).
[CrossRef]

Sheik-Bahae, M.

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

M. Sheik-Bahae, D. J. Hagan, 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 (1990).
[CrossRef] [PubMed]

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

M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, “High-sensitivity, single-beam n2measurement,” Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

M. Sheik-Bahae, H. S. Kwok, “Picosecond CO2laser-induced self-focusing in InSb,” IEEE J. Quantum Electron. QE-23, 1974 (1987).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. J. Canto-Said, Y. Y. Wu, J. Young, T. H. Wei, E. W. Van Stryland, “Nonlinearities in semiconductors for optical limiting,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soleau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 294 (1990).
[CrossRef]

Shekhter, D. Sh.

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

Smirl, A. L.

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

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

A. L. Smirl, T. F. Boggess, J. Dubard, A. G. Cui, “Single and multiple beam nonlinear absorption and refraction measurements in semiconductors,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 251 (1990).
[CrossRef]

Smith, S. D.

A. K. Kar, J. G. H. Mathew, S. D. Smith, B. Davis, W. Prettl, “Optical bistability in InSb at room temperature with two photon absorption,” Appl. Phys. Lett. 42, 334 (1983).
[CrossRef]

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

D. A. B. Miller, S. D. Smith, A. M. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low power effects in InSb,” App. Phys. Lett. 35, 658 (1979).
[CrossRef]

Smith, W. L.

J. H. Bechtel, W. L. Smith, “Two-photon absorption in semiconductors with picosecond pulses,” Phys. Rev. B 13, 3515 (1976).
[CrossRef]

Soileau, M. J.

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1981 (1988).

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

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490 (1985).
[CrossRef] [PubMed]

S. Guha, E. W. Van Stryland, M. J. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption,” Opt. Lett. 10, 285 (1985).
[CrossRef] [PubMed]

Sukhorukov, A. P.

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

Teschke, O.

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

Tooley, F. A. P.

B. S. Wherrett, A. C. Walker, F. A. P. Tooley, “Nonlinear refraction for cw optical bistability,” in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, New York, 1988), p. 239.
[CrossRef]

Van Stryland, E. W.

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

E. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, “Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991); D. J. Hagan, E. Canto, E. Meisak, M. J. Soileau, E. W. Van Stryland, “Picosecond degenerate four-wave mixing studies in ZnSe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 160.
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, 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 (1990).
[CrossRef] [PubMed]

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

M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, “High-sensitivity, single-beam n2measurement,” Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1981 (1988).

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

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490 (1985).
[CrossRef] [PubMed]

S. Guha, E. W. Van Stryland, M. J. Soileau, “Self-defocusing in CdSe induced by charge carriers created by two-photon absorption,” Opt. Lett. 10, 285 (1985).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. J. Canto-Said, Y. Y. Wu, J. Young, T. H. Wei, E. W. Van Stryland, “Nonlinearities in semiconductors for optical limiting,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soleau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 294 (1990).
[CrossRef]

Vanherzeele, H.

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490 (1985).
[CrossRef] [PubMed]

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

Venkatesan, T. N.

H. M. Gibbs, S. L. McCall, T. N. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451 (1979).
[CrossRef]

Walker, A. C.

B. S. Wherrett, A. C. Walker, F. A. P. Tooley, “Nonlinear refraction for cw optical bistability,” in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, New York, 1988), p. 239.
[CrossRef]

Wei, T. H.

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

A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. J. Canto-Said, Y. Y. Wu, J. Young, T. H. Wei, E. W. Van Stryland, “Nonlinearities in semiconductors for optical limiting,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soleau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 294 (1990).
[CrossRef]

Weiler, M.

M. Weiler, “Nonparabolicity and exciton effects in two photon absorption in zinc-blende semiconductors,” Solid State Commun. 39, 937 (1981).
[CrossRef]

Wherrett, B. S.

B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1, 67 (1984).
[CrossRef]

B. S. Wherrett, A. C. Walker, F. A. P. Tooley, “Nonlinear refraction for cw optical bistability,” in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, New York, 1988), p. 239.
[CrossRef]

Wiegmann, W.

H. M. Gibbs, S. L. McCall, T. N. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451 (1979).
[CrossRef]

Woodall, M. A.

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

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490 (1985).
[CrossRef] [PubMed]

Wu, Y. Y.

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1981 (1988).

A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. J. Canto-Said, Y. Y. Wu, J. Young, T. H. Wei, E. W. Van Stryland, “Nonlinearities in semiconductors for optical limiting,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soleau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 294 (1990).
[CrossRef]

Young, J.

E. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, “Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991); D. J. Hagan, E. Canto, E. Meisak, M. J. Soileau, E. W. Van Stryland, “Picosecond degenerate four-wave mixing studies in ZnSe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 160.
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. J. Canto-Said, Y. Y. Wu, J. Young, T. H. Wei, E. W. Van Stryland, “Nonlinearities in semiconductors for optical limiting,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soleau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 294 (1990).
[CrossRef]

App. Phys. Lett. (1)

D. A. B. Miller, S. D. Smith, A. M. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low power effects in InSb,” App. Phys. Lett. 35, 658 (1979).
[CrossRef]

Appl. Phys. Lett. (2)

H. M. Gibbs, S. L. McCall, T. N. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451 (1979).
[CrossRef]

A. K. Kar, J. G. H. Mathew, S. D. Smith, B. Davis, W. Prettl, “Optical bistability in InSb at room temperature with two photon absorption,” Appl. Phys. Lett. 42, 334 (1983).
[CrossRef]

IEEE J. Quantum Electron. (5)

E. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, “Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors,” IEEE J. Quantum Electron. 27, 2274 (1991); D. J. Hagan, E. Canto, E. Meisak, M. J. Soileau, E. W. Van Stryland, “Picosecond degenerate four-wave mixing studies in ZnSe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 160.
[CrossRef]

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

M. Sheik-Bahae, H. S. Kwok, “Picosecond CO2laser-induced self-focusing in InSb,” IEEE J. Quantum Electron. QE-23, 1974 (1987).
[CrossRef]

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

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

J. Chem. Phys. Solids (1)

E. O. Kane, “Band structure of InSb,” J. Chem. Phys. Solids 1, 249 (1957).
[CrossRef]

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

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1981 (1988).

B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1, 67 (1984).
[CrossRef]

Opt. Eng. (1)

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

Opt. Lett. (3)

Phys. Rev. B (2)

J. H. Bechtel, W. L. Smith, “Two-photon absorption in semiconductors with picosecond pulses,” Phys. Rev. B 13, 3515 (1976).
[CrossRef]

C. C. Lee, H. Y. Fan, “Two photon absorption with exciton effects for degenerate valence bands,” Phys. Rev. B 9, 3502 (1974).
[CrossRef]

Phys. Rev. Lett. (2)

D. A. B. Miller, C. T. Seaton, M. E. Prise, 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, 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 (1990).
[CrossRef] [PubMed]

Phys. Status Solidi B (1)

T. S. Moss, “Theory of intensity dependence of refractive index,” Phys. Status Solidi B 101, 555 (1980).
[CrossRef]

Radiophys. Quantum Electron. (1)

A. E. Kaplan, “External self-focusing of light by a nonlinear lens,” Radiophys. Quantum Electron. 12, 692 (1969).
[CrossRef]

So. Phys. Solid State (1)

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

Solid State Commun. (1)

M. Weiler, “Nonparabolicity and exciton effects in two photon absorption in zinc-blende semiconductors,” Solid State Commun. 39, 937 (1981).
[CrossRef]

Solid State Electron. (1)

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

Z. Phys. B (1)

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

Other (10)

S. W. Koch, Optical Sciences Center, University of Arizona, Tucson, Ariz. 85721 (personal communication).

K.-H. Hellwege, editor, Landolt–Börnstein Numerical Data and Functional Relationships in Science and Technology, Vol. 17, Semiconductors (Springer-Verlag, New York, 1982), Subvol. (b).

R. K. Jain, M. B. Klein, “Degenerate four-wave mixing in semiconductors,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 335.

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

B. S. Wherrett, A. C. Walker, F. A. P. Tooley, “Nonlinear refraction for cw optical bistability,” in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, New York, 1988), p. 239.
[CrossRef]

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

The ZnSe sample was obtained from Heriot-Watt University, Edinburgh, UK; CdTe II–VI, from Saxonburgh, Pa.; GaAs from the Massachusetts Institute of Technology, Boston, Mass.; and ZnTe from Cleveland Crystals, Cleveland, Ohio.

A. L. Smirl, T. F. Boggess, J. Dubard, A. G. Cui, “Single and multiple beam nonlinear absorption and refraction measurements in semiconductors,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 251 (1990).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. J. Canto-Said, Y. Y. Wu, J. Young, T. H. Wei, E. W. Van Stryland, “Nonlinearities in semiconductors for optical limiting,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soleau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1307, 294 (1990).
[CrossRef]

A. Miller, D. Duncan, “Optical nonlinearities in narrow gap semiconductors,” in Optical Properties of Narrow-Gap Low-Dimensional Structures, C. M. Sotomayor Torres, J. C. Portal, J. C. Maan, R. A. Stradling, eds. (Plenum, New York, 1987).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Z-scan experimental setup. D2/D1 is measured as a function of the sample position z. D1, D2, detectors.

Fig. 2
Fig. 2

Normalized transmittance for an open-aperture Z scan at z = 0 as a function of βI0Leff = q(0,0,0). From this curve β can be determined without fitting the data.

Fig. 3
Fig. 3

Normalized Z-scan data of a 2.7-mm ZnSe sample measured with 27-ps (FWHM) pulses and λ = 532 nm at low irradiance (I0 = 0.21 GW/cm2). The solid curves are the theoretical fits. (a) Open-aperture data (S = 1) were fitted with β = 5.8 cm/GW. (b) 40%-aperture data were fitted with β = 5.8 cm/GW and n2 = −4.4 × 10−11 esu.

Fig. 4
Fig. 4

Closed-aperture Z-scan data (S = 0.4) and theoretical fits (solid curves) of the ZnSe sample taken at high irradiance levels of (a) I0 = 0.57 GW/cm2 and (b) I0 = 2.4 GW/cm2, where free-carrier refraction is significant. The data in (a) and (b) were fitted with β = 5.8 cm/GW, n2 = −4.0 × 10−11 esu, and σr = −0.8 × 10−2 cm3.

Fig. 5
Fig. 5

Closed-aperture Z-scan data (S = 0.4) for a 3-mm CdTe sample with 1.06-μm, 40-ps (FWHM) pulses at I0 = 300 MW/cm2. The theoretical fit (solid curve) was obtained with β = 26 cm/GW, n2 = −2.0 × 10−10 esu, and σr = −5.0 × 10−21 cm3.

Fig. 6
Fig. 6

Closed-aperture Z-scan data (S = 0.4) for a 1.2-mm GaAs sample with 1.06-μm, 40-ps (FWHM) pulses at I0 = 450 MW/cm2. The theoretical fit (solid curve) was obtained with β = 26 cm/GW, n2 = −2.7 × 10−10 esu, and σr = −6.5 × 10−21 cm3.

Fig. 7
Fig. 7

Closed-aperture Z-scan data (S = 0.4) and theoretical fit (solid curve) of the ZnTe sample at I0 = 1.4 GW/cm2. The data were fitted with β = 4.2 cm/GW, n2 = +8.3 × 10−11 esu, and σr =0.75 × 10−21 cm3. No definite peak–valley or valley–peak signature can be observed.

Fig. 8
Fig. 8

Closed-aperture Z-scan data (S = 0.4) and theoretical fit (solid curve) of the ZnTe sample at I0 = 0.6 GW/cm2. The data were fitted with the same parameters used in Fig. 7. The valley–peak configuration indicates that the positive bound electronic Kerr effect is dominant at this irradiance level.

Fig. 9
Fig. 9

Closed-aperture (S = 0.4) Z-scan experimental data of ZnSe at 1.06 μm (filled circles) and 532 nm (open circles) in units of z0 = πw02/λ. This figure clearly shows the dispersion in n2 as it changes its sign from positive at 1.06 μm to negative at 532 nm.

Fig. 10
Fig. 10

Δn/I0 directly derived from ΔTpv plotted as a function of I0 for ZnSe. The intercept of the straight-line best fit to the data yields γ = −6.4 × 10−14 cm2/W, and the slope gives σr = −1.1 × 10−21 cm3.

Fig. 11
Fig. 11

Δn/I0 plotted as a function of I0 for CdTe (filled circles) and GaAs open circles). The best fits to the data give γ = −2.7 × 10−13 cm2/W and σr = −5.2 × 10−21 cm3 for CdTe and γ = −4.1 × 10−13 cm2/W and σr = −5.9 × 10−21 cm3 for GaAs.

Tables (3)

Tables Icon

Table 1 Comparison of Experimental and Theoretical Values of n2 and Two-Photon Absorption Coefficient β

Tables Icon

Table 2 Contributions to the Change in the Index of Refraction Caused by Plasma and Blocking from Various Interband Transitionsa

Tables Icon

Table 3 Comparison of Experimental and Theoretical Values for the Index Change per Unit Carrier Density σra

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

d Δ ϕ d z = k Δ n ,
d I d z = - ( α 0 + β I ) I ,
Δ n = γ I + σ r N ,
d N d t = β I 2 2 ω .
I ( L , r , t , z ) = I ( 0 , r , t , z ) exp ( - α 0 L ) 1 + q ( r , t , z ) ,
I ( 0 , r , t , z ) = I 0 exp [ - 2 ( r / w 0 ) 2 - ( t / t 0 ) 2 ] 1 + ( z / z 0 ) 2 ,
T ( z ) = 1 π 1 / 2 q ( 0 , 0 , z ) - ln [ 1 + q ( 0 , 0 , z ) exp ( - τ 2 ) ] d τ .
Δ ϕ ( r , t , z ) = k γ β ln [ 1 + q ( r , t , z ) ] + k σ r 2 ω β - t d t F ( t ) ,
F ( t ) = α 0 ln [ 1 + q ( r , t , z ) ] - q ( r , t , z ) L eff [ 1 - exp ( - α 0 L ) 1 + q ( r , t , z ) ] .
E a ( r , t , z ) = 2 π i λ ( d - z ) exp [ i π r 2 λ ( d - z ) ] × 0 r d r E ( L , r , t , z ) exp [ i π r 2 λ ( d - z ) ] × J 0 [ 2 π r r λ ( d - z ) ] ,
P T ( z , t ) = c 0 n 0 π 0 r a E a ( r , t ) 2 r d r ,
T ( z , S ) = - P T ( t ) d t S - P i ( t ) d t ,
Δ n = - 2 π N e 2 n 0 ω 2 m c v E g 2 E g 2 - ( ω ) 2 ,
Δ n = - 2 π e 2 n 0 ω 2 { Δ N c m c [ 1 + Z ( m c h m J h c + m c l m J l c ) ] + Δ P h m h ( 1 + Z m c h m J h h ) + Δ P l m l ( 1 + Z m c l m J l l ) } ,
Z = 4 3 π 1 / 2 m P 2 2 k B T ,
J i j = 0 x 2 exp ( - x 2 ) x 2 + a i j d x ,
a i j = E g - ω k B T m c i m j .
Δ N c Δ P h 1 + ( m l m h ) 3 / 2 ,             Δ N c Δ P l 1 + ( m h m l ) 3 / 2 .
F i j = - 2 J ( m c i m j E g k B T ) + J ( m c i m j E g - ω k B T ) + J ( m c i m j E g + ω k B T ) .
Δ n ( blocking ) ( ω ) 2 / [ E g 2 - ( ω ) 2 ] ,
Δ T p - v p ( i ) Δ Φ 0 ,
C 0.23 ( β t 0 / ω )
Δ T p - v Δ T p - v ( 3 ) + Δ T p - v ( 5 ) p ( 3 ) k Δ n ( 3 ) L eff + p ( 5 ) k Δ n ( 5 ) × [ 1 - exp ( - 2 α L ) ] / ( 2 α ) ,
Δ n ( 5 ) - σ r N ( t ) I 0 ( t ) d t - I 0 ( t ) d t ,
( Δ n ) / I 0 γ + C σ r I 0 ,

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