Abstract

An algorithm is presented for the calculation of the nondegenerate two-photon absorption coefficient by using second-order perturbation theory and a Kane band-structure model, including the effects of nonparabolicity and nonzone-center wave functions. The polarization dependence is included by correctly accounting for the symmetry of the electronic wave functions. A comparison is made with degenerate two-photon absorption data in various zinc blende semiconductors, and excellent agreement is found without the use of fitting parameters. Comparisons are also made with nondegenerate two-photon absorption spectra measured in ZnSe and ZnS by using a picosecond continuum and with some polarization-dependent measurements obtained by a two-color Z-scan measurement.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Nathan, A. H. Guenther, and S. S. Mitra, “Review of multi-photon absorption in crystalline solids,” J. Opt. Soc. Am. B 2, 294–316 (1985).
    [CrossRef]
  2. M. H. Weiler, “Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors,” Solid State Commun. 39, 937–940 (1981).
    [CrossRef]
  3. 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, 613–623 (1985).
  4. J. Bolger, A. K. Kar, B. S. Wherrett, R. DeSalvo, D. C. Hutchings, and D. J. Hagan, “Nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO,” Opt. Commun. (to be published).
  5. M. Sheik-Bahae, J. Wang, J. R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a 2-color Z-scan,” Opt. Lett. 17, 258–260 (1992).
    [CrossRef] [PubMed]
  6. D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers–Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1–30 (1992), tutorial review.
    [CrossRef]
  7. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
    [CrossRef]
  8. B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1, 67–72 (1984).
    [CrossRef]
  9. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).
  10. N. G. Basov, A. Z. Grasyuk, I. G. Zubarev, V. A. Katulin, and O. N. Krokhin, “Semiconductor quantum generator with two-photon optical excitation,” Sov. Phys. JETP 23, 366–371 (1966).
  11. E. O. Kane, “Band structure of narrow gap semiconductors,” in Lecture Notes in Physics: Narrow Gap Semiconductors Physics and Applications, W. Zawadzki, ed. (Springer-Verlag, New York, 1980), Vol. 133, pp. 13–31.
    [CrossRef]
  12. E. O. Kane, “Band structure of indium antimonide,” J. Phys. Chem. Solids 1, 249–261 (1957).
    [CrossRef]
  13. C. C. Lee and H. Y. Fan, “Two-photon absorption with exciton effect for degenerate bands,” Phys. Rev. B 9, 3502–3516 (1974).
    [CrossRef]
  14. C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, “Two-photon absorption in zinc-blende semiconductors,” Phys. Rev. Lett. 42, 1785–1788 (1979).
    [CrossRef]
  15. J. H. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515–3522 (1976).
    [CrossRef]
  16. H. D. Jones and H. R. Reiss, “Intense-field effects in solids,” Phys. Rev. B 16, 2466–2473 (1977).
    [CrossRef]
  17. H. S. Brandi and C. B. de Araújo, “Multiphoton absorption coefficients in solids: a universal curve,” J. Phys. C 16, 5929–5936 (1983).
    [CrossRef]
  18. E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena HI, Vol. 23 of Chemical Physics, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, Berlin, 1982), pp. 368–371.
    [CrossRef]
  19. A. Miller, A. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
    [CrossRef]
  20. A. M. Johnson, C. R. Pidgeon, and J. Dempsey, “Frequency dependence of two-photon absorption in InSb and HgCdTe,” Phys. Rev. B 22, 825–831 (1980).
    [CrossRef]
  21. M. Sheik-Bahae, P. Mukherjee, and H. S. Kwok, “Two-photon and three-photon absorption coefficients in InSb,” J. Opt. Soc. Am. B 3, 379–385 (1986).
    [CrossRef]
  22. M. Sheik-Bahae, T. Rossi, and H. S. Kwok, “Frequency dependence of the two-photon absorption coefficient in InSb: tunneling effects,” J. Opt. Soc. Am. B 4, 1964–1969 (1987).
    [CrossRef]
  23. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound and free-carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).
    [CrossRef]
  24. J. Bolger, Department of Physics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK(personal communication).
  25. R. J. Elliott, “Intensity of optical obsorption by excitons,” Phys. Rev. 6, 1384–1389 (1957).
    [CrossRef]
  26. K.-H. Hellwege, ed., Landolt-Börstein Numerical Data and Functional Relationships in Science and Technology (Springer-Verlag, Berlin, 1982), Vols. 17a, 17b, Group III.

1992 (3)

1991 (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

1987 (1)

1986 (1)

1985 (2)

V. Nathan, A. H. Guenther, and S. S. Mitra, “Review of multi-photon absorption in crystalline solids,” J. Opt. Soc. Am. B 2, 294–316 (1985).
[CrossRef]

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, 613–623 (1985).

1984 (1)

1983 (1)

H. S. Brandi and C. B. de Araújo, “Multiphoton absorption coefficients in solids: a universal curve,” J. Phys. C 16, 5929–5936 (1983).
[CrossRef]

1981 (1)

M. H. Weiler, “Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors,” Solid State Commun. 39, 937–940 (1981).
[CrossRef]

1980 (1)

A. M. Johnson, C. R. Pidgeon, and J. Dempsey, “Frequency dependence of two-photon absorption in InSb and HgCdTe,” Phys. Rev. B 22, 825–831 (1980).
[CrossRef]

1979 (2)

A. Miller, A. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, “Two-photon absorption in zinc-blende semiconductors,” Phys. Rev. Lett. 42, 1785–1788 (1979).
[CrossRef]

1977 (1)

H. D. Jones and H. R. Reiss, “Intense-field effects in solids,” Phys. Rev. B 16, 2466–2473 (1977).
[CrossRef]

1976 (1)

J. H. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515–3522 (1976).
[CrossRef]

1974 (1)

C. C. Lee and H. Y. Fan, “Two-photon absorption with exciton effect for degenerate bands,” Phys. Rev. B 9, 3502–3516 (1974).
[CrossRef]

1966 (1)

N. G. Basov, A. Z. Grasyuk, I. G. Zubarev, V. A. Katulin, and O. N. Krokhin, “Semiconductor quantum generator with two-photon optical excitation,” Sov. Phys. JETP 23, 366–371 (1966).

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

1957 (2)

E. O. Kane, “Band structure of indium antimonide,” J. Phys. Chem. Solids 1, 249–261 (1957).
[CrossRef]

R. J. Elliott, “Intensity of optical obsorption by excitons,” Phys. Rev. 6, 1384–1389 (1957).
[CrossRef]

Basov, N. G.

N. G. Basov, A. Z. Grasyuk, I. G. Zubarev, V. A. Katulin, and O. N. Krokhin, “Semiconductor quantum generator with two-photon optical excitation,” Sov. Phys. JETP 23, 366–371 (1966).

Bechtel, J. H.

J. H. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515–3522 (1976).
[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, 613–623 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena HI, Vol. 23 of Chemical Physics, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, Berlin, 1982), pp. 368–371.
[CrossRef]

Bolger, J.

J. Bolger, A. K. Kar, B. S. Wherrett, R. DeSalvo, D. C. Hutchings, and D. J. Hagan, “Nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO,” Opt. Commun. (to be published).

J. Bolger, Department of Physics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK(personal communication).

Brandi, H. S.

H. S. Brandi and C. B. de Araújo, “Multiphoton absorption coefficients in solids: a universal curve,” J. Phys. C 16, 5929–5936 (1983).
[CrossRef]

de Araújo, C. B.

H. S. Brandi and C. B. de Araújo, “Multiphoton absorption coefficients in solids: a universal curve,” J. Phys. C 16, 5929–5936 (1983).
[CrossRef]

Dempsey, J.

A. M. Johnson, C. R. Pidgeon, and J. Dempsey, “Frequency dependence of two-photon absorption in InSb and HgCdTe,” Phys. Rev. B 22, 825–831 (1980).
[CrossRef]

A. Miller, A. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, “Two-photon absorption in zinc-blende semiconductors,” Phys. Rev. Lett. 42, 1785–1788 (1979).
[CrossRef]

DeSalvo, J. R.

DeSalvo, R.

J. Bolger, A. K. Kar, B. S. Wherrett, R. DeSalvo, D. C. Hutchings, and D. J. Hagan, “Nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO,” Opt. Commun. (to be published).

Elliott, R. J.

R. J. Elliott, “Intensity of optical obsorption by excitons,” Phys. Rev. 6, 1384–1389 (1957).
[CrossRef]

Fan, H. Y.

C. C. Lee and H. Y. Fan, “Two-photon absorption with exciton effect for degenerate bands,” Phys. Rev. B 9, 3502–3516 (1974).
[CrossRef]

Grasyuk, A. Z.

N. G. Basov, A. Z. Grasyuk, I. G. Zubarev, V. A. Katulin, and O. N. Krokhin, “Semiconductor quantum generator with two-photon optical excitation,” Sov. Phys. JETP 23, 366–371 (1966).

Guenther, A. H.

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, 613–623 (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, 1–30 (1992), tutorial review.
[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 and free-carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

M. Sheik-Bahae, J. Wang, J. R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a 2-color Z-scan,” Opt. Lett. 17, 258–260 (1992).
[CrossRef] [PubMed]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

J. Bolger, A. K. Kar, B. S. Wherrett, R. DeSalvo, D. C. Hutchings, and D. J. Hagan, “Nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO,” Opt. Commun. (to be published).

Holah, G. D.

A. Miller, A. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

Hopf, F. A.

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena HI, Vol. 23 of Chemical Physics, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, Berlin, 1982), pp. 368–371.
[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, 1–30 (1992), tutorial review.
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

J. Bolger, A. K. Kar, B. S. Wherrett, R. DeSalvo, D. C. Hutchings, and D. J. Hagan, “Nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO,” Opt. Commun. (to be published).

Johnson, A.

A. Miller, A. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

Johnson, A. M.

A. M. Johnson, C. R. Pidgeon, and J. Dempsey, “Frequency dependence of two-photon absorption in InSb and HgCdTe,” Phys. Rev. B 22, 825–831 (1980).
[CrossRef]

Johnston, A. M.

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, “Two-photon absorption in zinc-blende semiconductors,” Phys. Rev. Lett. 42, 1785–1788 (1979).
[CrossRef]

Jones, H. D.

H. D. Jones and H. R. Reiss, “Intense-field effects in solids,” Phys. Rev. B 16, 2466–2473 (1977).
[CrossRef]

Kane, E. O.

E. O. Kane, “Band structure of indium antimonide,” J. Phys. Chem. Solids 1, 249–261 (1957).
[CrossRef]

E. O. Kane, “Band structure of narrow gap semiconductors,” in Lecture Notes in Physics: Narrow Gap Semiconductors Physics and Applications, W. Zawadzki, ed. (Springer-Verlag, New York, 1980), Vol. 133, pp. 13–31.
[CrossRef]

Kar, A. K.

J. Bolger, A. K. Kar, B. S. Wherrett, R. DeSalvo, D. C. Hutchings, and D. J. Hagan, “Nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO,” Opt. Commun. (to be published).

Katulin, V. A.

N. G. Basov, A. Z. Grasyuk, I. G. Zubarev, V. A. Katulin, and O. N. Krokhin, “Semiconductor quantum generator with two-photon optical excitation,” Sov. Phys. JETP 23, 366–371 (1966).

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Krokhin, O. N.

N. G. Basov, A. Z. Grasyuk, I. G. Zubarev, V. A. Katulin, and O. N. Krokhin, “Semiconductor quantum generator with two-photon optical excitation,” Sov. Phys. JETP 23, 366–371 (1966).

Kwok, H. S.

Lee, C. C.

C. C. Lee and H. Y. Fan, “Two-photon absorption with exciton effect for degenerate bands,” Phys. Rev. B 9, 3502–3516 (1974).
[CrossRef]

Miller, A.

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, “Two-photon absorption in zinc-blende semiconductors,” Phys. Rev. Lett. 42, 1785–1788 (1979).
[CrossRef]

A. Miller, A. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

Mitra, S. S.

Mukherjee, P.

Nathan, V.

Pidgeon, C. R.

A. M. Johnson, C. R. Pidgeon, and J. Dempsey, “Frequency dependence of two-photon absorption in InSb and HgCdTe,” Phys. Rev. B 22, 825–831 (1980).
[CrossRef]

A. Miller, A. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, “Two-photon absorption in zinc-blende semiconductors,” Phys. Rev. Lett. 42, 1785–1788 (1979).
[CrossRef]

Reiss, H. R.

H. D. Jones and H. R. Reiss, “Intense-field effects in solids,” Phys. Rev. B 16, 2466–2473 (1977).
[CrossRef]

Rossi, T.

Said, A. A.

Sheik-Bahae, M.

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, 613–623 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena HI, Vol. 23 of Chemical Physics, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, Berlin, 1982), pp. 368–371.
[CrossRef]

Smith, J.

A. Miller, A. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

Smith, W. L.

J. H. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515–3522 (1976).
[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, 613–623 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena HI, Vol. 23 of Chemical Physics, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, Berlin, 1982), pp. 368–371.
[CrossRef]

Van Stryland, E. W.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers–Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1–30 (1992), tutorial review.
[CrossRef]

M. Sheik-Bahae, J. Wang, J. R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a 2-color Z-scan,” Opt. Lett. 17, 258–260 (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 and free-carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

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, 613–623 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena HI, Vol. 23 of Chemical Physics, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, Berlin, 1982), pp. 368–371.
[CrossRef]

Vanherzeele, H.

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, 613–623 (1985).

Wang, J.

Wei, T. H.

Weiler, M. H.

M. H. Weiler, “Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors,” Solid State Commun. 39, 937–940 (1981).
[CrossRef]

Wherrett, B. S.

B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1, 67–72 (1984).
[CrossRef]

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, “Two-photon absorption in zinc-blende semiconductors,” Phys. Rev. Lett. 42, 1785–1788 (1979).
[CrossRef]

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena HI, Vol. 23 of Chemical Physics, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, Berlin, 1982), pp. 368–371.
[CrossRef]

J. Bolger, A. K. Kar, B. S. Wherrett, R. DeSalvo, D. C. Hutchings, and D. J. Hagan, “Nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO,” Opt. Commun. (to be published).

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, 613–623 (1985).

Young, J.

Zubarev, I. G.

N. G. Basov, A. Z. Grasyuk, I. G. Zubarev, V. A. Katulin, and O. N. Krokhin, “Semiconductor quantum generator with two-photon optical excitation,” Sov. Phys. JETP 23, 366–371 (1966).

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

J. Opt. Soc. Am. B (5)

J. Phys. C (2)

A. Miller, A. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

H. S. Brandi and C. B. de Araújo, “Multiphoton absorption coefficients in solids: a universal curve,” J. Phys. C 16, 5929–5936 (1983).
[CrossRef]

J. Phys. Chem. Solids (1)

E. O. Kane, “Band structure of indium antimonide,” J. Phys. Chem. Solids 1, 249–261 (1957).
[CrossRef]

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, 613–623 (1985).

Opt. Lett. (1)

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, 1–30 (1992), tutorial review.
[CrossRef]

Phys. Rev. (1)

R. J. Elliott, “Intensity of optical obsorption by excitons,” Phys. Rev. 6, 1384–1389 (1957).
[CrossRef]

Phys. Rev. B (4)

A. M. Johnson, C. R. Pidgeon, and J. Dempsey, “Frequency dependence of two-photon absorption in InSb and HgCdTe,” Phys. Rev. B 22, 825–831 (1980).
[CrossRef]

C. C. Lee and H. Y. Fan, “Two-photon absorption with exciton effect for degenerate bands,” Phys. Rev. B 9, 3502–3516 (1974).
[CrossRef]

J. H. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515–3522 (1976).
[CrossRef]

H. D. Jones and H. R. Reiss, “Intense-field effects in solids,” Phys. Rev. B 16, 2466–2473 (1977).
[CrossRef]

Phys. Rev. Lett. (1)

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, “Two-photon absorption in zinc-blende semiconductors,” Phys. Rev. Lett. 42, 1785–1788 (1979).
[CrossRef]

Solid State Commun. (1)

M. H. Weiler, “Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors,” Solid State Commun. 39, 937–940 (1981).
[CrossRef]

Sov. Phys. JETP (2)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

N. G. Basov, A. Z. Grasyuk, I. G. Zubarev, V. A. Katulin, and O. N. Krokhin, “Semiconductor quantum generator with two-photon optical excitation,” Sov. Phys. JETP 23, 366–371 (1966).

Other (5)

E. O. Kane, “Band structure of narrow gap semiconductors,” in Lecture Notes in Physics: Narrow Gap Semiconductors Physics and Applications, W. Zawadzki, ed. (Springer-Verlag, New York, 1980), Vol. 133, pp. 13–31.
[CrossRef]

J. Bolger, A. K. Kar, B. S. Wherrett, R. DeSalvo, D. C. Hutchings, and D. J. Hagan, “Nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO,” Opt. Commun. (to be published).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” in Picosecond Phenomena HI, Vol. 23 of Chemical Physics, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, and A. Laubereau, eds. (Springer-Verlag, Berlin, 1982), pp. 368–371.
[CrossRef]

K.-H. Hellwege, ed., Landolt-Börstein Numerical Data and Functional Relationships in Science and Technology (Springer-Verlag, Berlin, 1982), Vols. 17a, 17b, Group III.

J. Bolger, Department of Physics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK(personal communication).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Band structure for a zinc blende semiconductor near the center of the Brillouin zone as given by Kane.12 Only the set of four doubly degenerate (in spin) bands are considered: conduction band (cb), heavy-hole band (hh), light-hole band (lh), and split-off band (so).

Fig. 2
Fig. 2

Theoretical frequency dependence of the nondegenerate 2PA for three different pump frequencies, ℏω2 = 0.3, 0.5, 0.7 for a two-parabolic-band model.

Fig. 3
Fig. 3

Frequency dependence of the degenerate 2PA in InSb. Included for comparison are various experimentally determined values at 10.6 and 9.6 μm: △, Ref. 19; ○, Ref. 20; □, Ref. 21; ♢, Ref. 22.

Fig. 4
Fig. 4

Comparison of the present calculation (solid curves) with the fitted two-parabolic-band result (dashed curves), i.e., setting Kpb = 3100 cm/GW (eV)5/2, for the degenerate 2PA in InSb, GaAs, and ZnSe.

Fig. 5
Fig. 5

Frequency dependence of the degenerate 2PA in ZnSe. The solid curve shows the present calculation; the short-dashed curve and the long-dashed curve show Weiler’s nonparabolic expressions in the limits Δ ≫ Eg and Δ ≪ Eg, respectively. The dotted–dashed curve shows nondegenerate 2PA where the two wavelengths are identical but the optical polarizations are perpendicular. Also included are some data points with appropriate error bars taken from Refs. 3 and 23.

Fig. 6
Fig. 6

Nondegenerate 2PA in ZnSe at the second-harmonic frequency that is due to the presence of light at the fundamental frequency. The solid curve corresponds to parallel optical polarizations; the dashed curve; to perpendicular. Two data points are shown, measured at 0.532 μm because of the presence of a beam at 1.064 μm, by the two color Z-scan technique.5 The square corresponds to parallel polarizations, and the triangle to perpendicular.

Fig. 7
Fig. 7

Nondegenerate 2PA in ZnSe as a function of probe frequency for a fixed pump frequency at 0.705 μm (parallel polarizations). The data are from Ref. 4. The circles correspond to a high irradiance, I2 = 8 GW/cm2 (errors ±30%), and the squares and triangles to a lower irradiance measurement, I2 = 0.7 GW/cm2 (errors ±45%).

Fig. 8
Fig. 8

Nondegenerate 2PA in ZnS as a function of probe frequency for a fixed pump frequency at 0.705 μm (parallel polarizations). The data are from Ref. 4. The circles correspond to a high irradiance, I2 = 8 GW/cm2 (errors ±30%), the squares to a medium irradiance, I2 = 1.8 GW/cm2 (errors ±45%), and the triangles to a lower irradiance I2 = 0.7 GW/cm2 (errors ±45%).

Tables (3)

Tables Icon

Table 1 z Components of the Scaled Momentum Matrix Element Mij = 〈i|pz|j〉ℏ/m0P as a Function of the Electronic k Vector in Polar Coordinatesa

Tables Icon

Table 2 x Components of the Scaled Momentum Matrix Element Mij = 〈i|px|j〉ℏ/m0P as a Function of the Electronic k Vector in Polar Coordinatesa

Tables Icon

Table 3 Degenerate 2PA in a Variety of Zinc Blende Semiconductors

Equations (19)

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

W 2 = 2 π vc | i ψ c | Ĥ opt | ψ i ψ i | Ĥ opt | ψ υ E i υ ( k ) ω | 2 δ ( E cv ( k ) 2 ω ) ,
β ( ω ) = K pb E p n 0 2 ( ω ) E g 3 F 2 ( ω E g ) , F 2 = ( 2 x 1 ) 3 / 2 ( 2 x ) 5 ,
K pb = 2 9 π 5 e 4 m 0 c 2 = 1940 cm / GW ( eV ) 5 / 2 .
I 1 z = β 11 I 1 2 2 β 12 I 1 I 2 , I 2 z = β 22 I 2 2 2 β 21 I 1 I 2 .
β 12 = K pb E p n 0 ( ω 1 ) n 0 ( ω 2 ) E g 3 F 2 nd ( ω 1 E g ; ω 2 E g ) ,
F 2 nd ( x 1 ; x 2 ) = ( x 1 + x 2 1 ) 3 / 2 2 7 x 1 x 2 2 ( 1 x 1 + 1 x 2 ) 2 ,
E = 0 , E ( E E g ) ( E + Δ ) ( k P ) 2 ( E + 2 Δ / 3 ) = 0 ,
P = i m 0 S | p x | X = i m 0 S | p y | Y = i m 0 S | p z | Z .
ϕ i α = a i ( i S ) + b i [ ( X i Y ) / 2 ] + c i ( Z ) , ϕ i β = a i ( i S ) + b i [ ( X + i Y ) / 2 ] + c i ( Z ) , ϕ hh α = [ ( X + i Y ) / 2 ] , ϕ hh β = [ ( X i Y ) / 2 ] ,
a i = k P ( E i + 2 Δ / 3 ) / N , b i = ( 2 Δ / 3 ) ( E i E g ) / N , c i = ( E i E g ) ( E i + 2 Δ / 3 ) / N ,
W 2 nd = 2 π vc | i [ c | Ĥ 2 | i i | Ĥ 1 | υ E i υ ( k ) ω 1 + c | Ĥ 1 | i i | Ĥ 2 | υ E i υ ( k ) ω 2 ] | 2 × δ [ E cv ( k ) ω 1 ω 2 ] ,
Ĥ j = e m 0 c A j p ̂ , = e i m 0 ω j [ 2 π I j n 0 ( ω j ) c ] 1 / 2 â j p ̂ .
M i j ( n ) ( k ) = m 0 P â n j , k | p ̂ | i , k .
M i β , j β = M i α , j α , M i α , j β = M j β , i α . *
β 12 ( ω 1 ; ω 2 ) = ( e 2 c ) 2 P 2 n 0 ( ω 1 ) n 0 ( ω 2 ) E g 3 f 2 ( ω 1 E g ; ω 2 E g ) , = K E p n 0 ( ω 1 ) n 0 ( ω 2 ) E g 3 f 2 ( ω 1 E g ; ω 2 E g ) ,
f 2 ( x 1 ; x 2 ) = 1 x 1 x 2 2 vc 0 2 π d ϕ 0 π sin θ d θ 0 ( k P E g ) 2 d ( k P ) E g × | i [ M c i ( 2 ) M i υ ( 1 ) E i υ ( k ) / E g x 1 + M c i ( 1 ) M i υ ( 2 ) E i υ ( k ) / E g x 2 ] | 2 × δ [ E cv ( k ) E g x 1 x 2 ] .
K = ( e 2 c ) 2 2 2 2 m 0 ,
f 2 np ( x ) = 8 π ( 2 x 1 ) 3 / 2 3 x 3 × [ 4 ( 3 x ) 1 / 2 ( 3 x 1 ) 2 + ( 3 x + 3 2 ) 3 / 2 ( 9 x 4 + 10 x 2 + 6 ) 90 x 5 ] .
f 2 pb ( x ) = 8 π ( 2 x 1 ) 3 / 2 6 x 5 ( 4 + 29 2 12 ) .

Metrics