Abstract

We extend the z-scan technique to provide for measurements of the sign and the magnitude of all the independent components of χ(3) for isotropic and cubic-symmetry materials. This technique is used to measure the dispersion of the tensor components of the real and the imaginary parts of χ(3) for various wide-gap semiconductor materials by use of femtosecond laser pulses. Our measurements of the polarization dichroism of the nonlinear-index and two-photon absorption coefficients are in fair agreement with recent theoretical calculations; however, substantial discrepancies exist between the measured and predicted values for the corresponding anisotropy parameters.

© 1995 Optical Society of America

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  1. L. Dahlström, Opt. Commun. 5, 157 (1972); M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, A. J. Schmidt, Opt. Lett. 16, 502 (1991).
    [CrossRef] [PubMed]
  2. A. L. Smirl, J. Dubard, A. G. Cui, T. F. Boggess, G. C. Valley, Opt. Lett. 14, 242 (1989).
    [CrossRef] [PubMed]
  3. A. Owyoung, IEEE J. Quantum Electron. QE-11, 1064 (1973); M. D. Levenson, N. Bloembergen, Phys. Rev. B 10, 4447 (1974).
    [CrossRef]
  4. E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
    [CrossRef]
  5. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  6. M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Phys. Rev. Lett. 65, 96 (1990); M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
    [CrossRef] [PubMed]
  7. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
    [CrossRef]
  8. T. D. Krauss, F. W. Wise, Appl. Phys. Lett. 65, 1739 (1994).
    [CrossRef]
  9. R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, E. W. Van Stryland, Opt. Lett. 18, 194 (1993).
    [CrossRef] [PubMed]
  10. M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, IEEE J. Quantum Electron. 30, 256 (1994).
    [CrossRef]
  11. W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, J. Opt. Soc. Am. B 12, 401 (1995).
    [CrossRef]
  12. D. C. Hutchings, B. S. Wherrett, Opt. Mater. 3, 53 (1994); J. Mod. Opt. 41, 1141 (1994).
    [CrossRef]
  13. D. C. Hutchings, B. S. Wherrett, Phys. Rev. B 49, 2418 (1994).
    [CrossRef]
  14. D. C. Hutchings, B. S. Wherrett, Opt. Commun. 111, 507 (1994).
    [CrossRef]
  15. D. C. Hutchings, B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zincblende semiconductors,” Phys. Rev. B (to be published).
  16. J. Yumoto, Otsuka, Phys. Rev. Lett. 54, 1806 (1985).
    [CrossRef] [PubMed]
  17. P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1967).
  18. Y. Pang, V. Yanovsky, F. Wise, B. I. Minkov, Opt. Lett. 18, 1168 (1993).
    [CrossRef] [PubMed]
  19. M. Shiek-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
    [CrossRef]

1995 (1)

1994 (5)

D. C. Hutchings, B. S. Wherrett, Opt. Mater. 3, 53 (1994); J. Mod. Opt. 41, 1141 (1994).
[CrossRef]

D. C. Hutchings, B. S. Wherrett, Phys. Rev. B 49, 2418 (1994).
[CrossRef]

D. C. Hutchings, B. S. Wherrett, Opt. Commun. 111, 507 (1994).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, IEEE J. Quantum Electron. 30, 256 (1994).
[CrossRef]

T. D. Krauss, F. W. Wise, Appl. Phys. Lett. 65, 1739 (1994).
[CrossRef]

1993 (2)

1992 (1)

1991 (2)

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

M. Shiek-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

1990 (2)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Phys. Rev. Lett. 65, 96 (1990); M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef] [PubMed]

1989 (1)

1985 (1)

J. Yumoto, Otsuka, Phys. Rev. Lett. 54, 1806 (1985).
[CrossRef] [PubMed]

1973 (1)

A. Owyoung, IEEE J. Quantum Electron. QE-11, 1064 (1973); M. D. Levenson, N. Bloembergen, Phys. Rev. B 10, 4447 (1974).
[CrossRef]

1972 (1)

L. Dahlström, Opt. Commun. 5, 157 (1972); M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, A. J. Schmidt, Opt. Lett. 16, 502 (1991).
[CrossRef] [PubMed]

1967 (1)

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1967).

Andersen, D. R.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, J. Opt. Soc. Am. B 12, 401 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, IEEE J. Quantum Electron. 30, 256 (1994).
[CrossRef]

Boggess, T. F.

Canto-Said, E. J.

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

Cui, A. G.

Dahlström, L.

L. Dahlström, Opt. Commun. 5, 157 (1972); M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, A. J. Schmidt, Opt. Lett. 16, 502 (1991).
[CrossRef] [PubMed]

DeSalvo, R.

Dubard, J.

Dvorak, M. D.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, J. Opt. Soc. Am. B 12, 401 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, IEEE J. Quantum Electron. 30, 256 (1994).
[CrossRef]

Hagan, D. J.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, E. W. Van Stryland, Opt. Lett. 18, 194 (1993).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

M. Shiek-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Phys. Rev. Lett. 65, 96 (1990); M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef] [PubMed]

Harken, D. R.

Hutchings, D. C.

D. C. Hutchings, B. S. Wherrett, Opt. Mater. 3, 53 (1994); J. Mod. Opt. 41, 1141 (1994).
[CrossRef]

D. C. Hutchings, B. S. Wherrett, Phys. Rev. B 49, 2418 (1994).
[CrossRef]

D. C. Hutchings, B. S. Wherrett, Opt. Commun. 111, 507 (1994).
[CrossRef]

D. C. Hutchings, B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zincblende semiconductors,” Phys. Rev. B (to be published).

Krauss, T. D.

T. D. Krauss, F. W. Wise, Appl. Phys. Lett. 65, 1739 (1994).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1967).

McCallum, D. S.

Minkov, B. I.

Otsuka,

J. Yumoto, Otsuka, Phys. Rev. Lett. 54, 1806 (1985).
[CrossRef] [PubMed]

Owyoung, A.

A. Owyoung, IEEE J. Quantum Electron. QE-11, 1064 (1973); M. D. Levenson, N. Bloembergen, Phys. Rev. B 10, 4447 (1974).
[CrossRef]

Pang, Y.

Said, A. A.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, E. W. Van Stryland, Opt. Lett. 18, 194 (1993).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Shiek-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Schroeder, W. A.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, J. Opt. Soc. Am. B 12, 401 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, IEEE J. Quantum Electron. 30, 256 (1994).
[CrossRef]

Sheik-Bahae, M.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, E. W. Van Stryland, Opt. Lett. 18, 194 (1993).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Phys. Rev. Lett. 65, 96 (1990); M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef] [PubMed]

Shiek-Bahae, M.

M. Shiek-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Smirl, A. L.

Soileau, M. J.

M. Shiek-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1967).

Valley, G. C.

Van Stryland, E. W.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, E. W. Van Stryland, Opt. Lett. 18, 194 (1993).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

M. Shiek-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Phys. Rev. Lett. 65, 96 (1990); M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef] [PubMed]

Wang, J.

Wei, T. H.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wherrett, B. S.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, B. S. Wherrett, J. Opt. Soc. Am. B 12, 401 (1995).
[CrossRef]

D. C. Hutchings, B. S. Wherrett, Opt. Mater. 3, 53 (1994); J. Mod. Opt. 41, 1141 (1994).
[CrossRef]

D. C. Hutchings, B. S. Wherrett, Opt. Commun. 111, 507 (1994).
[CrossRef]

D. C. Hutchings, B. S. Wherrett, Phys. Rev. B 49, 2418 (1994).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, IEEE J. Quantum Electron. 30, 256 (1994).
[CrossRef]

D. C. Hutchings, B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zincblende semiconductors,” Phys. Rev. B (to be published).

Wise, F.

Wise, F. W.

T. D. Krauss, F. W. Wise, Appl. Phys. Lett. 65, 1739 (1994).
[CrossRef]

Yanovsky, V.

Young, J.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

Yumoto, J.

J. Yumoto, Otsuka, Phys. Rev. Lett. 54, 1806 (1985).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

T. D. Krauss, F. W. Wise, Appl. Phys. Lett. 65, 1739 (1994).
[CrossRef]

IEEE J. Quantum Electron. (4)

A. Owyoung, IEEE J. Quantum Electron. QE-11, 1064 (1973); M. D. Levenson, N. Bloembergen, Phys. Rev. B 10, 4447 (1974).
[CrossRef]

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, B. S. Wherrett, IEEE J. Quantum Electron. 30, 256 (1994).
[CrossRef]

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

Opt. Commun. (2)

D. C. Hutchings, B. S. Wherrett, Opt. Commun. 111, 507 (1994).
[CrossRef]

L. Dahlström, Opt. Commun. 5, 157 (1972); M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, A. J. Schmidt, Opt. Lett. 16, 502 (1991).
[CrossRef] [PubMed]

Opt. Eng. (1)

M. Shiek-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Opt. Lett. (3)

Opt. Mater. (1)

D. C. Hutchings, B. S. Wherrett, Opt. Mater. 3, 53 (1994); J. Mod. Opt. 41, 1141 (1994).
[CrossRef]

Phys. Rev. A (1)

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1967).

Phys. Rev. B (1)

D. C. Hutchings, B. S. Wherrett, Phys. Rev. B 49, 2418 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

J. Yumoto, Otsuka, Phys. Rev. Lett. 54, 1806 (1985).
[CrossRef] [PubMed]

M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Phys. Rev. Lett. 65, 96 (1990); M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef] [PubMed]

Other (1)

D. C. Hutchings, B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zincblende semiconductors,” Phys. Rev. B (to be published).

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Figures (2)

Fig. 1
Fig. 1

Measured values of the polarization dichroism parameters (a) δr and (b) δi associated with the real and imaginary parts of χ(3) plotted as a function of the ratio of the photon energy ħω to the energy gap Eg for various semiconductor samples. The solid curves are theoretical calculations of (a) δr and (b) δi for GaAs from Refs. 15 and 13, respectively. The dashed curve is the theoretical prediction of an isotropic model (Ref. 15), which is appropriate for the polycrystalline samples.

Fig. 2
Fig. 2

Measured values for ZnTe and GaAs of the anisotropy parameters (a) σr and (b) σi associated with the real and imaginary parts of χ(3) plotted as a function of the ratio of the photon energy ħω to the energy gap Eg. The solid curves are theoretical calculations of (a) σr and (b) σi for GaAs from Refs. 15 and 13, respectively.

Equations (4)

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d E x , y d z = i ( χ 1 E x , y 2 + 2 χ 2 E y , x 2 ) E x , y + i χ 3 E y , x 2 E x , y * ,
n 2 ( 0 ) + i c 2 ω β ( 0 ) = 2 π n 0 ω χ 1 ,
n 2 ( 45 ) + i c 2 ω β ( 45 ) = 2 π n 0 ω [ ( 1 - σ r 2 ) χ 1 r + i ( 1 - σ i 2 ) χ 1 i ] ,
n 2 circ + i c 2 ω β circ = 2 π n 0 ω [ ( 2 χ 2 r + σ r 2 χ 1 r ) + i ( 2 χ 2 i + σ i 2 χ 1 i ) ] ,

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