Abstract

We calculate the spectrum of three-photon absorption (3PA) in zinc blende semiconductors using Kane’s four-band model. We apply this to ZnSe and measure the 3PA spectrum using femtosecond pulses, obtaining excellent agreement. The spectrum shows the apparent onset of 3PA from the split-off band and also shows quantum interference between the several possible evolution pathways when exciting carriers from valence to conduction band.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. M. Balu, L. A. Padilha, D. J. Hagan, E. W. Van Stryland, S. Yao, K. Belfield, S. Zheng, S. Barlow, and S. Marder, J. Opt. Soc. Am. B 25, 159 (2008).
    [CrossRef]
  4. H. D. Jones and H. R. Reiss, Phys. Rev. B 16, 2466 (1977).
    [CrossRef]
  5. B. S. Wherrett, J. Opt. Soc. Am. B 1, 67 (1984).
    [CrossRef]
  6. H. S. Brandi and C. B. de Araujo, J. Phys. C 16, 5929 (1983).
    [CrossRef]
  7. D. C. Hutchings and E. W. Van Stryland, J. Opt. Soc. Am. B 9, 2065 (1992).
    [CrossRef]
  8. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
    [CrossRef]
  9. I. M. Catalano, A. Cingolani, and A. Minafra, Opt. Commun. 7, 270 (1973).
    [CrossRef]
  10. M. Lepore, R. Tommasi, and I. M. Catalano, Solid State Commun. 84, 463 (1992).
    [CrossRef]
  11. J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 65, 147 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
  13. L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).
  14. E. O. Kane, J. Phys. Chem. Solids 1, 249 (1957).
    [CrossRef]
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    [CrossRef]
  16. K. H. Hellwege, ed., Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology (Springer-Verlag, 1982), 17a, 17b, Group III.
  17. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  18. D. C. Hutchings and B. S. Wherrett, Phys. Rev. B 49, 2418 (1994).
    [CrossRef]
  19. M. Weiler, Solid State Commun. 39, 937 (1981).
    [CrossRef]

2008 (1)

2005 (1)

2003 (1)

M. Dinu, IEEE J. Quantum Electron. 39, 1498 (2003).
[CrossRef]

1994 (2)

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

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 65, 147 (1994).
[CrossRef]

1992 (3)

1991 (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

1990 (1)

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

1985 (1)

1984 (1)

1983 (1)

H. S. Brandi and C. B. de Araujo, J. Phys. C 16, 5929 (1983).
[CrossRef]

1981 (1)

M. Weiler, Solid State Commun. 39, 937 (1981).
[CrossRef]

1977 (1)

H. D. Jones and H. R. Reiss, Phys. Rev. B 16, 2466 (1977).
[CrossRef]

1973 (1)

I. M. Catalano, A. Cingolani, and A. Minafra, Opt. Commun. 7, 270 (1973).
[CrossRef]

1965 (1)

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

1957 (1)

E. O. Kane, J. Phys. Chem. Solids 1, 249 (1957).
[CrossRef]

Aitchison, J. S.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 65, 147 (1994).
[CrossRef]

Al-hemyari, K.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 65, 147 (1994).
[CrossRef]

Balu, M.

Barlow, S.

Belfield, K.

Brandi, H. S.

H. S. Brandi and C. B. de Araujo, J. Phys. C 16, 5929 (1983).
[CrossRef]

Catalano, I. M.

M. Lepore, R. Tommasi, and I. M. Catalano, Solid State Commun. 84, 463 (1992).
[CrossRef]

I. M. Catalano, A. Cingolani, and A. Minafra, Opt. Commun. 7, 270 (1973).
[CrossRef]

Cingolani, A.

I. M. Catalano, A. Cingolani, and A. Minafra, Opt. Commun. 7, 270 (1973).
[CrossRef]

de Araujo, C. B.

H. S. Brandi and C. B. de Araujo, J. Phys. C 16, 5929 (1983).
[CrossRef]

Dinu, M.

M. Dinu, IEEE J. Quantum Electron. 39, 1498 (2003).
[CrossRef]

Hagan, D. J.

M. Balu, L. A. Padilha, D. J. Hagan, E. W. Van Stryland, S. Yao, K. Belfield, S. Zheng, S. Barlow, and S. Marder, J. Opt. Soc. Am. B 25, 159 (2008).
[CrossRef]

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

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, 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, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

He, J.

Hellwege, K. H.

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

Hutchings, D. C.

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

D. C. Hutchings and E. W. Van Stryland, J. Opt. Soc. Am. B 9, 2065 (1992).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

Ironside, C. N.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 65, 147 (1994).
[CrossRef]

Ji, W.

Jones, H. D.

H. D. Jones and H. R. Reiss, Phys. Rev. B 16, 2466 (1977).
[CrossRef]

Kane, E. O.

E. O. Kane, J. Phys. Chem. Solids 1, 249 (1957).
[CrossRef]

Kang, J. U.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 65, 147 (1994).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Lepore, M.

M. Lepore, R. Tommasi, and I. M. Catalano, Solid State Commun. 84, 463 (1992).
[CrossRef]

Li, H.

Marder, S.

Mi, J.

Minafra, A.

I. M. Catalano, A. Cingolani, and A. Minafra, Opt. Commun. 7, 270 (1973).
[CrossRef]

Padilha, L. A.

Qu, Y.

Reiss, H. R.

H. D. Jones and H. R. Reiss, Phys. Rev. B 16, 2466 (1977).
[CrossRef]

Said, A. A.

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

Sheik-Bahae, M.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 65, 147 (1994).
[CrossRef]

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

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, 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, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Soileau, M. J.

Stegeman, G. I.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 65, 147 (1994).
[CrossRef]

Tommasi, R.

M. Lepore, R. Tommasi, and I. M. Catalano, Solid State Commun. 84, 463 (1992).
[CrossRef]

Van Stryland, E. W.

Vanherzeele, H.

Villeneuve, A.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 65, 147 (1994).
[CrossRef]

Wang, J.

Wei, T. H.

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

Weiler, M.

M. Weiler, Solid State Commun. 39, 937 (1981).
[CrossRef]

Wherrett, B. S.

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

B. S. Wherrett, J. Opt. Soc. Am. B 1, 67 (1984).
[CrossRef]

Woodall, M. A.

Yao, S.

Young, J.

Zheng, S.

Appl. Phys. Lett. (1)

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 65, 147 (1994).
[CrossRef]

IEEE J. Quantum Electron. (3)

M. Dinu, IEEE J. Quantum Electron. 39, 1498 (2003).
[CrossRef]

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

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. C (1)

H. S. Brandi and C. B. de Araujo, J. Phys. C 16, 5929 (1983).
[CrossRef]

J. Phys. Chem. Solids (1)

E. O. Kane, J. Phys. Chem. Solids 1, 249 (1957).
[CrossRef]

Opt. Commun. (1)

I. M. Catalano, A. Cingolani, and A. Minafra, Opt. Commun. 7, 270 (1973).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (2)

H. D. Jones and H. R. Reiss, Phys. Rev. B 16, 2466 (1977).
[CrossRef]

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

Solid State Commun. (2)

M. Weiler, Solid State Commun. 39, 937 (1981).
[CrossRef]

M. Lepore, R. Tommasi, and I. M. Catalano, Solid State Commun. 84, 463 (1992).
[CrossRef]

Sov. Phys. JETP (1)

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Other (1)

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

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Figures (2)

Fig. 1
Fig. 1

(a) Contributions to the degenerate 3PA coefficient due to transitions from the (1) heavy-hole, (2) light-hole, and (3) split-off bands as a function of photon energy. (b) (1) Calculated degenerate 3PA spectrum compared to previous theories of (2) Wherrett and (3) Brandi and de Araujo.

Fig. 2
Fig. 2

Experimentally obtained spectrum of 3PA coefficient compared to our calculation scaled by a factor of 3.2. Inset shows typical experimental Z scans performed at λ = 1200 nm .

Equations (2)

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H = ( p 2 2 m ) + 2 k 2 2 m + V + ( m ) k p + ( 4 m 2 c 2 ) ( V × p ) σ ,
W 3 = 2 π v , c i , j Ψ c H int Ψ j Ψ j H int Ψ i Ψ i H int Ψ v ( E j v ( k ) 2 ω ) ( E i v ( k ) ω ) 2 δ ( E c v ( k ) 3 ω ) .

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