Abstract

We present measurements of the two-photon absorption coefficients β2 of 10 different semiconductors having band-gap energies between 1.4 and 3.7 eV. We find that β2 varies as Eg−3, as predicted by theory. In addition, the absolute values of β2 agree with theory, which includes the effect of nonparabolic bands, the average difference being less than 26%. This agreement permits confident predictions of two-photon absorption coefficients of other materials at other wavelengths.

© 1985 Optical Society of America

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  1. E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).
  2. J. H. Bechtel, W. L. Smith, Phys. Rev. B 13, 3515 (1976).
    [CrossRef]
  3. Ep = 2P2m/ħ2, where P is the Kane momentum parameter and m is the electron mass;E. O. Kane, J. Chem. Phys. Solids 1, 249 (1957).
    [CrossRef]
  4. C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, A. Miller, Phys. Rev. Lett. 42, 1785 (1979).
    [CrossRef]
  5. M. Weiler, Solid State Commun. 39, 937 (1981).
    [CrossRef]
  6. B. S. Wherrett, J. Opt. Soc. Am. B 1, 67 (1984).
    [CrossRef]
  7. A. Miller, A. Johnston, J. Dempsey, J. Smith, C. R. Pidgeon, G. D. Holah, J. Phys. 12, 4839 (1979).
  8. S. Guha, E. W. Van Stryland, M. J. Soileau, Opt. Lett. 10, 285 (1985).
    [CrossRef] [PubMed]
  9. T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. (to be published).
  10. Values taken from E. O. Kane, in Narrow Gap Semiconductors—Physics and Applications, W. Zawadzki, ed. (Springer-Verlag, New York, 1980 ), p. 13;for values not listed in this reference the value of 21 eV was assumed.
    [CrossRef]
  11. Cleveland Crystals, P.O. Box 17157, Euclid, Ohio 44117.
  12. II-VI, Inc., Saxonburg Boulevard, Saxonburg, Pa. 16056.
  13. Morgan Semiconductors, 2623 National Circle, Garland, Tex. 75041.
  14. CVD Inc., 35 Industrial Parkway, Woburn, Mass. 01801.
  15. Raytheon Company, Missile Systems Division, Hartwell Road, Bedford, Mass. 01730.
  16. Atomergic Chemetals, 100 Fairchild Avenue, Plainview, N.Y. 11803.
  17. K. H. Hellwege, ed., Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology, Vol. 17, Subvols. (a) and (b), Semiconductors (Springer-Verlag, New York, 1982).
  18. M. Neuberger, “II-VI semiconducting compound tables,” (Hughes Aircraft Company, Culver City, Calif., 1969).
  19. Y. S. Park, D. C. Reynolds, Phys. Rev. 132, 2450 (1963).
    [CrossRef]
  20. These values were obtained by linear extrapolation as a function of composition between the known values for CdS and CdSe. Y. S. Park, D. C. Reynolds, Phys. Rev. 132, 2450 (1963).
    [CrossRef]
  21. R. H. Bube, Photoconductivity of Solids (Wiley, New York, 1960).
  22. C. C. Lee, H. Y. Fan, Phys. Rev. B 9, 3502 (1974).
    [CrossRef]
  23. P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, Phys. Rev. B 17, 4620 (1978).
    [CrossRef]

1985 (2)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

S. Guha, E. W. Van Stryland, M. J. Soileau, Opt. Lett. 10, 285 (1985).
[CrossRef] [PubMed]

1984 (1)

1981 (1)

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

1979 (2)

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, A. Miller, Phys. Rev. Lett. 42, 1785 (1979).
[CrossRef]

A. Miller, A. Johnston, J. Dempsey, J. Smith, C. R. Pidgeon, G. D. Holah, J. Phys. 12, 4839 (1979).

1978 (1)

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, Phys. Rev. B 17, 4620 (1978).
[CrossRef]

1976 (1)

J. H. Bechtel, W. L. Smith, Phys. Rev. B 13, 3515 (1976).
[CrossRef]

1974 (1)

C. C. Lee, H. Y. Fan, Phys. Rev. B 9, 3502 (1974).
[CrossRef]

1963 (2)

Y. S. Park, D. C. Reynolds, Phys. Rev. 132, 2450 (1963).
[CrossRef]

These values were obtained by linear extrapolation as a function of composition between the known values for CdS and CdSe. Y. S. Park, D. C. Reynolds, Phys. Rev. 132, 2450 (1963).
[CrossRef]

1957 (1)

Ep = 2P2m/ħ2, where P is the Kane momentum parameter and m is the electron mass;E. O. Kane, J. Chem. Phys. Solids 1, 249 (1957).
[CrossRef]

Bechtel, J. H.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, Phys. Rev. B 17, 4620 (1978).
[CrossRef]

J. H. Bechtel, W. L. Smith, Phys. Rev. B 13, 3515 (1976).
[CrossRef]

Bloembergen, N.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, Phys. Rev. B 17, 4620 (1978).
[CrossRef]

Boggess, T. F.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. (to be published).

Boyd, I. W.

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. (to be published).

Bube, R. H.

R. H. Bube, Photoconductivity of Solids (Wiley, New York, 1960).

Dempsey, J.

A. Miller, A. Johnston, J. Dempsey, J. Smith, C. R. Pidgeon, G. D. Holah, J. Phys. 12, 4839 (1979).

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, A. Miller, Phys. Rev. Lett. 42, 1785 (1979).
[CrossRef]

Fan, H. Y.

C. C. Lee, H. Y. Fan, Phys. Rev. B 9, 3502 (1974).
[CrossRef]

Guha, S.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

S. Guha, E. W. Van Stryland, M. J. Soileau, Opt. Lett. 10, 285 (1985).
[CrossRef] [PubMed]

Holah, G. D.

A. Miller, A. Johnston, J. Dempsey, J. Smith, C. R. Pidgeon, G. D. Holah, J. Phys. 12, 4839 (1979).

Johnston, A.

A. Miller, A. Johnston, J. Dempsey, J. Smith, C. R. Pidgeon, G. D. Holah, J. Phys. 12, 4839 (1979).

Johnston, A. M.

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, A. Miller, Phys. Rev. Lett. 42, 1785 (1979).
[CrossRef]

Kane, E. O.

Ep = 2P2m/ħ2, where P is the Kane momentum parameter and m is the electron mass;E. O. Kane, J. Chem. Phys. Solids 1, 249 (1957).
[CrossRef]

Values taken from E. O. Kane, in Narrow Gap Semiconductors—Physics and Applications, W. Zawadzki, ed. (Springer-Verlag, New York, 1980 ), p. 13;for values not listed in this reference the value of 21 eV was assumed.
[CrossRef]

Lee, C. C.

C. C. Lee, H. Y. Fan, Phys. Rev. B 9, 3502 (1974).
[CrossRef]

Liu, P.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, Phys. Rev. B 17, 4620 (1978).
[CrossRef]

Lotem, H.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, Phys. Rev. B 17, 4620 (1978).
[CrossRef]

Miller, A.

A. Miller, A. Johnston, J. Dempsey, J. Smith, C. R. Pidgeon, G. D. Holah, J. Phys. 12, 4839 (1979).

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, A. Miller, Phys. Rev. Lett. 42, 1785 (1979).
[CrossRef]

Moss, S. C.

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. (to be published).

Neuberger, M.

M. Neuberger, “II-VI semiconducting compound tables,” (Hughes Aircraft Company, Culver City, Calif., 1969).

Park, Y. S.

Y. S. Park, D. C. Reynolds, Phys. Rev. 132, 2450 (1963).
[CrossRef]

These values were obtained by linear extrapolation as a function of composition between the known values for CdS and CdSe. Y. S. Park, D. C. Reynolds, Phys. Rev. 132, 2450 (1963).
[CrossRef]

Pidgeon, C. R.

A. Miller, A. Johnston, J. Dempsey, J. Smith, C. R. Pidgeon, G. D. Holah, J. Phys. 12, 4839 (1979).

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, A. Miller, Phys. Rev. Lett. 42, 1785 (1979).
[CrossRef]

Reynolds, D. C.

Y. S. Park, D. C. Reynolds, Phys. Rev. 132, 2450 (1963).
[CrossRef]

These values were obtained by linear extrapolation as a function of composition between the known values for CdS and CdSe. Y. S. Park, D. C. Reynolds, Phys. Rev. 132, 2450 (1963).
[CrossRef]

Smirl, A. L.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. (to be published).

Smith, J.

A. Miller, A. Johnston, J. Dempsey, J. Smith, C. R. Pidgeon, G. D. Holah, J. Phys. 12, 4839 (1979).

Smith, W. L.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, Phys. Rev. B 17, 4620 (1978).
[CrossRef]

J. H. Bechtel, W. L. Smith, Phys. Rev. B 13, 3515 (1976).
[CrossRef]

Soileau, M. J.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

S. Guha, E. W. Van Stryland, M. J. Soileau, Opt. Lett. 10, 285 (1985).
[CrossRef] [PubMed]

Van Stryland, E. W.

S. Guha, E. W. Van Stryland, M. J. Soileau, 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, Opt. Eng. 24, 613 (1985).

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. (to be published).

Vanherzeele, H.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Weiler, M.

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

Wherrett, B. S.

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

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, A. Miller, Phys. Rev. Lett. 42, 1785 (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, Opt. Eng. 24, 613 (1985).

J. Chem. Phys. Solids (1)

Ep = 2P2m/ħ2, where P is the Kane momentum parameter and m is the electron mass;E. O. Kane, J. Chem. Phys. Solids 1, 249 (1957).
[CrossRef]

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

J. Phys. (1)

A. Miller, A. Johnston, J. Dempsey, J. Smith, C. R. Pidgeon, G. D. Holah, J. Phys. 12, 4839 (1979).

Opt. Eng. (1)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Opt. Lett. (1)

Phys. Rev. (2)

Y. S. Park, D. C. Reynolds, Phys. Rev. 132, 2450 (1963).
[CrossRef]

These values were obtained by linear extrapolation as a function of composition between the known values for CdS and CdSe. Y. S. Park, D. C. Reynolds, Phys. Rev. 132, 2450 (1963).
[CrossRef]

Phys. Rev. B (3)

C. C. Lee, H. Y. Fan, Phys. Rev. B 9, 3502 (1974).
[CrossRef]

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, Phys. Rev. B 17, 4620 (1978).
[CrossRef]

J. H. Bechtel, W. L. Smith, Phys. Rev. B 13, 3515 (1976).
[CrossRef]

Phys. Rev. Lett. (1)

C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, A. Miller, Phys. Rev. Lett. 42, 1785 (1979).
[CrossRef]

Solid State Commun. (1)

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

Other (11)

R. H. Bube, Photoconductivity of Solids (Wiley, New York, 1960).

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. (to be published).

Values taken from E. O. Kane, in Narrow Gap Semiconductors—Physics and Applications, W. Zawadzki, ed. (Springer-Verlag, New York, 1980 ), p. 13;for values not listed in this reference the value of 21 eV was assumed.
[CrossRef]

Cleveland Crystals, P.O. Box 17157, Euclid, Ohio 44117.

II-VI, Inc., Saxonburg Boulevard, Saxonburg, Pa. 16056.

Morgan Semiconductors, 2623 National Circle, Garland, Tex. 75041.

CVD Inc., 35 Industrial Parkway, Woburn, Mass. 01801.

Raytheon Company, Missile Systems Division, Hartwell Road, Bedford, Mass. 01730.

Atomergic Chemetals, 100 Fairchild Avenue, Plainview, N.Y. 11803.

K. H. Hellwege, ed., Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology, Vol. 17, Subvols. (a) and (b), Semiconductors (Springer-Verlag, New York, 1982).

M. Neuberger, “II-VI semiconducting compound tables,” (Hughes Aircraft Company, Culver City, Calif., 1969).

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Figures (2)

Fig. 1
Fig. 1

A log–log plot of the scaled 2PA coefficient versus energy gap assuming parabolic band structure. The solid line is a least-squares fit of the data to a line of slope −3 (omitting ZnTe). The ×’s shown for GaAs, CdTe, CdSe, and ZnTe are data from Ref. 11. Data to the left of the vertical dotted line were taken with 1-μm light; those to the right, with 0.5-μm light.

Fig. 2
Fig. 2

The function F2 plotted versus 2ħw/Eg using K = 3100 in Eq. (1). (Ep and Eg are in electron volts, and β2 is in centimeters per gigawatt.)

Tables (1)

Tables Icon

Table 1 Material Parameters and Two-Photon Absorption Coefficients of the Materials Studied

Equations (2)

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

β 2 = K E p F ( 2 w / E g ) / n 2 E g 3 ,
F ( 2 w / E g ) = ( 2 w / E g - 1 ) 3 / 2 / ( 2 w / E g ) 5 .

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