Abstract

An investigation was made of a photoacoustic technique for determining the optical absorption coefficient in solids. A train of laser pulses was passed through the solid, and a piezoelectric transducer attached directly to the sample measured the amplitude of the elastic wave generated by the absorbed radiation. Calibration was performed at a wavelength of known absorption. The sensitivity of the technique was found to be limited to about 1 × 10−5 cm−1 in our samples due to radiation scattered onto the transducer, but the technique is capable of measuring absorption coefficients in the 10−6 cm−1 range using laser powers of about 1 W.

© 1977 Optical Society of America

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References

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  1. For a review see, e.g., L. Skolnik, in Optical Properties of Highly Transparent Solids, S. S. Mitra, B. Bendow, Eds. (Plenum, New York, 1975), p. 405.
    [CrossRef]
  2. M. Hass, J. W. Davison, H. B. Rosenstock, J. Babiskin, Appl. Opt. 14, 1128 (1975).
    [CrossRef] [PubMed]
  3. K. I. White, J. E. Midwinter, Opto-Electronics 5, 323 (1973).
    [CrossRef]
  4. L. Skolnik, A. Hordvik, A. Kahan, Appl. Phys. Lett. 23, 477 (1973).
    [CrossRef]
  5. D. L. Stierwalt, Appl. Opt. 5, 1911 (1966).
    [CrossRef] [PubMed]
  6. L. Skolnik, M. Clark, R. Koch, W. McCann, W. Shields, in Proc. Fourth Annual Conf. on IR Laser Window Materials, AFMS-TR-75-79 (1975), p. 197.
  7. A. Hordvik, H. Schlossberg, J. Opt. Soc. Am. 65, 1165 (1975).
  8. A. G. Bell, Am. J. Sci.-Third Ser. 20, 305 (1880).
  9. A. G. Bell, Philos. Mag. 11, 510 (1881).
  10. J. Tyndall, Proc. R. Soc. London 31, 307 (1881).
  11. W. C. Roentgen, Philos. Mag. 11, 308 (1881).
  12. M. I. Delaney, Sci. Prog. 47, 459 (1959).
  13. L. K. Kreuzer, J. Appl. Phys. 42, 2934 (1971).
    [CrossRef]
  14. W. R. Harshbarger, M. B. Robin, Acc. Chem. Res. 6, 329 (1973).
    [CrossRef]
  15. F. C. Dewey, Opt. Eng. 13, 483 (1974).
    [CrossRef]
  16. A. Rosencwaig, Opt. Commun. 7, 305 (1973).
    [CrossRef]
  17. A. Rosencwaig, Phys. Today, 28 (9), 23 (1975).
    [CrossRef]
  18. A. Rosencwaig, A. Gersho, J. Appl. Phys. 47, 64 (1976); Science 190, 556 (1975).
    [CrossRef]
  19. E. L. Kerr, Appl. Opt. 12, 2520 (1973).
    [CrossRef] [PubMed]
  20. J. G. Parker, Appl. Opt. 12, 2974 (1973).
    [CrossRef] [PubMed]
  21. H. S. Bennet, R. A. Forman, Appl. Opt. 14, 3031 (1975); Appl. Opt. 15, 1313 (1976).
    [CrossRef] [PubMed]
  22. Y. N. Lokhov, V. S. Mospanov, Y. D. Fiveiskii, Kvantovaya Elektron. (Moscow) 1 (3), 67 (1971) [Sov. J. Quantum Electron. 1, 252 (1971)].
  23. The particular ceramic used has the tradename PZT-5H. The manufacturer is Vernitron Piezoelectric Division, Bedford, Ohio 44146.
  24. A publication is being prepared which describes the use of the photoacoustic technique for measuring surface absorption.
  25. Information on the absorption coefficients compiled from a variety of sources can be found in “Infrared Laser Window Materials Property Data for ZnSe, KCl, NaCl, CaF2, SaF2, BaF2” by S. K. Dickinson, AFCRL Report, AFCRL-TR-75-0318 (1975).
  26. T. G. McGill, R. W. Hellwarth, M. Mangir, H. V. Winston, J. Phys. Chem. Solids 34, 2105 (1973).
    [CrossRef]
  27. T. F. Deutsch, J. Phys. Chem. Solids 34, 2091 (1973).
    [CrossRef]
  28. A number of papers on this topic can be found in Ref. 1.

1976 (1)

A. Rosencwaig, A. Gersho, J. Appl. Phys. 47, 64 (1976); Science 190, 556 (1975).
[CrossRef]

1975 (5)

A. Rosencwaig, Phys. Today, 28 (9), 23 (1975).
[CrossRef]

M. Hass, J. W. Davison, H. B. Rosenstock, J. Babiskin, Appl. Opt. 14, 1128 (1975).
[CrossRef] [PubMed]

L. Skolnik, M. Clark, R. Koch, W. McCann, W. Shields, in Proc. Fourth Annual Conf. on IR Laser Window Materials, AFMS-TR-75-79 (1975), p. 197.

A. Hordvik, H. Schlossberg, J. Opt. Soc. Am. 65, 1165 (1975).

H. S. Bennet, R. A. Forman, Appl. Opt. 14, 3031 (1975); Appl. Opt. 15, 1313 (1976).
[CrossRef] [PubMed]

1974 (1)

F. C. Dewey, Opt. Eng. 13, 483 (1974).
[CrossRef]

1973 (8)

A. Rosencwaig, Opt. Commun. 7, 305 (1973).
[CrossRef]

W. R. Harshbarger, M. B. Robin, Acc. Chem. Res. 6, 329 (1973).
[CrossRef]

E. L. Kerr, Appl. Opt. 12, 2520 (1973).
[CrossRef] [PubMed]

J. G. Parker, Appl. Opt. 12, 2974 (1973).
[CrossRef] [PubMed]

K. I. White, J. E. Midwinter, Opto-Electronics 5, 323 (1973).
[CrossRef]

L. Skolnik, A. Hordvik, A. Kahan, Appl. Phys. Lett. 23, 477 (1973).
[CrossRef]

T. G. McGill, R. W. Hellwarth, M. Mangir, H. V. Winston, J. Phys. Chem. Solids 34, 2105 (1973).
[CrossRef]

T. F. Deutsch, J. Phys. Chem. Solids 34, 2091 (1973).
[CrossRef]

1971 (2)

Y. N. Lokhov, V. S. Mospanov, Y. D. Fiveiskii, Kvantovaya Elektron. (Moscow) 1 (3), 67 (1971) [Sov. J. Quantum Electron. 1, 252 (1971)].

L. K. Kreuzer, J. Appl. Phys. 42, 2934 (1971).
[CrossRef]

1966 (1)

1959 (1)

M. I. Delaney, Sci. Prog. 47, 459 (1959).

1881 (3)

A. G. Bell, Philos. Mag. 11, 510 (1881).

J. Tyndall, Proc. R. Soc. London 31, 307 (1881).

W. C. Roentgen, Philos. Mag. 11, 308 (1881).

1880 (1)

A. G. Bell, Am. J. Sci.-Third Ser. 20, 305 (1880).

Babiskin, J.

Bell, A. G.

A. G. Bell, Philos. Mag. 11, 510 (1881).

A. G. Bell, Am. J. Sci.-Third Ser. 20, 305 (1880).

Bennet, H. S.

Clark, M.

L. Skolnik, M. Clark, R. Koch, W. McCann, W. Shields, in Proc. Fourth Annual Conf. on IR Laser Window Materials, AFMS-TR-75-79 (1975), p. 197.

Davison, J. W.

Delaney, M. I.

M. I. Delaney, Sci. Prog. 47, 459 (1959).

Deutsch, T. F.

T. F. Deutsch, J. Phys. Chem. Solids 34, 2091 (1973).
[CrossRef]

Dewey, F. C.

F. C. Dewey, Opt. Eng. 13, 483 (1974).
[CrossRef]

Dickinson, S. K.

Information on the absorption coefficients compiled from a variety of sources can be found in “Infrared Laser Window Materials Property Data for ZnSe, KCl, NaCl, CaF2, SaF2, BaF2” by S. K. Dickinson, AFCRL Report, AFCRL-TR-75-0318 (1975).

Fiveiskii, Y. D.

Y. N. Lokhov, V. S. Mospanov, Y. D. Fiveiskii, Kvantovaya Elektron. (Moscow) 1 (3), 67 (1971) [Sov. J. Quantum Electron. 1, 252 (1971)].

Forman, R. A.

Gersho, A.

A. Rosencwaig, A. Gersho, J. Appl. Phys. 47, 64 (1976); Science 190, 556 (1975).
[CrossRef]

Harshbarger, W. R.

W. R. Harshbarger, M. B. Robin, Acc. Chem. Res. 6, 329 (1973).
[CrossRef]

Hass, M.

Hellwarth, R. W.

T. G. McGill, R. W. Hellwarth, M. Mangir, H. V. Winston, J. Phys. Chem. Solids 34, 2105 (1973).
[CrossRef]

Hordvik, A.

A. Hordvik, H. Schlossberg, J. Opt. Soc. Am. 65, 1165 (1975).

L. Skolnik, A. Hordvik, A. Kahan, Appl. Phys. Lett. 23, 477 (1973).
[CrossRef]

Kahan, A.

L. Skolnik, A. Hordvik, A. Kahan, Appl. Phys. Lett. 23, 477 (1973).
[CrossRef]

Kerr, E. L.

Koch, R.

L. Skolnik, M. Clark, R. Koch, W. McCann, W. Shields, in Proc. Fourth Annual Conf. on IR Laser Window Materials, AFMS-TR-75-79 (1975), p. 197.

Kreuzer, L. K.

L. K. Kreuzer, J. Appl. Phys. 42, 2934 (1971).
[CrossRef]

Lokhov, Y. N.

Y. N. Lokhov, V. S. Mospanov, Y. D. Fiveiskii, Kvantovaya Elektron. (Moscow) 1 (3), 67 (1971) [Sov. J. Quantum Electron. 1, 252 (1971)].

Mangir, M.

T. G. McGill, R. W. Hellwarth, M. Mangir, H. V. Winston, J. Phys. Chem. Solids 34, 2105 (1973).
[CrossRef]

McCann, W.

L. Skolnik, M. Clark, R. Koch, W. McCann, W. Shields, in Proc. Fourth Annual Conf. on IR Laser Window Materials, AFMS-TR-75-79 (1975), p. 197.

McGill, T. G.

T. G. McGill, R. W. Hellwarth, M. Mangir, H. V. Winston, J. Phys. Chem. Solids 34, 2105 (1973).
[CrossRef]

Midwinter, J. E.

K. I. White, J. E. Midwinter, Opto-Electronics 5, 323 (1973).
[CrossRef]

Mospanov, V. S.

Y. N. Lokhov, V. S. Mospanov, Y. D. Fiveiskii, Kvantovaya Elektron. (Moscow) 1 (3), 67 (1971) [Sov. J. Quantum Electron. 1, 252 (1971)].

Parker, J. G.

Robin, M. B.

W. R. Harshbarger, M. B. Robin, Acc. Chem. Res. 6, 329 (1973).
[CrossRef]

Roentgen, W. C.

W. C. Roentgen, Philos. Mag. 11, 308 (1881).

Rosencwaig, A.

A. Rosencwaig, A. Gersho, J. Appl. Phys. 47, 64 (1976); Science 190, 556 (1975).
[CrossRef]

A. Rosencwaig, Phys. Today, 28 (9), 23 (1975).
[CrossRef]

A. Rosencwaig, Opt. Commun. 7, 305 (1973).
[CrossRef]

Rosenstock, H. B.

Schlossberg, H.

A. Hordvik, H. Schlossberg, J. Opt. Soc. Am. 65, 1165 (1975).

Shields, W.

L. Skolnik, M. Clark, R. Koch, W. McCann, W. Shields, in Proc. Fourth Annual Conf. on IR Laser Window Materials, AFMS-TR-75-79 (1975), p. 197.

Skolnik, L.

L. Skolnik, M. Clark, R. Koch, W. McCann, W. Shields, in Proc. Fourth Annual Conf. on IR Laser Window Materials, AFMS-TR-75-79 (1975), p. 197.

L. Skolnik, A. Hordvik, A. Kahan, Appl. Phys. Lett. 23, 477 (1973).
[CrossRef]

For a review see, e.g., L. Skolnik, in Optical Properties of Highly Transparent Solids, S. S. Mitra, B. Bendow, Eds. (Plenum, New York, 1975), p. 405.
[CrossRef]

Stierwalt, D. L.

Tyndall, J.

J. Tyndall, Proc. R. Soc. London 31, 307 (1881).

White, K. I.

K. I. White, J. E. Midwinter, Opto-Electronics 5, 323 (1973).
[CrossRef]

Winston, H. V.

T. G. McGill, R. W. Hellwarth, M. Mangir, H. V. Winston, J. Phys. Chem. Solids 34, 2105 (1973).
[CrossRef]

Acc. Chem. Res. (1)

W. R. Harshbarger, M. B. Robin, Acc. Chem. Res. 6, 329 (1973).
[CrossRef]

Am. J. Sci.-Third Ser. (1)

A. G. Bell, Am. J. Sci.-Third Ser. 20, 305 (1880).

Appl. Opt. (5)

Appl. Phys. Lett. (1)

L. Skolnik, A. Hordvik, A. Kahan, Appl. Phys. Lett. 23, 477 (1973).
[CrossRef]

J. Appl. Phys. (2)

L. K. Kreuzer, J. Appl. Phys. 42, 2934 (1971).
[CrossRef]

A. Rosencwaig, A. Gersho, J. Appl. Phys. 47, 64 (1976); Science 190, 556 (1975).
[CrossRef]

J. Opt. Soc. Am. (1)

A. Hordvik, H. Schlossberg, J. Opt. Soc. Am. 65, 1165 (1975).

J. Phys. Chem. Solids (2)

T. G. McGill, R. W. Hellwarth, M. Mangir, H. V. Winston, J. Phys. Chem. Solids 34, 2105 (1973).
[CrossRef]

T. F. Deutsch, J. Phys. Chem. Solids 34, 2091 (1973).
[CrossRef]

Kvantovaya Elektron. (Moscow) (1)

Y. N. Lokhov, V. S. Mospanov, Y. D. Fiveiskii, Kvantovaya Elektron. (Moscow) 1 (3), 67 (1971) [Sov. J. Quantum Electron. 1, 252 (1971)].

Opt. Commun. (1)

A. Rosencwaig, Opt. Commun. 7, 305 (1973).
[CrossRef]

Opt. Eng. (1)

F. C. Dewey, Opt. Eng. 13, 483 (1974).
[CrossRef]

Opto-Electronics (1)

K. I. White, J. E. Midwinter, Opto-Electronics 5, 323 (1973).
[CrossRef]

Philos. Mag. (2)

A. G. Bell, Philos. Mag. 11, 510 (1881).

W. C. Roentgen, Philos. Mag. 11, 308 (1881).

Phys. Today (1)

A. Rosencwaig, Phys. Today, 28 (9), 23 (1975).
[CrossRef]

Proc. Fourth Annual Conf. on IR Laser Window Materials (1)

L. Skolnik, M. Clark, R. Koch, W. McCann, W. Shields, in Proc. Fourth Annual Conf. on IR Laser Window Materials, AFMS-TR-75-79 (1975), p. 197.

Proc. R. Soc. London (1)

J. Tyndall, Proc. R. Soc. London 31, 307 (1881).

Sci. Prog. (1)

M. I. Delaney, Sci. Prog. 47, 459 (1959).

Other (5)

For a review see, e.g., L. Skolnik, in Optical Properties of Highly Transparent Solids, S. S. Mitra, B. Bendow, Eds. (Plenum, New York, 1975), p. 405.
[CrossRef]

The particular ceramic used has the tradename PZT-5H. The manufacturer is Vernitron Piezoelectric Division, Bedford, Ohio 44146.

A publication is being prepared which describes the use of the photoacoustic technique for measuring surface absorption.

Information on the absorption coefficients compiled from a variety of sources can be found in “Infrared Laser Window Materials Property Data for ZnSe, KCl, NaCl, CaF2, SaF2, BaF2” by S. K. Dickinson, AFCRL Report, AFCRL-TR-75-0318 (1975).

A number of papers on this topic can be found in Ref. 1.

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Figures (6)

Fig. 1
Fig. 1

Schematic of experimental arrangement.

Fig. 2
Fig. 2

Transducer output voltage vs transmitted power at a fixed position and chopping frequency.

Fig. 3
Fig. 3

Transducer output voltage vs distance beam to transducer at fixed input power and chopping frequency.

Fig. 4
Fig. 4

Absorption coefficient of CaF2 vs wavenumber. The dashed line is drawn with the slope found by Deutsch.27

Fig. 5
Fig. 5

Absorption coefficient of SrF2 vs wavenumber. The dashed line is drawn with the slope found by Deutsch.27

Fig. 6
Fig. 6

Absorption coefficient of BaF2 vs wavenumber. The dashed line is drawn with the slope found by Deutsch.27

Tables (1)

Tables Icon

Table I Optical Absorption Coefficient of Various Materials at Selected Wavelengths

Equations (12)

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

u = Φ ;
2 Φ - 1 v 2 2 Φ t 2 = 1 + σ 1 - σ α 0 T ;
2 T + β 2 P ( t ) π a 2 exp ( - 2 r 2 / a 2 ) = ρ C κ T t ;
P ( t ) = P [ 1 - exp ( - t / τ ) ] ;
r r = 2 Φ r 2 , θ θ = 1 r Φ r .
r r ( r , t ) = β P α 0 v 2 ( 1 + σ ) 2 π C ρ ( 1 - σ ) 0 exp ( - s 2 a 2 / 8 ) × [ - s J 0 ( s r ) + 1 r J 1 ( s r ) ] × { v 2 [ exp ( - α 2 s 2 t ) - 1 ] - α 4 s 2 α 2 s 2 v 2 ( α 4 s 2 + v 2 ) + τ ( 1 + v 2 s 2 τ 2 ) exp ( - α 2 s 2 t ) - τ 3 s 2 ( α 4 s 2 + v 2 ) exp ( - t / τ ) ( 1 - α 2 τ s 2 ) ( 1 + v 2 s 2 τ ) ( α 4 s 2 + v 2 ) + ( α 2 - τ v 2 ) cos v s t v 2 ( 1 + v 2 τ 2 s 2 ) ( α 4 s 2 + v 2 ) + ( 1 + α 2 s 2 τ ) sin v s t s v ( 1 + v 2 τ 2 s 2 ) ( α 4 s 2 + v 2 ) } d s .
r r = - θ θ = - β P α 0 ( 1 + σ ) t 2 π C ρ ( 1 - σ ) r 2 .
Δ W = 1 2 ( 1 - R ) f [ exp ( β l ) - ( 1 - R ) - R exp ( - β l ) ] P t ,
Δ W = 1 2 ( 1 + R ) ( 1 - R ) f β l ( 1 + 1 2 β l 1 - R 1 + R ) P t .
β = A exp ( γ ω ω 0 ) ,
V β P α 0 ( 1 + σ ) t 2 π C ρ ( 1 - σ ) r 2
V · C · ρ ( 1 - σ ) β · P · α 0 ( 1 + σ ) = const

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