Abstract

A model for the thermal lens which approximates the refractive shape as a parabola is compared with a model which accounts for the aberrant nature of the lens; both models are tested against experimental results. The comparison suggests how the inaccuracies of the parabolic lens model may be corrected while retaining its mathematical simplicity and better predictive power for stronger thermal lenses.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. C. C. Leite, R. S. Moore, J. R. Whinnery, Appl. Phys. Lett. 5, 141 (1964).
    [CrossRef]
  2. D. Solimini, J. Appl. Phys. 37, 3314 (1966).
    [CrossRef]
  3. Y. Kohanzadeh, D. H. Auston, IEEE J. Quantum Electron. QE-6, 475 (1970).
    [CrossRef]
  4. S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
    [CrossRef]
  5. R. L. Carman, P. L. Kelley, Appl. Phys. Lett. 12, 241 (1968).
    [CrossRef]
  6. F. W. Dabby, R. W. Boyko, C. V. Shank, J. R. Whinnery, IEEE J. Quantum Electron. QE-5, 516 (1969).
    [CrossRef]
  7. P. Calmettes, C. Laj, J. Phys. Paris C-1, 125 (1972).
  8. J. Stone, J. Opt. Soc. Am. 62, 327 (1972).
    [CrossRef]
  9. C. Hu, J. R. Whinnery, Appl. Opt. 12, 72 (1973).
    [CrossRef] [PubMed]
  10. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
    [CrossRef]
  11. S. J. Sheldon, L. V. Knight, J. M. Thorne, Appl. Opt. 21, 1663 (1982).
    [CrossRef] [PubMed]
  12. J. R. Whinnery, Acc. Chem. Res. 7, 225 (1974).
    [CrossRef]
  13. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1972), p. 228.
  14. H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
    [CrossRef]
  15. J. M. Harris, N. J. Dovichi, Anal. Chem. 52, 695A (1980).
    [CrossRef]
  16. C. A. Carter, J. M. Harris, Anal. Chem. 54, 163 (1983).
  17. R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).
    [CrossRef]
  18. A. C. Tam, C. K. N. Patel, Appl. Opt. 18, 3348 (1979).
    [CrossRef] [PubMed]
  19. J. H. Brannon, D. Magde, J. Phys. Chem. 82, 705 (1978).
    [CrossRef]
  20. N. J. Dovichi, J. M. Harris, Anal. Chem. 53, 106 (1981).
    [CrossRef]
  21. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
  22. G. Abbate, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 11, 1167 (1968).
    [CrossRef]
  23. E. W. Washburn, Ed., International Critical Tables, Vol. 7 (McGraw-Hill, New York, 1930), p. 12.
  24. G. S. Kell, J. Chem. Eng. Data 20, 97 (1975).
    [CrossRef]
  25. D. Beysens, P. Calmettes, J. Chem. Phys. 66, 766 (1977).
    [CrossRef]
  26. G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 9, 1945 (1976).
    [CrossRef]
  27. K. Chu, A. R. Thompson, J. Chem. Eng. Data 7, 358 (1962).
    [CrossRef]
  28. R. E. Bolz, G. L. Tuve, Eds., Handbook of Tables for Applied Engineering Science (CRC Press, Cleveland, 1973), p. 88.
  29. J. E. S. Venart, R. S. Prasad, D. G. Stocker, in Water and Steam, J. Straub, K. Scheffler, Eds. (Pergamon, New York, 1980), p. 392.
  30. R. E. Bolz, G. L. Tuve, Eds., Handbook of Tables for Applied Engineering Science (CRC Press, Cleveland, 1973) p. 92.
  31. H. L. Mason, Trans. ASME 76, 817 (1954).
  32. R. C. Weast, M. J. Astle, Eds., CRC Handbook of Chemistry and Physics (CRC Press, West Palm Beach, Fla.1978) p. C-461.
  33. L. S. Shraiber, N. G. Pechenyuk, Russ. J. Phys. Chem. 39, 219 (1965).
  34. J. E. Grolier, G. C. Benson, P. Picker, J. Chem. Eng. Data 20, 243 (1975).
    [CrossRef]
  35. D. Harrison, E. A. Moelwyn-Hughes, Proc. R. Soc. London Ser. A 239, 230 (1957).
    [CrossRef]
  36. R. Anthore, P. Flament, G. Gouesbet, M. Rhazi, M. E. Weill, Appl. Opt. 21, 2 (1982).
    [CrossRef] [PubMed]
  37. G. Gouesbet, M. Rhazi, M. E. Weill, Appl. Opt. 22, 304 (1983).
    [CrossRef] [PubMed]

1983 (2)

C. A. Carter, J. M. Harris, Anal. Chem. 54, 163 (1983).

G. Gouesbet, M. Rhazi, M. E. Weill, Appl. Opt. 22, 304 (1983).
[CrossRef] [PubMed]

1982 (2)

1981 (1)

N. J. Dovichi, J. M. Harris, Anal. Chem. 53, 106 (1981).
[CrossRef]

1980 (1)

J. M. Harris, N. J. Dovichi, Anal. Chem. 52, 695A (1980).
[CrossRef]

1979 (1)

1978 (1)

J. H. Brannon, D. Magde, J. Phys. Chem. 82, 705 (1978).
[CrossRef]

1977 (1)

D. Beysens, P. Calmettes, J. Chem. Phys. 66, 766 (1977).
[CrossRef]

1976 (1)

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 9, 1945 (1976).
[CrossRef]

1975 (2)

G. S. Kell, J. Chem. Eng. Data 20, 97 (1975).
[CrossRef]

J. E. Grolier, G. C. Benson, P. Picker, J. Chem. Eng. Data 20, 243 (1975).
[CrossRef]

1974 (1)

J. R. Whinnery, Acc. Chem. Res. 7, 225 (1974).
[CrossRef]

1973 (1)

1972 (3)

P. Calmettes, C. Laj, J. Phys. Paris C-1, 125 (1972).

J. Stone, J. Opt. Soc. Am. 62, 327 (1972).
[CrossRef]

R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).
[CrossRef]

1970 (1)

Y. Kohanzadeh, D. H. Auston, IEEE J. Quantum Electron. QE-6, 475 (1970).
[CrossRef]

1969 (1)

F. W. Dabby, R. W. Boyko, C. V. Shank, J. R. Whinnery, IEEE J. Quantum Electron. QE-5, 516 (1969).
[CrossRef]

1968 (3)

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

R. L. Carman, P. L. Kelley, Appl. Phys. Lett. 12, 241 (1968).
[CrossRef]

G. Abbate, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 11, 1167 (1968).
[CrossRef]

1966 (2)

D. Solimini, J. Appl. Phys. 37, 3314 (1966).
[CrossRef]

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

1965 (2)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

L. S. Shraiber, N. G. Pechenyuk, Russ. J. Phys. Chem. 39, 219 (1965).

1964 (1)

R. C. C. Leite, R. S. Moore, J. R. Whinnery, Appl. Phys. Lett. 5, 141 (1964).
[CrossRef]

1962 (1)

K. Chu, A. R. Thompson, J. Chem. Eng. Data 7, 358 (1962).
[CrossRef]

1957 (1)

D. Harrison, E. A. Moelwyn-Hughes, Proc. R. Soc. London Ser. A 239, 230 (1957).
[CrossRef]

1954 (1)

H. L. Mason, Trans. ASME 76, 817 (1954).

Abbate, G.

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 9, 1945 (1976).
[CrossRef]

G. Abbate, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 11, 1167 (1968).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Anthore, R.

Attanasio, A.

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 9, 1945 (1976).
[CrossRef]

Auston, D. H.

Y. Kohanzadeh, D. H. Auston, IEEE J. Quantum Electron. QE-6, 475 (1970).
[CrossRef]

Benson, G. C.

J. E. Grolier, G. C. Benson, P. Picker, J. Chem. Eng. Data 20, 243 (1975).
[CrossRef]

Bernini, U.

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 9, 1945 (1976).
[CrossRef]

G. Abbate, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 11, 1167 (1968).
[CrossRef]

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Beysens, D.

D. Beysens, P. Calmettes, J. Chem. Phys. 66, 766 (1977).
[CrossRef]

Boyko, R. W.

F. W. Dabby, R. W. Boyko, C. V. Shank, J. R. Whinnery, IEEE J. Quantum Electron. QE-5, 516 (1969).
[CrossRef]

Brannon, J. H.

J. H. Brannon, D. Magde, J. Phys. Chem. 82, 705 (1978).
[CrossRef]

Burke, R. W.

R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).
[CrossRef]

Calmettes, P.

D. Beysens, P. Calmettes, J. Chem. Phys. 66, 766 (1977).
[CrossRef]

P. Calmettes, C. Laj, J. Phys. Paris C-1, 125 (1972).

Carman, R. L.

R. L. Carman, P. L. Kelley, Appl. Phys. Lett. 12, 241 (1968).
[CrossRef]

Carter, C. A.

C. A. Carter, J. M. Harris, Anal. Chem. 54, 163 (1983).

Chu, K.

K. Chu, A. R. Thompson, J. Chem. Eng. Data 7, 358 (1962).
[CrossRef]

Dabby, F. W.

F. W. Dabby, R. W. Boyko, C. V. Shank, J. R. Whinnery, IEEE J. Quantum Electron. QE-5, 516 (1969).
[CrossRef]

Deardorff, E. R.

R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).
[CrossRef]

Dovichi, N. J.

N. J. Dovichi, J. M. Harris, Anal. Chem. 53, 106 (1981).
[CrossRef]

J. M. Harris, N. J. Dovichi, Anal. Chem. 52, 695A (1980).
[CrossRef]

Flament, P.

Gordon, J. P.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Gouesbet, G.

Grolier, J. E.

J. E. Grolier, G. C. Benson, P. Picker, J. Chem. Eng. Data 20, 243 (1975).
[CrossRef]

Harris, J. M.

C. A. Carter, J. M. Harris, Anal. Chem. 54, 163 (1983).

N. J. Dovichi, J. M. Harris, Anal. Chem. 53, 106 (1981).
[CrossRef]

J. M. Harris, N. J. Dovichi, Anal. Chem. 52, 695A (1980).
[CrossRef]

Harrison, D.

D. Harrison, E. A. Moelwyn-Hughes, Proc. R. Soc. London Ser. A 239, 230 (1957).
[CrossRef]

Hu, C.

Kell, G. S.

G. S. Kell, J. Chem. Eng. Data 20, 97 (1975).
[CrossRef]

Kelley, P. L.

R. L. Carman, P. L. Kelley, Appl. Phys. Lett. 12, 241 (1968).
[CrossRef]

Khokhlov, R. V.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Knight, L. V.

Kogelnik, H.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Kohanzadeh, Y.

Y. Kohanzadeh, D. H. Auston, IEEE J. Quantum Electron. QE-6, 475 (1970).
[CrossRef]

Krindach, D. P.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Laj, C.

P. Calmettes, C. Laj, J. Phys. Paris C-1, 125 (1972).

Leite, R. C. C.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, J. R. Whinnery, Appl. Phys. Lett. 5, 141 (1964).
[CrossRef]

Li, T.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Magde, D.

J. H. Brannon, D. Magde, J. Phys. Chem. 82, 705 (1978).
[CrossRef]

Mason, H. L.

H. L. Mason, Trans. ASME 76, 817 (1954).

Menis, O.

R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).
[CrossRef]

Migulin, A. V.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Moelwyn-Hughes, E. A.

D. Harrison, E. A. Moelwyn-Hughes, Proc. R. Soc. London Ser. A 239, 230 (1957).
[CrossRef]

Moore, R. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, J. R. Whinnery, Appl. Phys. Lett. 5, 141 (1964).
[CrossRef]

Patel, C. K. N.

Pechenyuk, N. G.

L. S. Shraiber, N. G. Pechenyuk, Russ. J. Phys. Chem. 39, 219 (1965).

Picker, P.

J. E. Grolier, G. C. Benson, P. Picker, J. Chem. Eng. Data 20, 243 (1975).
[CrossRef]

Porto, S. P. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Prasad, R. S.

J. E. S. Venart, R. S. Prasad, D. G. Stocker, in Water and Steam, J. Straub, K. Scheffler, Eds. (Pergamon, New York, 1980), p. 392.

Ragozzino, E.

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 9, 1945 (1976).
[CrossRef]

G. Abbate, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 11, 1167 (1968).
[CrossRef]

Rhazi, M.

Shank, C. V.

F. W. Dabby, R. W. Boyko, C. V. Shank, J. R. Whinnery, IEEE J. Quantum Electron. QE-5, 516 (1969).
[CrossRef]

Sheldon, S. J.

Shraiber, L. S.

L. S. Shraiber, N. G. Pechenyuk, Russ. J. Phys. Chem. 39, 219 (1965).

Solimini, D.

D. Solimini, J. Appl. Phys. 37, 3314 (1966).
[CrossRef]

Somma, F.

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 9, 1945 (1976).
[CrossRef]

G. Abbate, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 11, 1167 (1968).
[CrossRef]

Stocker, D. G.

J. E. S. Venart, R. S. Prasad, D. G. Stocker, in Water and Steam, J. Straub, K. Scheffler, Eds. (Pergamon, New York, 1980), p. 392.

Stone, J.

Sukhorukov, A. P.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Tam, A. C.

Thompson, A. R.

K. Chu, A. R. Thompson, J. Chem. Eng. Data 7, 358 (1962).
[CrossRef]

Thorne, J. M.

Venart, J. E. S.

J. E. S. Venart, R. S. Prasad, D. G. Stocker, in Water and Steam, J. Straub, K. Scheffler, Eds. (Pergamon, New York, 1980), p. 392.

Weill, M. E.

Whinnery, J. R.

J. R. Whinnery, Acc. Chem. Res. 7, 225 (1974).
[CrossRef]

C. Hu, J. R. Whinnery, Appl. Opt. 12, 72 (1973).
[CrossRef] [PubMed]

F. W. Dabby, R. W. Boyko, C. V. Shank, J. R. Whinnery, IEEE J. Quantum Electron. QE-5, 516 (1969).
[CrossRef]

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, J. R. Whinnery, Appl. Phys. Lett. 5, 141 (1964).
[CrossRef]

Acc. Chem. Res. (1)

J. R. Whinnery, Acc. Chem. Res. 7, 225 (1974).
[CrossRef]

Anal. Chem. (3)

J. M. Harris, N. J. Dovichi, Anal. Chem. 52, 695A (1980).
[CrossRef]

C. A. Carter, J. M. Harris, Anal. Chem. 54, 163 (1983).

N. J. Dovichi, J. M. Harris, Anal. Chem. 53, 106 (1981).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (2)

R. L. Carman, P. L. Kelley, Appl. Phys. Lett. 12, 241 (1968).
[CrossRef]

R. C. C. Leite, R. S. Moore, J. R. Whinnery, Appl. Phys. Lett. 5, 141 (1964).
[CrossRef]

IEEE J. Quantum Electron. (3)

Y. Kohanzadeh, D. H. Auston, IEEE J. Quantum Electron. QE-6, 475 (1970).
[CrossRef]

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

F. W. Dabby, R. W. Boyko, C. V. Shank, J. R. Whinnery, IEEE J. Quantum Electron. QE-5, 516 (1969).
[CrossRef]

J. Appl. Phys. (2)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

D. Solimini, J. Appl. Phys. 37, 3314 (1966).
[CrossRef]

J. Chem. Eng. Data (3)

K. Chu, A. R. Thompson, J. Chem. Eng. Data 7, 358 (1962).
[CrossRef]

G. S. Kell, J. Chem. Eng. Data 20, 97 (1975).
[CrossRef]

J. E. Grolier, G. C. Benson, P. Picker, J. Chem. Eng. Data 20, 243 (1975).
[CrossRef]

J. Chem. Phys. (1)

D. Beysens, P. Calmettes, J. Chem. Phys. 66, 766 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Chem. (1)

J. H. Brannon, D. Magde, J. Phys. Chem. 82, 705 (1978).
[CrossRef]

J. Phys. D (2)

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 9, 1945 (1976).
[CrossRef]

G. Abbate, U. Bernini, E. Ragozzino, F. Somma, J. Phys. D 11, 1167 (1968).
[CrossRef]

J. Phys. Paris (1)

P. Calmettes, C. Laj, J. Phys. Paris C-1, 125 (1972).

J. Res. Natl. Bur. Stand. Sect. A (1)

R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).
[CrossRef]

Proc. IEEE (1)

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

D. Harrison, E. A. Moelwyn-Hughes, Proc. R. Soc. London Ser. A 239, 230 (1957).
[CrossRef]

Russ. J. Phys. Chem. (1)

L. S. Shraiber, N. G. Pechenyuk, Russ. J. Phys. Chem. 39, 219 (1965).

Trans. ASME (1)

H. L. Mason, Trans. ASME 76, 817 (1954).

Other (7)

R. C. Weast, M. J. Astle, Eds., CRC Handbook of Chemistry and Physics (CRC Press, West Palm Beach, Fla.1978) p. C-461.

E. W. Washburn, Ed., International Critical Tables, Vol. 7 (McGraw-Hill, New York, 1930), p. 12.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

R. E. Bolz, G. L. Tuve, Eds., Handbook of Tables for Applied Engineering Science (CRC Press, Cleveland, 1973), p. 88.

J. E. S. Venart, R. S. Prasad, D. G. Stocker, in Water and Steam, J. Straub, K. Scheffler, Eds. (Pergamon, New York, 1980), p. 392.

R. E. Bolz, G. L. Tuve, Eds., Handbook of Tables for Applied Engineering Science (CRC Press, Cleveland, 1973) p. 92.

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1972), p. 228.

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 (2)

Fig. 1(a)
Fig. 1(a)

Thermal lens position dependence. Weak thermal lens case. Solid line is the parabolic lens model, Eq. (7), for θ = 0.021 and Zc = 5.37 cm. Dashed line is the aberrant lens model, Eq. (8), for θ = 0.040 and Zc = 3.10 cm.

Fig. 1(b)
Fig. 1(b)

Thermal lens position dependence. Stronger thermal lens case. Solid line as above for θ = 0.21. Dashed line as above for θ = 0.40.

Tables (5)

Tables Icon

Table I Formulas for the Parabolic and Aberrant Thermal Lens Model a

Tables Icon

Table II Fit of Equations for Position Dependence to Experimental Values of ΔI/Ia

Tables Icon

Table III Time Constants for Selected Solvents

Tables Icon

Table IV From Time-Resolved Thermal Lens Measurements on Aqueous Solutions

Tables Icon

Table V Physical Constants of Selected Solvents for Prediction of Thermal Lens Parameters

Equations (14)

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

Δ T ( r , t ) = ( 1 4 π k ) ( P 2.303 a b ) [ E i ( - 2 r 2 ω 2 ) - E i ( - 1 1 + 2 t / t c · 2 r 2 ω 2 ) ] ,
t c = ω 2 ρ C p / 4 k .
f ( t ) = π k ω 2 ρ 2.303 A ( d n / d T ) ( 1 + t c 2 t ) .
Z c = π ω 0 2 / λ
Δ I / I = [ I ( 0 ) - I ( ) ] / I ( ) = θ + θ 2 / 2 ,
Δ I / I = - 1 + [ 1 - θ tan - 1 ( 1 / 3 ) ] - 1 .
Δ I / I = 0.52 θ + 0.13 θ 2 + .
Δ I / I = 0.52 θ mod + 0.135 θ mod 2 .
I ( t ) = I ( 0 ) [ 1 - θ ( 1 + t c / 2 t ) - 1 ] ,
I ( t ) = I ( 0 ) { 1 - θ tan - 1 [ ( 1 / 3 ) ( 1 + t c / t ) - 1 ] } I ( 0 ) [ 1 - 0.58 θ ( 1 + t c / t ) - 1 ] .
I ( 0 ) - I ( ) I ( ) = θ ( 2 γ 1 + γ 2 ) + θ 2 ( 1 1 + γ 2 )
I ( 0 ) - I ( ) I ( ) = - 1 + { 1 - θ tan - 1 ( 2 γ 3 + γ 2 ) + [ θ 2 tan - 1 ( 2 γ 3 + γ 2 ) ] 2 + [ θ 4 ln ( 1 + γ 2 9 + γ 2 ) ] 2 } - 1
I ( t ) = I ( 0 ) { 1 + θ ( 1 + t c / 2 t ) ( 2 γ 1 + γ 2 ) + [ θ ( 1 + t c / 2 t ) ] 2 ( 1 1 + γ 2 ) } - 1
I ( t ) = I ( 0 ) [ 1 - θ tan - 1 [ 2 γ 3 + γ 2 + ( 9 + γ 2 ) t c / 2 t ] + { θ 2 tan - 1 [ 2 γ 3 + γ 2 + ( 9 + γ 2 ) t c / 2 t ] } 2 + ( θ 4 ln { [ ( 2 + t c / t ) ( 3 + γ 2 ) + 6 t c / t ] 2 + 16 γ 2 ( 9 + γ 2 ) 2 ( 2 + t c / t ) 2 } ) 2 ]

Metrics