Abstract

Time-resolved temperature-dependent beam-deflection spectroscopy has been used to investigate Ti:sapphire. Signals produced by thermal and nonthermal changes in the index of refraction were observed. The temperature behavior of the thermal part of the signal is in agreement with a theoretical model that includes the temperature dependence of the thermal diffusivity D. To our knowledge this is the first time that temperature-dependent beam-deflection spectroscopy has been carried out down to 20 K.

© 1993 Optical Society of America

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References

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  1. P. Hess and J. Pelzl, eds., Photoacoustic and Photothermal Phenomena, Springer Series in Optical Science (Springer-Verlag, Berlin, 1988).
    [CrossRef]
  2. J. C. Murphy, J. W. Maclachlan Spicer, L. C. Aamodt, and B. S. H. Royce, eds., Photoacoustic and Photothermal Phenomena, Springer Series in Optical Science (Springer-Verlag, Berlin, 1990).
    [CrossRef]
  3. D. Bicanic, ed., Photoacoustic and Photothermal Phenomena III, Springer Series in Optical Science (Springer-Verlag, Berlin, 1992).
    [CrossRef]
  4. W. B. Jackson, N. M. Amer, A. C. Boccara, and D. Fournier, “Photothermal deflection spectroscopy and detection,” Appl. Opt. 20, 1333 (1981).
    [CrossRef] [PubMed]
  5. A. Rose, R. Vyas, and R. Gupta, “Pulsed photothermal deflection spectroscopy in a flowing medium: a quantitative investigation,” Appl. Opt. 25, 4626 (1986).
    [CrossRef] [PubMed]
  6. H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti3+ doped sapphire,” Phys. Rev. B 45, 9604 (1992).
    [CrossRef]
  7. U. Hömmerich, H. Eilers, E. Strauss, and W. M. Yen, “Optically induced lensing effects in Nd3+-doped laser glass measured by photothermal beam-deflection spectroscopy,” Opt. Lett. 17, 213 (1992).
    [CrossRef] [PubMed]
  8. E. Strauss, “Bulk and local elastic relaxation around optically excited centers,” Phys. Rev. B 42, 1917 (1990).
    [CrossRef]
  9. E. Strauss and S. Walder, “Photorefractive effect and observation of the matrix relaxation around photo-excited centres in condensed matter,” Europhys. Lett. 6, 713 (1988).
    [CrossRef]
  10. H. Eilers, F. Kieseling, E. Strauss, and W. M. Yen, “Photoelastic law explains optically induced changes in the index of refraction in Ti:Al2O3,” Ref. 3, p. 320.
  11. P. F. Moulton, Opt. News 8, 9 (1982).
    [CrossRef]
  12. T. S. Narasimhamurty, Photoelastic and Electro-Optic Properties of Crystals (Plenum Press, New York, 1981).
    [CrossRef]
  13. P. F. Moulton, “Spectroscopic and laser characteristics of Ti:Al2O3,” J. Opt. Soc. Am. B 3, 125 (1986).
    [CrossRef]
  14. Y. S. Touloukian and C. Y. Ho, eds., Thermal Conductivity, Vol. 2 of TPRC Data Series (IFI/Plenum, New York, 1970) p. 97.
  15. K. Schäfer and E. Lax, eds., Landolt-Börnstein, Zahlenwerke aus Naturwissenschaft und Technik (Springer-Verlag, Berlin, 1961), Vol. II/4, p. 495.
  16. B. Yates, R. F. Cooper, and A. F. Pojur, “Thermal expansion at elevated temperatures: II. Aluminum oxide: experimental data between 100 and 800 K and their analysis,” J. Phys. C 5, 1046 (1972).
    [CrossRef]

1992 (2)

1990 (1)

E. Strauss, “Bulk and local elastic relaxation around optically excited centers,” Phys. Rev. B 42, 1917 (1990).
[CrossRef]

1988 (1)

E. Strauss and S. Walder, “Photorefractive effect and observation of the matrix relaxation around photo-excited centres in condensed matter,” Europhys. Lett. 6, 713 (1988).
[CrossRef]

1986 (2)

1982 (1)

P. F. Moulton, Opt. News 8, 9 (1982).
[CrossRef]

1981 (1)

1972 (1)

B. Yates, R. F. Cooper, and A. F. Pojur, “Thermal expansion at elevated temperatures: II. Aluminum oxide: experimental data between 100 and 800 K and their analysis,” J. Phys. C 5, 1046 (1972).
[CrossRef]

Amer, N. M.

Boccara, A. C.

Cooper, R. F.

B. Yates, R. F. Cooper, and A. F. Pojur, “Thermal expansion at elevated temperatures: II. Aluminum oxide: experimental data between 100 and 800 K and their analysis,” J. Phys. C 5, 1046 (1972).
[CrossRef]

Eilers, H.

H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti3+ doped sapphire,” Phys. Rev. B 45, 9604 (1992).
[CrossRef]

U. Hömmerich, H. Eilers, E. Strauss, and W. M. Yen, “Optically induced lensing effects in Nd3+-doped laser glass measured by photothermal beam-deflection spectroscopy,” Opt. Lett. 17, 213 (1992).
[CrossRef] [PubMed]

H. Eilers, F. Kieseling, E. Strauss, and W. M. Yen, “Photoelastic law explains optically induced changes in the index of refraction in Ti:Al2O3,” Ref. 3, p. 320.

Fournier, D.

Gupta, R.

Hömmerich, U.

Jackson, W. B.

Kieseling, F.

H. Eilers, F. Kieseling, E. Strauss, and W. M. Yen, “Photoelastic law explains optically induced changes in the index of refraction in Ti:Al2O3,” Ref. 3, p. 320.

Moulton, P. F.

Narasimhamurty, T. S.

T. S. Narasimhamurty, Photoelastic and Electro-Optic Properties of Crystals (Plenum Press, New York, 1981).
[CrossRef]

Pojur, A. F.

B. Yates, R. F. Cooper, and A. F. Pojur, “Thermal expansion at elevated temperatures: II. Aluminum oxide: experimental data between 100 and 800 K and their analysis,” J. Phys. C 5, 1046 (1972).
[CrossRef]

Rose, A.

Strauss, E.

H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti3+ doped sapphire,” Phys. Rev. B 45, 9604 (1992).
[CrossRef]

U. Hömmerich, H. Eilers, E. Strauss, and W. M. Yen, “Optically induced lensing effects in Nd3+-doped laser glass measured by photothermal beam-deflection spectroscopy,” Opt. Lett. 17, 213 (1992).
[CrossRef] [PubMed]

E. Strauss, “Bulk and local elastic relaxation around optically excited centers,” Phys. Rev. B 42, 1917 (1990).
[CrossRef]

E. Strauss and S. Walder, “Photorefractive effect and observation of the matrix relaxation around photo-excited centres in condensed matter,” Europhys. Lett. 6, 713 (1988).
[CrossRef]

H. Eilers, F. Kieseling, E. Strauss, and W. M. Yen, “Photoelastic law explains optically induced changes in the index of refraction in Ti:Al2O3,” Ref. 3, p. 320.

Vyas, R.

Walder, S.

E. Strauss and S. Walder, “Photorefractive effect and observation of the matrix relaxation around photo-excited centres in condensed matter,” Europhys. Lett. 6, 713 (1988).
[CrossRef]

Yates, B.

B. Yates, R. F. Cooper, and A. F. Pojur, “Thermal expansion at elevated temperatures: II. Aluminum oxide: experimental data between 100 and 800 K and their analysis,” J. Phys. C 5, 1046 (1972).
[CrossRef]

Yen, W. M.

H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti3+ doped sapphire,” Phys. Rev. B 45, 9604 (1992).
[CrossRef]

U. Hömmerich, H. Eilers, E. Strauss, and W. M. Yen, “Optically induced lensing effects in Nd3+-doped laser glass measured by photothermal beam-deflection spectroscopy,” Opt. Lett. 17, 213 (1992).
[CrossRef] [PubMed]

H. Eilers, F. Kieseling, E. Strauss, and W. M. Yen, “Photoelastic law explains optically induced changes in the index of refraction in Ti:Al2O3,” Ref. 3, p. 320.

Appl. Opt. (2)

Europhys. Lett. (1)

E. Strauss and S. Walder, “Photorefractive effect and observation of the matrix relaxation around photo-excited centres in condensed matter,” Europhys. Lett. 6, 713 (1988).
[CrossRef]

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

J. Phys. C (1)

B. Yates, R. F. Cooper, and A. F. Pojur, “Thermal expansion at elevated temperatures: II. Aluminum oxide: experimental data between 100 and 800 K and their analysis,” J. Phys. C 5, 1046 (1972).
[CrossRef]

Opt. Lett. (1)

Opt. News (1)

P. F. Moulton, Opt. News 8, 9 (1982).
[CrossRef]

Phys. Rev. B (2)

E. Strauss, “Bulk and local elastic relaxation around optically excited centers,” Phys. Rev. B 42, 1917 (1990).
[CrossRef]

H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti3+ doped sapphire,” Phys. Rev. B 45, 9604 (1992).
[CrossRef]

Other (7)

P. Hess and J. Pelzl, eds., Photoacoustic and Photothermal Phenomena, Springer Series in Optical Science (Springer-Verlag, Berlin, 1988).
[CrossRef]

J. C. Murphy, J. W. Maclachlan Spicer, L. C. Aamodt, and B. S. H. Royce, eds., Photoacoustic and Photothermal Phenomena, Springer Series in Optical Science (Springer-Verlag, Berlin, 1990).
[CrossRef]

D. Bicanic, ed., Photoacoustic and Photothermal Phenomena III, Springer Series in Optical Science (Springer-Verlag, Berlin, 1992).
[CrossRef]

H. Eilers, F. Kieseling, E. Strauss, and W. M. Yen, “Photoelastic law explains optically induced changes in the index of refraction in Ti:Al2O3,” Ref. 3, p. 320.

T. S. Narasimhamurty, Photoelastic and Electro-Optic Properties of Crystals (Plenum Press, New York, 1981).
[CrossRef]

Y. S. Touloukian and C. Y. Ho, eds., Thermal Conductivity, Vol. 2 of TPRC Data Series (IFI/Plenum, New York, 1970) p. 97.

K. Schäfer and E. Lax, eds., Landolt-Börnstein, Zahlenwerke aus Naturwissenschaft und Technik (Springer-Verlag, Berlin, 1961), Vol. II/4, p. 495.

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Figures (4)

Fig. 1
Fig. 1

The experimental setup for the beam-defection experiments. For more details see Refs. 6 and 9. L1, L2, lenses; M, mirror; IF, interference filter; D, position-sensitive detector; DA, difference amplifier; DSO, digital storage oscilloscope; BD, beam dump, and PC, computer.

Fig. 2
Fig. 2

Beam deflection signal at T = 293 K.

Fig. 3
Fig. 3

Beam-deflection signal at T = 40 K.

Fig. 4
Fig. 4

Simulated behavior of the thermal part of Eq. (2) for different values of the thermal diffusivity D (in units of μm2/μs).

Tables (1)

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Table 1 Values for k,15 cp,14 and the calculated D valuesa

Equations (2)

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d n d T = n T + d n d T | exp .
H ( t ) = { H f + H s [ 1 - exp ( - t / τ ) } 2 r ( σ 2 + 4 D t ) 2 × exp [ - r 2 / ( σ 2 + 4 D t ) ] N + C exp ( - t / τ ) ,

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