Abstract

The finite-size effect on the thermal mirror (TM) experiments is described. The time-resolved thermoelastic deformation equation is solved and compared to the semi-infinite solution. To determine the applicability of the semi-infinite model, experiments were performed in optical glasses and the quantitative results compared to both models. The analytical results presented here were found to be in excellent agreement with the numerical finite elemental analysis model. Modeling and experiment showed that the TM transient signal is strongly affected as the sample thickness is reduced. The results of the finite-size model demonstrate that it is intrinsically more accurate to characterize physical properties of low optical absorption thin samples, which suggests that the model and the TM method could even be applied to study very thin films down to the micrometer scale.

© 2011 Optical Society of America

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  1. S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).
  2. A.Mandelis, ed., Progress in Photoacoustic and Photothermal Science and Technology (Elsevier, 1991).
  3. D. P. Almond and P. M. Patel, Photothermal Science and Techniques (Chapman and Hall, 1996).
  4. M. A. Olmstead, N. M. Amer, and S. Kohn, “Photothermal displacement spectroscopy—an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
    [CrossRef]
  5. P. Kuo and M. Munidasa, “Single-beam interferometry of a thermal bump,” Appl. Opt. 29, 5326–5331 (1990).
    [CrossRef] [PubMed]
  6. J. Cheng and S. Zhang, “3-dimensional theory to study photothermal phenomena of semiconductors. 1. Modulated optical reflectance,” J. Appl. Phys. 70, 6999–7006 (1991).
    [CrossRef]
  7. B. C. Li, Z. Zhen, and S. He, “Modulated photothermal deformation in solids,” J. Phys. D: Appl. Phys. 24, 2196–2201 (1991).
    [CrossRef]
  8. P. S. Jeon, J. H. Kim, H. J. Kim, and J. Yoo, “The measurement of thermal diffusivities for semi-infinite solids using the photothermal displacement method,” Thermochim. Acta 494, 65–70(2009).
    [CrossRef]
  9. D. Albagli, M. Dark, C. von Rosenberg, L. Perelman, I. Itzkan, and M. S. Feld, “Laser-induced thermoelastic deformation—a 3-dimensional solution and its application to the ablation of biological tissue,” Med. Phys. 21, 1323–1331 (1994).
    [CrossRef] [PubMed]
  10. T. Elperin and G. Rudin, “Thermal mirror method for measuring physical properties of multilayered coatings,” Int. J. Thermophys. 28, 60–82 (2007).
    [CrossRef]
  11. J. W. Fang and S. Y. Zhang, “Modeling for laser-induced surface thermal lens in semiconductors,” Appl. Phys. B 67, 633–639(1998).
    [CrossRef]
  12. J. C. Cheng, L. Wu, and S. Y. Zhang, “Thermoelastic response of pulsed photothermal deformation of thin plates,” J. Appl. Phys. 76, 716–722 (1994).
    [CrossRef]
  13. G. L. Bennis, R. Vyas, R. Gupta, S. Ang, and W. D. Brown, “Thermal diffusivity measurement of solid materials by the pulsed photothermal displacement technique,” J. Appl. Phys. 84, 3602–3610 (1998).
    [CrossRef]
  14. B. C. Li, “Three-dimensional theory of pulsed photothermal deformation,” J. Appl. Phys. 68, 482–487 (1990).
    [CrossRef]
  15. N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
    [CrossRef]
  16. L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
    [CrossRef]
  17. F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
    [CrossRef]
  18. F. B. G. Astrath, N. G. C. Astrath, J. Shen, J. Zhou, L. C. Malacarne, P. R. B. Pedreira, and M. L. Baesso, “Time-resolved thermal mirror technique with top-hat cw laser excitation,” Opt. Express 16, 12214–12219 (2008).
    [CrossRef] [PubMed]
  19. N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
    [CrossRef]
  20. W. Nowacki, Thermoelasticity (Pergamon, 1982).
  21. L. C. Malacarne, N. G. C. Astrath, G. V. B. Lukasievicz, E. K. Lenzi, M. L. Baesso, and S. E. Bialkowski, “Time-resolved thermal lens and thermal mirror spectroscopy with sample-fluid heat coupling: a complete model for material characterization,” Appl. Spectrosc. 65, 99–104(2011).
    [CrossRef] [PubMed]

2011 (1)

2009 (2)

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

P. S. Jeon, J. H. Kim, H. J. Kim, and J. Yoo, “The measurement of thermal diffusivities for semi-infinite solids using the photothermal displacement method,” Thermochim. Acta 494, 65–70(2009).
[CrossRef]

2008 (3)

L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
[CrossRef]

F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

F. B. G. Astrath, N. G. C. Astrath, J. Shen, J. Zhou, L. C. Malacarne, P. R. B. Pedreira, and M. L. Baesso, “Time-resolved thermal mirror technique with top-hat cw laser excitation,” Opt. Express 16, 12214–12219 (2008).
[CrossRef] [PubMed]

2007 (2)

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

T. Elperin and G. Rudin, “Thermal mirror method for measuring physical properties of multilayered coatings,” Int. J. Thermophys. 28, 60–82 (2007).
[CrossRef]

1998 (2)

J. W. Fang and S. Y. Zhang, “Modeling for laser-induced surface thermal lens in semiconductors,” Appl. Phys. B 67, 633–639(1998).
[CrossRef]

G. L. Bennis, R. Vyas, R. Gupta, S. Ang, and W. D. Brown, “Thermal diffusivity measurement of solid materials by the pulsed photothermal displacement technique,” J. Appl. Phys. 84, 3602–3610 (1998).
[CrossRef]

1994 (2)

J. C. Cheng, L. Wu, and S. Y. Zhang, “Thermoelastic response of pulsed photothermal deformation of thin plates,” J. Appl. Phys. 76, 716–722 (1994).
[CrossRef]

D. Albagli, M. Dark, C. von Rosenberg, L. Perelman, I. Itzkan, and M. S. Feld, “Laser-induced thermoelastic deformation—a 3-dimensional solution and its application to the ablation of biological tissue,” Med. Phys. 21, 1323–1331 (1994).
[CrossRef] [PubMed]

1991 (2)

J. Cheng and S. Zhang, “3-dimensional theory to study photothermal phenomena of semiconductors. 1. Modulated optical reflectance,” J. Appl. Phys. 70, 6999–7006 (1991).
[CrossRef]

B. C. Li, Z. Zhen, and S. He, “Modulated photothermal deformation in solids,” J. Phys. D: Appl. Phys. 24, 2196–2201 (1991).
[CrossRef]

1990 (2)

B. C. Li, “Three-dimensional theory of pulsed photothermal deformation,” J. Appl. Phys. 68, 482–487 (1990).
[CrossRef]

P. Kuo and M. Munidasa, “Single-beam interferometry of a thermal bump,” Appl. Opt. 29, 5326–5331 (1990).
[CrossRef] [PubMed]

1983 (1)

M. A. Olmstead, N. M. Amer, and S. Kohn, “Photothermal displacement spectroscopy—an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Albagli, D.

D. Albagli, M. Dark, C. von Rosenberg, L. Perelman, I. Itzkan, and M. S. Feld, “Laser-induced thermoelastic deformation—a 3-dimensional solution and its application to the ablation of biological tissue,” Med. Phys. 21, 1323–1331 (1994).
[CrossRef] [PubMed]

Almond, D. P.

D. P. Almond and P. M. Patel, Photothermal Science and Techniques (Chapman and Hall, 1996).

Amer, N. M.

M. A. Olmstead, N. M. Amer, and S. Kohn, “Photothermal displacement spectroscopy—an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Ang, S.

G. L. Bennis, R. Vyas, R. Gupta, S. Ang, and W. D. Brown, “Thermal diffusivity measurement of solid materials by the pulsed photothermal displacement technique,” J. Appl. Phys. 84, 3602–3610 (1998).
[CrossRef]

Astrath, F. B. G.

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

F. B. G. Astrath, N. G. C. Astrath, J. Shen, J. Zhou, L. C. Malacarne, P. R. B. Pedreira, and M. L. Baesso, “Time-resolved thermal mirror technique with top-hat cw laser excitation,” Opt. Express 16, 12214–12219 (2008).
[CrossRef] [PubMed]

Astrath, N. G. C.

L. C. Malacarne, N. G. C. Astrath, G. V. B. Lukasievicz, E. K. Lenzi, M. L. Baesso, and S. E. Bialkowski, “Time-resolved thermal lens and thermal mirror spectroscopy with sample-fluid heat coupling: a complete model for material characterization,” Appl. Spectrosc. 65, 99–104(2011).
[CrossRef] [PubMed]

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

F. B. G. Astrath, N. G. C. Astrath, J. Shen, J. Zhou, L. C. Malacarne, P. R. B. Pedreira, and M. L. Baesso, “Time-resolved thermal mirror technique with top-hat cw laser excitation,” Opt. Express 16, 12214–12219 (2008).
[CrossRef] [PubMed]

F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
[CrossRef]

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

Baesso, M. L.

L. C. Malacarne, N. G. C. Astrath, G. V. B. Lukasievicz, E. K. Lenzi, M. L. Baesso, and S. E. Bialkowski, “Time-resolved thermal lens and thermal mirror spectroscopy with sample-fluid heat coupling: a complete model for material characterization,” Appl. Spectrosc. 65, 99–104(2011).
[CrossRef] [PubMed]

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

F. B. G. Astrath, N. G. C. Astrath, J. Shen, J. Zhou, L. C. Malacarne, P. R. B. Pedreira, and M. L. Baesso, “Time-resolved thermal mirror technique with top-hat cw laser excitation,” Opt. Express 16, 12214–12219 (2008).
[CrossRef] [PubMed]

F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
[CrossRef]

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

Belancon, M. P.

F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

Bennis, G. L.

G. L. Bennis, R. Vyas, R. Gupta, S. Ang, and W. D. Brown, “Thermal diffusivity measurement of solid materials by the pulsed photothermal displacement technique,” J. Appl. Phys. 84, 3602–3610 (1998).
[CrossRef]

Bento, A. C.

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
[CrossRef]

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

Bialkowski, S. E.

Brown, W. D.

G. L. Bennis, R. Vyas, R. Gupta, S. Ang, and W. D. Brown, “Thermal diffusivity measurement of solid materials by the pulsed photothermal displacement technique,” J. Appl. Phys. 84, 3602–3610 (1998).
[CrossRef]

Cheng, J.

J. Cheng and S. Zhang, “3-dimensional theory to study photothermal phenomena of semiconductors. 1. Modulated optical reflectance,” J. Appl. Phys. 70, 6999–7006 (1991).
[CrossRef]

Cheng, J. C.

J. C. Cheng, L. Wu, and S. Y. Zhang, “Thermoelastic response of pulsed photothermal deformation of thin plates,” J. Appl. Phys. 76, 716–722 (1994).
[CrossRef]

Dark, M.

D. Albagli, M. Dark, C. von Rosenberg, L. Perelman, I. Itzkan, and M. S. Feld, “Laser-induced thermoelastic deformation—a 3-dimensional solution and its application to the ablation of biological tissue,” Med. Phys. 21, 1323–1331 (1994).
[CrossRef] [PubMed]

Elperin, T.

T. Elperin and G. Rudin, “Thermal mirror method for measuring physical properties of multilayered coatings,” Int. J. Thermophys. 28, 60–82 (2007).
[CrossRef]

Fang, J. W.

J. W. Fang and S. Y. Zhang, “Modeling for laser-induced surface thermal lens in semiconductors,” Appl. Phys. B 67, 633–639(1998).
[CrossRef]

Feld, M. S.

D. Albagli, M. Dark, C. von Rosenberg, L. Perelman, I. Itzkan, and M. S. Feld, “Laser-induced thermoelastic deformation—a 3-dimensional solution and its application to the ablation of biological tissue,” Med. Phys. 21, 1323–1331 (1994).
[CrossRef] [PubMed]

Gu, C. E.

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

Gupta, R.

G. L. Bennis, R. Vyas, R. Gupta, S. Ang, and W. D. Brown, “Thermal diffusivity measurement of solid materials by the pulsed photothermal displacement technique,” J. Appl. Phys. 84, 3602–3610 (1998).
[CrossRef]

He, S.

B. C. Li, Z. Zhen, and S. He, “Modulated photothermal deformation in solids,” J. Phys. D: Appl. Phys. 24, 2196–2201 (1991).
[CrossRef]

Itzkan, I.

D. Albagli, M. Dark, C. von Rosenberg, L. Perelman, I. Itzkan, and M. S. Feld, “Laser-induced thermoelastic deformation—a 3-dimensional solution and its application to the ablation of biological tissue,” Med. Phys. 21, 1323–1331 (1994).
[CrossRef] [PubMed]

Jeon, P. S.

P. S. Jeon, J. H. Kim, H. J. Kim, and J. Yoo, “The measurement of thermal diffusivities for semi-infinite solids using the photothermal displacement method,” Thermochim. Acta 494, 65–70(2009).
[CrossRef]

Kim, H. J.

P. S. Jeon, J. H. Kim, H. J. Kim, and J. Yoo, “The measurement of thermal diffusivities for semi-infinite solids using the photothermal displacement method,” Thermochim. Acta 494, 65–70(2009).
[CrossRef]

Kim, J. H.

P. S. Jeon, J. H. Kim, H. J. Kim, and J. Yoo, “The measurement of thermal diffusivities for semi-infinite solids using the photothermal displacement method,” Thermochim. Acta 494, 65–70(2009).
[CrossRef]

Kohn, S.

M. A. Olmstead, N. M. Amer, and S. Kohn, “Photothermal displacement spectroscopy—an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Kuo, P.

Lenzi, E. K.

Li, B. C.

B. C. Li, Z. Zhen, and S. He, “Modulated photothermal deformation in solids,” J. Phys. D: Appl. Phys. 24, 2196–2201 (1991).
[CrossRef]

B. C. Li, “Three-dimensional theory of pulsed photothermal deformation,” J. Appl. Phys. 68, 482–487 (1990).
[CrossRef]

Lukasievicz, G. V. B.

Malacarne, L. C.

L. C. Malacarne, N. G. C. Astrath, G. V. B. Lukasievicz, E. K. Lenzi, M. L. Baesso, and S. E. Bialkowski, “Time-resolved thermal lens and thermal mirror spectroscopy with sample-fluid heat coupling: a complete model for material characterization,” Appl. Spectrosc. 65, 99–104(2011).
[CrossRef] [PubMed]

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

F. B. G. Astrath, N. G. C. Astrath, J. Shen, J. Zhou, L. C. Malacarne, P. R. B. Pedreira, and M. L. Baesso, “Time-resolved thermal mirror technique with top-hat cw laser excitation,” Opt. Express 16, 12214–12219 (2008).
[CrossRef] [PubMed]

F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
[CrossRef]

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

Mendes, R. S.

L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
[CrossRef]

F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

Munidasa, M.

Nowacki, W.

W. Nowacki, Thermoelasticity (Pergamon, 1982).

Olmstead, M. A.

M. A. Olmstead, N. M. Amer, and S. Kohn, “Photothermal displacement spectroscopy—an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Patel, P. M.

D. P. Almond and P. M. Patel, Photothermal Science and Techniques (Chapman and Hall, 1996).

Pedreira, P. R. B.

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

F. B. G. Astrath, N. G. C. Astrath, J. Shen, J. Zhou, L. C. Malacarne, P. R. B. Pedreira, and M. L. Baesso, “Time-resolved thermal mirror technique with top-hat cw laser excitation,” Opt. Express 16, 12214–12219 (2008).
[CrossRef] [PubMed]

F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
[CrossRef]

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

Perelman, L.

D. Albagli, M. Dark, C. von Rosenberg, L. Perelman, I. Itzkan, and M. S. Feld, “Laser-induced thermoelastic deformation—a 3-dimensional solution and its application to the ablation of biological tissue,” Med. Phys. 21, 1323–1331 (1994).
[CrossRef] [PubMed]

Rudin, G.

T. Elperin and G. Rudin, “Thermal mirror method for measuring physical properties of multilayered coatings,” Int. J. Thermophys. 28, 60–82 (2007).
[CrossRef]

Sato, F.

L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
[CrossRef]

F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

Shen, J.

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

F. B. G. Astrath, N. G. C. Astrath, J. Shen, J. Zhou, L. C. Malacarne, P. R. B. Pedreira, and M. L. Baesso, “Time-resolved thermal mirror technique with top-hat cw laser excitation,” Opt. Express 16, 12214–12219 (2008).
[CrossRef] [PubMed]

F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
[CrossRef]

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

von Rosenberg, C.

D. Albagli, M. Dark, C. von Rosenberg, L. Perelman, I. Itzkan, and M. S. Feld, “Laser-induced thermoelastic deformation—a 3-dimensional solution and its application to the ablation of biological tissue,” Med. Phys. 21, 1323–1331 (1994).
[CrossRef] [PubMed]

Vyas, R.

G. L. Bennis, R. Vyas, R. Gupta, S. Ang, and W. D. Brown, “Thermal diffusivity measurement of solid materials by the pulsed photothermal displacement technique,” J. Appl. Phys. 84, 3602–3610 (1998).
[CrossRef]

Wu, L.

J. C. Cheng, L. Wu, and S. Y. Zhang, “Thermoelastic response of pulsed photothermal deformation of thin plates,” J. Appl. Phys. 76, 716–722 (1994).
[CrossRef]

Yoo, J.

P. S. Jeon, J. H. Kim, H. J. Kim, and J. Yoo, “The measurement of thermal diffusivities for semi-infinite solids using the photothermal displacement method,” Thermochim. Acta 494, 65–70(2009).
[CrossRef]

Zhang, S.

J. Cheng and S. Zhang, “3-dimensional theory to study photothermal phenomena of semiconductors. 1. Modulated optical reflectance,” J. Appl. Phys. 70, 6999–7006 (1991).
[CrossRef]

Zhang, S. Y.

J. W. Fang and S. Y. Zhang, “Modeling for laser-induced surface thermal lens in semiconductors,” Appl. Phys. B 67, 633–639(1998).
[CrossRef]

J. C. Cheng, L. Wu, and S. Y. Zhang, “Thermoelastic response of pulsed photothermal deformation of thin plates,” J. Appl. Phys. 76, 716–722 (1994).
[CrossRef]

Zhen, Z.

B. C. Li, Z. Zhen, and S. He, “Modulated photothermal deformation in solids,” J. Phys. D: Appl. Phys. 24, 2196–2201 (1991).
[CrossRef]

Zhou, J.

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

F. B. G. Astrath, N. G. C. Astrath, J. Shen, J. Zhou, L. C. Malacarne, P. R. B. Pedreira, and M. L. Baesso, “Time-resolved thermal mirror technique with top-hat cw laser excitation,” Opt. Express 16, 12214–12219 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. A (1)

M. A. Olmstead, N. M. Amer, and S. Kohn, “Photothermal displacement spectroscopy—an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Appl. Phys. B (2)

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, C. E. Gu, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, and M. L. Baesso, “Top-hat cw laser induced thermal mirror: a complete model for material characterization,” Appl. Phys. B 94, 473–481(2009).
[CrossRef]

J. W. Fang and S. Y. Zhang, “Modeling for laser-induced surface thermal lens in semiconductors,” Appl. Phys. B 67, 633–639(1998).
[CrossRef]

Appl. Phys. Lett. (2)

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

L. C. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bento, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror,” Appl. Phys. Lett. 92, 131903(2008).
[CrossRef]

Appl. Spectrosc. (1)

Int. J. Thermophys. (1)

T. Elperin and G. Rudin, “Thermal mirror method for measuring physical properties of multilayered coatings,” Int. J. Thermophys. 28, 60–82 (2007).
[CrossRef]

J. Appl. Phys. (5)

J. Cheng and S. Zhang, “3-dimensional theory to study photothermal phenomena of semiconductors. 1. Modulated optical reflectance,” J. Appl. Phys. 70, 6999–7006 (1991).
[CrossRef]

J. C. Cheng, L. Wu, and S. Y. Zhang, “Thermoelastic response of pulsed photothermal deformation of thin plates,” J. Appl. Phys. 76, 716–722 (1994).
[CrossRef]

G. L. Bennis, R. Vyas, R. Gupta, S. Ang, and W. D. Brown, “Thermal diffusivity measurement of solid materials by the pulsed photothermal displacement technique,” J. Appl. Phys. 84, 3602–3610 (1998).
[CrossRef]

B. C. Li, “Three-dimensional theory of pulsed photothermal deformation,” J. Appl. Phys. 68, 482–487 (1990).
[CrossRef]

F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M. L. Baesso, N. G. C. Astrath, and J. Shen, “Time-resolved thermal mirror method: a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

B. C. Li, Z. Zhen, and S. He, “Modulated photothermal deformation in solids,” J. Phys. D: Appl. Phys. 24, 2196–2201 (1991).
[CrossRef]

Med. Phys. (1)

D. Albagli, M. Dark, C. von Rosenberg, L. Perelman, I. Itzkan, and M. S. Feld, “Laser-induced thermoelastic deformation—a 3-dimensional solution and its application to the ablation of biological tissue,” Med. Phys. 21, 1323–1331 (1994).
[CrossRef] [PubMed]

Opt. Express (1)

Thermochim. Acta (1)

P. S. Jeon, J. H. Kim, H. J. Kim, and J. Yoo, “The measurement of thermal diffusivities for semi-infinite solids using the photothermal displacement method,” Thermochim. Acta 494, 65–70(2009).
[CrossRef]

Other (4)

W. Nowacki, Thermoelasticity (Pergamon, 1982).

S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).

A.Mandelis, ed., Progress in Photoacoustic and Photothermal Science and Technology (Elsevier, 1991).

D. P. Almond and P. M. Patel, Photothermal Science and Techniques (Chapman and Hall, 1996).

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Figures (4)

Fig. 1
Fig. 1

Displacement profile for a standard glass [21] at t = 200 ms using the finite model for different sample thicknesses (solid curves) and the FEA (open circles). Dashed curve represents the semi-infinite solution.

Fig. 2
Fig. 2

Simulated TM signal for a standard glass and different thicknesses using the finite model. The inset shows the divergence between the parameters θ TM and D used to simulate the TM finite model curves and the ones obtained fitting with the semi-infinite model.

Fig. 3
Fig. 3

(a) Normalized TM signal, I ( t ) / I ( 0 ) , for glass samples; λ p = 632.8 nm , λ ex = 488 nm , and P e = 550 mW . Solid curves represent the theoretical fits using Eq. (10). (b) Thermal diffusivity and (c)  θ TM as a function of the excitation power. The parameters were obtained fitting the experimental transients to the semi-infinite and finite models.

Fig. 4
Fig. 4

Steady-state TM signal, [ I ( 0 ) I ( ) ] / I ( 0 ) , as function of P e and l. The parameters used in this simulation are listed in Fig. 3, and θ TM / P e = 660 W 1 m 1 .

Equations (11)

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2 Ψ ( r , z , t ) = 1 + ν 1 ν α T T ( r , z , t ) ,
2 2 ψ ( r , z , t ) = 0.
u i ( r , z , t ) = i Ψ ( r , z , t ) + 1 1 2 ν [ 2 ( 1 ν ) δ z i 2 z i ] ψ ( r , z , t ) ,
σ i j = 2 μ [ i j δ i j 2 ] Ψ ( r , z , t ) + 2 μ 1 2 ν [ z ( ν δ i j 2 i j ) + ( 1 ν ) 2 ( δ i z j + δ j z i ) ] ψ ( r , z , t ) ,
Ψ ( r , z , t ) = 1 + ν 1 ν α T 2 π 0 0 T ( α , λ , t ) ( α 2 + λ 2 ) Cos ( λ ) J 0 ( α r ) α d α d λ ,
ψ ( r , z , t ) = 0 [ ( A + α z B ) e α z + ( F + α z G ) e α z ] α 2 J 0 ( α r ) d α ,
u z ( r , 0 , t ) = 0 2 α T ( 1 + ν ) α 2 ϑ ( α , t ) J 0 ( α r ) 1 + 2 l 2 α 2 Cosh ( 2 l α ) d α ,
ϑ ( α , t ) = 2 π 0 T ( α , λ , t ) ( α 2 + λ 2 ) { [ 2 l α + Sinh ( 2 l α ) ] 2 [ l α Cosh ( l α ) + Sinh ( l α ) ] Cos ( λ l ) [ 2 l Sinh ( l α ) ] λ Sin ( λ l ) } d λ .
T ( α , λ , t ) = 2 π Q 0 c ρ δ ( λ ) ω 2 4 e ω 2 α 2 8 0 t e D α 2 τ d τ .
u z ( g , 0 , t ) = θ TM λ p 4 π ω 2 t c 0 Cosh ( l α ) - 1 l α + Sinh ( l α ) ( 0 t e ω 2 8 ( 1 + 2 τ t c ) α 2 d τ ) J 0 ( α ω m g ) d α .
U ( Z 1 + Z 2 , t ) = C 0 e ( 1 + i V ) g i ϕ TM ( g , t ) d g ,

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