Abstract

A simple method for optically measuring the thermal diffusivity of solids is demonstrated. The thermal displacement created on a substrate by a focused laser beam is determined from the divergence that it induces in a weak probe beam. The dynamics of the surface lens and the amplitude of the probe beam’s divergence are then used to determine the thermal diffusivity of the substrate. Several materials that span a wide range of thermal properties are studied.

© 2004 Optical Society of America

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References

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  1. M. C. Gupta, S. D. Hong, A. Gupta, J. Moacanin, “Thermal diffusivity measurements using a pulsed dual-beam thermal lens technique,” Appl. Phys. Lett. 37, 505–507 (1980).
    [CrossRef]
  2. A. Marcano, C. Loper, N. Melikechi, “High-sensitivity absorption measurement in water and glass samples using a mode-mismatched pump-probe thermal lens method,” Appl. Phys. Lett. 78, 3415–3417 (2001).
    [CrossRef]
  3. G. T. Fraser, A. S. Pine, W. J. Lafferty, R. E. Miller, “Sub-Doppler infrared spectrum of the carbon dioxide trimer,” J. Chem. Phys. 87, 1502–1508 (1987).
    [CrossRef]
  4. J. Shen, M. L. Baesso, R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
    [CrossRef]
  5. J. Shen, A. J. Soroka, D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry based on probe beam profile image detection,” J. Appl. Phys. 78, 700–708 (1995).
    [CrossRef]
  6. S. S. Gupte, A. Marcano, R. D. Pradhan, C. F. Desai, N. Melikechi, “Pump-probe thermal lens near-infrared spectroscopy and Z-scan study of zinc (tris)thiourea sulfate,” J. Appl. Phys. 89, 4939–4943 (2001).
    [CrossRef]
  7. M. Terazima, T. Azumi, “Observation of transient absorption by using the thermal lens method,” Appl. Phys. Lett. 54, 2398–2399 (1989).
    [CrossRef]
  8. D. Comeau, A. Haché, N. Melikechi, “Reflective thermal lensing and optical measurement of thermal diffusivity in liquids,” Appl. Phys. Lett. 83, 246–248 (2003).
    [CrossRef]

2003 (1)

D. Comeau, A. Haché, N. Melikechi, “Reflective thermal lensing and optical measurement of thermal diffusivity in liquids,” Appl. Phys. Lett. 83, 246–248 (2003).
[CrossRef]

2001 (2)

S. S. Gupte, A. Marcano, R. D. Pradhan, C. F. Desai, N. Melikechi, “Pump-probe thermal lens near-infrared spectroscopy and Z-scan study of zinc (tris)thiourea sulfate,” J. Appl. Phys. 89, 4939–4943 (2001).
[CrossRef]

A. Marcano, C. Loper, N. Melikechi, “High-sensitivity absorption measurement in water and glass samples using a mode-mismatched pump-probe thermal lens method,” Appl. Phys. Lett. 78, 3415–3417 (2001).
[CrossRef]

1995 (1)

J. Shen, A. J. Soroka, D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry based on probe beam profile image detection,” J. Appl. Phys. 78, 700–708 (1995).
[CrossRef]

1994 (1)

J. Shen, M. L. Baesso, R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
[CrossRef]

1989 (1)

M. Terazima, T. Azumi, “Observation of transient absorption by using the thermal lens method,” Appl. Phys. Lett. 54, 2398–2399 (1989).
[CrossRef]

1987 (1)

G. T. Fraser, A. S. Pine, W. J. Lafferty, R. E. Miller, “Sub-Doppler infrared spectrum of the carbon dioxide trimer,” J. Chem. Phys. 87, 1502–1508 (1987).
[CrossRef]

1980 (1)

M. C. Gupta, S. D. Hong, A. Gupta, J. Moacanin, “Thermal diffusivity measurements using a pulsed dual-beam thermal lens technique,” Appl. Phys. Lett. 37, 505–507 (1980).
[CrossRef]

Azumi, T.

M. Terazima, T. Azumi, “Observation of transient absorption by using the thermal lens method,” Appl. Phys. Lett. 54, 2398–2399 (1989).
[CrossRef]

Baesso, M. L.

J. Shen, M. L. Baesso, R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
[CrossRef]

Comeau, D.

D. Comeau, A. Haché, N. Melikechi, “Reflective thermal lensing and optical measurement of thermal diffusivity in liquids,” Appl. Phys. Lett. 83, 246–248 (2003).
[CrossRef]

Desai, C. F.

S. S. Gupte, A. Marcano, R. D. Pradhan, C. F. Desai, N. Melikechi, “Pump-probe thermal lens near-infrared spectroscopy and Z-scan study of zinc (tris)thiourea sulfate,” J. Appl. Phys. 89, 4939–4943 (2001).
[CrossRef]

Fraser, G. T.

G. T. Fraser, A. S. Pine, W. J. Lafferty, R. E. Miller, “Sub-Doppler infrared spectrum of the carbon dioxide trimer,” J. Chem. Phys. 87, 1502–1508 (1987).
[CrossRef]

Gupta, A.

M. C. Gupta, S. D. Hong, A. Gupta, J. Moacanin, “Thermal diffusivity measurements using a pulsed dual-beam thermal lens technique,” Appl. Phys. Lett. 37, 505–507 (1980).
[CrossRef]

Gupta, M. C.

M. C. Gupta, S. D. Hong, A. Gupta, J. Moacanin, “Thermal diffusivity measurements using a pulsed dual-beam thermal lens technique,” Appl. Phys. Lett. 37, 505–507 (1980).
[CrossRef]

Gupte, S. S.

S. S. Gupte, A. Marcano, R. D. Pradhan, C. F. Desai, N. Melikechi, “Pump-probe thermal lens near-infrared spectroscopy and Z-scan study of zinc (tris)thiourea sulfate,” J. Appl. Phys. 89, 4939–4943 (2001).
[CrossRef]

Haché, A.

D. Comeau, A. Haché, N. Melikechi, “Reflective thermal lensing and optical measurement of thermal diffusivity in liquids,” Appl. Phys. Lett. 83, 246–248 (2003).
[CrossRef]

Hong, S. D.

M. C. Gupta, S. D. Hong, A. Gupta, J. Moacanin, “Thermal diffusivity measurements using a pulsed dual-beam thermal lens technique,” Appl. Phys. Lett. 37, 505–507 (1980).
[CrossRef]

Lafferty, W. J.

G. T. Fraser, A. S. Pine, W. J. Lafferty, R. E. Miller, “Sub-Doppler infrared spectrum of the carbon dioxide trimer,” J. Chem. Phys. 87, 1502–1508 (1987).
[CrossRef]

Loper, C.

A. Marcano, C. Loper, N. Melikechi, “High-sensitivity absorption measurement in water and glass samples using a mode-mismatched pump-probe thermal lens method,” Appl. Phys. Lett. 78, 3415–3417 (2001).
[CrossRef]

Marcano, A.

A. Marcano, C. Loper, N. Melikechi, “High-sensitivity absorption measurement in water and glass samples using a mode-mismatched pump-probe thermal lens method,” Appl. Phys. Lett. 78, 3415–3417 (2001).
[CrossRef]

S. S. Gupte, A. Marcano, R. D. Pradhan, C. F. Desai, N. Melikechi, “Pump-probe thermal lens near-infrared spectroscopy and Z-scan study of zinc (tris)thiourea sulfate,” J. Appl. Phys. 89, 4939–4943 (2001).
[CrossRef]

Melikechi, N.

D. Comeau, A. Haché, N. Melikechi, “Reflective thermal lensing and optical measurement of thermal diffusivity in liquids,” Appl. Phys. Lett. 83, 246–248 (2003).
[CrossRef]

S. S. Gupte, A. Marcano, R. D. Pradhan, C. F. Desai, N. Melikechi, “Pump-probe thermal lens near-infrared spectroscopy and Z-scan study of zinc (tris)thiourea sulfate,” J. Appl. Phys. 89, 4939–4943 (2001).
[CrossRef]

A. Marcano, C. Loper, N. Melikechi, “High-sensitivity absorption measurement in water and glass samples using a mode-mismatched pump-probe thermal lens method,” Appl. Phys. Lett. 78, 3415–3417 (2001).
[CrossRef]

Miller, R. E.

G. T. Fraser, A. S. Pine, W. J. Lafferty, R. E. Miller, “Sub-Doppler infrared spectrum of the carbon dioxide trimer,” J. Chem. Phys. 87, 1502–1508 (1987).
[CrossRef]

Moacanin, J.

M. C. Gupta, S. D. Hong, A. Gupta, J. Moacanin, “Thermal diffusivity measurements using a pulsed dual-beam thermal lens technique,” Appl. Phys. Lett. 37, 505–507 (1980).
[CrossRef]

Pine, A. S.

G. T. Fraser, A. S. Pine, W. J. Lafferty, R. E. Miller, “Sub-Doppler infrared spectrum of the carbon dioxide trimer,” J. Chem. Phys. 87, 1502–1508 (1987).
[CrossRef]

Pradhan, R. D.

S. S. Gupte, A. Marcano, R. D. Pradhan, C. F. Desai, N. Melikechi, “Pump-probe thermal lens near-infrared spectroscopy and Z-scan study of zinc (tris)thiourea sulfate,” J. Appl. Phys. 89, 4939–4943 (2001).
[CrossRef]

Shen, J.

J. Shen, A. J. Soroka, D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry based on probe beam profile image detection,” J. Appl. Phys. 78, 700–708 (1995).
[CrossRef]

J. Shen, M. L. Baesso, R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
[CrossRef]

Snook, D.

J. Shen, A. J. Soroka, D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry based on probe beam profile image detection,” J. Appl. Phys. 78, 700–708 (1995).
[CrossRef]

Snook, R. D.

J. Shen, M. L. Baesso, R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
[CrossRef]

Soroka, A. J.

J. Shen, A. J. Soroka, D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry based on probe beam profile image detection,” J. Appl. Phys. 78, 700–708 (1995).
[CrossRef]

Terazima, M.

M. Terazima, T. Azumi, “Observation of transient absorption by using the thermal lens method,” Appl. Phys. Lett. 54, 2398–2399 (1989).
[CrossRef]

Appl. Phys. Lett. (4)

M. C. Gupta, S. D. Hong, A. Gupta, J. Moacanin, “Thermal diffusivity measurements using a pulsed dual-beam thermal lens technique,” Appl. Phys. Lett. 37, 505–507 (1980).
[CrossRef]

A. Marcano, C. Loper, N. Melikechi, “High-sensitivity absorption measurement in water and glass samples using a mode-mismatched pump-probe thermal lens method,” Appl. Phys. Lett. 78, 3415–3417 (2001).
[CrossRef]

M. Terazima, T. Azumi, “Observation of transient absorption by using the thermal lens method,” Appl. Phys. Lett. 54, 2398–2399 (1989).
[CrossRef]

D. Comeau, A. Haché, N. Melikechi, “Reflective thermal lensing and optical measurement of thermal diffusivity in liquids,” Appl. Phys. Lett. 83, 246–248 (2003).
[CrossRef]

J. Appl. Phys. (3)

J. Shen, M. L. Baesso, R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
[CrossRef]

J. Shen, A. J. Soroka, D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry based on probe beam profile image detection,” J. Appl. Phys. 78, 700–708 (1995).
[CrossRef]

S. S. Gupte, A. Marcano, R. D. Pradhan, C. F. Desai, N. Melikechi, “Pump-probe thermal lens near-infrared spectroscopy and Z-scan study of zinc (tris)thiourea sulfate,” J. Appl. Phys. 89, 4939–4943 (2001).
[CrossRef]

J. Chem. Phys. (1)

G. T. Fraser, A. S. Pine, W. J. Lafferty, R. E. Miller, “Sub-Doppler infrared spectrum of the carbon dioxide trimer,” J. Chem. Phys. 87, 1502–1508 (1987).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental layout. A strong heating beam (dashed lines) is modulated and focused onto a thin film deposited upon a substrate, creating a small thermal displacement. A weaker beam (solid lines) probes the surface at the same location; its phase front is deformed by the convexity of the bump.

Fig. 2
Fig. 2

Normalized, real-time signal of the probe beam power transmitted through a circular aperture over one full on-off cycle of the pump beam.

Fig. 3
Fig. 3

Real-time signal with a Ge substrate fitted to curves of the form T(t) = A + B exp(-Ct). Best fits give C parameters of 1.35 × 103 s-1 for the rise portion and 1.33 × 103 s-1 for the fall portion of the data.

Fig. 4
Fig. 4

Values of the C parameter (averaged for each instance of on and off) obtained from the best fit, as a function of thermal diffusivity of the sample material. Solid curve, quadratic fit that is usable as a calibration standard.

Fig. 5
Fig. 5

Amplitude modulation of the probe power transmitted through the circular aperture, measured by the lock-in amplifier, versus the thermal diffusivity of the substrate. The fitting curve has a logarithmic form.

Tables (1)

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Table 1 Physical Constants of the Substrate Materials Used in This Study

Equations (2)

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dTdt=Ht-δT-T0,
Tt=A+B exp-Ct,

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