Abstract

A frequency-resolved thermal lensing (TL) approach to measure thermal diffusivity properties of both diluted liquid solutions and silver nanoparticle colloidal suspensions is demonstrated. The experiment is based on a classical two-color pump–probe TL configuration, which is adapted to measure the induced TL signal as a function of the chopping frequency of the pump beam. Because of the thermal diffusivity lengths in the samples, the TL signal decreases exponentially with the increment of the frequency. The exponential decay factor can be associated with the thermal diffusivity of the medium. Measurements are performed on diluted liquid solutions and silver nanoparticles suspended in a PVP solution. A suitable fitting to a theoretical model based on the Fresnel diffraction approximation of the experimental data is obtained. This work demonstrates the feasibility of using this approach for the thermal characterization of nanoparticles in liquid solutions. Thermal diffusivity as low as 0.094×107m2s1 can be estimated by using this approach.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. J. Sheldon, L. V. Knight, and J. M. Thorne, Appl. Opt. 21, 1663 (1982).
    [CrossRef]
  2. M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, Appl. Phys. A 32, 141 (1983).
    [CrossRef]
  3. D. G. Cahill, Rev. Sci. Instrum. 75, 5119 (2004).
    [CrossRef]
  4. S. Doiron and A. Haché, Appl. Opt. 43, 4250 (2004).
    [CrossRef]
  5. J. C. Murphy and L. C. Aamodt, Appl. Phys. Lett. 38, 196 (1981).
    [CrossRef]
  6. J. Opsal, A. Rosenowaig, and D. L. Willenborg, Appl. Opt. 22, 3169 (1983).
    [CrossRef]
  7. J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
    [CrossRef]
  8. N. J. Dovichi and J. M. Harris, Anal. Chem. 51, 728 (1979).
    [CrossRef]
  9. J. Stone, J. Opt. Soc. Am. 62, 327 (1972).
    [CrossRef]
  10. J. Whinnery, D. Miller, and F. Dabby, IEEE J. Quantum Electron. 3, 382 (1967).
    [CrossRef]
  11. L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
    [CrossRef]
  12. D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
    [CrossRef]
  13. M. Selmke, M. Braun, and F. Cichos, Opt. Express 20, 8055 (2012).
    [CrossRef]

2013 (1)

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

2012 (1)

2004 (2)

D. G. Cahill, Rev. Sci. Instrum. 75, 5119 (2004).
[CrossRef]

S. Doiron and A. Haché, Appl. Opt. 43, 4250 (2004).
[CrossRef]

2003 (1)

D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
[CrossRef]

1992 (1)

J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
[CrossRef]

1983 (2)

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

J. Opsal, A. Rosenowaig, and D. L. Willenborg, Appl. Opt. 22, 3169 (1983).
[CrossRef]

1982 (1)

1981 (1)

J. C. Murphy and L. C. Aamodt, Appl. Phys. Lett. 38, 196 (1981).
[CrossRef]

1979 (1)

N. J. Dovichi and J. M. Harris, Anal. Chem. 51, 728 (1979).
[CrossRef]

1972 (1)

1967 (1)

J. Whinnery, D. Miller, and F. Dabby, IEEE J. Quantum Electron. 3, 382 (1967).
[CrossRef]

Aamodt, L. C.

J. C. Murphy and L. C. Aamodt, Appl. Phys. Lett. 38, 196 (1981).
[CrossRef]

Achete, C. A.

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Alves, A. P. P.

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Amer, N. M.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Anjos, V.

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Archanjo, B. S.

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Bell, M. J. V.

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Boccara, A. C.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Braun, M.

Cahill, D. G.

D. G. Cahill, Rev. Sci. Instrum. 75, 5119 (2004).
[CrossRef]

D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
[CrossRef]

Carvalho, E. A.

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Cichos, F.

Dabby, F.

J. Whinnery, D. Miller, and F. Dabby, IEEE J. Quantum Electron. 3, 382 (1967).
[CrossRef]

Doiron, S.

Dovichi, N. J.

N. J. Dovichi and J. M. Harris, Anal. Chem. 51, 728 (1979).
[CrossRef]

Ford, W. K.

D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
[CrossRef]

Fournier, D.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Fragneaud, B.

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Goodson, K. E.

D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
[CrossRef]

Haché, A.

Harris, J. M.

N. J. Dovichi and J. M. Harris, Anal. Chem. 51, 728 (1979).
[CrossRef]

Knight, L. V.

Kohn, S.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Lowe, R. D.

J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
[CrossRef]

Mahan, G. D.

D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
[CrossRef]

Majumdar, A.

D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
[CrossRef]

Maris, H. J.

D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
[CrossRef]

Merlin, R.

D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
[CrossRef]

Miller, D.

J. Whinnery, D. Miller, and F. Dabby, IEEE J. Quantum Electron. 3, 382 (1967).
[CrossRef]

Moreira, L. M.

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Murphy, J. C.

J. C. Murphy and L. C. Aamodt, Appl. Phys. Lett. 38, 196 (1981).
[CrossRef]

Olmstead, M. A.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Opsal, J.

Phillpot, S. R.

D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
[CrossRef]

Rosenowaig, A.

Sant’Ana, A. C.

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Selmke, M.

Sena, L. A.

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Sheldon, S. J.

Shen, J.

J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
[CrossRef]

Snook, R. D.

J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
[CrossRef]

Stone, J.

Thorne, J. M.

Whinnery, J.

J. Whinnery, D. Miller, and F. Dabby, IEEE J. Quantum Electron. 3, 382 (1967).
[CrossRef]

Willenborg, D. L.

Anal. Chem. (1)

N. J. Dovichi and J. M. Harris, Anal. Chem. 51, 728 (1979).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. A (1)

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Appl. Phys. Lett. (1)

J. C. Murphy and L. C. Aamodt, Appl. Phys. Lett. 38, 196 (1981).
[CrossRef]

Chem. Phys. (1)

J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Whinnery, D. Miller, and F. Dabby, IEEE J. Quantum Electron. 3, 382 (1967).
[CrossRef]

J. Appl. Phys. (1)

D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Therm. Anal. Calorim. (1)

L. M. Moreira, E. A. Carvalho, M. J. V. Bell, V. Anjos, A. C. Sant’Ana, A. P. P. Alves, B. Fragneaud, L. A. Sena, B. S. Archanjo, and C. A. Achete, J. Therm. Anal. Calorim. 114, 557 (2013).
[CrossRef]

Opt. Express (1)

Rev. Sci. Instrum. (1)

D. G. Cahill, Rev. Sci. Instrum. 75, 5119 (2004).
[CrossRef]

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 (4)

Fig. 1.
Fig. 1.

Experimental setup. The inset shows stationary signals for different chopping frequencies.

Fig. 2.
Fig. 2.

Absorbance spectra of PVPm, AgNPs and 0.5% samples.

Fig. 3.
Fig. 3.

Thermal distribution as a function of frequency from Eq. (2). The red line joins the points of maximum temperature rise which follows a thermal diffusive exponential decay.

Fig. 4.
Fig. 4.

Frequency-resolved PT measurements for selected samples. Solid lines are the fitting and red lines are the best fit ±10%. Note the vertical split range for better visualization of the different data sets.

Tables (1)

Tables Icon

Table 1. Summary of Experimental Results

Equations (6)

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

1rr(rΔTr)=1DΔTt+Qκ,
ΔT(r,ω)=A0η2πκ0exp(k2w02/8)k2+jω/DJ0(kr)kdk.
ϕ=(2πL/λ)(dn/dT)ΔT(r,ω),
U=C0(1jϕ)exp[(1+jV)r2/w12]rdr/w12,
U(ω,ϕ0)=Cw120exp[(1+jV)r2/w12]rdr+jϕ0C2πw1200exp(k2w02/8)(k2+jω/D)J0(kr)e(1+jV)r2/w12rdrkdk,
U(ω,ϕ0)=2πC{1+jϕ04πexp[jω(w02+2w12)/8D]E1[jω(w02+2w12)/8D]}.

Metrics