Abstract

We developed the theoretical model of the time-resolved thermal lens spectroscopy of a single particle with various pulse shape optical excitations. To account for the pulse shape optical excitation in the model, a heat diffusion equation of two media (the particle and liquid solvent) is solved using the numerical Laplace transform method. The model also incorporates the propagation of a diffracted Gaussian probe beam due to the thermal lens effect. Numerical results are presented to illustrate the effects of the excitation pulse shape and probe beam size on the evolution of the photothermal lens signal. The developed model is utilized for the thermal diffusivity and size extraction of a red polystyrene particle.

© 2010 Optical Society of America

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  1. C. V. Bindhu, S. S. Harihal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Thermal diffusivity measurements in organic liquids using transient thermal lens calorimetry,” Opt. Eng. 37, 2791-2794 (1998).
    [CrossRef]
  2. A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
    [CrossRef]
  3. S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry,” Phys. Rev. B 60, 15173-15178 (1999).
    [CrossRef]
  4. V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
    [CrossRef]
  5. D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nano-meter sized metal particles among scatterers,” Science 297, 1160-1163 (2002).
    [CrossRef] [PubMed]
  6. D. Lapotko, A. Shnip, and E. Lukianova, “Photothermal responses of individual cells,” J. Biomed. Opt. 10, 014006 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. D. Lapotko, T. Romanovskaya, and E. Gordiyko, “Photothermal monitoring of redox state of respiratory chain in single live cells,” Photochem. Photobiol. 75, 519-526 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. A. Marcano, L. Rodriguez, and Y. Alvarado, “Mode-mismatched thermal lens experiment in the pulse regime,” J. Opt. A, Pure Appl. Opt. 5, S256-S261 (2003).
    [CrossRef]
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    [CrossRef]
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  21. R. R. Letfullin, C. Joenathan, T. F. George, and V. P. Zharov, “Laser-induced explosion for gold nanoparticles: potential role for nanophotothermolysis of cancer,” Nanomedicine 1, 473-480 (2006).
    [CrossRef]
  22. K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, and T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316-5322 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
  26. L. Prod'homme, “A new approach to the thermal change in the refractive index of glasses,” Phys. Chem. Glasses 1, 119-122 (1962).
  27. M. L. Baesso, J. Shen, and R. D. Snook, “Mode-mismatched thermal lens determination of temperature coefficient optical path length in soda lime at different wavelengths,” J. Appl. Phys. 75, 3732-3737 (1994).
    [CrossRef]
  28. A. Tuntomo, C. L. Tien, and S. H. Park, “Internal distribution of radiant absorption in a spherical particle,” J. Heat Transfer 113, 407-412 (1991).
    [CrossRef]

2008 (1)

2006 (1)

R. R. Letfullin, C. Joenathan, T. F. George, and V. P. Zharov, “Laser-induced explosion for gold nanoparticles: potential role for nanophotothermolysis of cancer,” Nanomedicine 1, 473-480 (2006).
[CrossRef]

2005 (4)

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

D. Lapotko, A. Shnip, and E. Lukianova, “Photothermal responses of individual cells,” J. Biomed. Opt. 10, 014006 (2005).
[CrossRef]

D. A. Nedosekin, M. A. Proskurnin, and M. Y. Kononets, “Model for continuous-wave laser-induced thermal lens spectrometry of optically transparent surface-absorbing solids,” Appl. Opt. 44, 6296-6306 (2005).
[CrossRef] [PubMed]

D. Lapotko and V. P. Zharov, “Spectral evaluation of laser-induced cell damage with photothermal microscopy,” Lasers Surg. Med. 36, 22-30 (2005).
[CrossRef] [PubMed]

2004 (2)

R. Roscuni, L. Isa, and R. Piazza, “Thermal lensing measurement of particle thermophoresis in aqueous dispersions,” J. Opt. Soc. Am. B 21, 605-616 (2004).
[CrossRef]

A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
[CrossRef]

2003 (2)

A. Marcano, L. Rodriguez, and Y. Alvarado, “Mode-mismatched thermal lens experiment in the pulse regime,” J. Opt. A, Pure Appl. Opt. 5, S256-S261 (2003).
[CrossRef]

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316 (2003).
[CrossRef] [PubMed]

2002 (3)

D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nano-meter sized metal particles among scatterers,” Science 297, 1160-1163 (2002).
[CrossRef] [PubMed]

E. Tamaki, K. Sato, M. Tokeshi, K. Sato, M. Aihara, and T. Kitamori, “Single-cell analysis by a scanning thermal lens microscope with microchip: direct monitoring of cytochrome c distribution during apoptosis process,” Anal. Chem. 74, 1560-1564 (2002).
[CrossRef] [PubMed]

D. Lapotko, T. Romanovskaya, and E. Gordiyko, “Photothermal monitoring of redox state of respiratory chain in single live cells,” Photochem. Photobiol. 75, 519-526 (2002).
[CrossRef] [PubMed]

2000 (1)

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, and T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316-5322 (2000).
[CrossRef]

1999 (2)

S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry,” Phys. Rev. B 60, 15173-15178 (1999).
[CrossRef]

Y. Han, Z. L. Wu, J. S. Rosenshein, and M. Thomsen, “Pulsed photothermal deflection and diffraction effects: numerical modeling based on Fresnel diffraction theory,” Opt. Eng. 38, 2122-2128 (1999).
[CrossRef]

1998 (1)

C. V. Bindhu, S. S. Harihal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Thermal diffusivity measurements in organic liquids using transient thermal lens calorimetry,” Opt. Eng. 37, 2791-2794 (1998).
[CrossRef]

1995 (2)

K. Mawatari, T. Kitamori, and T. Sawada, “Individual detection of single nano-meter-sized particles in liquid by photothermal detection,” Anal. Chim. Acta 299, 343-347 (1995).
[CrossRef]

F. Jürgensen and W. Schroer, “Studies on the diffraction image of thermal lens,” Appl. Opt. 34, 41-50 (1995).
[CrossRef] [PubMed]

1994 (2)

A. Cheng, Y. Abousleiman, and P. Sidauruk, “Approximate inversion of the Laplace transform,” Math. J. 4, 78-81 (1994).

M. L. Baesso, J. Shen, and R. D. Snook, “Mode-mismatched thermal lens determination of temperature coefficient optical path length in soda lime at different wavelengths,” J. Appl. Phys. 75, 3732-3737 (1994).
[CrossRef]

1992 (1)

J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser-induced mode-mismatched dual beam thermal lens spectrometry,” Chem. Phys. 165, 385-396 (1992).
[CrossRef]

1991 (1)

A. Tuntomo, C. L. Tien, and S. H. Park, “Internal distribution of radiant absorption in a spherical particle,” J. Heat Transfer 113, 407-412 (1991).
[CrossRef]

1979 (1)

1962 (1)

L. Prod'homme, “A new approach to the thermal change in the refractive index of glasses,” Phys. Chem. Glasses 1, 119-122 (1962).

Abousleiman, Y.

A. Cheng, Y. Abousleiman, and P. Sidauruk, “Approximate inversion of the Laplace transform,” Math. J. 4, 78-81 (1994).

Ahluwalia, B.

Aihara, M.

E. Tamaki, K. Sato, M. Tokeshi, K. Sato, M. Aihara, and T. Kitamori, “Single-cell analysis by a scanning thermal lens microscope with microchip: direct monitoring of cytochrome c distribution during apoptosis process,” Anal. Chem. 74, 1560-1564 (2002).
[CrossRef] [PubMed]

Alvarado, Y.

A. Marcano, L. Rodriguez, and Y. Alvarado, “Mode-mismatched thermal lens experiment in the pulse regime,” J. Opt. A, Pure Appl. Opt. 5, S256-S261 (2003).
[CrossRef]

Andrade, A. A.

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

Anjos, V.

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

Baesso, M. L.

A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
[CrossRef]

S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry,” Phys. Rev. B 60, 15173-15178 (1999).
[CrossRef]

M. L. Baesso, J. Shen, and R. D. Snook, “Mode-mismatched thermal lens determination of temperature coefficient optical path length in soda lime at different wavelengths,” J. Appl. Phys. 75, 3732-3737 (1994).
[CrossRef]

Bell, M. J. V.

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

Bento, A. C.

A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
[CrossRef]

S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry,” Phys. Rev. B 60, 15173-15178 (1999).
[CrossRef]

Bindhu, C. V.

C. V. Bindhu, S. S. Harihal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Thermal diffusivity measurements in organic liquids using transient thermal lens calorimetry,” Opt. Eng. 37, 2791-2794 (1998).
[CrossRef]

Boyer, D.

D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nano-meter sized metal particles among scatterers,” Science 297, 1160-1163 (2002).
[CrossRef] [PubMed]

Carslaw, H. S.

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford Science Publications, 1986).

Castro, M. P. P.

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

Catunda, T.

A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
[CrossRef]

S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry,” Phys. Rev. B 60, 15173-15178 (1999).
[CrossRef]

Chen, G. C. K.

Cheng, A.

A. Cheng, Y. Abousleiman, and P. Sidauruk, “Approximate inversion of the Laplace transform,” Math. J. 4, 78-81 (1994).

da Silva, E. F.

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

de Vasconcelos, E. A.

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

Esquef, I. A.

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

Faria, R. T.

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

Franco, R. W. A.

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

George, T. F.

R. R. Letfullin, C. Joenathan, T. F. George, and V. P. Zharov, “Laser-induced explosion for gold nanoparticles: potential role for nanophotothermolysis of cancer,” Nanomedicine 1, 473-480 (2006).
[CrossRef]

Gittes, F.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316 (2003).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw Hill, 1996).

Gordiyko, E.

D. Lapotko, T. Romanovskaya, and E. Gordiyko, “Photothermal monitoring of redox state of respiratory chain in single live cells,” Photochem. Photobiol. 75, 519-526 (2002).
[CrossRef] [PubMed]

Han, Y.

Y. Han, Z. L. Wu, J. S. Rosenshein, and M. Thomsen, “Pulsed photothermal deflection and diffraction effects: numerical modeling based on Fresnel diffraction theory,” Opt. Eng. 38, 2122-2128 (1999).
[CrossRef]

Harihal, S. S.

C. V. Bindhu, S. S. Harihal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Thermal diffusivity measurements in organic liquids using transient thermal lens calorimetry,” Opt. Eng. 37, 2791-2794 (1998).
[CrossRef]

Hattori, M.

M. Hattori, “Thermal diffusivity of some linear polymers,” Kolloid-Zeitschrift und Zeitschrift fur polymers (1964).

Hernandes, A. C.

S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry,” Phys. Rev. B 60, 15173-15178 (1999).
[CrossRef]

Hibara, A.

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, and T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316-5322 (2000).
[CrossRef]

Isa, L.

Jaeger, J. C.

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford Science Publications, 1986).

Jaramillo, J. G.

Joenathan, C.

R. R. Letfullin, C. Joenathan, T. F. George, and V. P. Zharov, “Laser-induced explosion for gold nanoparticles: potential role for nanophotothermolysis of cancer,” Nanomedicine 1, 473-480 (2006).
[CrossRef]

Jürgensen, F.

Kimura, H.

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, and T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316-5322 (2000).
[CrossRef]

Kitamori, T.

E. Tamaki, K. Sato, M. Tokeshi, K. Sato, M. Aihara, and T. Kitamori, “Single-cell analysis by a scanning thermal lens microscope with microchip: direct monitoring of cytochrome c distribution during apoptosis process,” Anal. Chem. 74, 1560-1564 (2002).
[CrossRef] [PubMed]

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, and T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316-5322 (2000).
[CrossRef]

K. Mawatari, T. Kitamori, and T. Sawada, “Individual detection of single nano-meter-sized particles in liquid by photothermal detection,” Anal. Chim. Acta 299, 343-347 (1995).
[CrossRef]

Kononets, M. Y.

Lapotko, D.

D. Lapotko, A. Shnip, and E. Lukianova, “Photothermal responses of individual cells,” J. Biomed. Opt. 10, 014006 (2005).
[CrossRef]

D. Lapotko and V. P. Zharov, “Spectral evaluation of laser-induced cell damage with photothermal microscopy,” Lasers Surg. Med. 36, 22-30 (2005).
[CrossRef] [PubMed]

D. Lapotko, T. Romanovskaya, and E. Gordiyko, “Photothermal monitoring of redox state of respiratory chain in single live cells,” Photochem. Photobiol. 75, 519-526 (2002).
[CrossRef] [PubMed]

Lebullenger, R.

S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry,” Phys. Rev. B 60, 15173-15178 (1999).
[CrossRef]

Letfullin, R. R.

R. R. Letfullin, C. Joenathan, T. F. George, and V. P. Zharov, “Laser-induced explosion for gold nanoparticles: potential role for nanophotothermolysis of cancer,” Nanomedicine 1, 473-480 (2006).
[CrossRef]

Lima, S. M.

S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry,” Phys. Rev. B 60, 15173-15178 (1999).
[CrossRef]

Lounis, B.

D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nano-meter sized metal particles among scatterers,” Science 297, 1160-1163 (2002).
[CrossRef] [PubMed]

Lowe, R. D.

J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser-induced mode-mismatched dual beam thermal lens spectrometry,” Chem. Phys. 165, 385-396 (1992).
[CrossRef]

Lukianova, E.

D. Lapotko, A. Shnip, and E. Lukianova, “Photothermal responses of individual cells,” J. Biomed. Opt. 10, 014006 (2005).
[CrossRef]

Lytle, D.

Maali, A.

D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nano-meter sized metal particles among scatterers,” Science 297, 1160-1163 (2002).
[CrossRef] [PubMed]

Marcano, A.

A. Marcano, L. Rodriguez, and Y. Alvarado, “Mode-mismatched thermal lens experiment in the pulse regime,” J. Opt. A, Pure Appl. Opt. 5, S256-S261 (2003).
[CrossRef]

Mawatari, K.

K. Mawatari, T. Kitamori, and T. Sawada, “Individual detection of single nano-meter-sized particles in liquid by photothermal detection,” Anal. Chim. Acta 299, 343-347 (1995).
[CrossRef]

Medina, A. N.

A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
[CrossRef]

Miranda, L. C. M.

S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry,” Phys. Rev. B 60, 15173-15178 (1999).
[CrossRef]

Nampoori, V. P. N.

C. V. Bindhu, S. S. Harihal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Thermal diffusivity measurements in organic liquids using transient thermal lens calorimetry,” Opt. Eng. 37, 2791-2794 (1998).
[CrossRef]

Nedosekin, D. A.

Nunes, A. R.

A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
[CrossRef]

Nunes, L. A. O.

A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
[CrossRef]

Orrit, M.

D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nano-meter sized metal particles among scatterers,” Science 297, 1160-1163 (2002).
[CrossRef] [PubMed]

Park, S. H.

A. Tuntomo, C. L. Tien, and S. H. Park, “Internal distribution of radiant absorption in a spherical particle,” J. Heat Transfer 113, 407-412 (1991).
[CrossRef]

Pereira, J. R. D.

A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
[CrossRef]

Peterman, E. J. G.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316 (2003).
[CrossRef] [PubMed]

Piazza, R.

Prod'homme, L.

L. Prod'homme, “A new approach to the thermal change in the refractive index of glasses,” Phys. Chem. Glasses 1, 119-122 (1962).

Proskurnin, M. A.

Rodriguez, L.

A. Marcano, L. Rodriguez, and Y. Alvarado, “Mode-mismatched thermal lens experiment in the pulse regime,” J. Opt. A, Pure Appl. Opt. 5, S256-S261 (2003).
[CrossRef]

Rohling, J. H.

A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
[CrossRef]

Romanovskaya, T.

D. Lapotko, T. Romanovskaya, and E. Gordiyko, “Photothermal monitoring of redox state of respiratory chain in single live cells,” Photochem. Photobiol. 75, 519-526 (2002).
[CrossRef] [PubMed]

Roscuni, R.

Rosenshein, J. S.

Y. Han, Z. L. Wu, J. S. Rosenshein, and M. Thomsen, “Pulsed photothermal deflection and diffraction effects: numerical modeling based on Fresnel diffraction theory,” Opt. Eng. 38, 2122-2128 (1999).
[CrossRef]

Sato, K.

E. Tamaki, K. Sato, M. Tokeshi, K. Sato, M. Aihara, and T. Kitamori, “Single-cell analysis by a scanning thermal lens microscope with microchip: direct monitoring of cytochrome c distribution during apoptosis process,” Anal. Chem. 74, 1560-1564 (2002).
[CrossRef] [PubMed]

E. Tamaki, K. Sato, M. Tokeshi, K. Sato, M. Aihara, and T. Kitamori, “Single-cell analysis by a scanning thermal lens microscope with microchip: direct monitoring of cytochrome c distribution during apoptosis process,” Anal. Chem. 74, 1560-1564 (2002).
[CrossRef] [PubMed]

Sawada, T.

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, and T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316-5322 (2000).
[CrossRef]

K. Mawatari, T. Kitamori, and T. Sawada, “Individual detection of single nano-meter-sized particles in liquid by photothermal detection,” Anal. Chim. Acta 299, 343-347 (1995).
[CrossRef]

Schmidt, C. F.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316 (2003).
[CrossRef] [PubMed]

Schroer, W.

Shen, J.

M. L. Baesso, J. Shen, and R. D. Snook, “Mode-mismatched thermal lens determination of temperature coefficient optical path length in soda lime at different wavelengths,” J. Appl. Phys. 75, 3732-3737 (1994).
[CrossRef]

J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser-induced mode-mismatched dual beam thermal lens spectrometry,” Chem. Phys. 165, 385-396 (1992).
[CrossRef]

Shnip, A.

D. Lapotko, A. Shnip, and E. Lukianova, “Photothermal responses of individual cells,” J. Biomed. Opt. 10, 014006 (2005).
[CrossRef]

Sidauruk, P.

A. Cheng, Y. Abousleiman, and P. Sidauruk, “Approximate inversion of the Laplace transform,” Math. J. 4, 78-81 (1994).

Snook, R. D.

M. L. Baesso, J. Shen, and R. D. Snook, “Mode-mismatched thermal lens determination of temperature coefficient optical path length in soda lime at different wavelengths,” J. Appl. Phys. 75, 3732-3737 (1994).
[CrossRef]

J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser-induced mode-mismatched dual beam thermal lens spectrometry,” Chem. Phys. 165, 385-396 (1992).
[CrossRef]

Tamaki, E.

E. Tamaki, K. Sato, M. Tokeshi, K. Sato, M. Aihara, and T. Kitamori, “Single-cell analysis by a scanning thermal lens microscope with microchip: direct monitoring of cytochrome c distribution during apoptosis process,” Anal. Chem. 74, 1560-1564 (2002).
[CrossRef] [PubMed]

Tamarat, P.

D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nano-meter sized metal particles among scatterers,” Science 297, 1160-1163 (2002).
[CrossRef] [PubMed]

Thomsen, M.

Y. Han, Z. L. Wu, J. S. Rosenshein, and M. Thomsen, “Pulsed photothermal deflection and diffraction effects: numerical modeling based on Fresnel diffraction theory,” Opt. Eng. 38, 2122-2128 (1999).
[CrossRef]

Tien, C. L.

A. Tuntomo, C. L. Tien, and S. H. Park, “Internal distribution of radiant absorption in a spherical particle,” J. Heat Transfer 113, 407-412 (1991).
[CrossRef]

Tokeshi, M.

E. Tamaki, K. Sato, M. Tokeshi, K. Sato, M. Aihara, and T. Kitamori, “Single-cell analysis by a scanning thermal lens microscope with microchip: direct monitoring of cytochrome c distribution during apoptosis process,” Anal. Chem. 74, 1560-1564 (2002).
[CrossRef] [PubMed]

Tuntomo, A.

A. Tuntomo, C. L. Tien, and S. H. Park, “Internal distribution of radiant absorption in a spherical particle,” J. Heat Transfer 113, 407-412 (1991).
[CrossRef]

Uchiyama, K.

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, and T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316-5322 (2000).
[CrossRef]

Vallabhan, C. P. G.

C. V. Bindhu, S. S. Harihal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Thermal diffusivity measurements in organic liquids using transient thermal lens calorimetry,” Opt. Eng. 37, 2791-2794 (1998).
[CrossRef]

Vasudevan, S.

Wilkerson, G. W.

Wu, Z. L.

Y. Han, Z. L. Wu, J. S. Rosenshein, and M. Thomsen, “Pulsed photothermal deflection and diffraction effects: numerical modeling based on Fresnel diffraction theory,” Opt. Eng. 38, 2122-2128 (1999).
[CrossRef]

Zharov, V. P.

R. R. Letfullin, C. Joenathan, T. F. George, and V. P. Zharov, “Laser-induced explosion for gold nanoparticles: potential role for nanophotothermolysis of cancer,” Nanomedicine 1, 473-480 (2006).
[CrossRef]

D. Lapotko and V. P. Zharov, “Spectral evaluation of laser-induced cell damage with photothermal microscopy,” Lasers Surg. Med. 36, 22-30 (2005).
[CrossRef] [PubMed]

Anal. Chem. (1)

E. Tamaki, K. Sato, M. Tokeshi, K. Sato, M. Aihara, and T. Kitamori, “Single-cell analysis by a scanning thermal lens microscope with microchip: direct monitoring of cytochrome c distribution during apoptosis process,” Anal. Chem. 74, 1560-1564 (2002).
[CrossRef] [PubMed]

Anal. Chim. Acta (1)

K. Mawatari, T. Kitamori, and T. Sawada, “Individual detection of single nano-meter-sized particles in liquid by photothermal detection,” Anal. Chim. Acta 299, 343-347 (1995).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

A. R. Nunes, J. H. Rohling, A. N. Medina, J. R. D. Pereira, A. C. Bento, M. L. Baesso, L. A. O. Nunes, and T. Catunda, “Time-resolved thermal lens determination of thermo-optical coefficients in Nd-doped yttrium aluminium garnet as a function of temperature,” Appl. Phys. Lett. 84, 5183-5185 (2004).
[CrossRef]

Biophys. J. (1)

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316 (2003).
[CrossRef] [PubMed]

Chem. Phys. (1)

J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser-induced mode-mismatched dual beam thermal lens spectrometry,” Chem. Phys. 165, 385-396 (1992).
[CrossRef]

J. Appl. Phys. (1)

M. L. Baesso, J. Shen, and R. D. Snook, “Mode-mismatched thermal lens determination of temperature coefficient optical path length in soda lime at different wavelengths,” J. Appl. Phys. 75, 3732-3737 (1994).
[CrossRef]

J. Biomed. Opt. (1)

D. Lapotko, A. Shnip, and E. Lukianova, “Photothermal responses of individual cells,” J. Biomed. Opt. 10, 014006 (2005).
[CrossRef]

J. Heat Transfer (1)

A. Tuntomo, C. L. Tien, and S. H. Park, “Internal distribution of radiant absorption in a spherical particle,” J. Heat Transfer 113, 407-412 (1991).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

A. Marcano, L. Rodriguez, and Y. Alvarado, “Mode-mismatched thermal lens experiment in the pulse regime,” J. Opt. A, Pure Appl. Opt. 5, S256-S261 (2003).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, and T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316-5322 (2000).
[CrossRef]

Lasers Surg. Med. (1)

D. Lapotko and V. P. Zharov, “Spectral evaluation of laser-induced cell damage with photothermal microscopy,” Lasers Surg. Med. 36, 22-30 (2005).
[CrossRef] [PubMed]

Math. J. (1)

A. Cheng, Y. Abousleiman, and P. Sidauruk, “Approximate inversion of the Laplace transform,” Math. J. 4, 78-81 (1994).

Microelectron. J. (1)

V. Anjos, M. J. V. Bell, E. A. de Vasconcelos, E. F. da Silva, Jr., A. A. Andrade, R. W. A. Franco, M. P. P. Castro, I. A. Esquef, and R. T. Faria, Jr., “Thermal lens and photo-acoustic method for the determination of SiC thermal properties,” Microelectron. J. 36, 977-980 (2005).
[CrossRef]

Nanomedicine (1)

R. R. Letfullin, C. Joenathan, T. F. George, and V. P. Zharov, “Laser-induced explosion for gold nanoparticles: potential role for nanophotothermolysis of cancer,” Nanomedicine 1, 473-480 (2006).
[CrossRef]

Opt. Eng. (2)

Y. Han, Z. L. Wu, J. S. Rosenshein, and M. Thomsen, “Pulsed photothermal deflection and diffraction effects: numerical modeling based on Fresnel diffraction theory,” Opt. Eng. 38, 2122-2128 (1999).
[CrossRef]

C. V. Bindhu, S. S. Harihal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Thermal diffusivity measurements in organic liquids using transient thermal lens calorimetry,” Opt. Eng. 37, 2791-2794 (1998).
[CrossRef]

Opt. Lett. (1)

Photochem. Photobiol. (1)

D. Lapotko, T. Romanovskaya, and E. Gordiyko, “Photothermal monitoring of redox state of respiratory chain in single live cells,” Photochem. Photobiol. 75, 519-526 (2002).
[CrossRef] [PubMed]

Phys. Chem. Glasses (1)

L. Prod'homme, “A new approach to the thermal change in the refractive index of glasses,” Phys. Chem. Glasses 1, 119-122 (1962).

Phys. Rev. B (1)

S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry,” Phys. Rev. B 60, 15173-15178 (1999).
[CrossRef]

Science (1)

D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nano-meter sized metal particles among scatterers,” Science 297, 1160-1163 (2002).
[CrossRef] [PubMed]

Other (3)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw Hill, 1996).

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford Science Publications, 1986).

M. Hattori, “Thermal diffusivity of some linear polymers,” Kolloid-Zeitschrift und Zeitschrift fur polymers (1964).

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of an irradiated spherical particle with r = ( x 2 + y 2 + z 2 ) 1 / 2 .

Fig. 2
Fig. 2

Schematic experimental configuration of photothermal lens of single particle.

Fig. 3
Fig. 3

Experimental setup of photothermal lens technique.

Fig. 4
Fig. 4

Illustration of forces experienced by a particle (cross-sectional view). (a) Particle is pushed toward the focus. (b) Particle is pushed up by scattering force and escapes from the trap. (c) Particle is trapped against the cover slip.

Fig. 5
Fig. 5

Photothermal lens signal with various pulse shape functions. (a) Pulse duration ( t m ) is 0.1 μ s . (b) Pulse duration ( t m ) is 1 μ s while the relaxation time τ d is 6.6 μ s . 1, 2, 3, and 4 are referring to Gaussian, rectangular, exponential, and Dirac delta temporal pulse functions, respectively.

Fig. 6
Fig. 6

(a) Temporal fluctuation of excitation laser (Nd:YAG, 532 nm, 12   ns pulse width, Gaussian-like temporal pulse function). (b) Simulation result of photothermal lens signal with shifted peak Gaussian temporal pulse shape. Time to reach the maximum point ( t p ) for graphs 1, 2, and 3 are 0.3 μ s , 0.4 μ s , and 0.5 μ s .

Fig. 7
Fig. 7

Normalized transient TL signal with probe beam waist variation. (1) 5 μ m , (2) 10 μ m , and (3) 20 μ m probe beam waist radius, respectively. Size of the particle is 2.5 μ m .

Fig. 8
Fig. 8

Simulation result of temperature profile of spherical particle in sample medium with various time measurements. h = , where h is thermal contact conductance. Size of particle is 2 μ m . (1) Temperature difference between each point at central region; (2) temperature difference at the near surface of particle.

Fig. 9
Fig. 9

Schematic figure of z-scan measurement photothermal lens signal.

Fig. 10
Fig. 10

Simulated result of TL z-scan signal with different a / w G ratio. Particle radius a is 2.5 μ m and probe beam diameter w G are 2.5, 5, 7.5, and 10 μ m , respectively.

Fig. 11
Fig. 11

Curve-fitted photothermal lens of single RPS.

Fig. 12
Fig. 12

Plot of the extracted (a) thermal diffusivity and (b) size with three different temporal pulse shapes. (1), (2), and (3) are Gaussian, rectangular, and Dirac delta temporal pulse shapes, respectively. Standard deviation error for each pulse shape can be seen in Table 3.

Tables (3)

Tables Icon

Table 1 Pulse Shape Function and Their Laplace Transforms

Tables Icon

Table 2 Thermo-Optical Parameters of RPS [23, 24, 25]

Tables Icon

Table 3 Curve-Fitted Result of RPS with Different Pulse Shapes

Equations (34)

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

Q ( t ) = Φ φ ( t ) α ,
1 υ 1 T 1 t = 1 r 2 r ( r 2 T 1 r ) + Q ( t ) K 1 ,     0 r < a ,
1 υ 2 T 2 t = 1 r 2 r ( r 2 T 2 r ) ,     r > a .
K 1 | T 1 r | r = a = h ( T 1 T 2 ) = K 2 | T 2 r | r = a ,
T 1 = T 2 = 0 ,   when   t = 0 ,
d 2 d r 2 ( r T 1 ¯ ) r γ 1 T 1 ¯ = r Q ( s ) K 1 ,     0 r < a ,
d 2 d r 2 ( r T 2 ¯ ) r γ 2 T 2 ¯ = 0 ,     r > a ,
K 1 | d T 1 ¯ d r | r = a = h ( T 1 ¯ T 2 ¯ ) = K 2 | d T 2 ¯ d r | r = a
T 1 ¯ = T 2 ¯ ,   at   r = a ,
T 1 ¯   is   finite   as   r 0   and   T 2 ¯ 0   as   r ,
T 1 δ ¯ ( r , s ) = Φ α K 1 γ 1 [ 1 + a r K 2 K 1 sinh ( γ 1 1 / 2 r ) D ] ,     0 r < a ,
T 2 δ ¯ ( r , s ) = Φ α K 1 γ 1 a r [ sinh ( γ 1 1 / 2 a ) a γ 1 1 / 2   cosh ( γ 1 1 / 2 a ) ] ( 1 + γ 2 1 / 2 a ) D exp [ γ 2 ( r a ) ] ,     r > a ,
D = sinh ( γ 1 1 / 2 a ) γ 1 1 / 2 a   cosh ( γ 1 1 / 2 a ) ( 1 + γ 2 1 / 2 a ) ( 1 + K 2 γ 2 1 / 2 h + K 2 h a ) K 2 K 1 sinh ( γ 1 1 / 2 a ) .
D = sinh ( γ 1 1 / 2 a ) γ 1 1 / 2 a   cosh ( γ 1 1 / 2 a ) ( 1 + γ 2 1 / 2 a ) K 2 K 1 sinh ( γ 1 1 / 2 a ) ,
T i ¯ = φ ¯ ( s ) × T i δ ¯ ,
T i ( t ) = 1 2 π i σ i σ + i e s t T i ¯ ( r , s ) d s ,
f ( t ) ln   2 t n = 1 N c n F ( n   ln   2 t ) ,
c n = ( 1 ) n + N / 2 k = ( ( n + 1 ) / 2 ) min ( n , N / 2 ) k N / 2 ( 2 k ) ! ( N / 2 k ) ! k ! ( k 1 ) ! ( n k ) ! ( 2 k n ) !
U 1 ( x , y , z 1 ) = 1 w G 2 ( P e χ π ) 1 / 2 exp [ j k 2 q ( x 2 + y 2 ) ] exp ( j k z 1 ) ,
w G = w o ( 1 + z 1 2 z c 2 ) 1 / 2 ,
1 q = 1 R ( z ) j λ π w G 2 ,
exp [ j ( Δ ϑ ( x , y , t ) + Δ ϑ c ( x , y ) ) ] ,     r a ,
exp [ j Δ ϑ ( x , y , t ) ] ,     r > a ,
Δ ϑ ( x , y , t ) = k + η ( x , y , z ) T i ( x , y , z , t ) d z ,
η ( x , y , z ) = η o + Δ η ,     r a ,
η ( x , y , z ) = η o ,     r > a ,
Δ ϑ c ( x , y ) = 2 k Δ n c [ a 2 ( x 2 + y 2 ) ] 1 / 2 ,     r a .
U 1 ( x , y , z o ) = 1 w G 2 ( P e χ π ) 1 / 2 exp [ j k 2 q ( x 2 + y 2 ) ] exp ( j k z o )
exp [ j ( Δ ϑ ( x , y , t ) + Δ ϑ c ( x , y ) ) ] .
U d ( x , y , z 2 , t ) = 1 j λ ( z 2 z o ) exp ( j k ( z 2 z o ) ) exp [ j k 2 ( z 2 z o ) ( x 2 + y 2 ) ] U 1 ( ε , v , z o ) exp [ j k 2 ( z 2 z o ) ( ε 2 + ν 2 ) ] exp [ j π λ ( z 2 z o ) ( ε x + ν y ) ] d ε d ν .
I ( z 2 , t ) = R d R d R 2 2 y 2 R d 2 y 2 | U d ( x , y , z 2 , t ) | 2 d x d y ,
S ( z 2 , t ) = I ( z 2 , t ) I ( z 2 , ) I ( z 2 , ) ,
U 1 ( x , y , z o ) j n n = 0 ( x 2 + y 2 ) n ( n ! ) 2 n = 0 ( Δ ϑ ( x , y , t ) + Δ ϑ c ( x , y ) ) n w G 2 n .
d n d T = ζ ( n 2 1 ) ( n 2 + 2 ) 6 n ,

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