Abstract

To investigate the energy dissipation process after focusing a femtosecond laser pulse inside a zinc borosilicate glass, the time-dependent lens effect in the laser focal region was observed by a transient lens (TrL) method. We found that the TrL signal after 100 ns can be explained clearly by thermal diffusion. By fitting the observed signal, we obtained the phase change due to temperature increase, the initial diameter of the heated volume and the thermal diffusivity. On the basis of the results, the temperature increase and the cooling rate were estimated to be about 1800 K and 1.7×108 Ks-1, respectively. We have also observed the signal change on a 100 ns scale, which can not be explained by the thermal diffusion model. This change was attributed to the relaxation of the heated material.

© 2007 Optical Society of America

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  1. K.M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett 21, 1729-1731 (1996).
    [CrossRef] [PubMed]
  2. K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett 71, 3329-3331 (1997).
    [CrossRef]
  3. C.B. Schaffer, A. Brodeur, J.F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett 26, 93-95 (2001).
    [CrossRef]
  4. L. Shah, A.Y. Arai, S. M. Eaton, and P. R. Herman, "Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate," Opt. Express 13, 1999-2006 (2005).
    [CrossRef] [PubMed]
  5. R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Optical properties of waveguides written by a 26 MHz stretched cavity Ti:sapphire femtosecond oscillator," Opt. Express 13, 612-620 (2005).
    [CrossRef] [PubMed]
  6. R. R. Gattass, L. R. Cerami, and E. Mazur "Micromachining of bulk glass with bursts of femtosecond laser pulses at variable repetition rates," Opt. Express 14, 5279-5284 (2006).
    [CrossRef] [PubMed]
  7. S.M. Eaton, H. Zhang, P.R. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A.Y. Arai, "Heat accumulation effects in femtosecond laserwritten waveguides with variable repetition rate," Opt. Express 13, 4708-4716 (2005).
    [CrossRef] [PubMed]
  8. C.B Schaffer, J.F Garcia, and E. Mazur "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
    [CrossRef]
  9. A. Vogel, J. Noack, G. Huttman, and G. Paltauf, "Mechanisms of femtosecond laser nanosurgery of cells and tissues," Appl. Phys. B 81, 1015-1047 (2005).
    [CrossRef]
  10. L. Genberg, Q. Bao, S. Gracewski, and R. J. D. Miller, "Direct observation of global protein motion in hemoglobin and myoglobin on picosecond time scales," Science 251, 1051-1054 (1991).
    [CrossRef] [PubMed]
  11. M. Takezaki, N. Hirota, and M. Terazima, " Excited state dynamics of 9,10-diazaphenanthrene studied by the time-resolved transient grating method," J. Phys. Chem. 100, 10015-10020 (1996).
    [CrossRef]
  12. T. Hara, N. Hirota, and M. Terazima, "New application of the transient grating method to a photochemical reaction: the enthalpy, reaction volume change," J. Phys. Chem. 100, 10194-10200 (1996).
    [CrossRef]
  13. M. Terazima, and N. Hirota, "Rise profile of the thermal lens signal: contribution of the temperature lens and population lens," J. Chem. Phys 100, 2481-2486 (1994).
    [CrossRef]
  14. M. Sakakura, and M. Terazima, "Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass," Phys. Rev. B 71, 024113 (2005).
    [CrossRef]
  15. M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, "Observation of pressure wave generated by focusing a femtosecond laser pulse inside a glass," Opt. Express 15, 5674-5686 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  18. T. Yagi, and M. Susa, "Temperature dependence of the refractive index of Al2O3-Na2O-SiO2 melts: role of electronic polarizability of oxygen controlled by network structure," Meta. Mat. Trans. B 34B, 549-554 (2003).
    [CrossRef]
  19. Glass Technical Data of Corning 0211 http://www.eriesci.com/custom/cor0211-tech.aspx
  20. G. Ghosh, "Model for the thermo-optic coefficients of some standard optical glasses," J. Non-Cryst. Sol. 189, 191-196 (1995).
    [CrossRef]
  21. A. K. Varshneya, Fundamentals of Inorganic Glasses (Academic Press, 1994), Chap. 12.
  22. J. Yu, P-.F. Paradis, T. Ishikawa, and S. Yoda, "Microstructure and dielectric constant of BaTiO3 synthesized by roller quenching," Jpn. J. Appl. Phys. 43, 8135 (2004).
    [CrossRef]
  23. R. Bruckner, "Properties and structure of vitreous silica. I," J. Non-Cryst. Sol. 5, 123-175 (1970).
    [CrossRef]
  24. J. W. Chan, T. R. Huster, S. H. Risbud and D. M. Krol, "Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses," Appl. Phys. A 76, 367-372 (2003).
    [CrossRef]

2007

2006

2005

2004

J. Yu, P-.F. Paradis, T. Ishikawa, and S. Yoda, "Microstructure and dielectric constant of BaTiO3 synthesized by roller quenching," Jpn. J. Appl. Phys. 43, 8135 (2004).
[CrossRef]

2003

T. Yagi, and M. Susa, "Temperature dependence of the refractive index of Al2O3-Na2O-SiO2 melts: role of electronic polarizability of oxygen controlled by network structure," Meta. Mat. Trans. B 34B, 549-554 (2003).
[CrossRef]

J. W. Chan, T. R. Huster, S. H. Risbud and D. M. Krol, "Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses," Appl. Phys. A 76, 367-372 (2003).
[CrossRef]

C.B Schaffer, J.F Garcia, and E. Mazur "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
[CrossRef]

2001

C.B. Schaffer, A. Brodeur, J.F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett 26, 93-95 (2001).
[CrossRef]

1997

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett 71, 3329-3331 (1997).
[CrossRef]

1996

K.M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett 21, 1729-1731 (1996).
[CrossRef] [PubMed]

M. Takezaki, N. Hirota, and M. Terazima, " Excited state dynamics of 9,10-diazaphenanthrene studied by the time-resolved transient grating method," J. Phys. Chem. 100, 10015-10020 (1996).
[CrossRef]

T. Hara, N. Hirota, and M. Terazima, "New application of the transient grating method to a photochemical reaction: the enthalpy, reaction volume change," J. Phys. Chem. 100, 10194-10200 (1996).
[CrossRef]

1995

G. Ghosh, "Model for the thermo-optic coefficients of some standard optical glasses," J. Non-Cryst. Sol. 189, 191-196 (1995).
[CrossRef]

1994

M. Terazima, and N. Hirota, "Rise profile of the thermal lens signal: contribution of the temperature lens and population lens," J. Chem. Phys 100, 2481-2486 (1994).
[CrossRef]

1991

L. Genberg, Q. Bao, S. Gracewski, and R. J. D. Miller, "Direct observation of global protein motion in hemoglobin and myoglobin on picosecond time scales," Science 251, 1051-1054 (1991).
[CrossRef] [PubMed]

1990

1982

1970

R. Bruckner, "Properties and structure of vitreous silica. I," J. Non-Cryst. Sol. 5, 123-175 (1970).
[CrossRef]

Aiello, L.

Arai, A.Y.

Bao, Q.

L. Genberg, Q. Bao, S. Gracewski, and R. J. D. Miller, "Direct observation of global protein motion in hemoglobin and myoglobin on picosecond time scales," Science 251, 1051-1054 (1991).
[CrossRef] [PubMed]

Bovatsek, J.

Brodeur, A.

C.B. Schaffer, A. Brodeur, J.F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett 26, 93-95 (2001).
[CrossRef]

Bruckner, R.

R. Bruckner, "Properties and structure of vitreous silica. I," J. Non-Cryst. Sol. 5, 123-175 (1970).
[CrossRef]

Cerami, L. R.

Cerullo, G.

Chan, J. W.

J. W. Chan, T. R. Huster, S. H. Risbud and D. M. Krol, "Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses," Appl. Phys. A 76, 367-372 (2003).
[CrossRef]

Chiodo, N.

Davis, K.M.

K.M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett 21, 1729-1731 (1996).
[CrossRef] [PubMed]

De Nicola, S.

Eaton, S. M.

Eaton, S.M.

Ferraro, P.

Finizio, A.

Garcia, J.F

C.B Schaffer, J.F Garcia, and E. Mazur "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
[CrossRef]

Garcia, J.F.

C.B. Schaffer, A. Brodeur, J.F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett 26, 93-95 (2001).
[CrossRef]

Gattass, R. R.

Genberg, L.

L. Genberg, Q. Bao, S. Gracewski, and R. J. D. Miller, "Direct observation of global protein motion in hemoglobin and myoglobin on picosecond time scales," Science 251, 1051-1054 (1991).
[CrossRef] [PubMed]

Ghosh, G.

G. Ghosh, "Model for the thermo-optic coefficients of some standard optical glasses," J. Non-Cryst. Sol. 189, 191-196 (1995).
[CrossRef]

Gracewski, S.

L. Genberg, Q. Bao, S. Gracewski, and R. J. D. Miller, "Direct observation of global protein motion in hemoglobin and myoglobin on picosecond time scales," Science 251, 1051-1054 (1991).
[CrossRef] [PubMed]

Hara, T.

T. Hara, N. Hirota, and M. Terazima, "New application of the transient grating method to a photochemical reaction: the enthalpy, reaction volume change," J. Phys. Chem. 100, 10194-10200 (1996).
[CrossRef]

Herman, P. R.

Herman, P.R.

Hirao, K.

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, "Observation of pressure wave generated by focusing a femtosecond laser pulse inside a glass," Opt. Express 15, 5674-5686 (2007).
[CrossRef] [PubMed]

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett 71, 3329-3331 (1997).
[CrossRef]

K.M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett 21, 1729-1731 (1996).
[CrossRef] [PubMed]

Hirota, N.

T. Hara, N. Hirota, and M. Terazima, "New application of the transient grating method to a photochemical reaction: the enthalpy, reaction volume change," J. Phys. Chem. 100, 10194-10200 (1996).
[CrossRef]

M. Takezaki, N. Hirota, and M. Terazima, " Excited state dynamics of 9,10-diazaphenanthrene studied by the time-resolved transient grating method," J. Phys. Chem. 100, 10015-10020 (1996).
[CrossRef]

M. Terazima, and N. Hirota, "Rise profile of the thermal lens signal: contribution of the temperature lens and population lens," J. Chem. Phys 100, 2481-2486 (1994).
[CrossRef]

Huster, T. R.

J. W. Chan, T. R. Huster, S. H. Risbud and D. M. Krol, "Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses," Appl. Phys. A 76, 367-372 (2003).
[CrossRef]

Huttman, G.

A. Vogel, J. Noack, G. Huttman, and G. Paltauf, "Mechanisms of femtosecond laser nanosurgery of cells and tissues," Appl. Phys. B 81, 1015-1047 (2005).
[CrossRef]

Inouye, H.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett 71, 3329-3331 (1997).
[CrossRef]

Knight, L. V.

Krol, D. M.

J. W. Chan, T. R. Huster, S. H. Risbud and D. M. Krol, "Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses," Appl. Phys. A 76, 367-372 (2003).
[CrossRef]

Laporta, P.

Maselli, V.

Mazur, E.

R. R. Gattass, L. R. Cerami, and E. Mazur "Micromachining of bulk glass with bursts of femtosecond laser pulses at variable repetition rates," Opt. Express 14, 5279-5284 (2006).
[CrossRef] [PubMed]

C.B Schaffer, J.F Garcia, and E. Mazur "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
[CrossRef]

C.B. Schaffer, A. Brodeur, J.F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett 26, 93-95 (2001).
[CrossRef]

Miller, R. J. D.

L. Genberg, Q. Bao, S. Gracewski, and R. J. D. Miller, "Direct observation of global protein motion in hemoglobin and myoglobin on picosecond time scales," Science 251, 1051-1054 (1991).
[CrossRef] [PubMed]

Mitsuyu, T.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett 71, 3329-3331 (1997).
[CrossRef]

Miura, K.

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, "Observation of pressure wave generated by focusing a femtosecond laser pulse inside a glass," Opt. Express 15, 5674-5686 (2007).
[CrossRef] [PubMed]

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett 71, 3329-3331 (1997).
[CrossRef]

K.M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett 21, 1729-1731 (1996).
[CrossRef] [PubMed]

Noack, J.

A. Vogel, J. Noack, G. Huttman, and G. Paltauf, "Mechanisms of femtosecond laser nanosurgery of cells and tissues," Appl. Phys. B 81, 1015-1047 (2005).
[CrossRef]

Osellame, R.

Paltauf, G.

A. Vogel, J. Noack, G. Huttman, and G. Paltauf, "Mechanisms of femtosecond laser nanosurgery of cells and tissues," Appl. Phys. B 81, 1015-1047 (2005).
[CrossRef]

Pierattini, G.

Power, J.F.

Qiu, J.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett 71, 3329-3331 (1997).
[CrossRef]

Risbud, S. H.

J. W. Chan, T. R. Huster, S. H. Risbud and D. M. Krol, "Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses," Appl. Phys. A 76, 367-372 (2003).
[CrossRef]

Sakakura, M.

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, "Observation of pressure wave generated by focusing a femtosecond laser pulse inside a glass," Opt. Express 15, 5674-5686 (2007).
[CrossRef] [PubMed]

M. Sakakura, and M. Terazima, "Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass," Phys. Rev. B 71, 024113 (2005).
[CrossRef]

Schaffer, C.B

C.B Schaffer, J.F Garcia, and E. Mazur "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
[CrossRef]

Schaffer, C.B.

C.B. Schaffer, A. Brodeur, J.F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett 26, 93-95 (2001).
[CrossRef]

Shah, L.

Sheldon, S. J.

Shimotsuma, Y.

Sugimoto, N.

K.M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett 21, 1729-1731 (1996).
[CrossRef] [PubMed]

Susa, M.

T. Yagi, and M. Susa, "Temperature dependence of the refractive index of Al2O3-Na2O-SiO2 melts: role of electronic polarizability of oxygen controlled by network structure," Meta. Mat. Trans. B 34B, 549-554 (2003).
[CrossRef]

Takezaki, M.

M. Takezaki, N. Hirota, and M. Terazima, " Excited state dynamics of 9,10-diazaphenanthrene studied by the time-resolved transient grating method," J. Phys. Chem. 100, 10015-10020 (1996).
[CrossRef]

Terazima, M.

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, "Observation of pressure wave generated by focusing a femtosecond laser pulse inside a glass," Opt. Express 15, 5674-5686 (2007).
[CrossRef] [PubMed]

M. Sakakura, and M. Terazima, "Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass," Phys. Rev. B 71, 024113 (2005).
[CrossRef]

T. Hara, N. Hirota, and M. Terazima, "New application of the transient grating method to a photochemical reaction: the enthalpy, reaction volume change," J. Phys. Chem. 100, 10194-10200 (1996).
[CrossRef]

M. Takezaki, N. Hirota, and M. Terazima, " Excited state dynamics of 9,10-diazaphenanthrene studied by the time-resolved transient grating method," J. Phys. Chem. 100, 10015-10020 (1996).
[CrossRef]

M. Terazima, and N. Hirota, "Rise profile of the thermal lens signal: contribution of the temperature lens and population lens," J. Chem. Phys 100, 2481-2486 (1994).
[CrossRef]

Thorne, J. M.

Vogel, A.

A. Vogel, J. Noack, G. Huttman, and G. Paltauf, "Mechanisms of femtosecond laser nanosurgery of cells and tissues," Appl. Phys. B 81, 1015-1047 (2005).
[CrossRef]

Yagi, T.

T. Yagi, and M. Susa, "Temperature dependence of the refractive index of Al2O3-Na2O-SiO2 melts: role of electronic polarizability of oxygen controlled by network structure," Meta. Mat. Trans. B 34B, 549-554 (2003).
[CrossRef]

Yin, A.

Yoshino, F.

Yu, J.

J. Yu, P-.F. Paradis, T. Ishikawa, and S. Yoda, "Microstructure and dielectric constant of BaTiO3 synthesized by roller quenching," Jpn. J. Appl. Phys. 43, 8135 (2004).
[CrossRef]

Zavelani-Rossi, M.

Zhang, H.

Appl. Opt.

Appl. Phys. A

C.B Schaffer, J.F Garcia, and E. Mazur "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
[CrossRef]

J. W. Chan, T. R. Huster, S. H. Risbud and D. M. Krol, "Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses," Appl. Phys. A 76, 367-372 (2003).
[CrossRef]

Appl. Phys. B

A. Vogel, J. Noack, G. Huttman, and G. Paltauf, "Mechanisms of femtosecond laser nanosurgery of cells and tissues," Appl. Phys. B 81, 1015-1047 (2005).
[CrossRef]

Appl. Phys. Lett

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett 71, 3329-3331 (1997).
[CrossRef]

J. Chem. Phys

M. Terazima, and N. Hirota, "Rise profile of the thermal lens signal: contribution of the temperature lens and population lens," J. Chem. Phys 100, 2481-2486 (1994).
[CrossRef]

J. Non-Cryst. Sol.

R. Bruckner, "Properties and structure of vitreous silica. I," J. Non-Cryst. Sol. 5, 123-175 (1970).
[CrossRef]

G. Ghosh, "Model for the thermo-optic coefficients of some standard optical glasses," J. Non-Cryst. Sol. 189, 191-196 (1995).
[CrossRef]

J. Phys. Chem.

M. Takezaki, N. Hirota, and M. Terazima, " Excited state dynamics of 9,10-diazaphenanthrene studied by the time-resolved transient grating method," J. Phys. Chem. 100, 10015-10020 (1996).
[CrossRef]

T. Hara, N. Hirota, and M. Terazima, "New application of the transient grating method to a photochemical reaction: the enthalpy, reaction volume change," J. Phys. Chem. 100, 10194-10200 (1996).
[CrossRef]

Jpn. J. Appl. Phys.

J. Yu, P-.F. Paradis, T. Ishikawa, and S. Yoda, "Microstructure and dielectric constant of BaTiO3 synthesized by roller quenching," Jpn. J. Appl. Phys. 43, 8135 (2004).
[CrossRef]

Meta. Mat. Trans. B

T. Yagi, and M. Susa, "Temperature dependence of the refractive index of Al2O3-Na2O-SiO2 melts: role of electronic polarizability of oxygen controlled by network structure," Meta. Mat. Trans. B 34B, 549-554 (2003).
[CrossRef]

Opt. Express

Opt. Lett

K.M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett 21, 1729-1731 (1996).
[CrossRef] [PubMed]

C.B. Schaffer, A. Brodeur, J.F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett 26, 93-95 (2001).
[CrossRef]

Phys. Rev. B

M. Sakakura, and M. Terazima, "Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass," Phys. Rev. B 71, 024113 (2005).
[CrossRef]

Science

L. Genberg, Q. Bao, S. Gracewski, and R. J. D. Miller, "Direct observation of global protein motion in hemoglobin and myoglobin on picosecond time scales," Science 251, 1051-1054 (1991).
[CrossRef] [PubMed]

Other

Glass Technical Data of Corning 0211 http://www.eriesci.com/custom/cor0211-tech.aspx

A. K. Varshneya, Fundamentals of Inorganic Glasses (Academic Press, 1994), Chap. 12.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Experimental setup for a transient lens method. PD: photodiode; Lc: a collimation lens; the blue arrows depict electric pulses for a trigger. (b) Schematic picture of a TrL effect. Solid lines depict a probe beam without a TrL, and broken lines are a probe beam focused by a TrL. The focal position of the probe beam was changed by a beam expander.

Fig. 2.
Fig. 2.

(a) TrL signals measured at d=+0.07 mm and with excitation laser energy of 0.8, 0.6 and 0.4 µJ/pulse. (b) TrL signals simulated with wth =2.0 µm, Dth =0.46 µm2µs-1 and various Δφth. The signals were offset for clarity, and the broken lines are the baselines for each signal.

Fig. 3.
Fig. 3.

(a) TrL signals measured at four different d with excitation laser energy of 0.6 µJ/pulse. (b) TrL signals simulated with wth =2.0 µm, Dth =0.46 µm2µs-1, Δϕth =4.5, and various d. The signals were offset for clarity, and the broken lines are the baselines for each signal.

Fig. 4.
Fig. 4.

(a) TrL signals observed at Iex =0.6 µJ/pulse (open circles) and ones simulated (red lines) based on thermal diffusion models with Δϕth =5.8, wth =1.7 µm and Dth =0.75 µm2µs-1. (b) Temporal evolutions of temperature at the center of the photoexcited region.

Fig. 5.
Fig. 5.

(a) TrL signals in 1 µs measured at d=+0.03 mm. The solid lines are TrL signals simulated by Eqs. (4) and (5). The signal at Iex =0.6 µJ/pulse is offset for clarity. (b) TrL signals of 0.4 (opened circles) and 0.6 µJ/pulse (solid line) are plotted without offset.

Fig. 6.
Fig. 6.

Picture in which the dynamics observed in this study is summarized schematically.

Equations (6)

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I TrL ( t ) = I Sig ( t ) I probe ( t )
Δ T ( t = 0 , r ) = Δ T 0 exp [ ( r w th 2 ) 2 ( z l z ) 2 ]
Δ T ( t , r , z ) = Δ T 0 ( w th 2 ) 3 ( w th 2 ) 2 + 4 D th t · ( l z 2 l z 2 + 4 D th t ) 1 2 exp [ r 2 ( w th 2 ) 2 + 4 D th t z 2 l z 2 + 4 D th t ] .
Δ ϕ ( t , r ) = Δ ϕ th ( w th 2 ) 2 ( w th 2 ) 2 + 4 D th t exp [ r 2 ( w th 2 ) 2 + 4 D th t ]
I ( t , r ) = A 2 π λ probe z 0 0 E 0 ( t , r , d ) exp { i ( Δ ϕ ( t , r ) + π r 2 λ probe z 0 ) } J 0 ( 2 π λ probe z 0 r r ) r d r 2
Δ ϕ th = 2 π 3 2 n 0 λ ( dn dT ) Δ T 0 l z .

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