Abstract

A theoretical model for cw laser-induced thermal lens spectrometry of optically transparent surface-absorbing solids is developed. In the model, the sample is represented as a set of discrete layers with certain thicknesses and light absorptivities. The bloomed thermo-optical element in the sample is described with a summation of heat-flux functions for all the layers. The model employs simple mathematical expressions and can be used for both steady-state and time-resolved thermal lens experiments. Good coincidence of the experimental and theoretically predicted signal dependences is achieved. This model is verified for volume-absorbing samples (colored optical glasses) and used successfully to calculate absorbances and concentrations for various surface-absorbing samples.

© 2005 Optical Society of America

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  6. A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Electronic and thermal contributions to the non-linear refractive index of Nd3+ion-doped fluoride glasses,” J. Non-Cryst. Solids 273, 257–265 (2000).
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  7. S. M. Lima, A. A. Andrade, T. Catunda, R. Lebullenger, F. Smektala, Y. Jestin, M. L. Baesso, “Thermal and optical properties of chalcogalide glass,” J. Non-Cryst. Solids 284, 203–209 (2001).
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  8. J. A. Sampaio, T. Catunda, S. Gama, M. L. Baesso, “Thermo-optical properties of OH-free erbium-doped low silica calcium alumosilicate glass measured by thermal lens technique,” J. Non-Cryst. Solids 284, 210–216 (2001).
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  9. A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Thermal-lens measurements of fluores-cence quantum efficiency in Nd3+-doped fluoride glasses,” J. Non-Cryst. Solids 284, 255–260 (2001).
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    [CrossRef]
  30. D. A. Nedosekin, T. Yu. Chaikovskii, M. Yu. Kononets, M. A. Proskurnin, G. V. Lisichkin, “Thermooptical determination of vanadium and tin compounds at the surface of chemically modified silica,” J. Anal. Chem. (to be published).
  31. V. V. Chernysh, M. A. Proskurnin, M. Yu. Kononets, S. N. Bendrysheva, “Investigation of adsorption of nanogram quantities of iron(II) tris-(1,10-phenanthrolinate) on glasses and silica by thermal lens spectrometry,” Talanta 53, 1221–1227 (2001).
    [CrossRef]
  32. A. V. Pirogov, W. Buchberger, “Ionene-coated sulfonated silica as a packing material in the packed-capillary mode of electrochromatography,” J. Chromatogr. A 916, 51–59 (2001).
    [CrossRef] [PubMed]

2004 (1)

J. F. Power, “Fresnel diffraction model for the point spread of a laser light profile microscope (LPM),” Appl. Phys. B 78, 693–703 (2004).
[CrossRef]

2003 (1)

J. F. Power, “Linear Tikhonov regularization against an edge field: an improved reconstruction algorithm in photothermal depth profilometry,” Appl. Phys. B 76, 569–582 (2003).
[CrossRef]

2002 (1)

M. Yu. Kononets, S. N. Bendrysheva, M. A. Proskurnin, E. V. Proskurnina, E. M. Minkovskil, A. R. Tarasov, G. V. Lisichkin, “Thermal-lens spectrometry for studying molecular layers covalently bonded to a flat glass surface,” Mendeleev Commun. 12, 9–11 (2002).
[CrossRef]

2001 (6)

V. V. Chernysh, M. A. Proskurnin, M. Yu. Kononets, S. N. Bendrysheva, “Investigation of adsorption of nanogram quantities of iron(II) tris-(1,10-phenanthrolinate) on glasses and silica by thermal lens spectrometry,” Talanta 53, 1221–1227 (2001).
[CrossRef]

A. V. Pirogov, W. Buchberger, “Ionene-coated sulfonated silica as a packing material in the packed-capillary mode of electrochromatography,” J. Chromatogr. A 916, 51–59 (2001).
[CrossRef] [PubMed]

H. Hisamoto, T. Horiuchi, M. Tokeshi, A. Hibara, T. Kitamori, “On-chip integration of neutral ionophore-based ion pair extraction reaction,” Anal. Chem 73, 1382–1386 (2001).
[CrossRef]

S. M. Lima, A. A. Andrade, T. Catunda, R. Lebullenger, F. Smektala, Y. Jestin, M. L. Baesso, “Thermal and optical properties of chalcogalide glass,” J. Non-Cryst. Solids 284, 203–209 (2001).
[CrossRef]

J. A. Sampaio, T. Catunda, S. Gama, M. L. Baesso, “Thermo-optical properties of OH-free erbium-doped low silica calcium alumosilicate glass measured by thermal lens technique,” J. Non-Cryst. Solids 284, 210–216 (2001).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Thermal-lens measurements of fluores-cence quantum efficiency in Nd3+-doped fluoride glasses,” J. Non-Cryst. Solids 284, 255–260 (2001).
[CrossRef]

2000 (5)

S. M. Lima, J. A. Sampaio, T. Catunda, A. C. Bento, L. C. M. Miranda, M. L. Baesso, “Mode-mismatched thermal lens spectrometry for thermo-optical properties measurement in optical glasses: a review,” J. Non-Cryst. Solids 273, 215–227 (2000).
[CrossRef]

T. Shimosaka, T. Sugil, T. Hobo, J. B. A. Ross, K. Uchiyama, “Monitoring of dye adsorption phenomena at a silica glass/water interface with total internal reflection coupled with a thermal lens effect,” Anal. Chem. 72, 3532–3538 (2000).
[CrossRef] [PubMed]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Electronic and thermal contributions to the non-linear refractive index of Nd3+ion-doped fluoride glasses,” J. Non-Cryst. Solids 273, 257–265 (2000).
[CrossRef]

G. Gutierrez, T.-Ch. Jen, “Numerical simulation of non-linear heat conduction subjected to a laser source: the effect of variable thermal properties,” Int. J. Heat Mass Transfer 43, 2177–2182 (2000).
[CrossRef]

M. A. Proskurnin, V. V. Kuznetsova, “Optimization of the optical scheme of a dual-beam thermal lens spectrometer using expert estimation,” Anal. Chin. Acta 418, 101–111 (2000).
[CrossRef]

1999 (1)

S. M. Lima, J. A. Sampaio, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, F. C. G. Gandra, “Time-resolved thermal lens measurements of thermo-optical properties of fluoride glasses,” J. Non-Cryst. Solids 256, 337–342 (1999).
[CrossRef]

1998 (2)

H. Kawazumi, T. Kaieda, T. Inoue, T. Ogawa, “Development of an interfacial thermal lens technique: monitoring for the dissolving process of amphiphilic molecules at the hexane–water interface,” Chem. Phys. Lett. 282, 159–163 (1998).
[CrossRef]

R. D. Snook, R. D. Lowe, M. L. Baesso, “Photothermal spectrometry for membrane and interfacial region studies,” Analyst 123, 587–593 (1998).
[CrossRef]

1997 (1)

T. Catunda, M. L. Baesso, Y. Messaddeq, M. A. Aegerter, “Time-resolved Z-scan and thermal lens measurements in Er+3and Nd+3doped fluoroindate glasses,” J. Non-Cryst. Solids 213, 225–230 (1997).
[CrossRef]

1996 (1)

D. W. Tang, N. Araki, “Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance,” Int. J. Heat Mass Transfer 39, 1585–1590 (1996).
[CrossRef]

1995 (1)

R. D. Snook, R. D. Lowe, “Thermal lens spectrometry. A review,” Analyst 120, 2051–2068 (1995).
[CrossRef]

1994 (2)

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

M. A. Schweitzer, J. F. Power, “Optical depth profiling of thin films by impulse mirage-effect spectroscopy. Part I: theory,” Appl. Spectrosc. 48, 1054–1075 (1994).
[CrossRef]

1993 (1)

J. Shen, R. D. Snook, “A radial finite model of thermal lens spectrometry and the influence of sample radius upon the validity of the radial infinite model,” J. Appl. Phys. 73, 5286–5288 (1993).
[CrossRef]

1992 (3)

M. L. Baesso, J. Shen, R. D. Snook, “Time-resolved thermal lens measurements of thermal diffusivity of soda–lime glass,” Chem. Phys. Lett. 197, 255–258 (1992).
[CrossRef]

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

A. G. Abroskin, T. V. Belyaeva, V. A. Filichkina, E. K. Ivanova, M. A. Proscurnin, V. M. Savostina, Yu. A. Barbalat, “Thermal lens spectrometry in trace metal analysis,” Analyst 117, 1957–1962 (1992).
[CrossRef]

1990 (1)

Sh. Wu, N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[CrossRef]

1981 (1)

Abroskin, A. G.

A. G. Abroskin, T. V. Belyaeva, V. A. Filichkina, E. K. Ivanova, M. A. Proscurnin, V. M. Savostina, Yu. A. Barbalat, “Thermal lens spectrometry in trace metal analysis,” Analyst 117, 1957–1962 (1992).
[CrossRef]

Aegerter, M. A.

T. Catunda, M. L. Baesso, Y. Messaddeq, M. A. Aegerter, “Time-resolved Z-scan and thermal lens measurements in Er+3and Nd+3doped fluoroindate glasses,” J. Non-Cryst. Solids 213, 225–230 (1997).
[CrossRef]

Amer, N. M.

Andrade, A. A.

S. M. Lima, A. A. Andrade, T. Catunda, R. Lebullenger, F. Smektala, Y. Jestin, M. L. Baesso, “Thermal and optical properties of chalcogalide glass,” J. Non-Cryst. Solids 284, 203–209 (2001).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Thermal-lens measurements of fluores-cence quantum efficiency in Nd3+-doped fluoride glasses,” J. Non-Cryst. Solids 284, 255–260 (2001).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Electronic and thermal contributions to the non-linear refractive index of Nd3+ion-doped fluoride glasses,” J. Non-Cryst. Solids 273, 257–265 (2000).
[CrossRef]

Araki, N.

D. W. Tang, N. Araki, “Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance,” Int. J. Heat Mass Transfer 39, 1585–1590 (1996).
[CrossRef]

Baesso, M. L.

J. A. Sampaio, T. Catunda, S. Gama, M. L. Baesso, “Thermo-optical properties of OH-free erbium-doped low silica calcium alumosilicate glass measured by thermal lens technique,” J. Non-Cryst. Solids 284, 210–216 (2001).
[CrossRef]

S. M. Lima, A. A. Andrade, T. Catunda, R. Lebullenger, F. Smektala, Y. Jestin, M. L. Baesso, “Thermal and optical properties of chalcogalide glass,” J. Non-Cryst. Solids 284, 203–209 (2001).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Thermal-lens measurements of fluores-cence quantum efficiency in Nd3+-doped fluoride glasses,” J. Non-Cryst. Solids 284, 255–260 (2001).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, A. C. Bento, L. C. M. Miranda, M. L. Baesso, “Mode-mismatched thermal lens spectrometry for thermo-optical properties measurement in optical glasses: a review,” J. Non-Cryst. Solids 273, 215–227 (2000).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Electronic and thermal contributions to the non-linear refractive index of Nd3+ion-doped fluoride glasses,” J. Non-Cryst. Solids 273, 257–265 (2000).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, F. C. G. Gandra, “Time-resolved thermal lens measurements of thermo-optical properties of fluoride glasses,” J. Non-Cryst. Solids 256, 337–342 (1999).
[CrossRef]

R. D. Snook, R. D. Lowe, M. L. Baesso, “Photothermal spectrometry for membrane and interfacial region studies,” Analyst 123, 587–593 (1998).
[CrossRef]

T. Catunda, M. L. Baesso, Y. Messaddeq, M. A. Aegerter, “Time-resolved Z-scan and thermal lens measurements in Er+3and Nd+3doped fluoroindate glasses,” J. Non-Cryst. Solids 213, 225–230 (1997).
[CrossRef]

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

M. L. Baesso, J. Shen, R. D. Snook, “Time-resolved thermal lens measurements of thermal diffusivity of soda–lime glass,” Chem. Phys. Lett. 197, 255–258 (1992).
[CrossRef]

Barbalat, Yu. A.

A. G. Abroskin, T. V. Belyaeva, V. A. Filichkina, E. K. Ivanova, M. A. Proscurnin, V. M. Savostina, Yu. A. Barbalat, “Thermal lens spectrometry in trace metal analysis,” Analyst 117, 1957–1962 (1992).
[CrossRef]

Belyaeva, T. V.

A. G. Abroskin, T. V. Belyaeva, V. A. Filichkina, E. K. Ivanova, M. A. Proscurnin, V. M. Savostina, Yu. A. Barbalat, “Thermal lens spectrometry in trace metal analysis,” Analyst 117, 1957–1962 (1992).
[CrossRef]

Bendrysheva, S. N.

M. Yu. Kononets, S. N. Bendrysheva, M. A. Proskurnin, E. V. Proskurnina, E. M. Minkovskil, A. R. Tarasov, G. V. Lisichkin, “Thermal-lens spectrometry for studying molecular layers covalently bonded to a flat glass surface,” Mendeleev Commun. 12, 9–11 (2002).
[CrossRef]

V. V. Chernysh, M. A. Proskurnin, M. Yu. Kononets, S. N. Bendrysheva, “Investigation of adsorption of nanogram quantities of iron(II) tris-(1,10-phenanthrolinate) on glasses and silica by thermal lens spectrometry,” Talanta 53, 1221–1227 (2001).
[CrossRef]

Bento, A. C.

S. M. Lima, J. A. Sampaio, T. Catunda, A. C. Bento, L. C. M. Miranda, M. L. Baesso, “Mode-mismatched thermal lens spectrometry for thermo-optical properties measurement in optical glasses: a review,” J. Non-Cryst. Solids 273, 215–227 (2000).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, F. C. G. Gandra, “Time-resolved thermal lens measurements of thermo-optical properties of fluoride glasses,” J. Non-Cryst. Solids 256, 337–342 (1999).
[CrossRef]

Bialkowski, S. E.

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

Boccara, A. C.

Buchberger, W.

A. V. Pirogov, W. Buchberger, “Ionene-coated sulfonated silica as a packing material in the packed-capillary mode of electrochromatography,” J. Chromatogr. A 916, 51–59 (2001).
[CrossRef] [PubMed]

Catunda, T.

S. M. Lima, A. A. Andrade, T. Catunda, R. Lebullenger, F. Smektala, Y. Jestin, M. L. Baesso, “Thermal and optical properties of chalcogalide glass,” J. Non-Cryst. Solids 284, 203–209 (2001).
[CrossRef]

J. A. Sampaio, T. Catunda, S. Gama, M. L. Baesso, “Thermo-optical properties of OH-free erbium-doped low silica calcium alumosilicate glass measured by thermal lens technique,” J. Non-Cryst. Solids 284, 210–216 (2001).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Thermal-lens measurements of fluores-cence quantum efficiency in Nd3+-doped fluoride glasses,” J. Non-Cryst. Solids 284, 255–260 (2001).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Electronic and thermal contributions to the non-linear refractive index of Nd3+ion-doped fluoride glasses,” J. Non-Cryst. Solids 273, 257–265 (2000).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, A. C. Bento, L. C. M. Miranda, M. L. Baesso, “Mode-mismatched thermal lens spectrometry for thermo-optical properties measurement in optical glasses: a review,” J. Non-Cryst. Solids 273, 215–227 (2000).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, F. C. G. Gandra, “Time-resolved thermal lens measurements of thermo-optical properties of fluoride glasses,” J. Non-Cryst. Solids 256, 337–342 (1999).
[CrossRef]

T. Catunda, M. L. Baesso, Y. Messaddeq, M. A. Aegerter, “Time-resolved Z-scan and thermal lens measurements in Er+3and Nd+3doped fluoroindate glasses,” J. Non-Cryst. Solids 213, 225–230 (1997).
[CrossRef]

Chaikovskii, T. Yu.

D. A. Nedosekin, T. Yu. Chaikovskii, M. Yu. Kononets, M. A. Proskurnin, G. V. Lisichkin, “Thermooptical determination of vanadium and tin compounds at the surface of chemically modified silica,” J. Anal. Chem. (to be published).

Chernysh, V. V.

V. V. Chernysh, M. A. Proskurnin, M. Yu. Kononets, S. N. Bendrysheva, “Investigation of adsorption of nanogram quantities of iron(II) tris-(1,10-phenanthrolinate) on glasses and silica by thermal lens spectrometry,” Talanta 53, 1221–1227 (2001).
[CrossRef]

Dovichi, N. J.

Sh. Wu, N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[CrossRef]

Filichkina, V. A.

A. G. Abroskin, T. V. Belyaeva, V. A. Filichkina, E. K. Ivanova, M. A. Proscurnin, V. M. Savostina, Yu. A. Barbalat, “Thermal lens spectrometry in trace metal analysis,” Analyst 117, 1957–1962 (1992).
[CrossRef]

Fournier, D. A.

Gama, S.

J. A. Sampaio, T. Catunda, S. Gama, M. L. Baesso, “Thermo-optical properties of OH-free erbium-doped low silica calcium alumosilicate glass measured by thermal lens technique,” J. Non-Cryst. Solids 284, 210–216 (2001).
[CrossRef]

Gandra, F. C. G.

S. M. Lima, J. A. Sampaio, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, F. C. G. Gandra, “Time-resolved thermal lens measurements of thermo-optical properties of fluoride glasses,” J. Non-Cryst. Solids 256, 337–342 (1999).
[CrossRef]

Gutierrez, G.

G. Gutierrez, T.-Ch. Jen, “Numerical simulation of non-linear heat conduction subjected to a laser source: the effect of variable thermal properties,” Int. J. Heat Mass Transfer 43, 2177–2182 (2000).
[CrossRef]

Hernandes, A. C.

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Thermal-lens measurements of fluores-cence quantum efficiency in Nd3+-doped fluoride glasses,” J. Non-Cryst. Solids 284, 255–260 (2001).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Electronic and thermal contributions to the non-linear refractive index of Nd3+ion-doped fluoride glasses,” J. Non-Cryst. Solids 273, 257–265 (2000).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, F. C. G. Gandra, “Time-resolved thermal lens measurements of thermo-optical properties of fluoride glasses,” J. Non-Cryst. Solids 256, 337–342 (1999).
[CrossRef]

Hibara, A.

H. Hisamoto, T. Horiuchi, M. Tokeshi, A. Hibara, T. Kitamori, “On-chip integration of neutral ionophore-based ion pair extraction reaction,” Anal. Chem 73, 1382–1386 (2001).
[CrossRef]

Hisamoto, H.

H. Hisamoto, T. Horiuchi, M. Tokeshi, A. Hibara, T. Kitamori, “On-chip integration of neutral ionophore-based ion pair extraction reaction,” Anal. Chem 73, 1382–1386 (2001).
[CrossRef]

Hobo, T.

T. Shimosaka, T. Sugil, T. Hobo, J. B. A. Ross, K. Uchiyama, “Monitoring of dye adsorption phenomena at a silica glass/water interface with total internal reflection coupled with a thermal lens effect,” Anal. Chem. 72, 3532–3538 (2000).
[CrossRef] [PubMed]

Horiuchi, T.

H. Hisamoto, T. Horiuchi, M. Tokeshi, A. Hibara, T. Kitamori, “On-chip integration of neutral ionophore-based ion pair extraction reaction,” Anal. Chem 73, 1382–1386 (2001).
[CrossRef]

Inoue, T.

H. Kawazumi, T. Kaieda, T. Inoue, T. Ogawa, “Development of an interfacial thermal lens technique: monitoring for the dissolving process of amphiphilic molecules at the hexane–water interface,” Chem. Phys. Lett. 282, 159–163 (1998).
[CrossRef]

Ivanova, E. K.

A. G. Abroskin, T. V. Belyaeva, V. A. Filichkina, E. K. Ivanova, M. A. Proscurnin, V. M. Savostina, Yu. A. Barbalat, “Thermal lens spectrometry in trace metal analysis,” Analyst 117, 1957–1962 (1992).
[CrossRef]

Jackson, W. B.

Jen, T.-Ch.

G. Gutierrez, T.-Ch. Jen, “Numerical simulation of non-linear heat conduction subjected to a laser source: the effect of variable thermal properties,” Int. J. Heat Mass Transfer 43, 2177–2182 (2000).
[CrossRef]

Jestin, Y.

S. M. Lima, A. A. Andrade, T. Catunda, R. Lebullenger, F. Smektala, Y. Jestin, M. L. Baesso, “Thermal and optical properties of chalcogalide glass,” J. Non-Cryst. Solids 284, 203–209 (2001).
[CrossRef]

Kaieda, T.

H. Kawazumi, T. Kaieda, T. Inoue, T. Ogawa, “Development of an interfacial thermal lens technique: monitoring for the dissolving process of amphiphilic molecules at the hexane–water interface,” Chem. Phys. Lett. 282, 159–163 (1998).
[CrossRef]

Kawazumi, H.

H. Kawazumi, T. Kaieda, T. Inoue, T. Ogawa, “Development of an interfacial thermal lens technique: monitoring for the dissolving process of amphiphilic molecules at the hexane–water interface,” Chem. Phys. Lett. 282, 159–163 (1998).
[CrossRef]

Kitamori, T.

H. Hisamoto, T. Horiuchi, M. Tokeshi, A. Hibara, T. Kitamori, “On-chip integration of neutral ionophore-based ion pair extraction reaction,” Anal. Chem 73, 1382–1386 (2001).
[CrossRef]

Kononets, M. Yu.

M. Yu. Kononets, S. N. Bendrysheva, M. A. Proskurnin, E. V. Proskurnina, E. M. Minkovskil, A. R. Tarasov, G. V. Lisichkin, “Thermal-lens spectrometry for studying molecular layers covalently bonded to a flat glass surface,” Mendeleev Commun. 12, 9–11 (2002).
[CrossRef]

V. V. Chernysh, M. A. Proskurnin, M. Yu. Kononets, S. N. Bendrysheva, “Investigation of adsorption of nanogram quantities of iron(II) tris-(1,10-phenanthrolinate) on glasses and silica by thermal lens spectrometry,” Talanta 53, 1221–1227 (2001).
[CrossRef]

D. A. Nedosekin, T. Yu. Chaikovskii, M. Yu. Kononets, M. A. Proskurnin, G. V. Lisichkin, “Thermooptical determination of vanadium and tin compounds at the surface of chemically modified silica,” J. Anal. Chem. (to be published).

Kuznetsova, V. V.

M. A. Proskurnin, V. V. Kuznetsova, “Optimization of the optical scheme of a dual-beam thermal lens spectrometer using expert estimation,” Anal. Chin. Acta 418, 101–111 (2000).
[CrossRef]

Lebullenger, R.

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Thermal-lens measurements of fluores-cence quantum efficiency in Nd3+-doped fluoride glasses,” J. Non-Cryst. Solids 284, 255–260 (2001).
[CrossRef]

S. M. Lima, A. A. Andrade, T. Catunda, R. Lebullenger, F. Smektala, Y. Jestin, M. L. Baesso, “Thermal and optical properties of chalcogalide glass,” J. Non-Cryst. Solids 284, 203–209 (2001).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Electronic and thermal contributions to the non-linear refractive index of Nd3+ion-doped fluoride glasses,” J. Non-Cryst. Solids 273, 257–265 (2000).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, F. C. G. Gandra, “Time-resolved thermal lens measurements of thermo-optical properties of fluoride glasses,” J. Non-Cryst. Solids 256, 337–342 (1999).
[CrossRef]

Lima, S. M.

S. M. Lima, A. A. Andrade, T. Catunda, R. Lebullenger, F. Smektala, Y. Jestin, M. L. Baesso, “Thermal and optical properties of chalcogalide glass,” J. Non-Cryst. Solids 284, 203–209 (2001).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, A. C. Bento, L. C. M. Miranda, M. L. Baesso, “Mode-mismatched thermal lens spectrometry for thermo-optical properties measurement in optical glasses: a review,” J. Non-Cryst. Solids 273, 215–227 (2000).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, F. C. G. Gandra, “Time-resolved thermal lens measurements of thermo-optical properties of fluoride glasses,” J. Non-Cryst. Solids 256, 337–342 (1999).
[CrossRef]

Lisichkin, G. V.

M. Yu. Kononets, S. N. Bendrysheva, M. A. Proskurnin, E. V. Proskurnina, E. M. Minkovskil, A. R. Tarasov, G. V. Lisichkin, “Thermal-lens spectrometry for studying molecular layers covalently bonded to a flat glass surface,” Mendeleev Commun. 12, 9–11 (2002).
[CrossRef]

D. A. Nedosekin, T. Yu. Chaikovskii, M. Yu. Kononets, M. A. Proskurnin, G. V. Lisichkin, “Thermooptical determination of vanadium and tin compounds at the surface of chemically modified silica,” J. Anal. Chem. (to be published).

Lowe, R. D.

R. D. Snook, R. D. Lowe, M. L. Baesso, “Photothermal spectrometry for membrane and interfacial region studies,” Analyst 123, 587–593 (1998).
[CrossRef]

R. D. Snook, R. D. Lowe, “Thermal lens spectrometry. A review,” Analyst 120, 2051–2068 (1995).
[CrossRef]

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

Messaddeq, Y.

T. Catunda, M. L. Baesso, Y. Messaddeq, M. A. Aegerter, “Time-resolved Z-scan and thermal lens measurements in Er+3and Nd+3doped fluoroindate glasses,” J. Non-Cryst. Solids 213, 225–230 (1997).
[CrossRef]

Minkovskil, E. M.

M. Yu. Kononets, S. N. Bendrysheva, M. A. Proskurnin, E. V. Proskurnina, E. M. Minkovskil, A. R. Tarasov, G. V. Lisichkin, “Thermal-lens spectrometry for studying molecular layers covalently bonded to a flat glass surface,” Mendeleev Commun. 12, 9–11 (2002).
[CrossRef]

Miranda, L. C. M.

S. M. Lima, J. A. Sampaio, T. Catunda, A. C. Bento, L. C. M. Miranda, M. L. Baesso, “Mode-mismatched thermal lens spectrometry for thermo-optical properties measurement in optical glasses: a review,” J. Non-Cryst. Solids 273, 215–227 (2000).
[CrossRef]

Nedosekin, D. A.

D. A. Nedosekin, T. Yu. Chaikovskii, M. Yu. Kononets, M. A. Proskurnin, G. V. Lisichkin, “Thermooptical determination of vanadium and tin compounds at the surface of chemically modified silica,” J. Anal. Chem. (to be published).

Ogawa, T.

H. Kawazumi, T. Kaieda, T. Inoue, T. Ogawa, “Development of an interfacial thermal lens technique: monitoring for the dissolving process of amphiphilic molecules at the hexane–water interface,” Chem. Phys. Lett. 282, 159–163 (1998).
[CrossRef]

Pirogov, A. V.

A. V. Pirogov, W. Buchberger, “Ionene-coated sulfonated silica as a packing material in the packed-capillary mode of electrochromatography,” J. Chromatogr. A 916, 51–59 (2001).
[CrossRef] [PubMed]

Power, J. F.

J. F. Power, “Fresnel diffraction model for the point spread of a laser light profile microscope (LPM),” Appl. Phys. B 78, 693–703 (2004).
[CrossRef]

J. F. Power, “Linear Tikhonov regularization against an edge field: an improved reconstruction algorithm in photothermal depth profilometry,” Appl. Phys. B 76, 569–582 (2003).
[CrossRef]

M. A. Schweitzer, J. F. Power, “Optical depth profiling of thin films by impulse mirage-effect spectroscopy. Part I: theory,” Appl. Spectrosc. 48, 1054–1075 (1994).
[CrossRef]

Proscurnin, M. A.

A. G. Abroskin, T. V. Belyaeva, V. A. Filichkina, E. K. Ivanova, M. A. Proscurnin, V. M. Savostina, Yu. A. Barbalat, “Thermal lens spectrometry in trace metal analysis,” Analyst 117, 1957–1962 (1992).
[CrossRef]

Proskurnin, M. A.

M. Yu. Kononets, S. N. Bendrysheva, M. A. Proskurnin, E. V. Proskurnina, E. M. Minkovskil, A. R. Tarasov, G. V. Lisichkin, “Thermal-lens spectrometry for studying molecular layers covalently bonded to a flat glass surface,” Mendeleev Commun. 12, 9–11 (2002).
[CrossRef]

V. V. Chernysh, M. A. Proskurnin, M. Yu. Kononets, S. N. Bendrysheva, “Investigation of adsorption of nanogram quantities of iron(II) tris-(1,10-phenanthrolinate) on glasses and silica by thermal lens spectrometry,” Talanta 53, 1221–1227 (2001).
[CrossRef]

M. A. Proskurnin, V. V. Kuznetsova, “Optimization of the optical scheme of a dual-beam thermal lens spectrometer using expert estimation,” Anal. Chin. Acta 418, 101–111 (2000).
[CrossRef]

D. A. Nedosekin, T. Yu. Chaikovskii, M. Yu. Kononets, M. A. Proskurnin, G. V. Lisichkin, “Thermooptical determination of vanadium and tin compounds at the surface of chemically modified silica,” J. Anal. Chem. (to be published).

Proskurnina, E. V.

M. Yu. Kononets, S. N. Bendrysheva, M. A. Proskurnin, E. V. Proskurnina, E. M. Minkovskil, A. R. Tarasov, G. V. Lisichkin, “Thermal-lens spectrometry for studying molecular layers covalently bonded to a flat glass surface,” Mendeleev Commun. 12, 9–11 (2002).
[CrossRef]

Ross, J. B. A.

T. Shimosaka, T. Sugil, T. Hobo, J. B. A. Ross, K. Uchiyama, “Monitoring of dye adsorption phenomena at a silica glass/water interface with total internal reflection coupled with a thermal lens effect,” Anal. Chem. 72, 3532–3538 (2000).
[CrossRef] [PubMed]

Sampaio, J. A.

J. A. Sampaio, T. Catunda, S. Gama, M. L. Baesso, “Thermo-optical properties of OH-free erbium-doped low silica calcium alumosilicate glass measured by thermal lens technique,” J. Non-Cryst. Solids 284, 210–216 (2001).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, A. C. Bento, L. C. M. Miranda, M. L. Baesso, “Mode-mismatched thermal lens spectrometry for thermo-optical properties measurement in optical glasses: a review,” J. Non-Cryst. Solids 273, 215–227 (2000).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, F. C. G. Gandra, “Time-resolved thermal lens measurements of thermo-optical properties of fluoride glasses,” J. Non-Cryst. Solids 256, 337–342 (1999).
[CrossRef]

Savostina, V. M.

A. G. Abroskin, T. V. Belyaeva, V. A. Filichkina, E. K. Ivanova, M. A. Proscurnin, V. M. Savostina, Yu. A. Barbalat, “Thermal lens spectrometry in trace metal analysis,” Analyst 117, 1957–1962 (1992).
[CrossRef]

Schweitzer, M. A.

Shen, J.

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

J. Shen, R. D. Snook, “A radial finite model of thermal lens spectrometry and the influence of sample radius upon the validity of the radial infinite model,” J. Appl. Phys. 73, 5286–5288 (1993).
[CrossRef]

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

M. L. Baesso, J. Shen, R. D. Snook, “Time-resolved thermal lens measurements of thermal diffusivity of soda–lime glass,” Chem. Phys. Lett. 197, 255–258 (1992).
[CrossRef]

Shimosaka, T.

T. Shimosaka, T. Sugil, T. Hobo, J. B. A. Ross, K. Uchiyama, “Monitoring of dye adsorption phenomena at a silica glass/water interface with total internal reflection coupled with a thermal lens effect,” Anal. Chem. 72, 3532–3538 (2000).
[CrossRef] [PubMed]

Smektala, F.

S. M. Lima, A. A. Andrade, T. Catunda, R. Lebullenger, F. Smektala, Y. Jestin, M. L. Baesso, “Thermal and optical properties of chalcogalide glass,” J. Non-Cryst. Solids 284, 203–209 (2001).
[CrossRef]

Snook, R. D.

R. D. Snook, R. D. Lowe, M. L. Baesso, “Photothermal spectrometry for membrane and interfacial region studies,” Analyst 123, 587–593 (1998).
[CrossRef]

R. D. Snook, R. D. Lowe, “Thermal lens spectrometry. A review,” Analyst 120, 2051–2068 (1995).
[CrossRef]

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

J. Shen, R. D. Snook, “A radial finite model of thermal lens spectrometry and the influence of sample radius upon the validity of the radial infinite model,” J. Appl. Phys. 73, 5286–5288 (1993).
[CrossRef]

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

M. L. Baesso, J. Shen, R. D. Snook, “Time-resolved thermal lens measurements of thermal diffusivity of soda–lime glass,” Chem. Phys. Lett. 197, 255–258 (1992).
[CrossRef]

Sugil, T.

T. Shimosaka, T. Sugil, T. Hobo, J. B. A. Ross, K. Uchiyama, “Monitoring of dye adsorption phenomena at a silica glass/water interface with total internal reflection coupled with a thermal lens effect,” Anal. Chem. 72, 3532–3538 (2000).
[CrossRef] [PubMed]

Tang, D. W.

D. W. Tang, N. Araki, “Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance,” Int. J. Heat Mass Transfer 39, 1585–1590 (1996).
[CrossRef]

Tarasov, A. R.

M. Yu. Kononets, S. N. Bendrysheva, M. A. Proskurnin, E. V. Proskurnina, E. M. Minkovskil, A. R. Tarasov, G. V. Lisichkin, “Thermal-lens spectrometry for studying molecular layers covalently bonded to a flat glass surface,” Mendeleev Commun. 12, 9–11 (2002).
[CrossRef]

Tokeshi, M.

H. Hisamoto, T. Horiuchi, M. Tokeshi, A. Hibara, T. Kitamori, “On-chip integration of neutral ionophore-based ion pair extraction reaction,” Anal. Chem 73, 1382–1386 (2001).
[CrossRef]

Uchiyama, K.

T. Shimosaka, T. Sugil, T. Hobo, J. B. A. Ross, K. Uchiyama, “Monitoring of dye adsorption phenomena at a silica glass/water interface with total internal reflection coupled with a thermal lens effect,” Anal. Chem. 72, 3532–3538 (2000).
[CrossRef] [PubMed]

Uvarov, I. M.

I. M. Uvarov, The Book of USSR State Standards. 9411-81. Colored Optical Glass. Technical Conditions (Standards Publishing House, Moscow, 1981).

Wu, Sh.

Sh. Wu, N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[CrossRef]

Anal. Chem (1)

H. Hisamoto, T. Horiuchi, M. Tokeshi, A. Hibara, T. Kitamori, “On-chip integration of neutral ionophore-based ion pair extraction reaction,” Anal. Chem 73, 1382–1386 (2001).
[CrossRef]

Anal. Chem. (1)

T. Shimosaka, T. Sugil, T. Hobo, J. B. A. Ross, K. Uchiyama, “Monitoring of dye adsorption phenomena at a silica glass/water interface with total internal reflection coupled with a thermal lens effect,” Anal. Chem. 72, 3532–3538 (2000).
[CrossRef] [PubMed]

Anal. Chin. Acta (1)

M. A. Proskurnin, V. V. Kuznetsova, “Optimization of the optical scheme of a dual-beam thermal lens spectrometer using expert estimation,” Anal. Chin. Acta 418, 101–111 (2000).
[CrossRef]

Analyst (3)

A. G. Abroskin, T. V. Belyaeva, V. A. Filichkina, E. K. Ivanova, M. A. Proscurnin, V. M. Savostina, Yu. A. Barbalat, “Thermal lens spectrometry in trace metal analysis,” Analyst 117, 1957–1962 (1992).
[CrossRef]

R. D. Snook, R. D. Lowe, M. L. Baesso, “Photothermal spectrometry for membrane and interfacial region studies,” Analyst 123, 587–593 (1998).
[CrossRef]

R. D. Snook, R. D. Lowe, “Thermal lens spectrometry. A review,” Analyst 120, 2051–2068 (1995).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

J. F. Power, “Fresnel diffraction model for the point spread of a laser light profile microscope (LPM),” Appl. Phys. B 78, 693–703 (2004).
[CrossRef]

J. F. Power, “Linear Tikhonov regularization against an edge field: an improved reconstruction algorithm in photothermal depth profilometry,” Appl. Phys. B 76, 569–582 (2003).
[CrossRef]

Appl. Spectrosc. (1)

Chem. Phys (1)

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

Chem. Phys. Lett. (2)

H. Kawazumi, T. Kaieda, T. Inoue, T. Ogawa, “Development of an interfacial thermal lens technique: monitoring for the dissolving process of amphiphilic molecules at the hexane–water interface,” Chem. Phys. Lett. 282, 159–163 (1998).
[CrossRef]

M. L. Baesso, J. Shen, R. D. Snook, “Time-resolved thermal lens measurements of thermal diffusivity of soda–lime glass,” Chem. Phys. Lett. 197, 255–258 (1992).
[CrossRef]

Int. J. Heat Mass Transfer (2)

D. W. Tang, N. Araki, “Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance,” Int. J. Heat Mass Transfer 39, 1585–1590 (1996).
[CrossRef]

G. Gutierrez, T.-Ch. Jen, “Numerical simulation of non-linear heat conduction subjected to a laser source: the effect of variable thermal properties,” Int. J. Heat Mass Transfer 43, 2177–2182 (2000).
[CrossRef]

J. Appl. Phys. (3)

J. Shen, R. D. Snook, “A radial finite model of thermal lens spectrometry and the influence of sample radius upon the validity of the radial infinite model,” J. Appl. Phys. 73, 5286–5288 (1993).
[CrossRef]

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

Sh. Wu, N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[CrossRef]

J. Chromatogr. A (1)

A. V. Pirogov, W. Buchberger, “Ionene-coated sulfonated silica as a packing material in the packed-capillary mode of electrochromatography,” J. Chromatogr. A 916, 51–59 (2001).
[CrossRef] [PubMed]

J. Non-Cryst. Solids (7)

S. M. Lima, J. A. Sampaio, T. Catunda, A. C. Bento, L. C. M. Miranda, M. L. Baesso, “Mode-mismatched thermal lens spectrometry for thermo-optical properties measurement in optical glasses: a review,” J. Non-Cryst. Solids 273, 215–227 (2000).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Electronic and thermal contributions to the non-linear refractive index of Nd3+ion-doped fluoride glasses,” J. Non-Cryst. Solids 273, 257–265 (2000).
[CrossRef]

S. M. Lima, A. A. Andrade, T. Catunda, R. Lebullenger, F. Smektala, Y. Jestin, M. L. Baesso, “Thermal and optical properties of chalcogalide glass,” J. Non-Cryst. Solids 284, 203–209 (2001).
[CrossRef]

J. A. Sampaio, T. Catunda, S. Gama, M. L. Baesso, “Thermo-optical properties of OH-free erbium-doped low silica calcium alumosilicate glass measured by thermal lens technique,” J. Non-Cryst. Solids 284, 210–216 (2001).
[CrossRef]

A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, “Thermal-lens measurements of fluores-cence quantum efficiency in Nd3+-doped fluoride glasses,” J. Non-Cryst. Solids 284, 255–260 (2001).
[CrossRef]

T. Catunda, M. L. Baesso, Y. Messaddeq, M. A. Aegerter, “Time-resolved Z-scan and thermal lens measurements in Er+3and Nd+3doped fluoroindate glasses,” J. Non-Cryst. Solids 213, 225–230 (1997).
[CrossRef]

S. M. Lima, J. A. Sampaio, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, F. C. G. Gandra, “Time-resolved thermal lens measurements of thermo-optical properties of fluoride glasses,” J. Non-Cryst. Solids 256, 337–342 (1999).
[CrossRef]

Mendeleev Commun. (1)

M. Yu. Kononets, S. N. Bendrysheva, M. A. Proskurnin, E. V. Proskurnina, E. M. Minkovskil, A. R. Tarasov, G. V. Lisichkin, “Thermal-lens spectrometry for studying molecular layers covalently bonded to a flat glass surface,” Mendeleev Commun. 12, 9–11 (2002).
[CrossRef]

Talanta (1)

V. V. Chernysh, M. A. Proskurnin, M. Yu. Kononets, S. N. Bendrysheva, “Investigation of adsorption of nanogram quantities of iron(II) tris-(1,10-phenanthrolinate) on glasses and silica by thermal lens spectrometry,” Talanta 53, 1221–1227 (2001).
[CrossRef]

Other (4)

D. A. Nedosekin, T. Yu. Chaikovskii, M. Yu. Kononets, M. A. Proskurnin, G. V. Lisichkin, “Thermooptical determination of vanadium and tin compounds at the surface of chemically modified silica,” J. Anal. Chem. (to be published).

I. M. Uvarov, The Book of USSR State Standards. 9411-81. Colored Optical Glass. Technical Conditions (Standards Publishing House, Moscow, 1981).

M. Pons, S. Nonell, I. Garcia-Moreno, A. Costela, R. Sastre, “Thermal diffusion coefficients of solid polymeric laser dye solutions: a time-resolved thermal lens study,” presented at the Third Internet Photochemistry and Photobiology Conference, 24 November to 24 December 2000, http://www.photobiology.com/photobiology2000/nonell/index.htm .

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

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Figures (6)

Fig. 1
Fig. 1

Model representation of a sample as an assemblage of dsiscrete layers.

Fig. 2
Fig. 2

(a) Scheme of simulation of cw laser irradiation and (b) corresponding temperature rise in the sample by a series of pulses.

Fig. 3
Fig. 3

Calculated temperature profile in the sample with 1 μm light-absorbing layers on both sides of a glass plate (thickness of the plate, 1 mm; excitation laser power, 400 mW; other parameters are summarized in Table 4).

Fig. 4
Fig. 4

Schematic diagram of the probe beam propagation.

Fig. 5
Fig. 5

Experimental and calculated curves of the thermal lens signal development in the glass.1 Excitation laser power, 260 mW; λe = 488.0 nm. Parameters selected for calculations are given in Tables 2 and 3.

Fig. 6
Fig. 6

Experimental and theoretical dependences of the steady-state spectrometer signal ϑ(t → ∞) [Eqs. (5)(18)] on the sample absorption. Excitation laser power, 260 mW; λe = 488.0 nm.

Tables (5)

Tables Icon

Table 1 Requirements for Calculations of Temperature Profile Development in the Solid upon Laser Heating: Advantages and Disadvantages of the Existing Models

Tables Icon

Table 2 Thermal Lens Spectrometer Parameters

Tables Icon

Table 3 Thermo-Optical Parameters of Glassa Used for Calculation of the Temperature Rise [Eqs. (5)(11)]

Tables Icon

Table 4 Thermo-Optical Properties of the Colored Optical Glassesa (T = 298 K) (n = 3, P = 0.95)b

Tables Icon

Table 5 Estimation of the Parameters of Surface-Absorbing Samples of Glass (n = 10, P = 0.95)

Equations (23)

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

I ( r ) = 2 P e π ω e 2 exp ( - 2 r 2 ω e 2 ) .
t [ Δ T solid ( r , z , t ) ] - α solid 2 [ Δ T solid ( r , z , t ) ] = Q ( r , z , t ) C p ρ             for 0 z - 1 ,
t [ Δ T air ( r , z , t ) ] - α air 2 [ Δ T air ( r , z , t ) ] = 0             for z 0 and - l z .
Q ( r , z , t ) = 2 π β ( z ) I ( r ) r d r
Δ T ( r , z , t ) = 4 α t p π ω e 2 k π ( η i β i I i - 1 ) ( 4 α t ) - 3 / 2 ( Δ T long Δ T rad ) .
I i - 1 = I 0 exp ( - j = 1 i - 1 β j l j ) = 2 P e π ω e 2 exp ( - j = 1 i - 1 β j l j ) .
Δ T long , i ( z , t ) = exp [ β i ( z + l i - 1 ) ] × exp ( β i 2 α t ) 4 α t { erfc [ ( z + l i - 1 ) 4 α t + β i α t ] - erfc [ ( z + l i ) 4 α t + β i α t ] } .
Δ T rad , i ( r , t ) = 16 π α t ω e 2 ω c 2 exp ( - 2 r 2 ω c 2 ) ,
Δ T i ( r , z , t ) = 16 α π - 1 / 2 t p k [ exp ( - r 2 ω c 2 ) ω c 2 ] ( η i β i I i - 1 ) × ( exp [ β i ( z + l i - 1 ) ] exp ( β i 2 α t ) × { erfc [ ( z + l i - 1 ) 4 α t + β i α t ] - erfc [ ( z + l i ) 4 α t + β i α t ] } ) .
Δ T ( r , z , t ) = i = 1 M Δ T i ( r , z , t ) .
Δ T cw ( z , r , t ) = n = 1 N Δ T n ( z , r , t ) = n = 1 N i = 1 M Δ T n , i ( z , r , t ) ,
n ( z , r , t ) = n 0 + r 2 2 [ d 2 n ( z , t ) d r 2 ] = n 0 + r 2 2 ( d n d T ) p [ d 2 T cw ( z , t ) d r 2 ] .
d s d T = d n d T + γ p 3 ( n - 1 ) ( 1 + ν ) + n 0 3 4 γ p 3 E ( q + q ) .
d n d T ( n T ) p = - γ p ( n 2 - 1 ) ( n 2 + 2 ) 6 n .
1 f ( t ) = - l n air ( d n d T ) [ d 2 T cw ( r , z , t ) d r 2 ] r = 0 .
1 f ( t ) = - path d 2 n ( r , z , t ) d r 2 d z = - ( d n d T ) path d 2 T cw ( r , z , t ) d r 2 d z .
ϑ ( t ) = - [ 2 z d f ( t ) ] z w 2 + z 0 2 + z d z w ( z w + z d ) 2 + z 0 2 + [ z d f ( t ) ] 2 z w 2 + z 0 2 ( z w + z d ) 2 + z 0 2 .
A = i = 1 M β i l i = ϑ ( t ) - ϑ ( t = 0 ) a .
I p ( t ) I p ( 0 ) = 1 ϑ ( t ) + 1 .
I p ( t ) I p ( 0 ) = ( 1 - P e β l 2 k λ p d s d T × tan - 1 { 2 m V [ ( 1 + 2 m ) 2 + V 2 ] ( t c / 2 t ) + 1 + 2 m + V 2 } ) .
ϑ ZhS - 18 = - ( 0.8 ± 0.1 ) × 10 - 3 × P e - 0.002 ± 0.001 ( n = 8 , P = 0.95 , r = 0.9756 ) ,
ϑ ZhS - 17 = - ( 0.5 ± 0.1 ) × 10 - 3 × P e + 0.001 ± 0.001 ( n = 8 , P = 0.95 , r = 0.9786 ) .
ϑ = - 7.3 A - ϑ 0 .

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