Abstract

A model of the photothermal deflection signal in multilayer coatings is presented that takes into account optical interference effects and heat flow within the stack. Measurements are then taken of high-reflectivity HfO2/SiO2 ultraviolet mirrors made by plasma ion assisted deposition and compared to calculations. Good agreement is found between the experimental results and the model. Using this model for the calibration and the setup described, one can measure absorption in multilayer coatings accurately down to 10−7 of the incident power.

© 2005 Optical Society of America

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  1. A. C. Boccara, D. Fournier, W. Jackson, N. M. Amer, “Sensitive photothermal deflection technique for measuring absorption in optically thin media,” Opt. Lett. 5, 377–379 (1980).
    [CrossRef] [PubMed]
  2. J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
    [CrossRef]
  3. E. Welsh, D. Ristau, “Photothermal measurements on optical thin films,” Appl. Opt. 34, 7339–7253 (1995).
  4. M. Commandré, E. Pelletier, “Measurement of absorption losses in TiO2 films by a collinear photothermal deflection technique,” Appl. Opt. 29, 4276–4283 (1990).
    [CrossRef]
  5. M. Commandré, P. Roche, “Characterization of optical coatings by photothermal deflection,” Appl. Opt. 35, 5021–5034 (1996).
    [CrossRef] [PubMed]
  6. Z. Wu, M. Thomsen, P. Kuo, Y. Lu, C. Stolz, M. Koslowski, “Photothermal characterization of optical thin film coatings,” Opt. Eng. 36, 251–262 (1997).
    [CrossRef]
  7. V. Loriette, C. Boccara, “Absorption of low-loss optical materials measured at 1064 nm by a position-modulated collinear photothermal detection technique,” Appl. Opt. 42, 649–656 (2003).
    [CrossRef] [PubMed]
  8. A. During, C. Fossati, M. Commandré, “Photothermal deflection microscopy for imaging submicronic defects in optical materials,” Opt. Commun. 230, 279–286 (2004).
    [CrossRef]
  9. W. Mundy, J. Ermshar, P. Hanson, R. Hughes, “Photothermal deflection microscopy of HR and AR coatings,” in Laser-Induced Damage in Optical Materials: 1983, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Nat. Bur. Stand. (U.S.) Spec. Publ.688, 360–371 (1983).
  10. A. Papandrew, C. Stolz, Z. Wu, G. Loomis, S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, M. J. Soileau, eds., Proc. SPIE4347, 53–61 (2001).
  11. A. During, M. Commandré, C. Fossati, B. Bertussi, J. Y. Natoli, J. L. Rullier, H. Bercegol, P. Bouchut, “Integrated photothermal microscope and laser damage test facility for in-situ investigation of nanodefect induced damage,” Opt. Express 11, 2497–2501 (2003).
    [CrossRef] [PubMed]
  12. D. Ristau, X. Dang, J. Ebert, “Interface and bulk absorption of oxide layers and correlation to damage threshold,” inn Laser-Induced Damage in Optical Materials: 1985, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Natl. Bur. Stand. (U.S.) Spec. Publ.727, 298–312 (1986).
  13. E. Welsh, H. Walther, R. Wolf, D. Schafer, L. Wieczorek, “Measurement of optical losses and damage threshold of multilayer coatings,” Thin Solid Films 117, 87–94 (1984).
    [CrossRef]
  14. E. Welsh, H. Walther, D. Schafer, R. Wolf, “Measurement of optical losses and damage resistance of ZnS–Na3 AlF6 and TiO2–SiO2 laser mirrors depending on coating design,” Thin Solid Films 152, 433–442 (1987).
    [CrossRef]
  15. E. Welsh, H. Walther, D. Schafer, R. Wolf, H. Muller, “Correlation between morphology, optical losses and laser damage of MgF2–SiO2 multilayers,” Thin Solid Films 156, 1–10 (1988).
    [CrossRef]
  16. H. Walther, E. Welsh, J. Opfermann, “Calculation and measurement of the absorption in multilayer films by means of photoacoustics,” Thin Solid Films 142, 27–35 (1986).
    [CrossRef]
  17. W. Jackson, N. M. Amer, A. C. Boccara, D. Fournier, “Photothermal deflection spectroscopy and detection,” Appl. Opt. 20, 1333–1344 (1981).
    [CrossRef] [PubMed]
  18. M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. 32, 141–154 (1983).
    [CrossRef]
  19. P. Zimmermann, E. Welsch, “Modeling of signal detection by using the photothermal probe beam deflection technique,” Rev. Sci. Instrum. 65, 97–101 (1994).
    [CrossRef]
  20. G. Rousset, F. Charbonnier, F. Lepoutre, “Influence of radiative and convective transfers in a photothermal experiment,” J. Appl. Phys. 56, 2093–2096 (1984).
    [CrossRef]
  21. H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, 1986).
    [CrossRef]
  22. D. Decker, L. Koshigoe, E. Ashley, “Thermal properties of optical thin film materials,” in Laser-Induced Damage in Optical Materials: 1984, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Natl. Bur. Stand. (U.S.) Spec. Publ.727, 291–297 (1986).
  23. D. Ristau, J. Ebert, “Development of a thermographic laser calorimeter,” Appl. Opt. 25, 4571–4578 (1986).
    [CrossRef] [PubMed]
  24. J. Lambropoulos, M. Jolly, C. Amsden, S. Gilman, M. Sinicropi, D. Diakomihalis, S. Jacobs, “Thermal conductivity of dielectric thin films,” J. Appl. Phys. 66, 4230–4242 (1989).
    [CrossRef]
  25. S. Lee, D. Cahill, T. Allen, “Thermal conductivity of sputtered oxide films,” Phys. Rev. B 52, 253–257 (1995).
    [CrossRef]
  26. E. Drouard, P. Huguet-Chantõme, L. Escoubas, F. Flory, “∂n/∂T measurements performed with guided waves and their application to the temperature sensitivity of wavelength-division multiplexing filters,” Appl. Opt. 41, 3192–3136 (2002).
    [CrossRef]
  27. L. Gallais, H. Hinsch, M.-L. Lay, M. Commandré, “Photothermal facility for optical characterization of DUV materials,” in Advances in Optical Thin Films,C. Amra, N. Kaiser, H. Angus Macleod, eds. Proc. SPIE5250, 597–602 (2004).
    [CrossRef]
  28. L. Gallais, M. Commandré, “Simultaneous absorption, scattering, and luminescence mappings for the characterization of optical coatings and surfaces,” Appl. Opt. (to be published).mc
  29. P. Torchio, A. Gatto, M. Alvisi, G. Albrand, N. Kaiser, C. Amra, “High-reflectivity HfO2/SiO2 ultraviolet mirrors,” Appl. Opt. 41, 3156–3261 (2002).
    [CrossRef]
  30. S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys. 83, 5150–5153 (1998).
    [CrossRef]

2004

A. During, C. Fossati, M. Commandré, “Photothermal deflection microscopy for imaging submicronic defects in optical materials,” Opt. Commun. 230, 279–286 (2004).
[CrossRef]

2003

2002

P. Torchio, A. Gatto, M. Alvisi, G. Albrand, N. Kaiser, C. Amra, “High-reflectivity HfO2/SiO2 ultraviolet mirrors,” Appl. Opt. 41, 3156–3261 (2002).
[CrossRef]

E. Drouard, P. Huguet-Chantõme, L. Escoubas, F. Flory, “∂n/∂T measurements performed with guided waves and their application to the temperature sensitivity of wavelength-division multiplexing filters,” Appl. Opt. 41, 3192–3136 (2002).
[CrossRef]

1998

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys. 83, 5150–5153 (1998).
[CrossRef]

1997

Z. Wu, M. Thomsen, P. Kuo, Y. Lu, C. Stolz, M. Koslowski, “Photothermal characterization of optical thin film coatings,” Opt. Eng. 36, 251–262 (1997).
[CrossRef]

1996

1995

E. Welsh, D. Ristau, “Photothermal measurements on optical thin films,” Appl. Opt. 34, 7339–7253 (1995).

S. Lee, D. Cahill, T. Allen, “Thermal conductivity of sputtered oxide films,” Phys. Rev. B 52, 253–257 (1995).
[CrossRef]

1994

P. Zimmermann, E. Welsch, “Modeling of signal detection by using the photothermal probe beam deflection technique,” Rev. Sci. Instrum. 65, 97–101 (1994).
[CrossRef]

1990

1989

J. Lambropoulos, M. Jolly, C. Amsden, S. Gilman, M. Sinicropi, D. Diakomihalis, S. Jacobs, “Thermal conductivity of dielectric thin films,” J. Appl. Phys. 66, 4230–4242 (1989).
[CrossRef]

1988

E. Welsh, H. Walther, D. Schafer, R. Wolf, H. Muller, “Correlation between morphology, optical losses and laser damage of MgF2–SiO2 multilayers,” Thin Solid Films 156, 1–10 (1988).
[CrossRef]

1987

E. Welsh, H. Walther, D. Schafer, R. Wolf, “Measurement of optical losses and damage resistance of ZnS–Na3 AlF6 and TiO2–SiO2 laser mirrors depending on coating design,” Thin Solid Films 152, 433–442 (1987).
[CrossRef]

1986

H. Walther, E. Welsh, J. Opfermann, “Calculation and measurement of the absorption in multilayer films by means of photoacoustics,” Thin Solid Films 142, 27–35 (1986).
[CrossRef]

D. Ristau, J. Ebert, “Development of a thermographic laser calorimeter,” Appl. Opt. 25, 4571–4578 (1986).
[CrossRef] [PubMed]

1984

G. Rousset, F. Charbonnier, F. Lepoutre, “Influence of radiative and convective transfers in a photothermal experiment,” J. Appl. Phys. 56, 2093–2096 (1984).
[CrossRef]

E. Welsh, H. Walther, R. Wolf, D. Schafer, L. Wieczorek, “Measurement of optical losses and damage threshold of multilayer coatings,” Thin Solid Films 117, 87–94 (1984).
[CrossRef]

1983

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. 32, 141–154 (1983).
[CrossRef]

1981

1980

A. C. Boccara, D. Fournier, W. Jackson, N. M. Amer, “Sensitive photothermal deflection technique for measuring absorption in optically thin media,” Opt. Lett. 5, 377–379 (1980).
[CrossRef] [PubMed]

J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
[CrossRef]

Aamodt, L. C.

J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
[CrossRef]

Adamik, M.

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys. 83, 5150–5153 (1998).
[CrossRef]

Albrand, G.

Allen, T.

S. Lee, D. Cahill, T. Allen, “Thermal conductivity of sputtered oxide films,” Phys. Rev. B 52, 253–257 (1995).
[CrossRef]

Alvisi, M.

Amer, N. M.

Amra, C.

Amsden, C.

J. Lambropoulos, M. Jolly, C. Amsden, S. Gilman, M. Sinicropi, D. Diakomihalis, S. Jacobs, “Thermal conductivity of dielectric thin films,” J. Appl. Phys. 66, 4230–4242 (1989).
[CrossRef]

Ashley, E.

D. Decker, L. Koshigoe, E. Ashley, “Thermal properties of optical thin film materials,” in Laser-Induced Damage in Optical Materials: 1984, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Natl. Bur. Stand. (U.S.) Spec. Publ.727, 291–297 (1986).

Bercegol, H.

Bertussi, B.

Boccara, A. C.

Boccara, C.

Bouchut, P.

Cahill, D.

S. Lee, D. Cahill, T. Allen, “Thermal conductivity of sputtered oxide films,” Phys. Rev. B 52, 253–257 (1995).
[CrossRef]

Charbonnier, F.

G. Rousset, F. Charbonnier, F. Lepoutre, “Influence of radiative and convective transfers in a photothermal experiment,” J. Appl. Phys. 56, 2093–2096 (1984).
[CrossRef]

Commandré, M.

A. During, C. Fossati, M. Commandré, “Photothermal deflection microscopy for imaging submicronic defects in optical materials,” Opt. Commun. 230, 279–286 (2004).
[CrossRef]

A. During, M. Commandré, C. Fossati, B. Bertussi, J. Y. Natoli, J. L. Rullier, H. Bercegol, P. Bouchut, “Integrated photothermal microscope and laser damage test facility for in-situ investigation of nanodefect induced damage,” Opt. Express 11, 2497–2501 (2003).
[CrossRef] [PubMed]

M. Commandré, P. Roche, “Characterization of optical coatings by photothermal deflection,” Appl. Opt. 35, 5021–5034 (1996).
[CrossRef] [PubMed]

M. Commandré, E. Pelletier, “Measurement of absorption losses in TiO2 films by a collinear photothermal deflection technique,” Appl. Opt. 29, 4276–4283 (1990).
[CrossRef]

L. Gallais, M. Commandré, “Simultaneous absorption, scattering, and luminescence mappings for the characterization of optical coatings and surfaces,” Appl. Opt. (to be published).mc

L. Gallais, H. Hinsch, M.-L. Lay, M. Commandré, “Photothermal facility for optical characterization of DUV materials,” in Advances in Optical Thin Films,C. Amra, N. Kaiser, H. Angus Macleod, eds. Proc. SPIE5250, 597–602 (2004).
[CrossRef]

Dang, X.

D. Ristau, X. Dang, J. Ebert, “Interface and bulk absorption of oxide layers and correlation to damage threshold,” inn Laser-Induced Damage in Optical Materials: 1985, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Natl. Bur. Stand. (U.S.) Spec. Publ.727, 298–312 (1986).

Decker, D.

D. Decker, L. Koshigoe, E. Ashley, “Thermal properties of optical thin film materials,” in Laser-Induced Damage in Optical Materials: 1984, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Natl. Bur. Stand. (U.S.) Spec. Publ.727, 291–297 (1986).

Diakomihalis, D.

J. Lambropoulos, M. Jolly, C. Amsden, S. Gilman, M. Sinicropi, D. Diakomihalis, S. Jacobs, “Thermal conductivity of dielectric thin films,” J. Appl. Phys. 66, 4230–4242 (1989).
[CrossRef]

Drouard, E.

E. Drouard, P. Huguet-Chantõme, L. Escoubas, F. Flory, “∂n/∂T measurements performed with guided waves and their application to the temperature sensitivity of wavelength-division multiplexing filters,” Appl. Opt. 41, 3192–3136 (2002).
[CrossRef]

During, A.

Ebert, J.

D. Ristau, J. Ebert, “Development of a thermographic laser calorimeter,” Appl. Opt. 25, 4571–4578 (1986).
[CrossRef] [PubMed]

D. Ristau, X. Dang, J. Ebert, “Interface and bulk absorption of oxide layers and correlation to damage threshold,” inn Laser-Induced Damage in Optical Materials: 1985, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Natl. Bur. Stand. (U.S.) Spec. Publ.727, 298–312 (1986).

Ermshar, J.

W. Mundy, J. Ermshar, P. Hanson, R. Hughes, “Photothermal deflection microscopy of HR and AR coatings,” in Laser-Induced Damage in Optical Materials: 1983, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Nat. Bur. Stand. (U.S.) Spec. Publ.688, 360–371 (1983).

Escoubas, L.

E. Drouard, P. Huguet-Chantõme, L. Escoubas, F. Flory, “∂n/∂T measurements performed with guided waves and their application to the temperature sensitivity of wavelength-division multiplexing filters,” Appl. Opt. 41, 3192–3136 (2002).
[CrossRef]

Falabella, S.

A. Papandrew, C. Stolz, Z. Wu, G. Loomis, S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, M. J. Soileau, eds., Proc. SPIE4347, 53–61 (2001).

Flory, F.

E. Drouard, P. Huguet-Chantõme, L. Escoubas, F. Flory, “∂n/∂T measurements performed with guided waves and their application to the temperature sensitivity of wavelength-division multiplexing filters,” Appl. Opt. 41, 3192–3136 (2002).
[CrossRef]

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys. 83, 5150–5153 (1998).
[CrossRef]

Fossati, C.

Fournier, D.

Gallais, L.

L. Gallais, H. Hinsch, M.-L. Lay, M. Commandré, “Photothermal facility for optical characterization of DUV materials,” in Advances in Optical Thin Films,C. Amra, N. Kaiser, H. Angus Macleod, eds. Proc. SPIE5250, 597–602 (2004).
[CrossRef]

L. Gallais, M. Commandré, “Simultaneous absorption, scattering, and luminescence mappings for the characterization of optical coatings and surfaces,” Appl. Opt. (to be published).mc

Gatto, A.

P. Torchio, A. Gatto, M. Alvisi, G. Albrand, N. Kaiser, C. Amra, “High-reflectivity HfO2/SiO2 ultraviolet mirrors,” Appl. Opt. 41, 3156–3261 (2002).
[CrossRef]

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys. 83, 5150–5153 (1998).
[CrossRef]

Gilman, S.

J. Lambropoulos, M. Jolly, C. Amsden, S. Gilman, M. Sinicropi, D. Diakomihalis, S. Jacobs, “Thermal conductivity of dielectric thin films,” J. Appl. Phys. 66, 4230–4242 (1989).
[CrossRef]

Hanson, P.

W. Mundy, J. Ermshar, P. Hanson, R. Hughes, “Photothermal deflection microscopy of HR and AR coatings,” in Laser-Induced Damage in Optical Materials: 1983, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Nat. Bur. Stand. (U.S.) Spec. Publ.688, 360–371 (1983).

Hinsch, H.

L. Gallais, H. Hinsch, M.-L. Lay, M. Commandré, “Photothermal facility for optical characterization of DUV materials,” in Advances in Optical Thin Films,C. Amra, N. Kaiser, H. Angus Macleod, eds. Proc. SPIE5250, 597–602 (2004).
[CrossRef]

Hughes, R.

W. Mundy, J. Ermshar, P. Hanson, R. Hughes, “Photothermal deflection microscopy of HR and AR coatings,” in Laser-Induced Damage in Optical Materials: 1983, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Nat. Bur. Stand. (U.S.) Spec. Publ.688, 360–371 (1983).

Huguet-Chantõme, P.

E. Drouard, P. Huguet-Chantõme, L. Escoubas, F. Flory, “∂n/∂T measurements performed with guided waves and their application to the temperature sensitivity of wavelength-division multiplexing filters,” Appl. Opt. 41, 3192–3136 (2002).
[CrossRef]

Jackson, W.

Jacobs, S.

J. Lambropoulos, M. Jolly, C. Amsden, S. Gilman, M. Sinicropi, D. Diakomihalis, S. Jacobs, “Thermal conductivity of dielectric thin films,” J. Appl. Phys. 66, 4230–4242 (1989).
[CrossRef]

Jolly, M.

J. Lambropoulos, M. Jolly, C. Amsden, S. Gilman, M. Sinicropi, D. Diakomihalis, S. Jacobs, “Thermal conductivity of dielectric thin films,” J. Appl. Phys. 66, 4230–4242 (1989).
[CrossRef]

Kaiser, N.

Kohn, S.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. 32, 141–154 (1983).
[CrossRef]

Koshigoe, L.

D. Decker, L. Koshigoe, E. Ashley, “Thermal properties of optical thin film materials,” in Laser-Induced Damage in Optical Materials: 1984, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Natl. Bur. Stand. (U.S.) Spec. Publ.727, 291–297 (1986).

Koslowski, M.

Z. Wu, M. Thomsen, P. Kuo, Y. Lu, C. Stolz, M. Koslowski, “Photothermal characterization of optical thin film coatings,” Opt. Eng. 36, 251–262 (1997).
[CrossRef]

Kovacs, I.

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys. 83, 5150–5153 (1998).
[CrossRef]

Kuo, P.

Z. Wu, M. Thomsen, P. Kuo, Y. Lu, C. Stolz, M. Koslowski, “Photothermal characterization of optical thin film coatings,” Opt. Eng. 36, 251–262 (1997).
[CrossRef]

Lambropoulos, J.

J. Lambropoulos, M. Jolly, C. Amsden, S. Gilman, M. Sinicropi, D. Diakomihalis, S. Jacobs, “Thermal conductivity of dielectric thin films,” J. Appl. Phys. 66, 4230–4242 (1989).
[CrossRef]

Lay, M.-L.

L. Gallais, H. Hinsch, M.-L. Lay, M. Commandré, “Photothermal facility for optical characterization of DUV materials,” in Advances in Optical Thin Films,C. Amra, N. Kaiser, H. Angus Macleod, eds. Proc. SPIE5250, 597–602 (2004).
[CrossRef]

Lee, S.

S. Lee, D. Cahill, T. Allen, “Thermal conductivity of sputtered oxide films,” Phys. Rev. B 52, 253–257 (1995).
[CrossRef]

Lepoutre, F.

G. Rousset, F. Charbonnier, F. Lepoutre, “Influence of radiative and convective transfers in a photothermal experiment,” J. Appl. Phys. 56, 2093–2096 (1984).
[CrossRef]

Loomis, G.

A. Papandrew, C. Stolz, Z. Wu, G. Loomis, S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, M. J. Soileau, eds., Proc. SPIE4347, 53–61 (2001).

Loriette, V.

Lu, Y.

Z. Wu, M. Thomsen, P. Kuo, Y. Lu, C. Stolz, M. Koslowski, “Photothermal characterization of optical thin film coatings,” Opt. Eng. 36, 251–262 (1997).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, 1986).
[CrossRef]

Muller, H.

E. Welsh, H. Walther, D. Schafer, R. Wolf, H. Muller, “Correlation between morphology, optical losses and laser damage of MgF2–SiO2 multilayers,” Thin Solid Films 156, 1–10 (1988).
[CrossRef]

Mundy, W.

W. Mundy, J. Ermshar, P. Hanson, R. Hughes, “Photothermal deflection microscopy of HR and AR coatings,” in Laser-Induced Damage in Optical Materials: 1983, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Nat. Bur. Stand. (U.S.) Spec. Publ.688, 360–371 (1983).

Murphy, J. C.

J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
[CrossRef]

Natoli, J. Y.

Olmstead, M. A.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. 32, 141–154 (1983).
[CrossRef]

Opfermann, J.

H. Walther, E. Welsh, J. Opfermann, “Calculation and measurement of the absorption in multilayer films by means of photoacoustics,” Thin Solid Films 142, 27–35 (1986).
[CrossRef]

Papandrew, A.

A. Papandrew, C. Stolz, Z. Wu, G. Loomis, S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, M. J. Soileau, eds., Proc. SPIE4347, 53–61 (2001).

Pelletier, E.

Ristau, D.

E. Welsh, D. Ristau, “Photothermal measurements on optical thin films,” Appl. Opt. 34, 7339–7253 (1995).

D. Ristau, J. Ebert, “Development of a thermographic laser calorimeter,” Appl. Opt. 25, 4571–4578 (1986).
[CrossRef] [PubMed]

D. Ristau, X. Dang, J. Ebert, “Interface and bulk absorption of oxide layers and correlation to damage threshold,” inn Laser-Induced Damage in Optical Materials: 1985, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newman, eds., Natl. Bur. Stand. (U.S.) Spec. Publ.727, 298–312 (1986).

Roche, P.

Rousset, G.

G. Rousset, F. Charbonnier, F. Lepoutre, “Influence of radiative and convective transfers in a photothermal experiment,” J. Appl. Phys. 56, 2093–2096 (1984).
[CrossRef]

Roux, L.

S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, I. Kovacs, “Titanium implantation in bulk and thin film amorphous silica,” J. Appl. Phys. 83, 5150–5153 (1998).
[CrossRef]

Rullier, J. L.

Schafer, D.

E. Welsh, H. Walther, D. Schafer, R. Wolf, H. Muller, “Correlation between morphology, optical losses and laser damage of MgF2–SiO2 multilayers,” Thin Solid Films 156, 1–10 (1988).
[CrossRef]

E. Welsh, H. Walther, D. Schafer, R. Wolf, “Measurement of optical losses and damage resistance of ZnS–Na3 AlF6 and TiO2–SiO2 laser mirrors depending on coating design,” Thin Solid Films 152, 433–442 (1987).
[CrossRef]

E. Welsh, H. Walther, R. Wolf, D. Schafer, L. Wieczorek, “Measurement of optical losses and damage threshold of multilayer coatings,” Thin Solid Films 117, 87–94 (1984).
[CrossRef]

Sinicropi, M.

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[CrossRef]

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[CrossRef]

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[CrossRef]

A. Papandrew, C. Stolz, Z. Wu, G. Loomis, S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, M. J. Soileau, eds., Proc. SPIE4347, 53–61 (2001).

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Opt. Commun.

A. During, C. Fossati, M. Commandré, “Photothermal deflection microscopy for imaging submicronic defects in optical materials,” Opt. Commun. 230, 279–286 (2004).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Configuration and notation used in our model transmission calculation: ni, ki, real and imaginary parts of complex index Ni of medium i (i = 0 for air, i = 1 for the first layer, …, i = N for the last layer, and i = S for the substrate), Ki is the thermal conductivity, ρi is the mass density, Ci is the heat capacity per unit mass, Ri is the thermal resistance at the interface between media i − 1 and i, ei is the film’s thickness, and 2a is the diameter at 1/e2 of the Gaussian pump beam.

Fig. 2
Fig. 2

Calculation of the spectral reflectance (R) and transmittance (T): (a) mirror M23, (b) Fabry–Perot filter: mirror M5, 12B, mirror M5. Materials: HfO2 (n = 2.4) and SiO2 (n = 1.5).

Fig. 3
Fig. 3

Electric-field distribution calculated at 244 nm in (a) mirror M23, (b) Fabry–Perot filter: mirror M5, 12B, mirror M5. Materials: HfO2 (n = 2.4) and SiO2 (n = 1.5).

Fig. 4
Fig. 4

Calculated photothermal deflection versus separation between pump and probe beams in (a), mirror M23, (b) Fabry–Perot filter: mirror M5, 12B, mirror M5. Materials: HfO2 (K = 0.1 Wm−1 K−1, ρC = 1.7 J m−3 K−1, ∂n/∂T = 5E − 5K−1) and SiO2 (K = 0.2 W m−1 K−1, ρC = 1.5 × 106 J m−3 K−1, ∂n/∂T = 5E − 5K−1).

Fig. 5
Fig. 5

Experimental setup for photothermal deflection measurements.

Fig. 6
Fig. 6

Calculation of the temperature distribution in mirror M23 in our experimental configuration along the z axis at the center of the pump beam.

Fig. 7
Fig. 7

Measurement and theoretical PD versus separation between pump and probe beams in mirror M23: (a) amplitude; (b) phase.

Fig. 8
Fig. 8

Measurement of the photothermal signal on the calibration samples and on the deep-ultraviolet mirror.

Tables (2)

Tables Icon

Table 1 Optical Parameters of the HfO2 Layers

Tables Icon

Table 2 Optical Parameters of the SiO2 Layers

Equations (23)

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2 T 0 ( r ,     z ,     t ) - ρ 0 C 0 K 0 T 0 t = 0 , 2 T i ( r ,     z ,     t ) - ρ i C i K i T i t = - Q i ( r ,     z ,     t ) K i , 2 T S ( r ,     z ,     t ) - ρ S C S K S T S t = - Q S ( r ,     z ,     t ) K S ,
Q i ( r ,     z ,     t ) = 4 π k i λ n i n 0 p 0 π a 2 exp ( - 2 r 2 a 2 ) × exp ( j ω t ) | E i E 0 + ( z ) | 2 ,
E i ( z ) = E i + exp ( - j 2 π N i λ z ) + E i - exp ( j 2 π N i λ z ) ,
T 0 ( r ,     z = 0 ) = T 1 ( r ,     z = 0 ) - Res 0 Φ 1 A , T i ( r ,     z = e i ) = T i + 1 ( r ,     z = e i ) - Res i Φ i + 1 i , T N ( r ,     z = e N ) = T S ( r ,     z = e N ) - Res N Φ S N ,
ϕ 1 A = K 0 T 0 z | z = 0 = K 1 T 1 z | z = 0 , ϕ i + 1 i = K i T i z | z = e i = K i + 1 T i + 1 z | z = e i , ϕ S N = K N T N z | z = e N = K S T S z | z = e N ,
T 0 ( r ,     z ,     t ) = 2 π 0 + σ J 0 ( 2 π σ r ) { A 0 ( σ ) × exp [ α 0 ( σ ) z ] } d σ exp ( j ω t ) , T i ( r ,     z ,     t ) = 2 π 0 + σ J 0 ( 2 π σ r ) { A i ( σ ) exp [ α i ( σ ) z ] + B i ( σ ) exp [ - α i ( σ ) z ] + F i ( σ ) [ E i + 2 × exp ( - 4 π k i λ z ) + E i - 2 exp ( 4 π k i λ z ) ] + G i ( σ ) [ E i + E i - * exp ( - j 4 π n i λ z ) + E i + * E i - exp ( j 4 π n i λ z ) ] } d σ exp ( j ω t ) , T s ( r ,     z ,     t ) = 2 π 0 + σ J 0 ( 2 π σ r ) { B S ( σ ) × exp [ - α S ( σ ) ( z ) ] + F S ( σ ) E S + 2 × exp ( - 4 π k S λ z ) } d σ exp ( j ω t ) ,
θ i = 1 n i n i T path i [ T i x ( x ,     y ,     z ,     t ) ] x = x 0 , y = y 0 d z ,
θ y air ( x 0 ,     y 0 ,     t ) = - 1 n 0 n 0 T 4 π 2 exp ( j ω t ) y 0 r 0 0 + × σ 2 J 1 ( 2 π σ r 0 ) A 0 α 0 d σ , θ y couche i ( x 0 ,     y 0 ,     t ) = - 1 n i n i T 4 π 2 exp ( j ω t ) y 0 r 0 0 + × σ 2 J 1 ( 2 π σ r 0 ) ( A i α i [ exp ( α i e i ) - exp ( α i e i - 1 ) ] + B i α i [ exp ( - α i e i - 1 ) - exp ( - α i e i ) ] + F i λ 4 π k i { E i + 2 × [ exp ( - 4 π k i λ e i - 1 ) - exp × ( - 4 π k i λ e i ) ] + E i - 2 [ exp ( 4 π k i λ e i ) - exp ( 4 π k i λ e i - 1 ) ] } + G i λ j 4 π n i × { E i + E i - * [ exp ( - j 4 π n i λ e i - 1 ) - exp ( - j 4 π n i λ e i ) ] + E i + * E i - × [ exp ( j 4 π n i λ e i ) - exp ( j 4 π n i λ e i - 1 ) ] } ) d σ , θ y substrate ( x 0 ,     y 0 ,     t ) = 1 n S n S T 4 π 2 exp ( j ω t ) y 0 r 0 0 + × σ 2 J 1 ( 2 π σ r 0 ) { B S α S [ exp ( - α S e N ) - exp ( - α S E ) ] + F S E S + 2 λ 4 π k S × [ exp ( - 4 π k S λ e N ) - exp ( - 4 π k S λ ) ] } d σ .
A CS = α × β CS × PDS CS ,
A sample = α × β S × PDS Sample .
A sample = A CS β S PDS sample β CS PDS CS .
A stack = i 4 π k i λ n i n 0 e i - 1 e i | E i E 0 + ( z ) | 2 d z .
2 T 0 ( r ,     z ,     t ) - ρ 0 C 0 K 0 T 0 t = 0 , 2 T i ( r ,     z ,     t ) - ρ i C i K i T i t = - 2 R i π a 2 exp ( - 2 r 2 a 2 ) × exp ( j ω t ) | E i E 0 + ( z ) | 2 , 2 T S ( r ,     z ,     t ) - ρ 2 C 2 K S T S t = - 2 R S π a 2 exp ( j ω t ) | E S E 0 + ( z ) | 2 ,
R i = P 0 2 K i n i n 0 4 π k i λ .
T i ( r ,     z ) = 2 π 0 + σ J 0 ( 2 π σ r ) T ˜ i ( σ ,     z ) d σ ,
2 z 2 T ˜ 0 ( σ ,     z ,     t ) - α 0 2 ( σ ) T ˜ 0 ( σ ,     z ,     t ) = 0 , 2 z 2 T ˜ i ( σ ,     z ,     t ) - α i 2 ( σ ) T ˜ i ( σ ,     z ,     t ) = - R i × exp ( - a 2 σ 2 π 2 2 ) exp ( j ω t ) | E i E 0 + ( z ) | 2 , 2 z 2 T ˜ S ( σ ,     z ,     t ) - α S 2 ( σ ) T ˜ S ( σ ,     z ,     t ) = - R S × exp ( - a 2 σ 2 π 2 2 ) exp ( j ω t ) | E S + E 0 + | 2 exp ( - 4 π k S λ z ) ,
μ i = ( K i ρ i C i π F ) 1 / 2 ,             α i 2 = 4 π 2 σ 2 + 2 j μ i 2 , R i = P 0 2 K i n i n 0 4 π k i λ .
T ˜ 0 ( σ ,     z ,     t ) = A 0 ( σ ) exp [ α 0 ( σ ) z ] exp ( j ω t ) , T ˜ i ( σ ,     z ,     t ) = { A i ( σ ) exp [ α i ( σ ) z ] + β i ( σ ) exp [ - α i ( σ ) z ] + F i ( σ ) [ E i + 2 exp ( - 4 π k i λ z ) + E i - 2 exp ( 4 π k i λ z ) ] + G i ( σ ) [ E i + E i - * × exp ( - j 4 π n i λ z ) + E i + * E i - exp ( j 4 π n i λ z ) ] } exp ( j ω t ) , T ˜ S ( σ ,     z ,     t ) = { B S ( σ ) exp [ - α 2 ( σ ) z ] + F S ( σ ) E S + 2 × exp ( - 4 π k S λ z ) } exp ( j ω t ) ,
F i ( σ ) = 1 E 0 + 2 R i exp ( a 2 σ 2 π 2 / 2 ) α i 2 ( σ ) - ( 4 π k i / λ ) 2 , G i ( σ ) = 1 E 0 + 2 B i exp [ - ( a 2 σ 2 π 2 / 2 ) ] α i 2 ( σ ) + ( 4 π n i / λ ) 2 .
T i ( r ,     z ,     t ) = 2 π 0 + σ J 0 ( 2 π σ r ) { A i ( σ ) exp [ α i ( σ ) z ] + B i ( σ ) exp [ - α i ( σ ) z ] + F i ( σ ) × [ E i + 2 exp ( 4 π k i λ z ) + E i - 2 exp ( 4 π k i λ z ) ] + G i ( σ ) [ E i + E i - * exp ( - j 4 π n i λ z ) + E i + * E i - exp ( j 4 π n i λ z ) ] } d σ exp ( j ω t ) ,
[ ( 1 + h 0 ) - 1 - 1 K 0 α 0 - K 1 α 1 K 1 α 1 ( 1 + h i ) exp ( - α i e i ) ( 1 - h i ) exp ( - α i e i ) - exp ( α i + 1 e i ) - exp ( - α i + 1 e i ) K i α i exp ( α i e i ) - K i α i exp ( - α i e i ) - K i + 1 α i + 1 exp ( α i + 1 e i ) K i + 1 α i + 1 exp ( - α i + 1 e i ) ( 1 + h N ) exp ( α N e N ) ( 1 - h N ) exp ( - α N e N ) - exp ( - α S e N ) K N α N exp ( α N e N ) - K N α N exp ( - α N e N ) K S α S exp ( - α S e N ) ] ( A 0 A 1 B 1 A i B i A i + 1 B i + 1 A N B N B S )
= [ F 1 a 1 ( 0 ) + G 1 b 1 ( 0 ) g 1 F 1 a 1 ( 0 ) + j f 1 G 1 b 1 ( 0 ) - F i a i ( e i ) - G i b i ( e i ) + F i + 1 a i + 1 ( e i ) + G i + 1 b i + 1 ( e i ) - Re s i g i F i a i ( e i ) - j Re s i f i G i b i ( e i ) - g i F i a i ( e i ) - j f i G i b i ( e i ) + g i + 1 F i + 1 a i + 1 ( e i ) + j f i + 1 G i + 1 b i + 1 ( e i ) - F N a N ( e N ) - G N b N ( e N ) + F S a S ( e N ) - g N Re s N F N a N ( e N ) - j Re s N f N G N b N ( e N ) - g N F N a N ( e N ) - j f N G N b N ( e N ) + g S F S a S ( e N ) ]
T 0 ( r ,     z ,     t ) = 2 π 0 + σ J 0 ( 2 π σ r ) { A 0 ( σ ) × exp [ α 0 ( σ ) z ] } d σ exp ( j ω t ) , T S ( r ,     z ,     t ) = 2 π 0 + σ J 0 ( 2 π σ r ) { B S ( σ ) exp [ - α 2 ( σ ) ( z ) ] + F S ( σ ) E S + 2 exp ( - 4 π k S λ z ) } d σ exp ( j ω t ) .

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