Abstract

A method is presented to evaluate optical absorption at a random wavelength by calculating temperature distribution in single-layer TiO2 films. Temperature distribution in single-layer TiO2 films was analyzed based on temperature field theory. Through our calculations, optical absorption variation was obtained to be similar to that of surface temperature rise in films. The surface temperature rise depends on film thickness, refractive index, extinction coefficient, specific heat, and thermal conductivity. Furthermore, the optical absorptions of the same single-layer TiO2 film at different wavelengths were deduced. As an example, the surface temperature rises were calculated for the 19 single-layer TiO2 films, which had been prepared by 12 different laboratories for the annual meeting of the Optical Society of America in 1986. The results agree well with the measured optical absorptions.

© 2009 Optical Society of America

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  1. M. Rahe, E. Oertel, L. Reinhardt, D. Ristau, and H. Welling, “Absorption calorimetry and laser induced damage threshold measurements of AR-coated ZnSe and metal mirrors at 10.6 mm,” Proc. SPIE 1441, 113-126 (1991).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008 (1)

F. Sato, L. C. Malacarne, and P. R. B. Pedreira, “Time-resolved thermal mirror method; a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

2007 (1)

J. K. Yao, H. Y. Li, Z. X. Fan, Y. X. Tang, Y. X. Jin, Y. A. Zhao, H. B. He, and J. D. Shao, “Comparison of TiO2 and ZrO2 films deposited by electron-beam evaporation and by sol-gel process,”Chin. Phys. Lett. 24, 1964-1066 (2007).
[CrossRef]

2005 (1)

1997 (1)

Q. Zhao, Z. X. Fan, and Z. J. Wang, “Role of interface absorption in laser induced local heating of optical coatings,” Opt. Eng. 36, 1530-1536 (1997).

1996 (2)

Z. X. Fan, Q. Zhao, and Z. L. Wu, “Temperature field design of optical thin film coatings,” Proc. SPIE 2966, 362-370(1996).

Z. L. Wu, M. Thompsen, P. K. Kuo, Y. S. Lu, C. J. Stolz, and M. R. Kozlowski, “Overview of photothermal characterization of optical thin film coatings,” Proc. SPIE 2714, 465-481(1996).

1995 (1)

1994 (1)

X. F. Tang, Z. X. Fan, and Z. J. Wang, “Surface inclusion adhesion of optical coatings,” Opt. Eng. 33, 3406-3410(1994).

1993 (1)

1991 (1)

M. Rahe, E. Oertel, L. Reinhardt, D. Ristau, and H. Welling, “Absorption calorimetry and laser induced damage threshold measurements of AR-coated ZnSe and metal mirrors at 10.6 mm,” Proc. SPIE 1441, 113-126 (1991).

1990 (1)

1982 (1)

Chow, R.

Commandre, M.

Falabella, S.

Fan, Z. X.

J. K. Yao, H. Y. Li, Z. X. Fan, Y. X. Tang, Y. X. Jin, Y. A. Zhao, H. B. He, and J. D. Shao, “Comparison of TiO2 and ZrO2 films deposited by electron-beam evaporation and by sol-gel process,”Chin. Phys. Lett. 24, 1964-1066 (2007).
[CrossRef]

Q. Zhao, Z. X. Fan, and Z. J. Wang, “Role of interface absorption in laser induced local heating of optical coatings,” Opt. Eng. 36, 1530-1536 (1997).

Z. X. Fan, Q. Zhao, and Z. L. Wu, “Temperature field design of optical thin film coatings,” Proc. SPIE 2966, 362-370(1996).

X. F. Tang, Z. X. Fan, and Z. J. Wang, “Surface inclusion adhesion of optical coatings,” Opt. Eng. 33, 3406-3410(1994).

Gallais, L.

Goodman, J. W.

He, H. B.

J. K. Yao, H. Y. Li, Z. X. Fan, Y. X. Tang, Y. X. Jin, Y. A. Zhao, H. B. He, and J. D. Shao, “Comparison of TiO2 and ZrO2 films deposited by electron-beam evaporation and by sol-gel process,”Chin. Phys. Lett. 24, 1964-1066 (2007).
[CrossRef]

Jin, Y. X.

J. K. Yao, H. Y. Li, Z. X. Fan, Y. X. Tang, Y. X. Jin, Y. A. Zhao, H. B. He, and J. D. Shao, “Comparison of TiO2 and ZrO2 films deposited by electron-beam evaporation and by sol-gel process,”Chin. Phys. Lett. 24, 1964-1066 (2007).
[CrossRef]

Kozlowski, M. R.

Z. L. Wu, M. Thompsen, P. K. Kuo, Y. S. Lu, C. J. Stolz, and M. R. Kozlowski, “Overview of photothermal characterization of optical thin film coatings,” Proc. SPIE 2714, 465-481(1996).

R. Chow, S. Falabella, G. E. Loomis, F. Rainer, C. J. Stolz, and M. R. Kozlowski, “Reactive evaporation of low-defect density hafnia,” Appl. Opt. 32, 5567-5574 (1993).
[CrossRef]

Kuo, P. K.

Z. L. Wu, M. Thompsen, P. K. Kuo, Y. S. Lu, C. J. Stolz, and M. R. Kozlowski, “Overview of photothermal characterization of optical thin film coatings,” Proc. SPIE 2714, 465-481(1996).

Li, H. Y.

J. K. Yao, H. Y. Li, Z. X. Fan, Y. X. Tang, Y. X. Jin, Y. A. Zhao, H. B. He, and J. D. Shao, “Comparison of TiO2 and ZrO2 films deposited by electron-beam evaporation and by sol-gel process,”Chin. Phys. Lett. 24, 1964-1066 (2007).
[CrossRef]

Loomis, G. E.

Lu, Y. S.

Z. L. Wu, M. Thompsen, P. K. Kuo, Y. S. Lu, C. J. Stolz, and M. R. Kozlowski, “Overview of photothermal characterization of optical thin film coatings,” Proc. SPIE 2714, 465-481(1996).

Malacarne, L. C.

F. Sato, L. C. Malacarne, and P. R. B. Pedreira, “Time-resolved thermal mirror method; a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

Mansuripur, M.

Neville Connell, G. A.

Oertel, E.

M. Rahe, E. Oertel, L. Reinhardt, D. Ristau, and H. Welling, “Absorption calorimetry and laser induced damage threshold measurements of AR-coated ZnSe and metal mirrors at 10.6 mm,” Proc. SPIE 1441, 113-126 (1991).

Pedreira, P. R. B.

F. Sato, L. C. Malacarne, and P. R. B. Pedreira, “Time-resolved thermal mirror method; a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

Pelletier, E.

Rahe, M.

M. Rahe, E. Oertel, L. Reinhardt, D. Ristau, and H. Welling, “Absorption calorimetry and laser induced damage threshold measurements of AR-coated ZnSe and metal mirrors at 10.6 mm,” Proc. SPIE 1441, 113-126 (1991).

Rainer, F.

Reinhardt, L.

M. Rahe, E. Oertel, L. Reinhardt, D. Ristau, and H. Welling, “Absorption calorimetry and laser induced damage threshold measurements of AR-coated ZnSe and metal mirrors at 10.6 mm,” Proc. SPIE 1441, 113-126 (1991).

Ristau, D.

E. Welsh and D. Ristau, “Photothermal measurements on optical thin films,” Appl. Opt. 34, 7239-7253 (1995).
[CrossRef]

M. Rahe, E. Oertel, L. Reinhardt, D. Ristau, and H. Welling, “Absorption calorimetry and laser induced damage threshold measurements of AR-coated ZnSe and metal mirrors at 10.6 mm,” Proc. SPIE 1441, 113-126 (1991).

Sato, F.

F. Sato, L. C. Malacarne, and P. R. B. Pedreira, “Time-resolved thermal mirror method; a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

Shao, J. D.

J. K. Yao, H. Y. Li, Z. X. Fan, Y. X. Tang, Y. X. Jin, Y. A. Zhao, H. B. He, and J. D. Shao, “Comparison of TiO2 and ZrO2 films deposited by electron-beam evaporation and by sol-gel process,”Chin. Phys. Lett. 24, 1964-1066 (2007).
[CrossRef]

Stolz, C. J.

Z. L. Wu, M. Thompsen, P. K. Kuo, Y. S. Lu, C. J. Stolz, and M. R. Kozlowski, “Overview of photothermal characterization of optical thin film coatings,” Proc. SPIE 2714, 465-481(1996).

R. Chow, S. Falabella, G. E. Loomis, F. Rainer, C. J. Stolz, and M. R. Kozlowski, “Reactive evaporation of low-defect density hafnia,” Appl. Opt. 32, 5567-5574 (1993).
[CrossRef]

Tang, X. F.

X. F. Tang, Z. X. Fan, and Z. J. Wang, “Surface inclusion adhesion of optical coatings,” Opt. Eng. 33, 3406-3410(1994).

Tang, Y. X.

J. K. Yao, H. Y. Li, Z. X. Fan, Y. X. Tang, Y. X. Jin, Y. A. Zhao, H. B. He, and J. D. Shao, “Comparison of TiO2 and ZrO2 films deposited by electron-beam evaporation and by sol-gel process,”Chin. Phys. Lett. 24, 1964-1066 (2007).
[CrossRef]

Thompsen, M.

Z. L. Wu, M. Thompsen, P. K. Kuo, Y. S. Lu, C. J. Stolz, and M. R. Kozlowski, “Overview of photothermal characterization of optical thin film coatings,” Proc. SPIE 2714, 465-481(1996).

Wang, Z. J.

Q. Zhao, Z. X. Fan, and Z. J. Wang, “Role of interface absorption in laser induced local heating of optical coatings,” Opt. Eng. 36, 1530-1536 (1997).

X. F. Tang, Z. X. Fan, and Z. J. Wang, “Surface inclusion adhesion of optical coatings,” Opt. Eng. 33, 3406-3410(1994).

Welling, H.

M. Rahe, E. Oertel, L. Reinhardt, D. Ristau, and H. Welling, “Absorption calorimetry and laser induced damage threshold measurements of AR-coated ZnSe and metal mirrors at 10.6 mm,” Proc. SPIE 1441, 113-126 (1991).

Welsh, E.

Wu, Z. L.

Z. X. Fan, Q. Zhao, and Z. L. Wu, “Temperature field design of optical thin film coatings,” Proc. SPIE 2966, 362-370(1996).

Z. L. Wu, M. Thompsen, P. K. Kuo, Y. S. Lu, C. J. Stolz, and M. R. Kozlowski, “Overview of photothermal characterization of optical thin film coatings,” Proc. SPIE 2714, 465-481(1996).

Yao, J. K.

J. K. Yao, H. Y. Li, Z. X. Fan, Y. X. Tang, Y. X. Jin, Y. A. Zhao, H. B. He, and J. D. Shao, “Comparison of TiO2 and ZrO2 films deposited by electron-beam evaporation and by sol-gel process,”Chin. Phys. Lett. 24, 1964-1066 (2007).
[CrossRef]

Zhao, Q.

Q. Zhao, Z. X. Fan, and Z. J. Wang, “Role of interface absorption in laser induced local heating of optical coatings,” Opt. Eng. 36, 1530-1536 (1997).

Z. X. Fan, Q. Zhao, and Z. L. Wu, “Temperature field design of optical thin film coatings,” Proc. SPIE 2966, 362-370(1996).

Zhao, Y. A.

J. K. Yao, H. Y. Li, Z. X. Fan, Y. X. Tang, Y. X. Jin, Y. A. Zhao, H. B. He, and J. D. Shao, “Comparison of TiO2 and ZrO2 films deposited by electron-beam evaporation and by sol-gel process,”Chin. Phys. Lett. 24, 1964-1066 (2007).
[CrossRef]

Appl. Opt. (5)

Chin. Phys. Lett. (1)

J. K. Yao, H. Y. Li, Z. X. Fan, Y. X. Tang, Y. X. Jin, Y. A. Zhao, H. B. He, and J. D. Shao, “Comparison of TiO2 and ZrO2 films deposited by electron-beam evaporation and by sol-gel process,”Chin. Phys. Lett. 24, 1964-1066 (2007).
[CrossRef]

J. Appl. Phys. (1)

F. Sato, L. C. Malacarne, and P. R. B. Pedreira, “Time-resolved thermal mirror method; a theoretical study,” J. Appl. Phys. 104, 053520 (2008).
[CrossRef]

Opt. Eng. (2)

X. F. Tang, Z. X. Fan, and Z. J. Wang, “Surface inclusion adhesion of optical coatings,” Opt. Eng. 33, 3406-3410(1994).

Q. Zhao, Z. X. Fan, and Z. J. Wang, “Role of interface absorption in laser induced local heating of optical coatings,” Opt. Eng. 36, 1530-1536 (1997).

Proc. SPIE (3)

Z. X. Fan, Q. Zhao, and Z. L. Wu, “Temperature field design of optical thin film coatings,” Proc. SPIE 2966, 362-370(1996).

M. Rahe, E. Oertel, L. Reinhardt, D. Ristau, and H. Welling, “Absorption calorimetry and laser induced damage threshold measurements of AR-coated ZnSe and metal mirrors at 10.6 mm,” Proc. SPIE 1441, 113-126 (1991).

Z. L. Wu, M. Thompsen, P. K. Kuo, Y. S. Lu, C. J. Stolz, and M. R. Kozlowski, “Overview of photothermal characterization of optical thin film coatings,” Proc. SPIE 2714, 465-481(1996).

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Figures (7)

Fig. 1
Fig. 1

Film thickness versus surface temperature rise T.

Fig. 2
Fig. 2

Refractive index n versus surface temperature rise T; the thickness of the Ti O 2 film is 300 nm (a) and 2000 nm (b).

Fig. 3
Fig. 3

Extinction coefficient k versus surface temperature rise T; the thickness of Ti O 2 film is 300 nm and 2000 nm .

Fig. 4
Fig. 4

Specific heat c versus surface temperature rise T; the thickness of the Ti O 2 film is 300 nm and 2000 nm .

Fig. 5
Fig. 5

Thermal conductivity K versus surface temperature rise T; the thickness of the Ti O 2 film is 300 nm and 2000 nm .

Fig. 6
Fig. 6

(a) Refractive index n and (b) extinction coefficient k of the single-layer Ti O 2 film.

Fig. 7
Fig. 7

Surface temperature rise and measured absorptions of Ti O 2 films versus refractive index.

Tables (5)

Tables Icon

Table 1 Summary of Parameters Used for the Calculations Presented in Fig. 1

Tables Icon

Table 2 Coating Parameters Used for the Calculations Presented in Fig. 2 to Fig. 5

Tables Icon

Table 3 Parameters Used for Calculating Surface Temperature Rise of the Film

Tables Icon

Table 4 Calculated Surface Temperature Rise of the Film at Three Wavelengths

Tables Icon

Table 5 Summary of Optical Constants, Thicknesses of Titanium Layers, Measured Absorptions [6], and the Calculated Surface Temperature Rises above Ambient

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