Abstract

The refractive indices of synthetic calcium fluoride for 69 wavelengths from 138 nm in the deep ultraviolet to 2326 nm in the near infrared were measured by the minimum-deviation method in a nitrogen environment. We made these measurements at 20° and 25 °C, respectively, to determine the thermal coefficients of the refractive index over this wide-wavelength region. These refractive indices were fitted to a four-term Sellmeier dispersion formula. The temperature coefficients of the refractive index were fitted to a Hoffman-type dispersion formula. The standard deviation of the residual between the observed values and the calculated values was 0.6 × 10-6 for the refractive index and was 0.13 × 10-6/°C for the temperature coefficient of the refractive index.

© 2002 Optical Society of America

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  1. T. M. Bloomstein, M. W. Horn, M. Rothschild, R. R. Kunz, S. T. Palmacci, R. B. Goodman, “Lithography with 157-nm lasers,” J. Vac. Sci. Technol. B 15, 2112–2116 (1997).
    [CrossRef]
  2. I. H. Malitson, “A redetermination of some optical properties of calcium fluoride,” Appl. Opt. 2, 1103–1107 (1963).
    [CrossRef]
  3. H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9, 161–289 (1980).
    [CrossRef]
  4. R. Gupta, J. H. Burnett, U. Griesmann, M. Walhout, “Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm,” Appl. Opt. 37, 5964–5968 (1998).
    [CrossRef]
  5. J. H. Burnett, R. Gupta, U. Griesmann, “Index of refraction and its temperature dependence of calcium fluoride near 157 nm,” in Optical Microlithography X II, L. Van den Hove, ed., Proc. SPIE3679, 1146–1152 (1999).
  6. J. H. Burnett, R. Gupta, U. Griesmann, “Absolute index of refraction and its temperature dependence of calcium fluoride, barium fluoride, and strontium fluoride near 157 nm,” in Optical Microlithography X III, C. J. Progler, ed., Proc. SPIE4000, 1503–1509 (2000).
  7. J. Reader, N. Acquista, C. J. Sansonetti, J. E. Sansonetti, “Wavelengths and intensities of a platinum/neon hollow cathode lamp in the region 1100–4000 Å,” Astrophys. J. Suppl. Ser. 72, 831–866 (1990).
    [CrossRef]
  8. J. E. Sansonetti, J. Reader, C. J. Sansonetti, N. Acquista, “Atlas of the spectrum of a platinum/neon hollow-cathode lamp in the region 1130–4330 Å,” http://physics.nist.gov/PhysRefData/platinum/contents.html/ .
  9. K. Watanabe, E. C. Y. Inn, M. Zelikoff, “Absorption coefficients of oxygen in the vacuum ultraviolet,” J. Chem. Phys. 21, 1026–1030 (1953).
    [CrossRef]
  10. K. Yoshino, D. E. Freeman, J. R. Esmond, W. H. Parkinson, “High resolution absorption cross section measurements and band oscillator strengths of the (1,0)–(12,0) Schumann–Runge bands of O2,” Planet. Space Sci. 31, 339–353 (1983).
    [CrossRef]
  11. J. Koch, “Uber die dispersion des lichtes in gasformigen korpern innerhalb des ultravioletten spektrums,” Ark. Mat. Astron. Fys. 9(6), 1–11 (1913).
  12. E. R. Peck, B. N. Khanna, “Dispersion of nitrogen,” J. Opt. Soc. Am. 56, 1059–1063 (1966).
    [CrossRef]
  13. U. Griesmann, J. H. Burnett, “Refractivity of nitrogen gas in the vacuum ultraviolet,” Opt. Lett. 24, 1699–1701 (1999).
    [CrossRef]
  14. B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
    [CrossRef]
  15. H. J. Hoffmann, W. W. Jochs, G. Westenberger, “A dispersion formula for the thermo-optic coefficient of optical glasses,” in Properties and Characteristics of Optical Glass II, A. J. Marker, ed., Proc. SPIE1327, 219–230 (1990).
    [CrossRef]

1999 (1)

1998 (1)

1997 (1)

T. M. Bloomstein, M. W. Horn, M. Rothschild, R. R. Kunz, S. T. Palmacci, R. B. Goodman, “Lithography with 157-nm lasers,” J. Vac. Sci. Technol. B 15, 2112–2116 (1997).
[CrossRef]

1990 (1)

J. Reader, N. Acquista, C. J. Sansonetti, J. E. Sansonetti, “Wavelengths and intensities of a platinum/neon hollow cathode lamp in the region 1100–4000 Å,” Astrophys. J. Suppl. Ser. 72, 831–866 (1990).
[CrossRef]

1983 (1)

K. Yoshino, D. E. Freeman, J. R. Esmond, W. H. Parkinson, “High resolution absorption cross section measurements and band oscillator strengths of the (1,0)–(12,0) Schumann–Runge bands of O2,” Planet. Space Sci. 31, 339–353 (1983).
[CrossRef]

1980 (1)

H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9, 161–289 (1980).
[CrossRef]

1966 (2)

1963 (1)

1953 (1)

K. Watanabe, E. C. Y. Inn, M. Zelikoff, “Absorption coefficients of oxygen in the vacuum ultraviolet,” J. Chem. Phys. 21, 1026–1030 (1953).
[CrossRef]

1913 (1)

J. Koch, “Uber die dispersion des lichtes in gasformigen korpern innerhalb des ultravioletten spektrums,” Ark. Mat. Astron. Fys. 9(6), 1–11 (1913).

Acquista, N.

J. Reader, N. Acquista, C. J. Sansonetti, J. E. Sansonetti, “Wavelengths and intensities of a platinum/neon hollow cathode lamp in the region 1100–4000 Å,” Astrophys. J. Suppl. Ser. 72, 831–866 (1990).
[CrossRef]

Bloomstein, T. M.

T. M. Bloomstein, M. W. Horn, M. Rothschild, R. R. Kunz, S. T. Palmacci, R. B. Goodman, “Lithography with 157-nm lasers,” J. Vac. Sci. Technol. B 15, 2112–2116 (1997).
[CrossRef]

Burnett, J. H.

U. Griesmann, J. H. Burnett, “Refractivity of nitrogen gas in the vacuum ultraviolet,” Opt. Lett. 24, 1699–1701 (1999).
[CrossRef]

R. Gupta, J. H. Burnett, U. Griesmann, M. Walhout, “Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm,” Appl. Opt. 37, 5964–5968 (1998).
[CrossRef]

J. H. Burnett, R. Gupta, U. Griesmann, “Index of refraction and its temperature dependence of calcium fluoride near 157 nm,” in Optical Microlithography X II, L. Van den Hove, ed., Proc. SPIE3679, 1146–1152 (1999).

J. H. Burnett, R. Gupta, U. Griesmann, “Absolute index of refraction and its temperature dependence of calcium fluoride, barium fluoride, and strontium fluoride near 157 nm,” in Optical Microlithography X III, C. J. Progler, ed., Proc. SPIE4000, 1503–1509 (2000).

Edlén, B.

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
[CrossRef]

Esmond, J. R.

K. Yoshino, D. E. Freeman, J. R. Esmond, W. H. Parkinson, “High resolution absorption cross section measurements and band oscillator strengths of the (1,0)–(12,0) Schumann–Runge bands of O2,” Planet. Space Sci. 31, 339–353 (1983).
[CrossRef]

Freeman, D. E.

K. Yoshino, D. E. Freeman, J. R. Esmond, W. H. Parkinson, “High resolution absorption cross section measurements and band oscillator strengths of the (1,0)–(12,0) Schumann–Runge bands of O2,” Planet. Space Sci. 31, 339–353 (1983).
[CrossRef]

Goodman, R. B.

T. M. Bloomstein, M. W. Horn, M. Rothschild, R. R. Kunz, S. T. Palmacci, R. B. Goodman, “Lithography with 157-nm lasers,” J. Vac. Sci. Technol. B 15, 2112–2116 (1997).
[CrossRef]

Griesmann, U.

U. Griesmann, J. H. Burnett, “Refractivity of nitrogen gas in the vacuum ultraviolet,” Opt. Lett. 24, 1699–1701 (1999).
[CrossRef]

R. Gupta, J. H. Burnett, U. Griesmann, M. Walhout, “Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm,” Appl. Opt. 37, 5964–5968 (1998).
[CrossRef]

J. H. Burnett, R. Gupta, U. Griesmann, “Absolute index of refraction and its temperature dependence of calcium fluoride, barium fluoride, and strontium fluoride near 157 nm,” in Optical Microlithography X III, C. J. Progler, ed., Proc. SPIE4000, 1503–1509 (2000).

J. H. Burnett, R. Gupta, U. Griesmann, “Index of refraction and its temperature dependence of calcium fluoride near 157 nm,” in Optical Microlithography X II, L. Van den Hove, ed., Proc. SPIE3679, 1146–1152 (1999).

Gupta, R.

R. Gupta, J. H. Burnett, U. Griesmann, M. Walhout, “Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm,” Appl. Opt. 37, 5964–5968 (1998).
[CrossRef]

J. H. Burnett, R. Gupta, U. Griesmann, “Absolute index of refraction and its temperature dependence of calcium fluoride, barium fluoride, and strontium fluoride near 157 nm,” in Optical Microlithography X III, C. J. Progler, ed., Proc. SPIE4000, 1503–1509 (2000).

J. H. Burnett, R. Gupta, U. Griesmann, “Index of refraction and its temperature dependence of calcium fluoride near 157 nm,” in Optical Microlithography X II, L. Van den Hove, ed., Proc. SPIE3679, 1146–1152 (1999).

Hoffmann, H. J.

H. J. Hoffmann, W. W. Jochs, G. Westenberger, “A dispersion formula for the thermo-optic coefficient of optical glasses,” in Properties and Characteristics of Optical Glass II, A. J. Marker, ed., Proc. SPIE1327, 219–230 (1990).
[CrossRef]

Horn, M. W.

T. M. Bloomstein, M. W. Horn, M. Rothschild, R. R. Kunz, S. T. Palmacci, R. B. Goodman, “Lithography with 157-nm lasers,” J. Vac. Sci. Technol. B 15, 2112–2116 (1997).
[CrossRef]

Inn, E. C. Y.

K. Watanabe, E. C. Y. Inn, M. Zelikoff, “Absorption coefficients of oxygen in the vacuum ultraviolet,” J. Chem. Phys. 21, 1026–1030 (1953).
[CrossRef]

Jochs, W. W.

H. J. Hoffmann, W. W. Jochs, G. Westenberger, “A dispersion formula for the thermo-optic coefficient of optical glasses,” in Properties and Characteristics of Optical Glass II, A. J. Marker, ed., Proc. SPIE1327, 219–230 (1990).
[CrossRef]

Khanna, B. N.

Koch, J.

J. Koch, “Uber die dispersion des lichtes in gasformigen korpern innerhalb des ultravioletten spektrums,” Ark. Mat. Astron. Fys. 9(6), 1–11 (1913).

Kunz, R. R.

T. M. Bloomstein, M. W. Horn, M. Rothschild, R. R. Kunz, S. T. Palmacci, R. B. Goodman, “Lithography with 157-nm lasers,” J. Vac. Sci. Technol. B 15, 2112–2116 (1997).
[CrossRef]

Li, H. H.

H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9, 161–289 (1980).
[CrossRef]

Malitson, I. H.

Palmacci, S. T.

T. M. Bloomstein, M. W. Horn, M. Rothschild, R. R. Kunz, S. T. Palmacci, R. B. Goodman, “Lithography with 157-nm lasers,” J. Vac. Sci. Technol. B 15, 2112–2116 (1997).
[CrossRef]

Parkinson, W. H.

K. Yoshino, D. E. Freeman, J. R. Esmond, W. H. Parkinson, “High resolution absorption cross section measurements and band oscillator strengths of the (1,0)–(12,0) Schumann–Runge bands of O2,” Planet. Space Sci. 31, 339–353 (1983).
[CrossRef]

Peck, E. R.

Reader, J.

J. Reader, N. Acquista, C. J. Sansonetti, J. E. Sansonetti, “Wavelengths and intensities of a platinum/neon hollow cathode lamp in the region 1100–4000 Å,” Astrophys. J. Suppl. Ser. 72, 831–866 (1990).
[CrossRef]

Rothschild, M.

T. M. Bloomstein, M. W. Horn, M. Rothschild, R. R. Kunz, S. T. Palmacci, R. B. Goodman, “Lithography with 157-nm lasers,” J. Vac. Sci. Technol. B 15, 2112–2116 (1997).
[CrossRef]

Sansonetti, C. J.

J. Reader, N. Acquista, C. J. Sansonetti, J. E. Sansonetti, “Wavelengths and intensities of a platinum/neon hollow cathode lamp in the region 1100–4000 Å,” Astrophys. J. Suppl. Ser. 72, 831–866 (1990).
[CrossRef]

Sansonetti, J. E.

J. Reader, N. Acquista, C. J. Sansonetti, J. E. Sansonetti, “Wavelengths and intensities of a platinum/neon hollow cathode lamp in the region 1100–4000 Å,” Astrophys. J. Suppl. Ser. 72, 831–866 (1990).
[CrossRef]

Walhout, M.

Watanabe, K.

K. Watanabe, E. C. Y. Inn, M. Zelikoff, “Absorption coefficients of oxygen in the vacuum ultraviolet,” J. Chem. Phys. 21, 1026–1030 (1953).
[CrossRef]

Westenberger, G.

H. J. Hoffmann, W. W. Jochs, G. Westenberger, “A dispersion formula for the thermo-optic coefficient of optical glasses,” in Properties and Characteristics of Optical Glass II, A. J. Marker, ed., Proc. SPIE1327, 219–230 (1990).
[CrossRef]

Yoshino, K.

K. Yoshino, D. E. Freeman, J. R. Esmond, W. H. Parkinson, “High resolution absorption cross section measurements and band oscillator strengths of the (1,0)–(12,0) Schumann–Runge bands of O2,” Planet. Space Sci. 31, 339–353 (1983).
[CrossRef]

Zelikoff, M.

K. Watanabe, E. C. Y. Inn, M. Zelikoff, “Absorption coefficients of oxygen in the vacuum ultraviolet,” J. Chem. Phys. 21, 1026–1030 (1953).
[CrossRef]

Appl. Opt. (2)

Ark. Mat. Astron. Fys. (1)

J. Koch, “Uber die dispersion des lichtes in gasformigen korpern innerhalb des ultravioletten spektrums,” Ark. Mat. Astron. Fys. 9(6), 1–11 (1913).

Astrophys. J. Suppl. Ser. (1)

J. Reader, N. Acquista, C. J. Sansonetti, J. E. Sansonetti, “Wavelengths and intensities of a platinum/neon hollow cathode lamp in the region 1100–4000 Å,” Astrophys. J. Suppl. Ser. 72, 831–866 (1990).
[CrossRef]

J. Chem. Phys. (1)

K. Watanabe, E. C. Y. Inn, M. Zelikoff, “Absorption coefficients of oxygen in the vacuum ultraviolet,” J. Chem. Phys. 21, 1026–1030 (1953).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Chem. Ref. Data (1)

H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9, 161–289 (1980).
[CrossRef]

J. Vac. Sci. Technol. B (1)

T. M. Bloomstein, M. W. Horn, M. Rothschild, R. R. Kunz, S. T. Palmacci, R. B. Goodman, “Lithography with 157-nm lasers,” J. Vac. Sci. Technol. B 15, 2112–2116 (1997).
[CrossRef]

Metrologia (1)

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
[CrossRef]

Opt. Lett. (1)

Planet. Space Sci. (1)

K. Yoshino, D. E. Freeman, J. R. Esmond, W. H. Parkinson, “High resolution absorption cross section measurements and band oscillator strengths of the (1,0)–(12,0) Schumann–Runge bands of O2,” Planet. Space Sci. 31, 339–353 (1983).
[CrossRef]

Other (4)

J. E. Sansonetti, J. Reader, C. J. Sansonetti, N. Acquista, “Atlas of the spectrum of a platinum/neon hollow-cathode lamp in the region 1130–4330 Å,” http://physics.nist.gov/PhysRefData/platinum/contents.html/ .

J. H. Burnett, R. Gupta, U. Griesmann, “Index of refraction and its temperature dependence of calcium fluoride near 157 nm,” in Optical Microlithography X II, L. Van den Hove, ed., Proc. SPIE3679, 1146–1152 (1999).

J. H. Burnett, R. Gupta, U. Griesmann, “Absolute index of refraction and its temperature dependence of calcium fluoride, barium fluoride, and strontium fluoride near 157 nm,” in Optical Microlithography X III, C. J. Progler, ed., Proc. SPIE4000, 1503–1509 (2000).

H. J. Hoffmann, W. W. Jochs, G. Westenberger, “A dispersion formula for the thermo-optic coefficient of optical glasses,” in Properties and Characteristics of Optical Glass II, A. J. Marker, ed., Proc. SPIE1327, 219–230 (1990).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Optical arrangement of the goniometer–spectrometer: M1, M4–M6, mirrors; M1, M4, parabolic off-axis mirrors. PMT, photomultiplier tube.

Fig. 2
Fig. 2

Schematic side view of the measurement setup: LS, light source; LC, light chopper; P, sample prism; OM, oxygen meter; BM, barometer; QTM, quartz thermometer; QS1, QS2, quartz thermo sensors; DMM, digital multimeter; SJ, standard junction; TC, thermocouple.

Fig. 3
Fig. 3

Comparison of our values for the refractive index of synthetic CaF2 in nitrogen gas at 25 °C and 1013.25 hPa with the values reported by Malitson.2 Our values computed from the dispersion formula are represented by the horizontal line, Δn = 0.

Fig. 4
Fig. 4

Comparison of our dispersion values for the refractive index of synthetic CaF2 in nitrogen gas at 20 °C and 1013.25 hPa with the dispersion values reported by Gupta et al.4 and by Burnett et al.6 Our values are represented by the horizontal line, Δn = 0.

Fig. 5
Fig. 5

Comparison of our dispersion values for dn rel(λ)/dt for synthetic CaF2 with values reported previously by Malitson,2 Gupta et al.,4 and Burnett et al.6 Our values are represented by the horizontal line Δ[dn rel(λ)/dt] = 0.

Tables (4)

Tables Icon

Table 1 Relative Refractive Indices and Relative dn/dt of CaF2

Tables Icon

Table 2 Dispersion Constants of Relative Refractive Indexa

Tables Icon

Table 3 Dispersion Constants of dn rel/dt a

Tables Icon

Table 4 Main Sources of Uncertainty

Equations (7)

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

n=sinθ+δ/2sinθ/2.
dnrelλdt=nλ, t1-nλ, t2t1-t2.
nλ, 20=nλ, t1-t1-20dnrelλ/dt,
nλ, 25=nλ, t2-t2-25dnrelλ/dt.
n2λ, t-1=i=14Aiλ2λ2-λi2,
dnλ, tdt=n2λ, t-12nλ, tDt+Etλ2-λ02t.
dnrelλdt=n2λ-12nλD0+E0λ2-λ02.

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