Abstract

Measurements of the ordinary and extraordinary refractive indexes of synthetic sapphire are reported. Direct independent measurements of the birefringence are given. Temperature and piezo-optical coefficients of birefringence are given and combined with published data and calculations of W. L. Bragg to yield order of magnitude values for the thermal coefficient of expansion and Young’s modulus.

© 1958 Optical Society of America

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References

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  1. Freed, McMurry, and Rosenbaum, J. Chem. Phys. 7, 853 (1939); Bauple, Gilles, Romand, and Vodar, J. Opt. Soc. Am. 40, 788 (1950).
    [Crossref]
  2. R. W. Kebler, “Optical properties of synthetic sapphire,” a brochure supplied by Linde Air Products Company, New York.
  3. Malitson, Murphy, and Rodney, J. Opt. Soc. Am. 48, 72 (1958).
    [Crossref]
  4. W. L. Bragg, Proc. Roy. Soc. (London) 106, 357 (1924).
  5. R. F. Galler and P. J. Yavorsky, J. Research Natl. Bur. Standards,  35, R. P. 1662 (1945).
  6. Furukawa, Douglas, McCoskey, and Ginnings, J. Research Natl. Bur. Standards 57, R. P. 2694 (1956).
    [Crossref]

1958 (1)

1956 (1)

Furukawa, Douglas, McCoskey, and Ginnings, J. Research Natl. Bur. Standards 57, R. P. 2694 (1956).
[Crossref]

1945 (1)

R. F. Galler and P. J. Yavorsky, J. Research Natl. Bur. Standards,  35, R. P. 1662 (1945).

1939 (1)

Freed, McMurry, and Rosenbaum, J. Chem. Phys. 7, 853 (1939); Bauple, Gilles, Romand, and Vodar, J. Opt. Soc. Am. 40, 788 (1950).
[Crossref]

1924 (1)

W. L. Bragg, Proc. Roy. Soc. (London) 106, 357 (1924).

Bragg, W. L.

W. L. Bragg, Proc. Roy. Soc. (London) 106, 357 (1924).

Douglas,

Furukawa, Douglas, McCoskey, and Ginnings, J. Research Natl. Bur. Standards 57, R. P. 2694 (1956).
[Crossref]

Freed,

Freed, McMurry, and Rosenbaum, J. Chem. Phys. 7, 853 (1939); Bauple, Gilles, Romand, and Vodar, J. Opt. Soc. Am. 40, 788 (1950).
[Crossref]

Furukawa,

Furukawa, Douglas, McCoskey, and Ginnings, J. Research Natl. Bur. Standards 57, R. P. 2694 (1956).
[Crossref]

Galler, R. F.

R. F. Galler and P. J. Yavorsky, J. Research Natl. Bur. Standards,  35, R. P. 1662 (1945).

Ginnings,

Furukawa, Douglas, McCoskey, and Ginnings, J. Research Natl. Bur. Standards 57, R. P. 2694 (1956).
[Crossref]

Kebler, R. W.

R. W. Kebler, “Optical properties of synthetic sapphire,” a brochure supplied by Linde Air Products Company, New York.

Malitson,

McCoskey,

Furukawa, Douglas, McCoskey, and Ginnings, J. Research Natl. Bur. Standards 57, R. P. 2694 (1956).
[Crossref]

McMurry,

Freed, McMurry, and Rosenbaum, J. Chem. Phys. 7, 853 (1939); Bauple, Gilles, Romand, and Vodar, J. Opt. Soc. Am. 40, 788 (1950).
[Crossref]

Murphy,

Rodney,

Rosenbaum,

Freed, McMurry, and Rosenbaum, J. Chem. Phys. 7, 853 (1939); Bauple, Gilles, Romand, and Vodar, J. Opt. Soc. Am. 40, 788 (1950).
[Crossref]

Yavorsky, P. J.

R. F. Galler and P. J. Yavorsky, J. Research Natl. Bur. Standards,  35, R. P. 1662 (1945).

J. Chem. Phys. (1)

Freed, McMurry, and Rosenbaum, J. Chem. Phys. 7, 853 (1939); Bauple, Gilles, Romand, and Vodar, J. Opt. Soc. Am. 40, 788 (1950).
[Crossref]

J. Opt. Soc. Am. (1)

J. Research Natl. Bur. Standards (2)

R. F. Galler and P. J. Yavorsky, J. Research Natl. Bur. Standards,  35, R. P. 1662 (1945).

Furukawa, Douglas, McCoskey, and Ginnings, J. Research Natl. Bur. Standards 57, R. P. 2694 (1956).
[Crossref]

Proc. Roy. Soc. (London) (1)

W. L. Bragg, Proc. Roy. Soc. (London) 106, 357 (1924).

Other (1)

R. W. Kebler, “Optical properties of synthetic sapphire,” a brochure supplied by Linde Air Products Company, New York.

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Figures (2)

Fig. 1
Fig. 1

Reproduction of spectrograms showing the multiple wave plate bands obtained with a sapphire plate 1.005 mm thick. (a) Prism spectrogram, 4300 A to 8800 A. Upper: channel spectrum. Middle: wave plate bands. Lower: mercury spectrum. (b) Grating spectrogram, 4300 A to 5500 A. Top: crystal at 20°C. Bottom: crystal at 70°C. (C) Gating spectrogram, 5790 A to 7000 A. Upper: no stress. Middle: 3600 N/cm2 perpendicular to the optic axis. Lower: 3600 N/cm2 parallel to the optic axis.

Fig. 2
Fig. 2

A plot of Bragg’s calculated values of the refractive indexes of Al2O3 for three different values of the parameter r.

Tables (3)

Tables Icon

Table I The indexes of refraction of sapphire at 24°C.

Tables Icon

Table II Constants for the Cornu dispersion formula n=a+b/(λ−λ0) for the ordinary and extraordinary indexes of sapphire.

Tables Icon

Table III Birefringence of a synthetic sapphire crystal plate at 23°C under different conditions of stress.

Equations (9)

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n = a + ( b / λ - λ 0 ) .
φ = ( 2 π / λ ) ( n O - n E ) t ,
( n O - n E ) t = m λ ,
B = Δ ( n O - n E ) / Δ S .
B = - 0.94 × 10 - 8 cm 2 / Newton , B = + 0.83 × 10 - 8 cm 2 / Newton .
d ( n O - n E ) d T = d ( n O - n E ) d r d r d T = r α d ( n O - n E ) d r
Δ ( n O - n E ) / Δ r = - 0.17 A - 1 .
Δ S = Y ( Δ r / r ) .
Y = Δ ( n O - n E ) r B Δ r = - 0.17 A - 1 × 1.45 A - 0.94 × 10 - 8 cm 2 / N = 26 × 10 6 N / cm 2 .