Abstract

This paper reports the index of refraction of CaWO4, CaF2, and BaF2 for wavelengths from 4350 to 18 460 Å and over the temperature range −180°C to room temperature. Measurements are made on dilute ruby at 5461 Å from −180° to 70°C. The results are applied to an interpretation of the output frequency of solid-state optical masers.

© 1963 Optical Society of America

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References

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  1. W. L. Bond (to be published).
  2. M. Barbaron, Ann. Phys. (Paris) 6, 899 (1951).
  3. R. A. McFarlane, “A Summary of Available Data on the Physical Properties of Synthetic Sapphire,” Adolf Meller Company, Providence (1961) and private communication. However, there is some spread in the values quoted in the literature. See also the publication of the Linde Company, “Thermal Properties of Clear Sapphire” (February1959).
  4. I. H. Malitson, F. V. Murphy, and W. S. Rodney, J. Opt. Soc. Am. 48, 72 (1958).
    [CrossRef]
  5. G. N. Ramachandran, Proc. Ind. Acad. Sci. 25A, 266 (1947).
  6. L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).
  7. L. Prod’homme, Rev. Opt. (France) 40, 407 (1961).
  8. F. Lukes, Czech. J. Phys. 10, 742 (1960).
    [CrossRef]
  9. International Critical Tables (McGraw-Hill Book Company, Inc., New York, 1928), Vol. 3, p. 43.
  10. T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhof, Phys. Rev. 123, 1151 (1961).
    [CrossRef]
  11. J. A. Ditzenberger (unpublished).
  12. M. Ciftan, A. Krutchkoff, and S. Koozekanani, Proc. IRE 50, 84 (1962).
  13. The coefficients of thermal expansion for CaWO4 are 7.9×10−6 (a axis) and 12.7×10−6 (c axis). See K. Nassau and A. M. Broyer, J. Appl. Phys. 33, 3064 (1962).
    [CrossRef]
  14. L. F. Johnson and R. A. Thomas (unpublished).
  15. L. F. Johnson, Quantum Electronics Conference, Paris, 1963.
  16. I. D. Abella and H. Z. Cummins, J. Appl. Phys. 32, 1177 (1961).
    [CrossRef]
  17. P. Kisliuk and W. S. Boyle, Proc. IRE 49, 1635 (1961).
    [CrossRef]

1962 (2)

M. Ciftan, A. Krutchkoff, and S. Koozekanani, Proc. IRE 50, 84 (1962).

The coefficients of thermal expansion for CaWO4 are 7.9×10−6 (a axis) and 12.7×10−6 (c axis). See K. Nassau and A. M. Broyer, J. Appl. Phys. 33, 3064 (1962).
[CrossRef]

1961 (4)

I. D. Abella and H. Z. Cummins, J. Appl. Phys. 32, 1177 (1961).
[CrossRef]

P. Kisliuk and W. S. Boyle, Proc. IRE 49, 1635 (1961).
[CrossRef]

L. Prod’homme, Rev. Opt. (France) 40, 407 (1961).

T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhof, Phys. Rev. 123, 1151 (1961).
[CrossRef]

1960 (2)

F. Lukes, Czech. J. Phys. 10, 742 (1960).
[CrossRef]

L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).

1958 (1)

1951 (1)

M. Barbaron, Ann. Phys. (Paris) 6, 899 (1951).

1947 (1)

G. N. Ramachandran, Proc. Ind. Acad. Sci. 25A, 266 (1947).

Abella, I. D.

I. D. Abella and H. Z. Cummins, J. Appl. Phys. 32, 1177 (1961).
[CrossRef]

Asawa, C. K.

T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhof, Phys. Rev. 123, 1151 (1961).
[CrossRef]

Barbaron, M.

M. Barbaron, Ann. Phys. (Paris) 6, 899 (1951).

Bond, W. L.

W. L. Bond (to be published).

Boyle, W. S.

P. Kisliuk and W. S. Boyle, Proc. IRE 49, 1635 (1961).
[CrossRef]

Broyer, A. M.

The coefficients of thermal expansion for CaWO4 are 7.9×10−6 (a axis) and 12.7×10−6 (c axis). See K. Nassau and A. M. Broyer, J. Appl. Phys. 33, 3064 (1962).
[CrossRef]

Ciftan, M.

M. Ciftan, A. Krutchkoff, and S. Koozekanani, Proc. IRE 50, 84 (1962).

Cummins, H. Z.

I. D. Abella and H. Z. Cummins, J. Appl. Phys. 32, 1177 (1961).
[CrossRef]

D’Haenens, I. J.

T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhof, Phys. Rev. 123, 1151 (1961).
[CrossRef]

Ditzenberger, J. A.

J. A. Ditzenberger (unpublished).

Evtuhof, V.

T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhof, Phys. Rev. 123, 1151 (1961).
[CrossRef]

Hoskins, R. H.

T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhof, Phys. Rev. 123, 1151 (1961).
[CrossRef]

Johnson, L. F.

L. F. Johnson and R. A. Thomas (unpublished).

L. F. Johnson, Quantum Electronics Conference, Paris, 1963.

Kisliuk, P.

P. Kisliuk and W. S. Boyle, Proc. IRE 49, 1635 (1961).
[CrossRef]

Koozekanani, S.

M. Ciftan, A. Krutchkoff, and S. Koozekanani, Proc. IRE 50, 84 (1962).

Krutchkoff, A.

M. Ciftan, A. Krutchkoff, and S. Koozekanani, Proc. IRE 50, 84 (1962).

Lukes, F.

F. Lukes, Czech. J. Phys. 10, 742 (1960).
[CrossRef]

Maiman, T. H.

T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhof, Phys. Rev. 123, 1151 (1961).
[CrossRef]

Malitson, I. H.

McFarlane, R. A.

R. A. McFarlane, “A Summary of Available Data on the Physical Properties of Synthetic Sapphire,” Adolf Meller Company, Providence (1961) and private communication. However, there is some spread in the values quoted in the literature. See also the publication of the Linde Company, “Thermal Properties of Clear Sapphire” (February1959).

Murphy, F. V.

Nassau, K.

The coefficients of thermal expansion for CaWO4 are 7.9×10−6 (a axis) and 12.7×10−6 (c axis). See K. Nassau and A. M. Broyer, J. Appl. Phys. 33, 3064 (1962).
[CrossRef]

Prod’homme, L.

L. Prod’homme, Rev. Opt. (France) 40, 407 (1961).

L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).

Ramachandran, G. N.

G. N. Ramachandran, Proc. Ind. Acad. Sci. 25A, 266 (1947).

Rodney, W. S.

Thomas, R. A.

L. F. Johnson and R. A. Thomas (unpublished).

Ann. Phys. (Paris) (1)

M. Barbaron, Ann. Phys. (Paris) 6, 899 (1951).

Czech. J. Phys. (1)

F. Lukes, Czech. J. Phys. 10, 742 (1960).
[CrossRef]

J. Appl. Phys. (2)

The coefficients of thermal expansion for CaWO4 are 7.9×10−6 (a axis) and 12.7×10−6 (c axis). See K. Nassau and A. M. Broyer, J. Appl. Phys. 33, 3064 (1962).
[CrossRef]

I. D. Abella and H. Z. Cummins, J. Appl. Phys. 32, 1177 (1961).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Chem. Glasses (1)

L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).

Phys. Rev. (1)

T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhof, Phys. Rev. 123, 1151 (1961).
[CrossRef]

Proc. Ind. Acad. Sci. (1)

G. N. Ramachandran, Proc. Ind. Acad. Sci. 25A, 266 (1947).

Proc. IRE (2)

M. Ciftan, A. Krutchkoff, and S. Koozekanani, Proc. IRE 50, 84 (1962).

P. Kisliuk and W. S. Boyle, Proc. IRE 49, 1635 (1961).
[CrossRef]

Rev. Opt. (France) (1)

L. Prod’homme, Rev. Opt. (France) 40, 407 (1961).

Other (6)

International Critical Tables (McGraw-Hill Book Company, Inc., New York, 1928), Vol. 3, p. 43.

R. A. McFarlane, “A Summary of Available Data on the Physical Properties of Synthetic Sapphire,” Adolf Meller Company, Providence (1961) and private communication. However, there is some spread in the values quoted in the literature. See also the publication of the Linde Company, “Thermal Properties of Clear Sapphire” (February1959).

L. F. Johnson and R. A. Thomas (unpublished).

L. F. Johnson, Quantum Electronics Conference, Paris, 1963.

W. L. Bond (to be published).

J. A. Ditzenberger (unpublished).

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Figures (14)

Fig. 1
Fig. 1

Positions of prism at which clinometer readings of the angle of incidence and angle of refraction are taken.

Fig. 2
Fig. 2

Orientation of c axis in CaWO4 and ruby prisms.

Fig. 3
Fig. 3

Apparatus constructed for measurement of refractive index as a function of temperature.

Fig. 4
Fig. 4

Path of light in detector method.

Fig. 5
Fig. 5

CaWO4n vs λ in the visible range at 20°C showing points from International Critical Tables and from the Handbook of Chemistry and Physics. nω is the refractive index of ordinary ray (E vector perpendicular to c axis). n is the refractive index of extraordinary ray (E vector parallel to c axis).

Fig. 6
Fig. 6

CaWO4n vs λ at 20°C including data of Bond.1

Fig. 7
Fig. 7

CaWO4n vs λ at −180°C for present work.

Fig. 8
Fig. 8

CaWO4(nn20) vs temperature, (a) ordinary ray, (b) extraordinary ray.

Fig. 9
Fig. 9

CaF2n vs λ at 25° and −190°C showing data from International Critical Tables and from Barbaron.2

Fig. 10
Fig. 10

CaF2(nn20) vs T measured by Barbaron2 for λ=5461Å.

Fig. 11
Fig. 11

BaF2n vs λ.

Fig. 12
Fig. 12

BaF2(nn25) vs T for λ=5461 and 10 140 Å.

Fig. 13
Fig. 13

The thermal coefficient of refractive index dn/dT vs T for CaWO4, BaF2, and CaF2.

Fig. 14
Fig. 14

Apparent refractive index vs temperature for ruby at 5461 Å. napp=sinθ/sinα0 where the prism angle α0 is measured at room temperature (see text).

Tables (5)

Tables Icon

Table I Temperature dependence of refractive indices of CaWO4 in the visible.

Tables Icon

Table II Temperature dependence of refractive indices of CaWO4 in the near infrared.

Tables Icon

Table III Temperature dependence of refractive index of BaF2.

Tables Icon

Table IV Temperature dependence of refractive index of CaF2.

Tables Icon

Table V Temperature coefficient of refractive indices of CaWO4, BaF2, and CaF2.

Equations (10)

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d n d T = 1 sin α d sin θ d T + cos α cot α sin θ ( C - C ) = ( d n d T ) a p p + Δ ,
d n ω / d T = 10.5 × 10 - 6 + 2.7 × 10 - 6 = + 13 × 10 - 6 ± 1 × 10 - 6 , d n / d T = 15 × 10 - 6 + 2.7 × 10 - 6 = + 17.5 × 10 - 6 ± 1 × 10 - 6 .
( n 2 - 1 ) / ( n 2 + 2 ) = ( 4 π / 3 ) ( L / M ) α ρ ,
m λ m = 2 n L ,
1 λ m d λ m d T = 1 ν m d ν m d T = 1 L d L d T + 1 n d n d T .
1 λ m d λ m d T = 7 × 10 - 6 - 1 1.43 ( 6.6 × 10 - 6 ) 2.4 × 10 - 6 ° K .
1 λ m d λ m d T = 7 × 10 - 6 - 1 1.47 ( 8.6 × 10 - 6 ) 1 × 10 - 6 ° K .
1 λ m d λ m d T = 12.7 × 10 - 6 - 1 1.9 ( 7.1 × 10 - 6 ) 9 × 10 - 6 ° K
1 λ m d λ m d T = 7.9 × 10 - 6 - 1 1.9 ( 7.1 × 10 - 6 ) 4 × 10 - 6 ° K
1 λ m d λ m d T = 5 × 10 - 6 + 1 1.77 ( 13 × 10 - 6 ) 12 × 10 - 6 ° K ,