Abstract

The optical constants of crystal quartz in the far infrared (10–400 cm−1) are presented along with the dispersion parameters for the two ordinary-ray bands measured in this study. The asymmetric Fourier-transform method was used for the quantitative measurement of the refractive indices of quartz. The advantages of this method as compared with the channeled-spectrum method usually employed for refractive-index measurements in the far infrared are discussed. The extrapolated, zero-frequency refractive indices of quartz are n0(0)=2.106±0.001 and ne(0)=2.154±0.001. A pseudocoherence effect is described which permits the measurement of the difference of the principle refractive indices in a birefringent sample without the use of a polarizer.

© 1967 Optical Society of America

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References

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  1. B. D. Saksena, Proc. Indian Acad. Sci. 12A, 93 (1940).
  2. W. G. Spitzer and D. A. Kleinman, Phys. Rev. 121, 1324 (1961).
    [CrossRef]
  3. M. Czerny, Z. Physik 53, 317 (1929).
    [CrossRef]
  4. J. E. Chamberlain, J. E. Gibbs, and H. A. Gebbie, Nature 198, 874 (1963).
    [CrossRef]
  5. J. E. Chamberlain and H. A. Gebbie, Appl. Opt. 5, 393 (1966).
    [CrossRef] [PubMed]
  6. E. E. Bell, Japan J. Appl. Phys. Suppl. 4, 412 (1965).
  7. E. E. Bell, Infrared Phys. 6, 57 (1966).
    [CrossRef]
  8. E. E. Bell, J. Physique (to be published).
  9. E. E. Russell, Ph.D. dissertation, Dept. of Physics, Ohio State Univ., June1966; order number 66–15, 128, University Microfilms Inc., Ann Arbor, Michigan.
  10. E. E. Russell and E. E. Bell, Infrared Phys. 6, 75 (1966).
    [CrossRef]
  11. J. E. Chamberlain and H. A. Gebbie, Appl. Opt. 5, 393 (1966).
    [CrossRef] [PubMed]
  12. S. Roberts and D. D. Coon, J. Opt. Soc. Am. 52, 1023 (1962).
    [CrossRef]
  13. See for example, F. Seitz, Modern Theory of Solids (McGraw–Hill Book Company, New York, 1940), Ch. XVII.
  14. J. E. Chamberlain, F. D. Findlay, and H. A. Gebbie, Appl. Opt. 4, 1382 (1965).
    [CrossRef]
  15. R. B. Barnes, Phys. Rev. 39, 562 (1932).
    [CrossRef]
  16. Y. Yamada, A. Mitsuishi, and H. Yoshinaga, J. Opt. Soc. Am. 52, 17 (1962).
    [CrossRef]
  17. This polarizer was prepared by M. Hass and M. O’Hara and loaned to us by E. D. Palik of the U. S. Naval Research Laboratory. The thick quartz sample was made available for this work by E. D. Palik, also.
  18. M. Hass and M. O’Hara, Appl. Opt. 4, 1027 (1965).
    [CrossRef]
  19. H. Happ and L. Genzel, Infrared Phys. 1, 39 (1961).
    [CrossRef]
  20. R. Geick, Z. Physik 161, 116 (1961).
    [CrossRef]
  21. J. E. Chamberlain and H. A. Gebbie, Nature 206, 602 (1965).
    [CrossRef]
  22. E. D. Palik, Appl. Opt. 4, 1017 (1965).
    [CrossRef]
  23. E. D. Palik (private communication).

1966 (4)

1965 (5)

1963 (1)

J. E. Chamberlain, J. E. Gibbs, and H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

1962 (2)

1961 (3)

W. G. Spitzer and D. A. Kleinman, Phys. Rev. 121, 1324 (1961).
[CrossRef]

H. Happ and L. Genzel, Infrared Phys. 1, 39 (1961).
[CrossRef]

R. Geick, Z. Physik 161, 116 (1961).
[CrossRef]

1940 (1)

B. D. Saksena, Proc. Indian Acad. Sci. 12A, 93 (1940).

1932 (1)

R. B. Barnes, Phys. Rev. 39, 562 (1932).
[CrossRef]

1929 (1)

M. Czerny, Z. Physik 53, 317 (1929).
[CrossRef]

Barnes, R. B.

R. B. Barnes, Phys. Rev. 39, 562 (1932).
[CrossRef]

Bell, E. E.

E. E. Bell, Infrared Phys. 6, 57 (1966).
[CrossRef]

E. E. Russell and E. E. Bell, Infrared Phys. 6, 75 (1966).
[CrossRef]

E. E. Bell, Japan J. Appl. Phys. Suppl. 4, 412 (1965).

E. E. Bell, J. Physique (to be published).

Chamberlain, J. E.

Coon, D. D.

Czerny, M.

M. Czerny, Z. Physik 53, 317 (1929).
[CrossRef]

Findlay, F. D.

Gebbie, H. A.

Geick, R.

R. Geick, Z. Physik 161, 116 (1961).
[CrossRef]

Genzel, L.

H. Happ and L. Genzel, Infrared Phys. 1, 39 (1961).
[CrossRef]

Gibbs, J. E.

J. E. Chamberlain, J. E. Gibbs, and H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

Happ, H.

H. Happ and L. Genzel, Infrared Phys. 1, 39 (1961).
[CrossRef]

Hass, M.

Kleinman, D. A.

W. G. Spitzer and D. A. Kleinman, Phys. Rev. 121, 1324 (1961).
[CrossRef]

Mitsuishi, A.

O’Hara, M.

Palik, E. D.

E. D. Palik, Appl. Opt. 4, 1017 (1965).
[CrossRef]

E. D. Palik (private communication).

Roberts, S.

Russell, E. E.

E. E. Russell and E. E. Bell, Infrared Phys. 6, 75 (1966).
[CrossRef]

E. E. Russell, Ph.D. dissertation, Dept. of Physics, Ohio State Univ., June1966; order number 66–15, 128, University Microfilms Inc., Ann Arbor, Michigan.

Saksena, B. D.

B. D. Saksena, Proc. Indian Acad. Sci. 12A, 93 (1940).

Seitz, F.

See for example, F. Seitz, Modern Theory of Solids (McGraw–Hill Book Company, New York, 1940), Ch. XVII.

Spitzer, W. G.

W. G. Spitzer and D. A. Kleinman, Phys. Rev. 121, 1324 (1961).
[CrossRef]

Yamada, Y.

Yoshinaga, H.

Appl. Opt. (5)

Infrared Phys. (3)

H. Happ and L. Genzel, Infrared Phys. 1, 39 (1961).
[CrossRef]

E. E. Bell, Infrared Phys. 6, 57 (1966).
[CrossRef]

E. E. Russell and E. E. Bell, Infrared Phys. 6, 75 (1966).
[CrossRef]

J. Opt. Soc. Am. (2)

Japan J. Appl. Phys. Suppl. (1)

E. E. Bell, Japan J. Appl. Phys. Suppl. 4, 412 (1965).

Nature (2)

J. E. Chamberlain, J. E. Gibbs, and H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

J. E. Chamberlain and H. A. Gebbie, Nature 206, 602 (1965).
[CrossRef]

Phys. Rev. (2)

W. G. Spitzer and D. A. Kleinman, Phys. Rev. 121, 1324 (1961).
[CrossRef]

R. B. Barnes, Phys. Rev. 39, 562 (1932).
[CrossRef]

Proc. Indian Acad. Sci. (1)

B. D. Saksena, Proc. Indian Acad. Sci. 12A, 93 (1940).

Z. Physik (2)

M. Czerny, Z. Physik 53, 317 (1929).
[CrossRef]

R. Geick, Z. Physik 161, 116 (1961).
[CrossRef]

Other (5)

See for example, F. Seitz, Modern Theory of Solids (McGraw–Hill Book Company, New York, 1940), Ch. XVII.

E. E. Bell, J. Physique (to be published).

E. E. Russell, Ph.D. dissertation, Dept. of Physics, Ohio State Univ., June1966; order number 66–15, 128, University Microfilms Inc., Ann Arbor, Michigan.

This polarizer was prepared by M. Hass and M. O’Hara and loaned to us by E. D. Palik of the U. S. Naval Research Laboratory. The thick quartz sample was made available for this work by E. D. Palik, also.

E. D. Palik (private communication).

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Figures (7)

Fig. 1
Fig. 1

Determination of the extrapolated, zero-frequency, ordinary- and extraordinary-ray refractive indices of quartz. The extrapolated values, n0(0)=2.1062 and ne(0)=2.1538, have an experimental uncertainty of ±0.001, which is much larger than is apparent from the consistency of the data.

Fig. 2
Fig. 2

Ordinary-ray refractive-indices and absorption coefficient of quartz.

Fig. 3
Fig. 3

Extraordinary-ray refractive indices and absorption coefficient of quartz.

Fig. 4
Fig. 4

Pseudocoherence between ordinary and extraordinary rays in a 4.79-mm, Y-cut quartz plate. The “transmittance” was observed with unpolarized radiation.

Fig. 5
Fig. 5

The refractive-index difference nen0 of quartz showing the dispersion through the weak band in the ordinary ray at 128.4 cm−1.

Fig. 6
Fig. 6

The power transmittance of a 0.0766-mm, Y-cut quartz plate. The solid curve is for the ordinary ray and the dashed curve for the extraordinary ray.

Fig. 7
Fig. 7

Ordinary-ray and extraordinary-ray refractive indices and absorption coefficients of quartz as determined from the 0.0766-mm plate.

Tables (3)

Tables Icon

Table I Optical constants of quartz in the far infrared.

Tables Icon

Table II Refractive-index differences |n0ne| for quartz measured using the pseudocoherence effect.

Tables Icon

Table III Dispersion parameters for crystal quartz which reproduce the measured far-infrared refraction spectra within experimental error.a

Equations (16)

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T ˆ = ( 1 - r ˆ 2 ) â ( 1 + â 2 r ˆ 2 + â 4 r ˆ 4 + ) = ( p 12 / p 11 ) exp i [ ϕ 12 - ϕ 11 + 2 π ν ( D + b ) ] .
T ˆ exp ( - i 2 π ν b ) = â ( 1 - r ˆ 2 ) [ 1 + â 2 r ˆ 2 W ( x ) + + â 2 m r ˆ 2 m W ( m x ) ] = ( p 12 / p 11 ) exp i ( ϕ 12 - ϕ 11 + 2 π ν D ) ,
n = 1 + D / b + ( ϕ 12 - ϕ 11 ) / ( 2 π ν b ) + L / ( ν b ) ,
T 2 = ( 1 - r 2 ) 2 a 2 ,
α = b - 1 ln [ ( 1 - r 2 ) 2 / T 2 ] .
T 2 = ( 1 - r 2 ) 2 a 2 / ( 1 - r 4 a 4 )
α = b - 1 ln 2 r 4 T 2 ( 1 - r 2 ) - 2 × { - 1 + [ 1 + 4 r 4 T 4 ( 1 - r 2 ) - 4 ] 1 2 } - 1 .
n calc = n [ 1 + β 2 ( 1 - n - 2 ) / 4 ] ,
n e , calc = n e [ 1 + β 2 ( 2 - n 0 - 2 - n e - 2 ) / 8 ]
n 0 - n e = m / ( 2 ν m b ) ,
ˆ = + i = ( n + i k ) 2 .
= n 2 - k 2 = + j S j ( 1 - Ω j 2 ) / [ ( 1 - Ω j 2 ) 2 + γ j 2 Ω j 2 ]
= 2 n k = j S j Ω j γ j / [ ( 1 - Ω j 2 ) 2 + γ j 2 Ω j 2 ] ,
( 0 ) = n 2 ( 0 ) = + j S j .
n 1 2 ( 0 ) { 1 + ν 2 j S j / [ 2 ( 0 ) ν j 2 ] } .
j th band 2 n k ν d ν = π ν j 2 S j / 2 ,