Abstract

We report the experimental demonstration of an optical quarter-wave plate having a retardation of 90°±1° in the region from 4000 to 8000 Å. The device is based on the synthesis procedure of Harris, Ammann, and Chang and consists of six sapphire wave plates with appropriately oriented principal axes. The device does not suffer from thermal or angular problems as do longer, narrow-band birefringent networks. Results comparing a 10-plate unit with the above 6-plate unit are given.

© 1968 Optical Society of America

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References

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  1. S. E. Harris, E. O. Ammann, and I. C. Chang, J. Opt. Soc. Am. 54, 1267 (1964).
    [CrossRef]
  2. E. O. Ammann and I. C. Chang, J. Opt. Soc. Am. 55, 835 (1965).
    [CrossRef]
  3. E. O. Ammann, J. Opt. Soc. Am. 56, 943 (1966).
    [CrossRef]
  4. E. O. Ammann, J. Opt. Soc. Am. 56, 952 (1966).
    [CrossRef]
  5. E. O. Ammann, J. Opt. Soc. Am. 56, 1081 (1966).
    [CrossRef]
  6. E. O. Ammann and J. M. Yarborough, J. Opt. Soc. Am. 57, 349 (1967).
    [CrossRef]
  7. C. D. West and A. S. Makas, J. Opt. Soc. Am. 39, 791 (1949).
    [CrossRef] [PubMed]
  8. M. G. Destriau and J. Prouteau, J. Phys. Radium 10, 53 (1949).
    [CrossRef]
  9. S. Pancharatnam, Proc. Indian Acad. Sci. A41, 130 (1955).
  10. S. Pancharatnam, Proc. Indian Acad. Sci. A41, 137 (1955).
  11. See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 51.
  12. Experimental results for networks of this type are reported by J. M. Yarborough and E. O. Ammann, J. Opt. Soc. Am. 58, 776 (1968).
    [CrossRef]
  13. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
    [CrossRef]
  14. E. O. Ammann, private communication.

1968 (1)

1967 (1)

1966 (3)

1965 (1)

1964 (1)

1955 (2)

S. Pancharatnam, Proc. Indian Acad. Sci. A41, 130 (1955).

S. Pancharatnam, Proc. Indian Acad. Sci. A41, 137 (1955).

1949 (2)

M. G. Destriau and J. Prouteau, J. Phys. Radium 10, 53 (1949).
[CrossRef]

C. D. West and A. S. Makas, J. Opt. Soc. Am. 39, 791 (1949).
[CrossRef] [PubMed]

1941 (1)

Ammann, E. O.

Born, M.

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 51.

Chang, I. C.

Destriau, M. G.

M. G. Destriau and J. Prouteau, J. Phys. Radium 10, 53 (1949).
[CrossRef]

Harris, S. E.

Jones, R. C.

Makas, A. S.

Pancharatnam, S.

S. Pancharatnam, Proc. Indian Acad. Sci. A41, 137 (1955).

S. Pancharatnam, Proc. Indian Acad. Sci. A41, 130 (1955).

Prouteau, J.

M. G. Destriau and J. Prouteau, J. Phys. Radium 10, 53 (1949).
[CrossRef]

West, C. D.

Wolf, E.

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 51.

Yarborough, J. M.

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Figures (6)

Fig. 1
Fig. 1

Basic configuration of achromatic wave plate.

Fig. 2
Fig. 2

Basic configuration of optical network including polarizers.

Fig. 3
Fig. 3

Individual crystal holder.

Fig. 4
Fig. 4

Eccentricity (a/b) vs wavelength for 10-element quarter-wave plate. – – – single-crystal λ/4 plate at 6000 Å. —— theory. ⋯ experiment, 10-crystal λ/4 plate.

Fig. 5
Fig. 5

Retardation vs wavelength for 10-element quarter-wave plate. – – – single-crystal λ/4 plate at 6000 Å. —— theory. ⋯ experiment, 10-crystal λ/4 plate.

Fig. 6
Fig. 6

Rate of change of retardation with crystal length vs wavelength for 6-element quarter-wave plate.

Tables (2)

Tables Icon

Table I Coefficients in the expansion of H(f) for a 6- and 10-element achromatic quarter-wave plate.

Tables Icon

Table II Crystal angles for a 6- and 10-element achromatic quarter-wave plate.

Equations (32)

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h ( t ) = m = 0 N C m δ ( t - m τ ) , τ = L ( Δ n ) / c , C m = f ( φ 1 , φ 2 , φ n , φ p ) ,
h ( t ) = m = - N / 2 N / 2 C m δ ( t - m τ ) ,
H ( f ) = m = - N / 2 N / 2 C m e - i m ω τ .
H ( f ) H * ( f ) + G ( f ) G * ( f ) = 1.
M = [ cos φ p - sin φ p sin φ p cos φ p ] [ H ( f ) G * ( f ) - G ( f ) H * ( f ) ]
H d ( f ) = e j θ / 2 ,             f 1 f f 2 ,
M = [ cos φ p - sin φ p sin φ p cos φ p ] [ e j θ / 2 0 0 e - j θ / 2 ] f 1 f f 2 .
Re [ H ( f ) ] = m = 0 N / 2 B m cos m ω τ .
C 0 = B 0 = cos θ / 2.
Im [ H ( f ) ] = m = 1 N / 2 K m sin m ω τ .
K l { f 1 f 2 [ sin θ 2 - m = 1 N / 2 K m sin m ω τ ] 2 d f } 1 l N / 2 = 0.
- A l + m = 1 N / 2 K m B m l = 0 ,
A l = f 1 f 2 sin θ 2 sin l ω τ d f
B m l = f 1 f 2 sin m ω τ sin l ω τ d f .
C 0 = cos θ / 2 C m = - 1 2 K m m > 0 C m = 1 2 K m m < 0.
τ { f 1 f 2 [ sin θ 2 - m = 1 N / 2 K m sin m ω τ ] 2 d f } = 0
θ = 2 π f l ( Δ n ) / c d θ / d l = 2 π f ( Δ n ) / c = 15.7 ( rad / cm )
f 0 = 5.625 × 10 14 Hz .
θ l = l tan - 1 Im [ H ( f ) ] Re [ H ( f ) ] .
d θ d l 0.5 rad cm             4200 Å λ 7800 Å .
M x , y = S ( φ p ) P S - 1 ( φ p ) S ( φ n ) N S - 1 ( φ n ) S ( φ n - 1 ) N S - 1 ( φ n - 1 ) S ( φ 1 ) N S - 1 ( φ 1 ) P = S ( φ p ) P A P ,
D 0 = M x , y D i .
[ D 0 x D 0 y ] = H ( f ) D i x [ cos φ p sin φ p ] ,
[ D 0 x D 0 y ] = a 11 D i x [ cos φ p sin φ p ]
[ D 0 x D 0 y ] = G ( f ) D i x [ sin φ p - cos φ p ] .
[ D 0 x D 0 y ] = a 21 D i x [ - sin φ p cos φ p ]
M x , y = S ( φ p ) P S - 1 ( φ p ) S ( φ n ) N * S - 1 ( φ n ) S ( φ n - 1 ) N * S - 1 ( φ n - 1 ) S ( φ 1 ) N * S - 1 ( φ 1 ) P ,
[ D 0 x D 0 y ] = H * ( f ) D i x [ cos φ p sin φ p ] .
[ D 0 x D 0 y ] = a 22 D i x [ cos φ p sin φ p ]
M = S ( φ p ) A = [ cos φ p - sin φ p sin φ p cos φ p ] [ H ( f ) G * ( f ) - G ( f ) H * ( f ) ] .
M = [ H ( f ) cos φ p - H * ( f ) sin φ p H ( f ) sin φ p H * ( f ) cos φ p ] ,
Re [ H ( f ) ] sin φ p = 0.