Abstract

The design of prisms utilizing total internal reflection to achieve particular phase retardation is considered. Two prisms are discussed that bend light by 90° without changing its polarization. Optimum design for Fresnel rhombs is considered, and designs for quarter-wave and half-wave are presented. The effect of light beam divergence and prism dispersion is treated.

© 1974 Optical Society of America

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References

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  1. P. G. Kard, Opt. Spectrosc. 6, 244, 339 (1959); P. B. Mauer, J. Opt. Soc. Am. 56, 1219 (1966), J. Opt. Soc. Am. 58, 1160 (1968).
    [CrossRef]
  2. R. W. Wood, Physical Optics (Macmillan, New York, 1934), pp. 416–418 and 354–355.
  3. The prism was constructed by Prismoid Optical, Maple Lake, Minnesota.
  4. F. Mooney, J. Opt. Soc. Am. 42, 181 (1952).
    [CrossRef]

1959 (1)

P. G. Kard, Opt. Spectrosc. 6, 244, 339 (1959); P. B. Mauer, J. Opt. Soc. Am. 56, 1219 (1966), J. Opt. Soc. Am. 58, 1160 (1968).
[CrossRef]

1952 (1)

Kard, P. G.

P. G. Kard, Opt. Spectrosc. 6, 244, 339 (1959); P. B. Mauer, J. Opt. Soc. Am. 56, 1219 (1966), J. Opt. Soc. Am. 58, 1160 (1968).
[CrossRef]

Mooney, F.

Wood, R. W.

R. W. Wood, Physical Optics (Macmillan, New York, 1934), pp. 416–418 and 354–355.

J. Opt. Soc. Am. (1)

Opt. Spectrosc. (1)

P. G. Kard, Opt. Spectrosc. 6, 244, 339 (1959); P. B. Mauer, J. Opt. Soc. Am. 56, 1219 (1966), J. Opt. Soc. Am. 58, 1160 (1968).
[CrossRef]

Other (2)

R. W. Wood, Physical Optics (Macmillan, New York, 1934), pp. 416–418 and 354–355.

The prism was constructed by Prismoid Optical, Maple Lake, Minnesota.

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Figures (5)

Fig. 1
Fig. 1

Relative indices of refraction, n, needed to produce various phase changes, Δ, as a function of the angle of incidence, Φ. The dashed lines give the values of n and Φ corresponding to Δ′ = 0 and Δ″ = 0.

Fig. 2
Fig. 2

Derivative of Δ with respect to Φ for different Δ as a function of Φ.

Fig. 3
Fig. 3

Second derivative of Δ with respect to Φ for different Δ as a function of Φ.

Fig. 4
Fig. 4

Derivative of Δ with respect to n for different Δ as a function of Φ.

Fig. 5
Fig. 5

Sketches of different rhomb designs. The light lines with arrows indicate light paths.

Equations (22)

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tan ½ Δ = cos Φ ( sin 2 Φ - 1 / n 2 ) 1 / 2 / sin 2 Φ ,
Δ = 2 cos 2 ( ½ Δ ) [ 2 - ( n 2 + 1 ) sin 2 Φ ] n sin 3 Φ [ n 2 sin 2 Φ - 1 ] 1 / 2
sin 2 Φ m = 2 / ( 1 + n 2 ) ;             tan ½ Δ m = ( n 2 - 1 ) / 2 n .
Δ m = - 8 n .
Δ / n = sin Δ / n ( n 2 sin 2 Φ - 1 ) .
Δ / n Φ m = 4 / ( 1 + n 2 ) .
cos Φ = cos Φ 0 cos θ + sin Φ 0 sin θ cos χ .
cos θ = cos ( θ cos χ ) and sin θ cos χ = sin ( θ cos χ )
Φ 0 - Φ = θ cos χ .
( Φ - Φ 0 ) n ¯ = ( - 1 ) n 0 θ m f ( θ ) θ n + 1 d θ 0 2 π cos n χ d χ 2 π 0 θ m f ( θ ) θ d θ .
( Φ - Φ 0 ) 2 m ¯ = f ( m ) 0 θ m f ( θ ) θ 2 m + 1 d θ / 0 θ m f ( θ ) θ d θ ,
Δ = Δ 0 + Δ 0 ( Φ - Φ 0 ) + ½ Δ 0 ( Φ - Φ 0 ) 2 + ,
Δ ¯ = Δ 0 + ½ Δ 0 ( Φ - Φ 0 ) 2 ¯ + ,
σ 2 = Δ 2 ¯ - Δ 2 ¯ = Δ 0 2 ( Φ - Φ 0 ) 2 ¯ + 1 4 Δ 0 2 [ ( Φ - Φ 0 ) 4 ¯ - ( Φ - Φ 0 ) 2 ¯ ] .
( Φ - Φ 0 ) 2 ¯ = ¼ θ m 2 ;             ( Φ - Φ 0 ) 4 ¯ = 1 8 θ m 4 .
Δ ¯ = Δ 0 + 1 8 Δ 0 θ m 2
σ 2 = ¼ Δ 0 θ m 2 + 1 64 Δ 0 2 θ m 4 .
σ = 1 8 Δ 0 θ m 2 .
( Φ - Φ 0 ) 2 ¯ = ¼ θ f 2 and ( Φ - Φ 0 ) 4 ¯ = 1 16 θ f 4 .
Δ ¯ = Δ 0 + 1 8 Δ 0 θ f 2
σ 2 = ¼ Δ 0 2 θ f 2 + 1 32 Δ 0 2 θ f 4 .
σ = Δ 0 θ f 2 / ( 32 ) 1 / 2 .

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