Abstract

When voltage is applied to a basal section of uniaxial crystal of the type XH2PO4, the crystal becomes biaxial. Between crossed polarizers it can be considered, then, to act as a light valve. The angular field of view is limited by the natural retardation of the crystal. This paper discusses methods by which this natural retardation can be minimized or effectively canceled so that the retardation with no voltage is essentially zero over a large angular field. In the first method a basal section of uniaxial crystal of opposite sign is placed in series with the slab to be excited. Another technique uses two slabs of similar crystal with a 90-degree optical rotator placed between them. Both these techniques are treated theoretically and experimental measurements are given to show the resulting angular polarization pattern. This pattern is shown both for the electrically excited case and the unexcited case.

© 1952 Optical Society of America

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References

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  1. Bruce H. Billings, J. Opt. Soc. Am. 39, 797–801 (1949).
    [Crossref]
  2. Bruce H. Billings, J. Opt. Soc. Am. 39, 802–808 (1949).
    [Crossref]
  3. Robert O’B. Carpenter, J. Opt. Soc. Am. 40, 225–229 (1950).
    [Crossref]
  4. Made by the Brush Development Company, Cleveland, Ohio, under the trademark “PN.”
  5. B. H. Billings and E. H. Land, J. Opt. Soc. Am. 38, 819–829 (1948).
    [Crossref] [PubMed]
  6. Carl Wiley, Goodyear Aircraft Company, Akron, Ohio (personal communication).
  7. Hans G. Baerwald, Brush Development Company, Cleveland, Ohio (personal communication).

1950 (1)

1949 (2)

1948 (1)

Baerwald, Hans G.

Hans G. Baerwald, Brush Development Company, Cleveland, Ohio (personal communication).

Billings, B. H.

Billings, Bruce H.

Carpenter, Robert O’B.

Land, E. H.

Wiley, Carl

Carl Wiley, Goodyear Aircraft Company, Akron, Ohio (personal communication).

J. Opt. Soc. Am. (4)

Other (3)

Carl Wiley, Goodyear Aircraft Company, Akron, Ohio (personal communication).

Hans G. Baerwald, Brush Development Company, Cleveland, Ohio (personal communication).

Made by the Brush Development Company, Cleveland, Ohio, under the trademark “PN.”

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Figures (11)

Fig. 1
Fig. 1

Polarization interference pattern observed with a basal section of ammonium dihydrogen phosphate between similar circular polarizers. The photograph was taken with monochromatic light of wavelength 590 millimicrons.

Fig. 2
Fig. 2

Polarization interference pattern observed with a basal section of rutile between similar circular polarizers. The photograph was taken with monochromatic light of wavelength 590 millimicrons.

Fig. 3
Fig. 3

Polarization interference pattern observed with the ammonium dihydrogen phosphate and rutile plate of Figs. 1 and 2 superposed.

Fig. 4
Fig. 4

A sketch showing the relationship between the various angles in a basal section of a biaxial crystal. OC ¯ is the direction of the refracted ray inside the crystal. OZ ¯ is the bisector of the angle between the axes and is normal to the crystal plate. OA ¯ and OB ¯ are the directions of the optic axes.

Fig. 5
Fig. 5

Transmission as a function of angle of incidence for an excited z cut ammonium dihydrogen phosphate crystal in series with a z cut positive crystal of the same retardation. The crystal thickness is 0.232-in. The wavelength is 590 millimicrons.

Fig. 6
Fig. 6

Transmission as a function of angle of incidence for an excited z cut ammonium dihydrogen phosphate crystal in series with a z cut positive crystal of the same retardation. The crystal thickness was 0.5 millimeter. The wavelength is 590 millimicrons.

Fig. 7
Fig. 7

Intensity as a function of angle of incidence of the light transmitted through a single basal section of ammonium dihydrogen phosphate between crossed linear polarizers. The wavelength is 590 millimicrons.

Fig. 8
Fig. 8

Theoretical intensity of the light transmitted through an electrically excited ammonium dihydrogen phosphate crystal in series with a rutile corrector plate. The combination is between crossed linear polarizers which are oriented at 45 degrees to the induced axes in the excited plate. The intensity is plotted as a function of the azimuth angle for various values of the angle of refraction inside the plate.

Fig. 9
Fig. 9

Theoretical plot of the maximum density in the polarization pattern observed with an excited ammonium dihydrogen phosphate plate in series with a rutile corrector plate. The combination is between crossed polarizers which are oriented at 45 degrees to the induced axes. The wavelength is 590 millimicrons.

Fig. 10
Fig. 10

Photograph of the polarization pattern observed with an excited ammonium dihydrogen phosphate plate in series with a rutile corrector plate. The combination is between crossed polarizers which are oriented at 45 degrees to the induced axes. The wavelength is 590 millimicrons.

Fig. 11
Fig. 11

Photograph of the pattern observed with an excited ammonium dihydrogen phosphate plate between circular polarizers. The wavelength is 590 millimicrons.

Tables (3)

Tables Icon

Table I Half-angular field to 1 percent and 0.1 percent transmission points for PN crystals of different thicknesses.

Tables Icon

Table II Indices of ammonia dihydrogen phosphate and rutile for D line of sodium.

Tables Icon

Table IV Specific rotation (for NaD line).

Equations (39)

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I = 1 2 sin 2 δ / 2 ,
δ = 2 π d λ ( ω 2 - 2 2 ω 2 ) sin 2 θ ,
= ω ( 2 cos 2 θ + ω 2 sin 2 θ ) 1 2 .
d rut = d ADP ( ω ADP 2 - ADP 2 ω rut 2 - rut 2 ) ( ω rut rut 2 ω ADP ADP 2 ) .
d rut = 0.578 d ADP .
δ = 2 π λ [ d ADP ( ω ADP 2 - ADP 2 ω A A 2 ) - d rut ( ω R 2 - R 2 ω R R 2 ) ] sin 2 θ .
I = 1 4 { 1 - ( cos 2 2 β 1 + sin 2 2 β 1 cos δ 1 ) × ( cos 2 2 β 2 + sin 2 2 β 2 cos δ 2 ) - [ cos 2 β 1 sin 2 β 1 ( 1 - cos δ 1 ) ] × [ cos 2 β 2 sin 2 β 2 ( 1 - cos δ 2 ) ] + ( sin 2 β 1 sin δ 1 ) ( sin 2 β 2 sin δ 2 ) } ,
I = 1 4 [ sin 2 2 β ( 1 - cos δ 1 + 1 - cos δ 2 ) - 4 ( 1 4 sin 2 4 β + sin 4 2 β ) ( 1 - cos δ 1 ) ( 1 - cos δ 2 ) + sin 2 2 β sin δ 1 sin δ 2 ] .
1 - cos δ 1 = 2 sin 2 δ 1 / 2 ,
I = 1 2 sin 2 2 β [ sin 2 δ 1 2 + sin 2 δ 2 2 - 2 sin 2 δ 1 2 sin 2 δ 2 2 + 2 sin δ 1 2 cos δ 1 2 sin δ 2 2 cos δ 2 2 ] ,
I = 1 2 sin 2 2 β sin 2 ( δ 1 + δ 2 ) / 2.
Γ k d = sin θ 1 sin θ 2 cos r ,
k = ( γ - α ) / λ ,
cos 2 θ 1 = ( sin 2 r cos 2 ζ + cos 2 r ) cos 2 ( φ 0 - Ω ) ,
cos 2 θ 2 = ( sin 2 r cos 2 ζ + cos 2 r ) cos 2 ( φ 0 + Ω ) ,
φ 0 = cos - 1 cos r ( sin 2 r cos 2 ζ + cos 2 r ) 1 2 .
( Γ k d ) 2 = [ 1 - a cos 2 ( φ 0 - Ω ) ] [ 1 - a cos 2 ( φ 0 + Ω ) ] cos 2 r ,
a = ( sin 2 r cos 2 ζ + cos 2 r ) .
( Γ k d ) = [ 1 - cos 2 ( r - Ω ) ] [ 1 - cos 2 ( r + Ω ) ] cos 2 r ,             ζ = 0 ,
Γ k d = [ 1 - cos 2 r cos 2 Ω ] cos r ,             ζ = π 2 .
I = 1 2 sin 2 1 2 [ 2 π k 1 d 1 ( 1 - cos 2 r cos 2 Ω ) cos r - π d 2 ω 1 λ ( ω 2 2 - 2 2 ω 2 2 2 ) sin 2 r ] ,
sin 2 Ω = Γ 0 / k d ,
Γ 0 = p V ,
k = ( ω - ) / λ .
Ω = 4 ° 1 7 .
ψ 2 + ξ = ψ 1 - ξ ,
ξ = 1 2 ( ψ 1 - ψ 2 ) .
cot ψ 1 = sin r [ cot Ω - cos ζ cot r ] sin ζ .
cot ψ 2 = sin r [ cot Ω + cos ζ cot r ] sin ζ .
tan ξ = cos r [ cos ζ - Δ sin ζ sin ζ + Δ cos ζ ] ,
Δ = a + ( a 2 + b 2 cos 2 Ω ) 1 2 b ,
a = cos 2 Ω ( 1 - sin 2 r sin 2 ζ ) - ( 1 - sin 2 r cos 2 ζ ) ,
b = 2 sin 2 r sin ζ cos ζ .
φ = π d ( n l - n r ) / λ ,
R = 2 ( 45° - ξ ) + 2 ξ = 90° .
R ( β , π ) R ( 0 , π ) = Q ,
R ( β , π ) = | 1 0 0 0 0 cos 4 β sin 4 β 0 0 sin 4 β - cos 4 β 0 0 0 0 - 1 | ,
R ( 0 , π ) = | 1 0 0 0 0 1 0 0 0 0 - 1 0 0 0 0 - 1 | .
Q = | 1 0 0 0 0 cos 4 β sin 4 β 0 0 - sin 4 β cos 4 β 0 0 0 0 1 | ,