Abstract

This paper discusses some of the general considerations relating to the use in optical instruments of polarization elements, with particular emphasis being given to partial polarizers of the dichroic type. A functional classification is provided for optical instruments which employ polarized light. Also provided is a functional classification for polarization elements, which classification involves four categories: polarizers, phase shifters, polarizing beam splitters, and depolarizers. The various methods of modulating light are discussed. A qualitative description of partial dichroic polarizers is included, and this is followed by the derivation of some of the basic mathematical relations which hold among the parameters which can be used to describe quantitatively the properties of partial dichroic polarizers.

© 1951 Optical Society of America

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References

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  1. G. Szivessy, Geiger-Scheel Handbuch d. Physik 20, 113 (1928).
  2. H. Fizeau, Compt. rend. 29, 90, 132 (1849).
  3. L. Foucault, Compt. rend. 55, 501, 792 (1862).
  4. W. Huxford and J. Platt, J. Opt. Soc. Am. 38, 253 (1948); H. Snyder and J. Platt, J. Opt. Soc. Am. 38, 269 (1948).
    [Crossref] [PubMed]
  5. A. C. Hardy, J. Opt. Soc. Am. 18, 96 (1929).
    [Crossref]
  6. A. Karolus and O. Mittelstädt, Physik. Z. 29, 698 (1928).
  7. E. Bergstrand, Arkiv. Fysik 2, 119–150 (1950).
  8. The adjective dichroic as used here means: exhibiting anisotropic absorption of light. This adjective is also used in two other distinct senses in the vocabulary of modern optics.
  9. Colloid Chemistry, ed. J. Alexander (Reinhold Publishing Corporation, New York, 1946), Chapter 6.
  10. (a)L. W. Chubb, Trans. Illum. Eng. Soc. 32, 523–527 (1937); (b)H. Sauer, VDI Ztschr. 82, 201–207 (1938).

1950 (1)

E. Bergstrand, Arkiv. Fysik 2, 119–150 (1950).

1948 (1)

1937 (1)

(a)L. W. Chubb, Trans. Illum. Eng. Soc. 32, 523–527 (1937); (b)H. Sauer, VDI Ztschr. 82, 201–207 (1938).

1929 (1)

1928 (2)

A. Karolus and O. Mittelstädt, Physik. Z. 29, 698 (1928).

G. Szivessy, Geiger-Scheel Handbuch d. Physik 20, 113 (1928).

1862 (1)

L. Foucault, Compt. rend. 55, 501, 792 (1862).

1849 (1)

H. Fizeau, Compt. rend. 29, 90, 132 (1849).

Bergstrand, E.

E. Bergstrand, Arkiv. Fysik 2, 119–150 (1950).

Chubb, L. W.

(a)L. W. Chubb, Trans. Illum. Eng. Soc. 32, 523–527 (1937); (b)H. Sauer, VDI Ztschr. 82, 201–207 (1938).

Fizeau, H.

H. Fizeau, Compt. rend. 29, 90, 132 (1849).

Foucault, L.

L. Foucault, Compt. rend. 55, 501, 792 (1862).

Hardy, A. C.

Huxford, W.

Karolus, A.

A. Karolus and O. Mittelstädt, Physik. Z. 29, 698 (1928).

Mittelstädt, O.

A. Karolus and O. Mittelstädt, Physik. Z. 29, 698 (1928).

Platt, J.

Szivessy, G.

G. Szivessy, Geiger-Scheel Handbuch d. Physik 20, 113 (1928).

Arkiv. Fysik (1)

E. Bergstrand, Arkiv. Fysik 2, 119–150 (1950).

Compt. rend. (2)

H. Fizeau, Compt. rend. 29, 90, 132 (1849).

L. Foucault, Compt. rend. 55, 501, 792 (1862).

Geiger-Scheel Handbuch d. Physik (1)

G. Szivessy, Geiger-Scheel Handbuch d. Physik 20, 113 (1928).

J. Opt. Soc. Am. (2)

Physik. Z. (1)

A. Karolus and O. Mittelstädt, Physik. Z. 29, 698 (1928).

Trans. Illum. Eng. Soc. (1)

(a)L. W. Chubb, Trans. Illum. Eng. Soc. 32, 523–527 (1937); (b)H. Sauer, VDI Ztschr. 82, 201–207 (1938).

Other (2)

The adjective dichroic as used here means: exhibiting anisotropic absorption of light. This adjective is also used in two other distinct senses in the vocabulary of modern optics.

Colloid Chemistry, ed. J. Alexander (Reinhold Publishing Corporation, New York, 1946), Chapter 6.

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Figures (6)

Fig. 1
Fig. 1

Showing the quantities k, H, ΔH, and ΔH/2k as functions of dz with Rd=7.5. The two arrows indicate the calculated positions of the maxima of ΔH and ΔH/2k. The confluence of the curves for k and ΔH/2k can be understood from the exact relation: ΔH/2k=kH/k.

Fig. 2
Fig. 2

Showing the quantities k, H, ΔH, and ΔH/2k as functions of dz with Rd=30.

Fig. 3
Fig. 3

Showing the quantities k, H, ΔH, and ΔH/2k as functions of dz with Rd=120.

Fig. 4
Fig. 4

Each straight line represents Malus’ law (Eq. (11)) for a pair of identical partial polarizers with a density ratio of 30 and with the specified value of the parameter dz, the latter running from zero to infinity. By inspection the maximum slope falls near d z = 3 2. The exact value of dz which maximizes ΔH for Rd=30 is (30 log10 30)/29≅1.528, according to Eqs. (13) and (19) of the following paper.

Fig. 5
Fig. 5

Showing the measured crossed transmittance 0.8493H as a function of the density ratio Rd and the measured transmittance 0.9216k. The labels on the curves give the value of 0.8493H, in percent.

Fig. 6
Fig. 6

Showing a schematic birefringent light modulator of high modulation efficiency. In the doubling system illustrated the polarizing beam splitter (BS) acts as its own beam uniter through an ordinary mirror (M). When the wave plate (P) has δ=0, the incident beam (I0) doubles back on itself; but when δ=90°, the beam emerges at I conserving its initial intensity and state of polarization. A possible natural rotation in P can be disregarded since it has to cancel itself on the return trip.

Equations (16)

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d y = - log 10 k y
d z = - log 10 k z ,
d y = a y C
d z = a z C ,
R t = k y / k z = 10 d z - d y = 10 ( a z - a y ) C
R d = d z / d y = a z / a y .
k = 1 2 ( k y + k z )
V = k y - k z k y + k z = R t - 1 R t + 1 .
T ( θ ) = k y cos 2 θ + k z sin 2 θ = ( k y - k z ) cos 2 θ + k z .
H ( θ ) = 1 2 ( k 1 y k 2 y + k 1 z k 2 z ) cos 2 θ + 1 2 ( k 1 y k 2 z + k 1 z k 2 y ) sin 2 θ .
H ( θ ) = H cos 2 θ + H sin 2 θ = Δ H cos 2 θ + H ,
H ( 0 ) H = 1 2 ( k y 2 + k z 2 )
H ( π / 2 ) H = k y k z ,
Δ H H - H = 1 2 ( k y - k z ) 2 .
H ( π / 4 ) H 45 = 1 2 ( H + H ) = 1 4 ( k y + k z ) 2 = k 2 ,
H H = k y 2 + k z 2 2 k y k z = 1 2 ( k y k z + k z k y ) .