Abstract

A method is presented, well suited to the ultraviolet region, for determining the degree of polarization produced by a polarizer at a given wavelength and for determining the polarization introduced by a grating monochromator. An analysis is made of the degree of polarization required by a polarizer for use in optical studies to determine, for example, the reflectance of a surface for light of parallel or perpendicular polarization. Data are given in the spectral region 500 to 1300 Å for gold and silver reflection-type polarizers and for a grating used in the Seya geometry.

© 1965 Optical Society of America

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References

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  1. M. Cardona, Solid State Commun. 1, 109 (1963); J. C. Phillips, Phys. Rev. 133, A452 (1964).
    [CrossRef]
  2. W. C. Walker, Appl. Opt. 3, 1457 (1964).
    [CrossRef]
  3. W. C. Johnson, Appl. Opt. 3, 1375 (1964).
  4. F. Abelés, Compt. Rend. 230, 1942 (1950).
  5. H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
    [CrossRef]
  6. L. R. Canfield, G. Hass, and W. R. Hunter, J. Phys. Radium 25, 124 (1964).

1964 (3)

W. C. Walker, Appl. Opt. 3, 1457 (1964).
[CrossRef]

W. C. Johnson, Appl. Opt. 3, 1375 (1964).

L. R. Canfield, G. Hass, and W. R. Hunter, J. Phys. Radium 25, 124 (1964).

1963 (1)

M. Cardona, Solid State Commun. 1, 109 (1963); J. C. Phillips, Phys. Rev. 133, A452 (1964).
[CrossRef]

1962 (1)

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

1950 (1)

F. Abelés, Compt. Rend. 230, 1942 (1950).

Abelés, F.

F. Abelés, Compt. Rend. 230, 1942 (1950).

Canfield, L. R.

L. R. Canfield, G. Hass, and W. R. Hunter, J. Phys. Radium 25, 124 (1964).

Cardona, M.

M. Cardona, Solid State Commun. 1, 109 (1963); J. C. Phillips, Phys. Rev. 133, A452 (1964).
[CrossRef]

Ehrenreich, H.

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

Hass, G.

L. R. Canfield, G. Hass, and W. R. Hunter, J. Phys. Radium 25, 124 (1964).

Hunter, W. R.

L. R. Canfield, G. Hass, and W. R. Hunter, J. Phys. Radium 25, 124 (1964).

Johnson, W. C.

W. C. Johnson, Appl. Opt. 3, 1375 (1964).

Philipp, H. R.

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

Walker, W. C.

Appl. Opt. (2)

W. C. Walker, Appl. Opt. 3, 1457 (1964).
[CrossRef]

W. C. Johnson, Appl. Opt. 3, 1375 (1964).

Compt. Rend. (1)

F. Abelés, Compt. Rend. 230, 1942 (1950).

J. Phys. Radium (1)

L. R. Canfield, G. Hass, and W. R. Hunter, J. Phys. Radium 25, 124 (1964).

Phys. Rev. (1)

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

Solid State Commun. (1)

M. Cardona, Solid State Commun. 1, 109 (1963); J. C. Phillips, Phys. Rev. 133, A452 (1964).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Evaluation of cos2θ dependence of reflection polarizer. △, 917 Å; ▲, 680 Å; ○, 509 Å.

Fig. 2
Fig. 2

(a), Rp/Rs for a platinized Bausch & Lomb grating blazed at 700 Å. (b), rp/rs for a 45° reflection from Au shown by dots; and (c), from Ag shown by triangles. ——, theory; ○, Au experimental; △, Ag experimental.

Fig. 3
Fig. 3

Relative error in the determination of rp and rs as a function of degree of polarization. – – –, rp; ——, rs. Value of rp/rs shown on each curve.

Fig. 4
Fig. 4

(a), Schematic diagram of and (b), polarization produced by 80°–70°–80° triple-reflection polarizer with Au surfaces. Dots represent experimental data and solid curve shows the results obtained by using optical constants of Au determined by Canfield, Hass, and Hunter.

Equations (33)

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I 1 = 1 2 I 0 [ R s r s r ¯ s + R p r p r ¯ p ] ,
I 2 = 1 2 I 0 [ R s r p r ¯ p + R p r s r ¯ s ] ,
I 3 = 1 2 I 0 [ R s r s r ¯ p + R p r p r ¯ s ] ,
I 4 = 1 2 I 0 [ R s r p r ¯ s + R p r s r ¯ p ] ,
P = R p / R s ,
ρ = r p / r s ,
ρ ¯ = r ¯ p / r ¯ s ,
I 1 = ( 1 2 I 0 R s r s r ¯ s ) [ 1 + P ρ ρ ¯ ] ,
I 2 = ( 1 2 I 0 R s r s r ¯ s ) [ ρ ρ ¯ + P ] ,
I 3 = ( 1 2 I 0 R s r s r ¯ s ) [ ρ ¯ + P ρ ] ,
I 4 = ( 1 2 I 0 R s r s r ¯ s ) [ ρ + P ρ ¯ ] .
P = A ± ( A 2 - 1 ) 1 2 ,
ρ = a ± ( a 2 - 1 ) 1 2 ,
ρ ¯ = a ¯ ± ( a ¯ 2 - 1 ) 1 2 ,
A = 1 2 ( I 1 2 + I 2 2 - I 3 2 - I 4 2 ) / ( I 1 I 2 - I 3 I 4 ) ,
a = 1 2 ( I 1 2 - I 2 2 - I 3 2 + I 4 2 ) / ( I 1 I 4 - I 2 I 3 ) ,
a ¯ = 1 2 ( I 1 2 - I 2 2 + I 3 2 - I 4 2 ) / ( I 1 I 3 - I 2 I 4 ) .
A = 1 2 ( I 1 2 + I 2 2 - 2 I 3 2 ) / ( I 1 I 2 - I 3 2 )
a = a ¯ = 1 2 ( I 1 + I 2 ) / I 3 .
r 45 ° = 1 2 ρ 45 ° ( 1 + ρ 45 ° ) .
Δ P = ( d P / d A ) Δ A .
Δ P P = 1 ( 1 - 1 / A 2 ) 1 2 | Δ A A | .
P = ( I 2 - I 1 ρ ) / ( I 1 - I 2 ρ ) ,
I 0 = 1 2 I 0 ( R s + R p ) ,
I 1 = 1 2 I 0 ( R s r s + R p r p ) ,
R 1 = I 1 / I 0 = ( r s + P r p ) / ( 1 + P ) ,
R 2 = ( P r s + r p ) / ( 1 + P ) .
r s = ( R 1 - R 2 P ) / ( 1 - P ) ,
r p = ( R 2 - R 1 P ) / ( 1 - P ) .
( Δ r s ) 2 = [ ( r s / R 1 ) Δ R 1 ] 2 + [ ( r s / R 2 ) Δ R 2 ] 2 + [ ( r s / P ) Δ P ] 2
( Δ r s r s ) 2 = [ 1 + P ρ 1 - P 2 Δ R 1 R 1 ] 2 + [ P ( ρ + P ) 1 - P 2 Δ R 2 R 2 ] 2 + [ P ( 1 - ρ ) 1 - P 2 Δ P P ] 2 ,
( Δ r p r p ) 2 = [ P ( 1 + P ρ ) ρ ( 1 - P 2 ) Δ R 1 R 1 ] 2 + [ ρ + P ρ ( 1 - P 2 ) Δ R 2 R 2 ] 2 + [ P ( 1 - ρ ) ρ ( 1 - P 2 ) Δ P P ] 2 ,
I ( θ ) = a · cos 2 θ + b .