Abstract

The ratio between the components of the complex amplitudes of a plane, completely polarized, electromagnetic wave describes the state of polarization. For partially polarized gaussian light, the average value of this ratio is found to be simply related to the elements of the coherency matrix. This average is related to the degree of polarization and the cross-correlation function. Its propagation through linear optical systems is discussed.

© 1973 Optical Society of America

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References

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  1. V. Rumsey, Proc. IRE 39, 535 (1951).
    [Crossref]
  2. H. G. Jerrard, J. Opt. Soc. Am. 44, 634 (1954).
    [Crossref]
  3. D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 57, 466 (1967).
    [Crossref] [PubMed]
  4. R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 222 (1972).
    [Crossref]
  5. E. L. O’Neill, Introduction to Statistical Optics (Addison–Wesley, Reading, Mass., 1963).
  6. W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, Mass., 1962).
  7. C. W. Helstrom, Statistical Theory of Signal Detection (Pergamon, Oxford, 1968).
  8. I am indebted to a reviewer for suggesting this simple proof of Eq. (7).

1972 (1)

1967 (1)

1954 (1)

1951 (1)

V. Rumsey, Proc. IRE 39, 535 (1951).
[Crossref]

Azzam, R. M. A.

Bashara, N. M.

Feucht, D. L.

Helstrom, C. W.

C. W. Helstrom, Statistical Theory of Signal Detection (Pergamon, Oxford, 1968).

Holmes, D. A.

Jerrard, H. G.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison–Wesley, Reading, Mass., 1963).

Rumsey, V.

V. Rumsey, Proc. IRE 39, 535 (1951).
[Crossref]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, Mass., 1962).

J. Opt. Soc. Am. (3)

Proc. IRE (1)

V. Rumsey, Proc. IRE 39, 535 (1951).
[Crossref]

Other (4)

E. L. O’Neill, Introduction to Statistical Optics (Addison–Wesley, Reading, Mass., 1963).

W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, Mass., 1962).

C. W. Helstrom, Statistical Theory of Signal Detection (Pergamon, Oxford, 1968).

I am indebted to a reviewer for suggesting this simple proof of Eq. (7).

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Figures (1)

F. 1
F. 1

The degree of polarization P as a function of the magnitude of the complex polarization number | R | for different values of the magnitude of the cross-correlation function.

Equations (24)

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r x y = E y / E x ,
J = [ J x x J x y J y x J y y ] = [ E x E x * E x E y * E y E x * E y E y * ] ,
I = J x x + J y y , M = J x x J y y , C = J y x + J x y , S = i ( J y x J x y ) ,
P = [ 1 4 det J / ( Tr J ) 2 ] 1 2 .
r x y | p = 2 J y x / [ J x x J y y + P ( J x x + J y y ) ] .
R x y = r x y ,
R x y = E y E x * / E x E x * = J y x / J x x ,
R x y = ( C + i S ) / ( I + M ) = ( I M ) / ( C + i S ) .
E y | E x = α E x
E y E x * | E x = α E x E x * .
E y E x * = α E x E x * ,
α = J y x / J x x .
E y / E x | E x = α ,
E y / E x = α = J y x / J x x .
μ x y = J x y / ( J x x J y y ) 1 2
P = [ 1 4 ( 1 μ 2 ) ( μ | R | + | R | μ ) 2 ] 1 2 ,
J = LJ L ,
L = [ T 11 T 12 T 21 T 22 ] .
R = T 11 * ( T 21 + T 22 R ) + T 12 * R * ( T 21 + T 22 R / μ 2 ) T 11 * ( T 11 + T 12 R ) + T 12 * R * ( T 11 + T 12 R / μ 2 ) ,
r = ( T 21 + T 22 r ) / ( T 11 + T 12 r ) .
[ cos 2 θ cos θ sin θ sin θ cos θ sin 2 θ ] ,
L = [ cos θ sin θ sin θ cos θ ] ,
R = ( tan θ + R ) + R tan θ ( tan θ + R μ 2 ) ( 1 + R tan θ ) + R tan θ ( 1 + R μ 2 tan θ ) .
R = R [ 1 + 1 μ 2 μ 2 R tan θ 1 + R tan θ ] .