Abstract

It has been known for some time that the degree of polarization of a light beam may change on propagation, even in free space. In this Letter we derive sufficiency conditions for the degree of polarization of a beam generated by a uniformly polarized stochastic, electromagnetic source of a wide class to be the same throughout the far zone and in the source plane.

© 2007 Optical Society of America

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References

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2005

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

O. Korotkova, B. Hoover, V. Gamiz, and E. Wolf, J. Opt. Soc. Am. A 22, 2597 (2005).
[CrossRef]

2004

2000

1994

J. Opt. Soc. Am. A

Opt. Commun.

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

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Equations (20)

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W ( 0 ) ( ρ 1 , ρ 2 , ω ) = [ W i j ( 0 ) ( ρ 1 , ρ 2 , ω ) ] = [ E i ( 0 ) * ( ρ 1 , ω ) E j ( 0 ) ( ρ 2 , ω ) ] , ( i = x , y , j = x , y ) ,
μ i j ( 0 ) ( ρ 1 , ρ 2 , ω ) = E i * ( ρ 1 , ω ) E j ( ρ 2 , ω ) S i ( 0 ) ( ρ 1 , ω ) S j ( 0 ) ( ρ 2 , ω ) ,
S α ( 0 ) ( ρ , ω ) = E α * ( ρ , ω ) E α ( ρ , ω ) , ( α = i , j ) ,
W i j ( 0 ) ( ρ 1 , ρ 2 , ω ) = S i ( 0 ) ( ρ 1 , ω ) S j ( 0 ) ( ρ 2 , ω ) μ i j ( 0 ) ( ρ 1 , ρ 2 , ω ) .
W i j ( 0 ) ( ρ 1 , ρ 2 , ω ) S i ( 0 ) ( ρ 1 + ρ 2 2 , ω ) S j ( 0 ) ( ρ 1 + ρ 2 2 , ω ) μ i j ( 0 ) ( ρ 2 ρ 1 , ω ) .
P ( 0 ) ( ω ) = [ S x ( 0 ) ( ω ) S y ( 0 ) ( ω ) ] 2 + 4 S x ( 0 ) ( ω ) S y ( 0 ) ( ω ) μ x y ( 0 ) ( 0 , ω ) 2 S x ( 0 ) ( ω ) + S y ( 0 ) ( ω ) .
μ x y ( 0 ) ( 0 , ω ) = 0.
P ( 0 ) ( ω ) = S x ( 0 ) ( ω ) S y ( 0 ) ( ω ) S x ( 0 ) ( ω ) + S y ( 0 ) ( ω ) .
S y ( 0 ) ( ω ) S x ( 0 ) ( ω ) = α ( ω )
P ( 0 ) ( ω ) = 1 α ( ω ) 1 + α ( ω ) .
P ( ) ( r s , ω ) = μ ̃ x x ( 0 ) ( k s , ω ) α ( ω ) μ ̃ y y ( 0 ) ( k s , ω ) μ ̃ x x ( 0 ) ( k s , ω ) + α ( ω ) μ ̃ y y ( 0 ) ( k s , ω ) .
μ ̃ j j ( 0 ) ( f , ω ) = 1 ( 2 π ) 2 μ j j ( 0 ) ( ρ , ω ) e i f ρ d 2 ρ ,
P ( ) ( r s , ω ) = 1 α ( ω ) β ( k s , ω ) 1 + α ( ω ) β ( k s , ω ) ,
β ( k s , ω ) = μ ̃ y y ( k s , ω ) μ ̃ x x ( k s , ω ) .
β ( k s , ω ) = 1 ,
P ( ) ( r s , ω ) = P ( 0 ) ( ω ) ,
μ ̃ y y ( 0 ) ( k s , ω ) = μ ̃ x x ( 0 ) ( k s , ω ) .
μ y y ( 0 ) ( ρ , ω ) = μ x x ( 0 ) ( ρ , ω ) .
μ x x ( 0 ) ( ρ 2 ρ 1 , ω ) = μ y y ( 0 ) ( ρ 2 ρ 1 , ω ) and μ x y ( 0 ) ( ρ 2 ρ 1 ) = 0
P ( ) ( r s , ω ) P ( ) ( ω ) = P ( 0 ) ( ω ) .

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