Abstract

Conditions for invariance of the degree and the state of polarization of beams radiated by electromagnetic quasi-homogeneous sources into the far-zone are derived. An example is given relating to electromagnetic Bessel-correlated sources.

© 2011 Optical Society of America

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References

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    [CrossRef]
  12. E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge University Press, 2007).
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2009

2008

R. A. Silverman, Proc. Cambridge Philos. Soc. 54, 530(2008).
[CrossRef]

2007

J. Pu, O. Korotkova, and E. Wolf, Phys. Rev. E 75, 056610(2007).
[CrossRef]

E. Wolf, Opt. Lett. 32, 3400 (2007).
[CrossRef] [PubMed]

2006

2005

1994

1987

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

1986

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

1957

R. A. Silverman, IRE Transactions Information Theory 3, 182 (1957).
[CrossRef]

Gamiz, V. L.

Gori, F.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Hoover, B. G.

James, D. F. V.

Korotkova, O.

J. Pu, O. Korotkova, and E. Wolf, Phys. Rev. E 75, 056610(2007).
[CrossRef]

J. Pu, O. Korotkova, and E. Wolf, Opt. Lett. 31, 2097 (2006).
[CrossRef] [PubMed]

O. Korotkova, J. Opt. A 8, 30 (2006).
[CrossRef]

O. Korotkova, B. G. Hoover, V. L. Gamiz, and E. Wolf, J. Opt. Soc. Am. A 22, 2547 (2005).
[CrossRef]

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

Liu, C.

Mandel, L.

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

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Pu, J.

J. Pu, O. Korotkova, and E. Wolf, Phys. Rev. E 75, 056610(2007).
[CrossRef]

J. Pu, O. Korotkova, and E. Wolf, Opt. Lett. 31, 2097 (2006).
[CrossRef] [PubMed]

Silverman, R. A.

R. A. Silverman, Proc. Cambridge Philos. Soc. 54, 530(2008).
[CrossRef]

R. A. Silverman, IRE Transactions Information Theory 3, 182 (1957).
[CrossRef]

Sun, Y.

Wolf, E.

E. Wolf, Opt. Lett. 32, 3400 (2007).
[CrossRef] [PubMed]

J. Pu, O. Korotkova, and E. Wolf, Phys. Rev. E 75, 056610(2007).
[CrossRef]

J. Pu, O. Korotkova, and E. Wolf, Opt. Lett. 31, 2097 (2006).
[CrossRef] [PubMed]

O. Korotkova, B. G. Hoover, V. L. Gamiz, and E. Wolf, J. Opt. Soc. Am. A 22, 2547 (2005).
[CrossRef]

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

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

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

E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge University Press, 2007).

Yao, Y.

Zhao, X.

IRE Transactions Information Theory

R. A. Silverman, IRE Transactions Information Theory 3, 182 (1957).
[CrossRef]

J. Opt. A

O. Korotkova, J. Opt. A 8, 30 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

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

Opt. Express

Opt. Lett.

Phys. Rev. E

J. Pu, O. Korotkova, and E. Wolf, Phys. Rev. E 75, 056610(2007).
[CrossRef]

Phys. Rev. Lett.

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

Proc. Cambridge Philos. Soc.

R. A. Silverman, Proc. Cambridge Philos. Soc. 54, 530(2008).
[CrossRef]

Other

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

E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge University Press, 2007).

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Figures (2)

Fig. 1
Fig. 1

Illustration of the concept of an electromagnetic quasi-homogeneous source.

Fig. 2
Fig. 2

Illustration of a source radiating into the far field.

Equations (27)

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W ( 0 ) ( ρ 1 , ρ 2 , ω ) = [ W α β ( 0 ) ( ρ 1 , ρ 2 , ω ) ] , ( α , β = x , y ) ,
W α β ( 0 ) ( ρ 1 , ρ 2 , ω ) S α ( 0 ) ( ρ 1 + ρ 2 2 , ω ) S β ( 0 ) ( ρ 1 + ρ 2 2 , ω ) × μ α β ( 0 ) ( ρ 1 ρ 2 , ω ) .
( r , ω ) = 1 4 det W ( r , r , ω ) [ tr W ( r , r , ω ) ] 2 ,
ϕ ( r , ω ) = 1 2 arctan [ 2 [ W x y ( r , r , ω ) ] W x x ( r , r , ω ) W y y ( r , r , ω ) ] ,
ϵ ( r , ω ) = A B A + B ,
A = [ W x x ( r , r , ω ) W y y ( r , r , ω ) ] 2 + 4 | W x y ( r , r , ω ) | 2 ,
B = [ W x x ( r , r , ω ) W y y ( r , r , ω ) ] 2 + 4 [ W x y ( r , r , ω ) ] 2 .
( 0 ) ( ρ , ω ) = [ S x ( 0 ) ( ρ ) S y ( 0 ) ( ρ ) ] 2 + 4 S x ( 0 ) ( ρ ) S y ( 0 ) ( ρ ) | μ x y ( 0 ) ( 0 ) | 2 S x ( 0 ) ( ρ ) + S y ( 0 ) ( ρ ) ,
ϕ ( 0 ) ( ρ , ω ) = 1 2 arctan [ 2 S x ( 0 ) ( ρ ) S y ( 0 ) ( ρ ) [ μ x y ( 0 ) ( 0 ) ] S x ( 0 ) ( ρ ) S y ( 0 ) ( ρ ) ] ,
ϵ ( 0 ) ( ρ , ω ) = A B A + B ,
A = [ S x ( 0 ) ( ρ ) S y ( 0 ) ( ρ ) ] 2 + 4 S x ( 0 ) ( ρ ) S y ( 0 ) ( ρ ) | μ x y ( 0 ) ( 0 ) | 2 ,
B = [ S x ( 0 ) ( ρ ) S y ( 0 ) ( ρ ) ] 2 + 4 S x ( 0 ) ( ρ ) S y ( 0 ) ( ρ ) [ μ x y ( 0 ) ( 0 ) ] 2 ,
S y ( 0 ) ( ρ , ω ) = χ ( ω ) S x ( 0 ) ( ρ , ω ) ,
( 0 ) ( ρ , ω ) = [ 1 χ ( ω ) ] 2 + 4 χ ( ω ) | μ x y ( 0 ) ( 0 , ω ) | 2 1 + χ ( ω ) ,
ϕ ( 0 ) ( ρ , ω ) = 1 2 arctan [ 2 χ ( ω ) [ μ x y ( 0 ) ( 0 , ω ) ] 1 χ ( ω ) ] ,
ϵ ( 0 ) ( ρ , ω ) = [ [ 1 χ ( ω ) ] 2 + 4 χ ( ω ) | μ x y ( 0 ) ( 0 , ω ) | 2 [ 1 χ ( ω ) ] 2 + 4 χ ( ω ) [ μ x y ( 0 ) ( 0 , ω ) ] 2 ] 1 / 2 × [ [ 1 χ ( ω ) ] 2 + 4 χ ( ω ) | μ x y ( 0 ) ( 0 , ω ) | 2 + [ 1 χ ( ω ) ] 2 + 4 χ ( ω ) [ μ x y ( 0 ) ( 0 , ω ) ] 2 ] 1 / 2 .
W α β ( ) ( r s , r s , ω ) = ( 2 π k ) 2 cos 2 θ r 2 S ˜ x ( 0 ) ( 0 , ω ) × χ α β ( ω ) μ ˜ α β ( 0 ) ( k s , ω ) ,
( ) ( r s ) = [ μ ˜ x x ( 0 ) ( k s ) χ μ ˜ y y ( 0 ) ( k s ) ] 2 + 4 χ | μ ˜ x y ( 0 ) ( k s ) | 2 μ ˜ x x ( 0 ) ( k s ) + χ μ ˜ y y ( 0 ) ( k s ) ,
ϕ ( ) ( r s ) = 1 2 arctan [ 2 χ [ μ ˜ x y ( 0 ) ( k s ) ] μ ˜ x x ( 0 ) ( k s ) χ μ ˜ y y ( 0 ) ( k s ) ] ,
ϵ ( ) ( r s ) = { [ μ ˜ x x ( 0 ) ( k s ) χ μ ˜ y y ( 0 ) ( k s ) ] 2 + 4 χ [ μ ˜ x y ( 0 ) ( k s ) ] 2 + [ μ ˜ x x ( 0 ) ( k s ) χ μ ˜ y y ( 0 ) ( k s ) ] 2 + 4 χ [ μ ˜ x y ( 0 ) ( k s ) ] 2 } 1 / 2 × { [ μ ˜ x x ( 0 ) ( k s ) χ μ ˜ y y ( 0 ) ( k s ) ] 2 + 4 χ [ μ ˜ x y ( 0 ) ( k s ) ] 2 [ μ ˜ x x ( 0 ) ( k s ) χ μ ˜ y y ( 0 ) ( k s ) ] 2 + 4 χ [ μ ˜ x y ( 0 ) ( k s ) ] 2 } 1 / 2 .
μ ˜ x x ( 0 ) ( k s , ω ) = a ( ω ) μ ˜ y y ( 0 ) ( k s , ω ) = b ( ω ) μ ˜ x y ( 0 ) ( k s , ω ) ,
μ x x ( 0 ) ( ρ 1 ρ 2 , ω ) = a ( ω ) μ y y ( 0 ) ( ρ 1 ρ 2 , ω ) = b ( ω ) μ x y ( 0 ) ( ρ 1 ρ 2 , ω ) .
μ x y ( 0 ) ( 0 , ω ) μ ˜ x x ( 0 ) ( k s , ω ) = μ x y ( 0 ) ( 0 , ω ) μ ˜ y y ( 0 ) ( k s , ω ) = μ ˜ x y ( 0 ) ( k s , ω ) .
μ ˜ x x ( 0 ) ( k s , ω ) = μ ˜ y y ( 0 ) ( k s , ω ) .
S α ( 0 ) ( ρ , ω ) = I α ( ω ) exp [ ρ 2 4 σ α 2 ( ω ) ] ,
μ α β ( 0 ) ( ρ 1 ρ 2 , ω ) = B α β ( ω ) J 0 [ δ α β ( ω ) | ρ 1 ρ 2 | ] ,
δ x x ( ω ) = δ y y ( ω ) = δ x y ( ω ) .

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