Abstract

We show that there is no unique form of the cross-spectral density matrix of completely polarized light beams. We present three kinds of such matrices, each of which represents a beam that is completely polarized at every point. Some of the beams do not imitate monochromatic beams, in contrast to the usual assumption made in polarization optics.

© 2009 Optical Society of America

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References

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  1. G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852), reprinted in W. Swindell, Polarized Light (Dowder, Hutchinson, P. Ross, 1975), pp. 124-141.
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  3. E. Wolf, Opt. Lett. 33, 642 (2008).
    [CrossRef] [PubMed]
  4. N. Wiener, J. Math. Phys. (MIT) 7, 109 (1927-28).
  5. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  6. H. Roychowdhury and E. Wolf, Opt. Lett. 226, 57 (2003).
  7. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  8. H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
    [CrossRef]
  9. J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Lett. 29, 1536 (2004).
    [CrossRef] [PubMed]

2008

2005

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

2004

2003

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Lett. 226, 57 (2003).

1852

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852), reprinted in W. Swindell, Polarized Light (Dowder, Hutchinson, P. Ross, 1975), pp. 124-141.

Dogariu, A.

Ellis, J.

Korotkova, O.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Mandel, L.

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

Ponomarenko, S.

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Lett. 226, 57 (2003).

Stokes, G. G.

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852), reprinted in W. Swindell, Polarized Light (Dowder, Hutchinson, P. Ross, 1975), pp. 124-141.

Wiener, N.

N. Wiener, J. Math. Phys. (MIT) 7, 109 (1927-28).

Wolf, E.

E. Wolf, Opt. Lett. 33, 642 (2008).
[CrossRef] [PubMed]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Lett. 29, 1536 (2004).
[CrossRef] [PubMed]

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Lett. 226, 57 (2003).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

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

J. Math. Phys. (MIT)

N. Wiener, J. Math. Phys. (MIT) 7, 109 (1927-28).

Opt. Commun.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Opt. Lett.

Phys. Lett. A

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

Trans. Cambridge Philos. Soc.

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852), reprinted in W. Swindell, Polarized Light (Dowder, Hutchinson, P. Ross, 1975), pp. 124-141.

Other

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

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

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Equations (34)

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W ( ρ 1 , ρ 2 , z ; ω ) [ W i j ( ρ 1 , ρ 2 , z ; ω ) ] = [ E i * ( ρ 1 , ω ) E j ( ρ 2 , z ; ω ) ] ,
( i = x , y ; j = x , y ) .
W ( p ) ( ρ 1 , ρ 2 , 0 ; ω ) = ( E x * ( ρ 1 , 0 ; ω ) E x ( ρ 2 , 0 ; ω ) E x * ( ρ 1 , 0 ; ω ) E y ( ρ 2 , 0 ; ω ) E y * ( ρ 1 , 0 ; ω ) E x ( ρ 2 , 0 ; ω ) E y * ( ρ 1 , 0 ; ω ) E y ( ρ 2 , 0 ; ω ) ) .
W i j ( p ) ( ρ 1 , ρ 2 , z ; ω ) = E i * ( ρ 1 , z ; ω ) E j ( ρ 2 , z ; ω ) ,
( i = x , y ; j = x , y ) ,
E i ( ρ , z , ω ) = E i ( ρ , ω ) exp [ i ( k z ω t ) ] , ( i = x , y ) .
W i j ( ρ 1 , ρ 2 , 0 ; ω ) = A i A j B i j exp [ ( ρ 1 2 4 σ i 2 + ρ 2 2 4 σ j 2 ) ] exp [ ( ρ 2 ρ 1 ) 2 2 δ i j 2 ] , ( i = x , y ; j = x , y ) .
B i j = 1 when i = j ,
B i j 1 when i j ,
B i j = B j i * ,
δ i j = δ j i .
σ x = σ y σ ( say ) ,
W i j ( ρ 1 , ρ 2 , z ; ω ) = A i A j B i j Δ i j 2 ( z ) exp [ ( ρ 1 + ρ 2 ) 2 8 σ 2 Δ i j 2 ( z ) ] exp [ ( ρ 2 ρ 1 ) 2 2 Ω i j 2 Δ i j 2 ( z ) ] exp [ i k ( ρ 2 2 ρ 1 2 ) 2 R i j ( z ) ] ,
R i j = z [ 1 + ( k σ Ω i j z ) 2 ] ,
1 Ω i j 2 = 1 4 σ 2 + 1 δ i j 2 ,
Δ i j ( z ) = 1 + ( z k σ Ω i j ) 2 .
δ x x = δ y y , B x y = 1 .
δ x x = δ y y = δ x y = δ y x δ ( say ) ,
Δ x x = Δ y y = Δ x y = Δ y x Δ ,
Ω x x = Ω y y = Ω x y = Ω y x Ω ,
R x x = R y y = R x y = R y x R .
W i j ( ρ 1 , ρ 2 , z ; ω ) = A i A j Δ 2 ( z ) exp { [ 1 2 Δ 2 ( z ) ( 1 2 σ 2 + 1 δ 2 ) + i k 2 R ( z ) ] ρ 1 2 } exp { [ 1 2 Δ 2 ( z ) ( 1 2 σ 2 + 1 δ 2 ) i k 2 R ( z ) ] ρ 2 2 } exp [ ρ 1 ρ 2 δ 2 Δ 2 ( z ) ] .
W i j ( ρ , ρ , z ; ω ) = A i A j Δ 2 ( z ) exp [ ρ 2 2 σ 2 Δ 2 ( z ) ] .
P ( ρ , z ; ω ) 1 4 Det W ( ρ , ρ , z ; ω ) [ Tr W ( ρ , ρ , z ; ω ) ] 2 = 1 .
E i ( r , ω ) = e i ( r , ω ) U ( r , ω ) , ( i = x , y ) ,
E i ( ρ , 0 , ω ) E j ( ρ , 0 , ω ) = e i ( ρ , 0 , ω ) e j ( ρ , 0 , ω ) , ( i = x , y ) .
E i ( ρ , z , ω ) = exp [ i k z ] z = 0 E i ( ρ , 0 , ω ) G ( ρ ρ , z , ω ) d 2 ρ ,
G ( ρ ρ , z , ω ) = i k 2 π z exp [ i k ( ρ ρ ) 2 2 z ] .
E i ( ρ , z , ω ) = exp [ i k z ] z = 0 e i ( ρ , 0 , ω ) U ( ρ , 0 , ω ) G ( ρ ρ , z , ω ) d 2 ρ .
E i ( ρ , z , ω ) E j ( ρ , z , ω ) = z = 0 e i ( ρ , 0 , ω ) U ( ρ , 0 , ω ) G ( ρ ρ , z , ω ) d 2 ρ z = 0 e j ( ρ , 0 , ω ) U ( ρ , 0 , ω ) G ( ρ ρ , z , ω ) d 2 ρ , ( i = x , y ) .
E i ( ρ , z , ω ) E j ( ρ , z , ω ) = e i ( ρ , z , ω ) e j ( ρ , z , ω ) , ( i = x , y ) .
W i j ( ρ 1 , ρ 2 , z ; ω )
= { { U * ( ω ) 2 e i * ( ρ 1 , z , ω ) } { U * ( ω ) 2 e j ( ρ 2 , z , ω ) } ( a ) e i * ( ω ) e j ( ω ) U * ( ρ 1 , z , ω ) U ( ρ 2 , z , ω ) ( b ) e 0 * ( ρ 1 , z , ω ) e 0 ( ρ 2 , z , ω ) U * ( ρ 1 , z , ω ) U ( ρ 2 , z , ω ) ( c ) } .
Det W ( ρ 1 , ρ 2 , z ; ω ) = 0 ,

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