Abstract

A new concept of vector and tensor densities is introduced into the general coherence theory of vector electromagnetic fields that is based on energy and energy-flow coherence tensors. Related coherence conservation laws are presented in the form of continuity equations that provide new insights into the propagation of second-order correlation tensors associated with stationary random classical electromagnetic fields.

© 2006 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  2. J. W. Goodman, Statistical Optics (Wiley, 2000).
  3. A. S. Marathay, Elements of Optical Coherence Theory (Wiley, 1982).
  4. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  5. E. Wolf, Nuovo Cimento 12, 884 (1954).
    [CrossRef]
  6. E. Wolf, in Proceedings of the Symposium on Astronomical Optics, Z.Kopal, ed. (North-Holland, 1956), pp. 177-185.
  7. P. Roman and E. Wolf, Nuovo Cimento 17, 462 (1960).
    [CrossRef]
  8. P. Roman and E. Wolf, Nuovo Cimento 17, 477 (1960).
    [CrossRef]
  9. H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
    [CrossRef] [PubMed]
  10. G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
    [CrossRef]
  11. W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
    [CrossRef] [PubMed]
  12. L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics, E.Wolf, ed. (North-Holland, 1999), Vol. 34, pp. 291-372.
    [CrossRef]
  13. W. Wang and M. Takeda, Phys. Rev. Lett. 96, 223904 (2006).
    [CrossRef] [PubMed]
  14. J. D. Jackson, Classical Electrodynamics (Wiley, 1998), Chap. 6.

2006 (2)

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

W. Wang and M. Takeda, Phys. Rev. Lett. 96, 223904 (2006).
[CrossRef] [PubMed]

2003 (3)

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
[CrossRef] [PubMed]

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

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

1960 (2)

P. Roman and E. Wolf, Nuovo Cimento 17, 462 (1960).
[CrossRef]

P. Roman and E. Wolf, Nuovo Cimento 17, 477 (1960).
[CrossRef]

1954 (1)

E. Wolf, Nuovo Cimento 12, 884 (1954).
[CrossRef]

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics, E.Wolf, ed. (North-Holland, 1999), Vol. 34, pp. 291-372.
[CrossRef]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics, E.Wolf, ed. (North-Holland, 1999), Vol. 34, pp. 291-372.
[CrossRef]

Duan, Z.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Gbur, G.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2000).

Hanson, S. G.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1998), Chap. 6.

Mandel, L.

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

Marathay, A. S.

A. S. Marathay, Elements of Optical Coherence Theory (Wiley, 1982).

Miyamoto, Y.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Padgett, M. J.

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics, E.Wolf, ed. (North-Holland, 1999), Vol. 34, pp. 291-372.
[CrossRef]

Roman, P.

P. Roman and E. Wolf, Nuovo Cimento 17, 477 (1960).
[CrossRef]

P. Roman and E. Wolf, Nuovo Cimento 17, 462 (1960).
[CrossRef]

Schouten, H. F.

Takeda, M.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

W. Wang and M. Takeda, Phys. Rev. Lett. 96, 223904 (2006).
[CrossRef] [PubMed]

Visser, T. D.

Wang, W.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

W. Wang and M. Takeda, Phys. Rev. Lett. 96, 223904 (2006).
[CrossRef] [PubMed]

Wolf, E.

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

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
[CrossRef] [PubMed]

P. Roman and E. Wolf, Nuovo Cimento 17, 477 (1960).
[CrossRef]

P. Roman and E. Wolf, Nuovo Cimento 17, 462 (1960).
[CrossRef]

E. Wolf, Nuovo Cimento 12, 884 (1954).
[CrossRef]

E. Wolf, in Proceedings of the Symposium on Astronomical Optics, Z.Kopal, ed. (North-Holland, 1956), pp. 177-185.

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

Nuovo Cimento (3)

E. Wolf, Nuovo Cimento 12, 884 (1954).
[CrossRef]

P. Roman and E. Wolf, Nuovo Cimento 17, 462 (1960).
[CrossRef]

P. Roman and E. Wolf, Nuovo Cimento 17, 477 (1960).
[CrossRef]

Opt. Commun. (1)

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

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

Phys. Rev. Lett. (2)

W. Wang and M. Takeda, Phys. Rev. Lett. 96, 223904 (2006).
[CrossRef] [PubMed]

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Other (6)

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics, E.Wolf, ed. (North-Holland, 1999), Vol. 34, pp. 291-372.
[CrossRef]

E. Wolf, in Proceedings of the Symposium on Astronomical Optics, Z.Kopal, ed. (North-Holland, 1956), pp. 177-185.

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

J. W. Goodman, Statistical Optics (Wiley, 2000).

A. S. Marathay, Elements of Optical Coherence Theory (Wiley, 1982).

J. D. Jackson, Classical Electrodynamics (Wiley, 1998), Chap. 6.

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Equations (23)

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ϵ j k l k 1 E l m 1 c τ S j m = 0 ,
ϵ j k l k 1 S l m + 1 c τ E j m = 0 ,
j 1 E j k = 0 ,
j 1 S j k = 0 ,
E j k ( x 1 , x 2 , τ ) = E j * ( x 1 , t ) E k ( x 2 , t + τ ) + H j * ( x 1 , t ) H k ( x 2 , t + τ ) ,
S j k ( x 1 , x 2 , τ ) = E j * ( x 1 , t ) H k ( x 2 , t + τ ) H j * ( x 1 , t ) E k ( x 2 , t + τ ) .
ϵ j k l ϵ i n j E n m k 1 E l m * 1 c ϵ i n j E n m τ S j m * = 0 .
E n m i 1 E n m * + E n m n 1 E i m * + E i m * n 1 E n m + 1 c ϵ i n j E n m τ S j m * = 0 ,
ϵ j k l ϵ i n j S n m k 1 S l m * + 1 c ϵ i n j S n m τ E j m * = 0 .
S n m i 1 S n m * + S n m n 1 S i m * + S i m * n 1 S n m + 1 c ϵ i n j S j m τ E n m * = 0 ,
τ T i ( x 1 , x 2 , τ ) + k 1 W k i ( x 1 , x 2 , τ ) = 0 ,
T i ( x 1 , x 2 , τ ) = 1 c ϵ i k j ( S k m E j m * + S k m * E j m ) ,
W k i ( x 1 , x 2 , τ ) = ( E k m E i m * + E k m * E i m ) δ k i ( E k m E k m * ) + ( S k m S i m * + S k m * S i m ) δ k i ( S k m S k m * ) .
d d τ V T i ( x 1 , x 2 , τ ) d 3 x 1 + S W k i ( x 1 , x 2 , τ ) n k d 2 x 1 = 0 .
ϵ m j i x j τ T i ( x 1 , x 2 , τ ) + ϵ m j i x j k 1 W k i ( x 1 , x 2 , τ ) = 0 .
τ ϵ m j i x j T i ( x 1 , x 2 , τ ) = ϵ m j i x j τ T i ( x 1 , x 2 , τ ) ,
L m ( x 1 , x 2 , τ ) = ϵ m j i x j T i ( x 1 , x 2 , τ ) ,
ϵ m j i x j k 1 W k i = k 1 ( ϵ m j i x j W k i ) ϵ m j i W k i δ k j = k 1 ( ϵ m j i x j W k i ) ϵ m j i W j i ,
ϵ m i j W i j = ϵ m j i W i j = ϵ m i j W j i = ϵ m i j W i j ,
ϵ m j i W j i = 0 .
τ L m ( x 1 , x 2 , τ ) + k 1 M m k ( x 1 , x 2 , τ ) = 0 ,
M m k ( x 1 , x 2 , τ ) = ϵ m j i x j W i k ( x 1 , x 2 , τ ) .
d d τ V L m ( x 1 , x 2 , τ ) d 3 x 1 + S M m k ( x 1 , x 2 , τ ) n k d 2 x 1 = 0 .

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