Abstract

In analogy with the separation of the total optical angular momentum into a spin and an orbital part in electrodynamics, we introduce a new concept of spin and orbital angular coherence momenta into the general coherence theory of vector electromagnetic fields. The properties of the newly introduced spin and orbital angular coherence momenta are investigated through the decomposition of the total coherence angular momentum into the sum of these two components, and their separate conservations have been derived for what is believed to be the first time.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  6. J. W. Goodman, Statistical Optics (Wiley, 2000).
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    [CrossRef] [PubMed]
  8. G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
    [CrossRef]
  9. D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., Phys. Rev. Lett. 92, 143905 (2004).
    [CrossRef] [PubMed]
  10. D. G. Fischer and T. D. Visser, J. Opt. Soc. Am. A 21, 2097 (2004).
    [CrossRef]
  11. W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
    [CrossRef] [PubMed]
  12. W. Wang and M. Takeda, Phys. Rev. Lett. 96, 223904 (2006).
    [CrossRef] [PubMed]
  13. W. Wang and M. Takeda, Opt. Lett. 31, 2520 (2006).
    [CrossRef] [PubMed]
  14. J. D. Jackson, Classical Electrodynamics (Wiley, 1998), Chap. 6.
  15. P. Roman and E. Wolf, Nuovo Cimento 17, 477 (1960).
    [CrossRef]
  16. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).
  17. S. J. van Enk and G. Nienhuis, J. Mod. Opt. 41, 963 (1994).
    [CrossRef]

2006

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]

W. Wang and M. Takeda, Opt. Lett. 31, 2520 (2006).
[CrossRef] [PubMed]

2004

D. G. Fischer and T. D. Visser, J. Opt. Soc. Am. A 21, 2097 (2004).
[CrossRef]

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef] [PubMed]

2003

1994

S. J. van Enk and G. Nienhuis, J. Mod. Opt. 41, 963 (1994).
[CrossRef]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

1960

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

1936

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

1909

J. H. Poynting, Proc. R. Soc. London, Ser. A 82, 560 (1909).
[CrossRef]

J. Mod. Opt.

S. J. van Enk and G. Nienhuis, J. Mod. Opt. 41, 963 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Nuovo Cimento

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

Opt. Commun.

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

Opt. Lett.

Phys. Rev.

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef] [PubMed]

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]

Proc. R. Soc. London, Ser. A

J. H. Poynting, Proc. R. Soc. London, Ser. A 82, 560 (1909).
[CrossRef]

Other

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2004).

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).

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

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

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

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Equations (20)

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E j m = ε j k l k 1 A l m ,
S j m = τ A j m ,
E j k ( r 1 , r 2 , τ ) = E j * ( r 1 , t ) E k ( r 2 , t + τ ) + H j * ( r 1 , t ) H k ( r 2 , t + τ ) ,
S j k ( r 1 , r 2 , τ ) = E j * ( r 1 , t ) H k ( r 2 , t + τ ) H j * ( r 1 , t ) E k ( r 2 , t + τ ) .
T i = c 1 ε i k j ( S k m E j m * + S k m * E j m ) = c 1 ε i k j [ S k m ( ε j n l n 1 A l m ) * + S k m * ( ε j n l n 1 A l m ) ] .
T i = c 1 [ S k m i 1 A k m * + S k m * i 1 A k m ( S k m k 1 A i m * + S k m * k 1 A i m ) ] = c 1 [ S k m i 1 A k m * + S k m * i 1 A k m k 1 ( S k m A i m * + S k m * A i m ) ] ,
L n ( r 1 , r 2 , τ ) ( r 1 r 0 ) × T ( r 1 , r 2 , τ ) = ε n j i ( r 1 j r 0 j ) T i ( r 1 , r 2 , τ ) ,
L n = c 1 ε n j i ( r 1 j r 0 j ) [ S k m i 1 A k m * + S k m * i 1 A k m k 1 ( S k m A i m * + S k m * A i m ) ] = c 1 ε n j i ( r 1 j r 0 j ) ( S k m i 1 A k m * + S k m * i 1 A k m ) c 1 ε n j i k 1 [ ( r 1 j r 0 j ) ( S k m A i m * + S k m * A i m ) ] + c 1 ε n j i [ k 1 ( r 1 j r 0 j ) ] ( S k m A i m * + S k m * A i m ) .
L n = c 1 S k m ε n j i ( r 1 j r 0 j ) i 1 A k m * + c 1 S k m * ε n j i ( r 1 j r 0 j ) i 1 A k m + c 1 ε n k i ( S k m A i m * + S k m * A i m ) c 1 ε n j i k 1 [ ( r 1 j r 0 j ) ( S k m A i m * + S k m * A i m ) ] = c 1 S k m [ ( r 1 r 0 ) × ] n A k m * + c 1 S k m * [ ( r 1 r 0 ) × ] n A k m + c 1 ε n k i ( S k m A i m * + S k m * A i m ) c 1 k 1 { S k m [ ( r 1 r 0 ) × A i m * ] + S k m * [ ( r 1 r 0 ) × A i m ] } .
L n = c 1 V [ S k m ε n j i ( r 1 j r 0 j ) i 1 A k m * + c 1 S k m * ε n j i ( r 1 j r 0 j ) i 1 A k m ] d r 1 3 + c 1 V [ ε n k i ( S k m A i m * + S k m * A i m ) ] d r 1 3 c 1 S { S k m [ ( r 1 r 0 ) × A i m * ] + S k m * [ ( r 1 r 0 ) × A i m ] } d r 1 2 = c 1 V { S k m [ ( r 1 r 0 ) × ] n A k m * + c 1 S k m * [ ( r 1 r 0 ) × ] n A k m } d r 1 3 + c 1 V [ ε n k i ( S k m A i m * + S k m * A i m ) ] d r 1 3 ,
L n = ( L s ) n + ( L o ) n ,
( L s ) n = c 1 V ε n k i ( S k m A i m * + S k m * A i m ) d r 1 3 ,
( L o ) n = c 1 V { S k m [ ( r 1 r 0 ) × ] n A k m * + c 1 S k m * [ ( r 1 r 0 ) × ] n A k m } d r 1 3 .
M n k = ε n j i ( r 1 j r 0 j ) [ ( E i m E k m * + E i m * E k m ) + ( S i m S k m * + S i m * S k m ) W δ i k ] = ε n j i ( r 1 j r 0 j ) { [ ( ε i l p l 1 A p m ) ( ε k f q f 1 A q m * ) + c.c. ] + ( S i m S k m * + S i m * S k m ) W δ i k } ,
M n k = ε n j i ( r 1 j r 0 j ) [ ( S i m S k m * + S i m * S k m ) W δ i k ] + { ε k f q [ ( r 1 j r 0 j ) ( n 1 A j m ) ( f 1 A q m * ) ( r 1 j r 0 j ) ( j 1 A n m ) ( f 1 A q m * ) ] + c.c. } = ε n j i ( r 1 j r 0 j ) [ ( S i m S k m * + S i m * S k m ) W δ i k ] + ( ε k f q ( f 1 A q m * ) { n 1 [ ( r 1 j r 0 j ) A j m ] j 1 [ ( r 1 j r 0 j ) A n m ] + 2 A n m } + c.c. ) , .
M n k = ( M s ) n k + ( M o ) n k ,
( M s ) n k = 2 V ε n f q [ ( f 1 A q m * ) A k m + ( f 1 A q m ) A k m * ] d r 1 3
( M o ) n k = V ( r 1 r 0 ) × [ ( S i m S k m * + S i m * S k m ) W δ i k ] d r 1 3
τ ( L s ) n + k 1 ( M s ) n k = 0 ,
τ ( L o ) n + k 1 ( M o ) n k = 0 .

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