Abstract

The definition of the orbital angular momentum established for coherent beams is extended to partially coherent beams, expressed in terms of two elements of the beam matrix. This extension is justified by use of the Mercer expansion of partially coherent fields. General Gauss–Schell-model fields are considered, and the relation between the twist parameter and the orbital angular momentum is analyzed.

© 2001 Optical Society of America

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  4. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
    [CrossRef] [PubMed]
  5. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
    [CrossRef]
  6. G. S. Agarwal, J. Opt. Soc. Am. A 16, 2914 (1999).
    [CrossRef]
  7. A. T. Friberg, C. Gao, B. Eppich, and H. Weber, Proc. SPIE 3110, 317 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1999 (2)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 59, 3950 (1999).
[CrossRef]

G. S. Agarwal, J. Opt. Soc. Am. A 16, 2914 (1999).
[CrossRef]

1997 (3)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, Proc. SPIE 3110, 317 (1997).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[CrossRef] [PubMed]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

1994 (1)

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

1993 (1)

1992 (1)

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

1985 (1)

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 2419 (1985).
[CrossRef]

1982 (1)

1979 (1)

Agarwal, G. S.

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 59, 3950 (1999).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[CrossRef] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

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

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 59, 3950 (1999).
[CrossRef]

Barnett, S. M.

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

Bastiaans, M. J.

Beijersbergen, M. W.

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

Courtial, J.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

Dholakia, K.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 59, 3950 (1999).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[CrossRef] [PubMed]

Encinas-Sanz, F.

J. Serna, F. Encinas-Sanz, and G. Nemeş, in Proceedings of the 5th International Workshop on Laser Beam and Optics Characterization, H. Weber and H. Laabs, eds. (Technische Universität–Optics Institut, Berlin, 2000).

Eppich, B.

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, Proc. SPIE 3110, 317 (1997).
[CrossRef]

Friberg, A. T.

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, Proc. SPIE 3110, 317 (1997).
[CrossRef]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Gao, C.

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, Proc. SPIE 3110, 317 (1997).
[CrossRef]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Mukunda, N.

R. Simon and N. Mukunda, J. Opt. Soc. Am. A 10, 95 (1993).
[CrossRef]

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 2419 (1985).
[CrossRef]

Nemes, G.

G. Nemeş and J. Serna, in 4th International Workshop on Laser Beam and Optics Characterization, A. Giesen and M. Morin, eds., (VDI-Technologiezentrum, Dusseldorf, Germany, 1997), pp. 92–105.

J. Serna, F. Encinas-Sanz, and G. Nemeş, in Proceedings of the 5th International Workshop on Laser Beam and Optics Characterization, H. Weber and H. Laabs, eds. (Technische Universität–Optics Institut, Berlin, 2000).

Padgett, M. J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 59, 3950 (1999).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Serna, J.

J. Serna, F. Encinas-Sanz, and G. Nemeş, in Proceedings of the 5th International Workshop on Laser Beam and Optics Characterization, H. Weber and H. Laabs, eds. (Technische Universität–Optics Institut, Berlin, 2000).

G. Nemeş and J. Serna, in 4th International Workshop on Laser Beam and Optics Characterization, A. Giesen and M. Morin, eds., (VDI-Technologiezentrum, Dusseldorf, Germany, 1997), pp. 92–105.

Simon, R.

R. Simon and N. Mukunda, J. Opt. Soc. Am. A 10, 95 (1993).
[CrossRef]

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 2419 (1985).
[CrossRef]

Simpson, N. B.

Spreeuw, R. J. C.

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

Sudarshan, E. C. G.

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 2419 (1985).
[CrossRef]

Weber, H.

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, Proc. SPIE 3110, 317 (1997).
[CrossRef]

Woerdman, J. P.

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

Wolf, E.

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (3)

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

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 2419 (1985).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 59, 3950 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Proc. SPIE (1)

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, Proc. SPIE 3110, 317 (1997).
[CrossRef]

Other (2)

J. Serna, F. Encinas-Sanz, and G. Nemeş, in Proceedings of the 5th International Workshop on Laser Beam and Optics Characterization, H. Weber and H. Laabs, eds. (Technische Universität–Optics Institut, Berlin, 2000).

G. Nemeş and J. Serna, in 4th International Workshop on Laser Beam and Optics Characterization, A. Giesen and M. Morin, eds., (VDI-Technologiezentrum, Dusseldorf, Germany, 1997), pp. 92–105.

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Equations (28)

Equations on this page are rendered with MathJax. Learn more.

L=Mrdxdy,
Ar=A0rexp-iωt-kze,
S¯=ϵ0c2/2ReEr×B*r,
L¯x=Iy-zv/c2,
L¯y=I-x+zu/c2,
L¯z=Ixv-yu/c2+s3/cω,
I=S¯zdxdy=ψ2dxdy,
ψr=iωϵ0c/2A0r,
x=1Ixψ2dxdy,
u=i2kIψψ*x-ψ*ψxdxdy,
xv=i2kIxψψ*x-ψ*ψydxdy,
yu=i2kIyψψ*x-ψ*ψxdxdy.
J¯z=Icxv-yu+s3ω.
J̅zS=s3ω,
J¯zL=Icxv-yu,
xv=1Ixvhx,y,u,vdxdydudv,
yu=1Iyuhx,y,u,vdxdydudv,
Γr1,r2=nΓnr1,r2,
Γnr1,r2=ψn*r1ψnr2
Γr1,r2ψnr1dxdy=Inψnr2,
ψn*rψmrdxdy=Inδn,m.
J¯zn=In/cxvn-yun.
J¯z=1cnInxvn-yun.
xv=1/InInxvn,
yu=1/InInyun,
J¯z=Icxv-yu,
J¯z=I2cTrR-1σI2-σI2R-1J-2τ TrσI2,
J=01-10.

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