Abstract

We investigate the role of the source coherence length in the two alternative definitions, [Phys. Rev. E 66, 016615 (2002)] and [Opt. Commun. 248, 333 (2005)], respectively, on the degree of polarization of a three-dimensional near field emitted by a random planar source. It is demonstrated that for the wide variety of statistically homogeneous sources, there are regimes where both definitions are identical. In particular, this occurs for fields from δ-correlated, such as thermal sources. Further, we discuss how the excitation of surface waves influence whether those two definitions coincide.

© 2012 Optical Society of America

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References

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  1. R. J. Glauber, Phys. Rev. 130, 2529 (1963).
    [CrossRef]
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ., 1995).
  3. T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
    [CrossRef]
  4. J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
    [CrossRef]
  5. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 328 (2004).
    [CrossRef]
  6. E. Wolf, Opt. Lett. 29, 1712 (2004).
    [CrossRef]
  7. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 1713 (2004).
    [CrossRef]
  8. R. Carminati and J. J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
    [CrossRef]
  9. J. M. Auñón and M. Nieto-Vesperinas, Opt. Lett. 36, 3410 (2011).
    [CrossRef]
  10. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (World Science, 2006).
  11. R. C. Bourret, Nuovo Cimento 18, 347 (1960).
    [CrossRef]
  12. R. Carminati, Phys. Rev. A 81, 053804 (2010).
    [CrossRef]
  13. W. H. Carter and E. Wolf, J. Opt. Soc. Am. A 65, 1067 (1975).
    [CrossRef]
  14. T. Jouttenus, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 72, 046611 (2005).
    [CrossRef]
  15. T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
    [CrossRef]

2011 (1)

2010 (1)

R. Carminati, Phys. Rev. A 81, 053804 (2010).
[CrossRef]

2005 (2)

T. Jouttenus, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 72, 046611 (2005).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

2004 (3)

2002 (2)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

1999 (1)

R. Carminati and J. J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

1975 (1)

W. H. Carter and E. Wolf, J. Opt. Soc. Am. A 65, 1067 (1975).
[CrossRef]

1963 (1)

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

1960 (1)

R. C. Bourret, Nuovo Cimento 18, 347 (1960).
[CrossRef]

Auñón, J. M.

Bourret, R. C.

R. C. Bourret, Nuovo Cimento 18, 347 (1960).
[CrossRef]

Carminati, R.

R. Carminati, Phys. Rev. A 81, 053804 (2010).
[CrossRef]

R. Carminati and J. J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

Carter, W. H.

W. H. Carter and E. Wolf, J. Opt. Soc. Am. A 65, 1067 (1975).
[CrossRef]

Dogariu, A.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

Ellis, J.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

Friberg, A. T.

T. Jouttenus, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 72, 046611 (2005).
[CrossRef]

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 1713 (2004).
[CrossRef]

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 328 (2004).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Glauber, R. J.

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

Greffet, J. J.

R. Carminati and J. J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

Jouttenus, T.

T. Jouttenus, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 72, 046611 (2005).
[CrossRef]

Kaivola, M.

T. Jouttenus, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 72, 046611 (2005).
[CrossRef]

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Mandel, L.

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

Nieto-Vesperinas, M.

J. M. Auñón and M. Nieto-Vesperinas, Opt. Lett. 36, 3410 (2011).
[CrossRef]

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (World Science, 2006).

Ponomarenko, S.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

Setälä, T.

T. Jouttenus, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 72, 046611 (2005).
[CrossRef]

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 328 (2004).
[CrossRef]

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 1713 (2004).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Shevchenko, A.

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Tervo, J.

Wolf, E.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

E. Wolf, Opt. Lett. 29, 1712 (2004).
[CrossRef]

W. H. Carter and E. Wolf, J. Opt. Soc. Am. A 65, 1067 (1975).
[CrossRef]

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

J. Opt. Soc. Am. A (1)

W. H. Carter and E. Wolf, J. Opt. Soc. Am. A 65, 1067 (1975).
[CrossRef]

Nuovo Cimento (1)

R. C. Bourret, Nuovo Cimento 18, 347 (1960).
[CrossRef]

Opt. Commun. (1)

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. (1)

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

Phys. Rev. A (1)

R. Carminati, Phys. Rev. A 81, 053804 (2010).
[CrossRef]

Phys. Rev. E (2)

T. Jouttenus, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 72, 046611 (2005).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

R. Carminati and J. J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

Other (2)

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

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (World Science, 2006).

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Figures (3)

Fig. 1.
Fig. 1.

Wzz(r,r,ω)/Wxx(r,r,ω) versus distance from the source (in units of wavelength λ), for different values of the source coherence length σ. The calculations are done at λ=500nm, (ϵ=4.2+i18.1).

Fig. 2.
Fig. 2.

DOP versus distance to the source for the two definitions: (a) Setälä et al. definition PS and (b) Ellis et al. definition PE, for different values of the coherence length σ of the source. Calculations of W are done at λ=500nm (ϵ=4.2+i18.1).

Fig. 3.
Fig. 3.

PS and PE versus distance to the source when SPPs are excited on its surface. The surface metal is Au at 620 nm (ϵ=9.1+i1.2).

Equations (10)

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

Wij(r1,r2,ω)=Ei*(r1,ω)Ej(r2,ω),
E(r,ω)=e(ks,ω)eiks·rd2s,
Wij(r,r,ω)=k2E˜ij(ks,ω)eik(szsz*)zd2s.
e(ks,ω)=es(ks,ω)s^+ep(ks,ω)p^,
E˜ij(ks,ω)=Ass(ks,ω)s^is^j+App(ks,ω)p^i*p^j+Asp(ks,ω)s^ip^j+Aps(ks,ω)p^i*s^j
E˜ij(ks,ω)=A(ks,ω)(s^is^j+p^i*p^j).
Wij(r,r,ω)=(Wxx000Wxx000Wzz).
PS(r,ω)=(λ1λ2)2+(λ1λ3)2+(λ2λ3)22(λ1+λ2+λ3),
PE(r,ω)=λ1λ2λ1+λ2+λ3.
Wij(r,r,ω)=k2A(ks,ω)×(sisj|ts|2+pi*pj|tp|2)eik(szsz*)zd2s,

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