Abstract

We introduce an extension of the van Cittert–Zernike theorem to spatially incoherent sources with partial polarization. We show through a simple example that fields generated by such sources can possess correlation matrices with interesting properties. In particular, we show that by suitable modulation of the polarization state across the incoherent source, the correlation between the orthogonal components of the field as well as the degree of polarization may drastically change on propagation.

© 2000 Optical Society of America

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References

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  1. D. F. V. James, J. Opt. Soc. Am. A 11, 1641 (1994).
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  2. R. Martínez-Herrero, P. M. Mejías, and J. M. Movilla, Opt. Lett. 22, 206 (1997).
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  3. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Eur. Opt. Soc. A Pure Appl. Opt. 7, 941 (1998).
  4. S. R. Seshadri, J. Opt. Soc. Am. A 16, 1373 (1999).
    [CrossRef]
  5. See, for example, L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
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  7. P. de Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
    [CrossRef]
  8. J. Turunen, A. Vasara, and A. T. Friberg, J. Opt. Soc. Am. A 8, 282 (1991).
    [CrossRef]
  9. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  10. F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, Opt. Commun. 163, 159 (1999).
    [CrossRef]
  11. L. Nikolova, M. Ivanov, T. Todorov, and S. Stoyanov, Bulg. J. Phys. 20, 46 (1993).
  12. P. Rochon, V. Drnoyan, and A. Natansohn, Proc. SPIE 3491, 306 (2000).
    [CrossRef]
  13. F. Gori, Opt. Lett. 24, 584 (1999).
    [CrossRef]
  14. C. G. Someda, Opt. Lett. 25, 1657 (2000).
    [CrossRef]
  15. P. De Santis, F. Gori, and G. Guattari, J. Opt. Soc. Am. A 3, 1258 (1986).
    [CrossRef]

2000 (2)

P. Rochon, V. Drnoyan, and A. Natansohn, Proc. SPIE 3491, 306 (2000).
[CrossRef]

C. G. Someda, Opt. Lett. 25, 1657 (2000).
[CrossRef]

1999 (3)

F. Gori, Opt. Lett. 24, 584 (1999).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, Opt. Commun. 163, 159 (1999).
[CrossRef]

S. R. Seshadri, J. Opt. Soc. Am. A 16, 1373 (1999).
[CrossRef]

1998 (1)

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Eur. Opt. Soc. A Pure Appl. Opt. 7, 941 (1998).

1997 (1)

1994 (1)

1993 (1)

L. Nikolova, M. Ivanov, T. Todorov, and S. Stoyanov, Bulg. J. Phys. 20, 46 (1993).

1991 (1)

1986 (1)

1979 (1)

P. de Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Borghi, R.

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, Opt. Commun. 163, 159 (1999).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Eur. Opt. Soc. A Pure Appl. Opt. 7, 941 (1998).

De Santis, P.

P. De Santis, F. Gori, and G. Guattari, J. Opt. Soc. Am. A 3, 1258 (1986).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Drnoyan, V.

P. Rochon, V. Drnoyan, and A. Natansohn, Proc. SPIE 3491, 306 (2000).
[CrossRef]

Friberg, A. T.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, Opt. Commun. 163, 159 (1999).
[CrossRef]

F. Gori, Opt. Lett. 24, 584 (1999).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Eur. Opt. Soc. A Pure Appl. Opt. 7, 941 (1998).

P. De Santis, F. Gori, and G. Guattari, J. Opt. Soc. Am. A 3, 1258 (1986).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Guattari, G.

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, Opt. Commun. 163, 159 (1999).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Eur. Opt. Soc. A Pure Appl. Opt. 7, 941 (1998).

P. De Santis, F. Gori, and G. Guattari, J. Opt. Soc. Am. A 3, 1258 (1986).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Ivanov, M.

L. Nikolova, M. Ivanov, T. Todorov, and S. Stoyanov, Bulg. J. Phys. 20, 46 (1993).

James, D. F. V.

Mandel, L.

See, for example, L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Martínez-Herrero, R.

Mejías, P. M.

Movilla, J. M.

Natansohn, A.

P. Rochon, V. Drnoyan, and A. Natansohn, Proc. SPIE 3491, 306 (2000).
[CrossRef]

Nikolova, L.

L. Nikolova, M. Ivanov, T. Todorov, and S. Stoyanov, Bulg. J. Phys. 20, 46 (1993).

Palma, C.

P. de Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Rochon, P.

P. Rochon, V. Drnoyan, and A. Natansohn, Proc. SPIE 3491, 306 (2000).
[CrossRef]

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, Opt. Commun. 163, 159 (1999).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Eur. Opt. Soc. A Pure Appl. Opt. 7, 941 (1998).

Seshadri, S. R.

Someda, C. G.

Stoyanov, S.

L. Nikolova, M. Ivanov, T. Todorov, and S. Stoyanov, Bulg. J. Phys. 20, 46 (1993).

Todorov, T.

L. Nikolova, M. Ivanov, T. Todorov, and S. Stoyanov, Bulg. J. Phys. 20, 46 (1993).

Turunen, J.

Vasara, A.

Vicalvi, S.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Eur. Opt. Soc. A Pure Appl. Opt. 7, 941 (1998).

Wolf, E.

See, for example, L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Bulg. J. Phys. (1)

L. Nikolova, M. Ivanov, T. Todorov, and S. Stoyanov, Bulg. J. Phys. 20, 46 (1993).

J. Eur. Opt. Soc. A Pure Appl. Opt. (1)

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Eur. Opt. Soc. A Pure Appl. Opt. 7, 941 (1998).

J. Opt. Soc. Am. A (4)

Opt. Commun. (2)

P. de Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, Opt. Commun. 163, 159 (1999).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (1)

P. Rochon, V. Drnoyan, and A. Natansohn, Proc. SPIE 3491, 306 (2000).
[CrossRef]

Other (3)

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

See, for example, L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

M. Born and E. Wolf, eds., Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Notation used in the evaluation of the BCP matrix for the field generated by the incoherent unpolarized primary source (S) covered by a polarizing filter.

Fig. 2
Fig. 2

Normalized elements of the BCP matrix versus Lν, where L is the width of the polarizer and ν=x2-x1/λz. The scalar-equivalent degree of coherence, jeq, is shown by the thicker solid curve.

Equations (12)

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

Jˆr1,r2,z=Jxxr1,r2,zJxyr1,r2,zJyxr1,r2,zJyyr1,r2,z,
Jαβr1,r2,z=Eα*r1,z;tEβr2,z;t,α,β=x,y.
Jαβρ1,ρ2,0=l2I0αβρ1δρ2-ρ1,
Jαβr1,r2,z=J0αβρ1,ρ2K*r1,ρ1,z×Kr2,ρ2,zd2ρ1d2ρ2,α,β=x,y.
Kr,ρ,z=-i expikzλzexpik2zr-ρ2,
Jαβr1,r2,z=expik2zr22-r12z2×I0αβρexp-2πiλzρ·r2-r1d2ρ,
Jˆinξ1,ξ2,0=λI0δξ2-ξ11001,
Jˆoutξ1,ξ2,0=Tˆξ1Jˆinξ1,ξ2,0Tˆξ2×rectξ1/Lrectξ2/L,
Tˆ=C2CSCSS2, C=cos πξ/L, S=sin πξ/L
jxxx1,x2,z=sincLν+12sincLν-1+12sincLν+1,jyyx1,x2,z=sincLν-12sincLν-1-12sincLν+1,jxyx1,x2,z=12isincLν-1-sincLν+1,
jeqx1,x2,z=sincLν.
Px,z=Jxx-Jyy2+4Jxy2Jxx+Jyy21/2,

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