Abstract

We develop an electromagnetic analysis for partially correlated thin annular sources. The elements of the correlation matrix are assumed to depend only on the angular distance between two typical points. For any such source, we show how the modal expansion can be found. Correlation changes upon free propagation are discussed. Further, examples and possible synthesis schemes are presented.

© 2010 Optical Society of America

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  1. F. Gori, M. Santarsiero, R. Borghi, and C. Li, “Partially correlated thin annular sources: the scalar case,” J. Opt. Soc. Am. A 25, 2826–2832 (2008).
    [CrossRef]
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  3. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  4. F. Gori, G. Guattari, and C. Padovani, “Modal expansion of J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
    [CrossRef]
  5. D. F. V. James, “Change of polarization of light beam on propagation in free-space,” J. Opt. Soc. Am. A 11, 1641–1643 (1994).
    [CrossRef]
  6. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 241–243 (1998).
    [CrossRef]
  7. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarisation matrix,” Pure Appl. Opt. 7, 941–951 (1998).
    [CrossRef]
  8. F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “The irradiance of partially polarized beams in a scalar treatment,” Opt. Commun. 163, 159–163 (1999).
    [CrossRef]
  9. S. R. Seshadri, “Partially coherent Gaussian Schell-model electromagnetic beam,” J. Opt. Soc. Am. A 16, 1373–1380 (1999).
    [CrossRef]
  10. F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert–Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291–1293 (2000).
    [CrossRef]
  11. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1–9 (2001).
    [CrossRef]
  12. G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, “Far field of beams generated by quasi-homogeneous sources passing through polarization gratings,” Opt. Commun. 195, 339–350 (2001).
    [CrossRef]
  13. J. Tervo, T. Setälä, and A. T. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11, 1137–1143 (2003).
    [CrossRef] [PubMed]
  14. E. Wolf, “Unified theory of coherence and polarization of statistical electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
    [CrossRef]
  15. F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, “Coherent-mode decomposition of partially polarized, partially coherent sources,” J. Opt. Soc. Am. A 20, 78–84 (2003).
    [CrossRef]
  16. J. Tervo, T. Setälä, and A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space-frequency domain,” J. Opt. Soc. Am. A 21, 2205–2215 (2004).
    [CrossRef]
  17. R. Martínez-Herrero, G. Piquero, and P. Mejías, “Parametric characterization of the spatial structure of partially coherent and partially polarized beams,” J. Opt. A, Pure Appl. Opt. 6, S67–S71 (2004).
    [CrossRef]
  18. O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29, 1173–1175 (2004).
    [CrossRef] [PubMed]
  19. P. Réfrégier and F. Goudail, “Invariant degrees of coherence of partially polarized light,” Opt. Express 13, 6051–6060 (2005).
    [CrossRef] [PubMed]
  20. H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (2005).
    [CrossRef]
  21. T. Shirai, “Polarization properties of a class of electromagnetic Gaussian Schell-model beams which have the same far-zone intensity distribution as a fully coherent laser beam,” Opt. Commun. 256, 197–209 (2005).
    [CrossRef]
  22. F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, “Effects of coherence on the degree of polarization in Young interference pattern,” Opt. Lett. 31, 688–690 (2006).
    [CrossRef] [PubMed]
  23. A. Luis, “Ray picture of polarization and coherence in a Young interferometer,” J. Opt. Soc. Am. A 23, 2855–2860 (2006).
    [CrossRef]
  24. M. Santarsiero, F. Gori, R. Borghi, and G. Guattari, “Vector-mode analysis of symmetric two-point sources,” J. Opt. A, Pure Appl. Opt. 9, 593–602 (2007).
    [CrossRef]
  25. F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33, 1857–1859 (2008).
    [CrossRef] [PubMed]
  26. S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10, 055001 (2008).
    [CrossRef]
  27. J. Tervo, T. Setl, A. Roueff, P. Rfrgier, and A. T. Friberg, “Two-point Stokes parameters: interpretation and properties,” Opt. Lett. 34, 3074–3076 (2009).
    [CrossRef] [PubMed]
  28. R. Borghi, F. Gori, and S. A. Ponomarenko, “On a class of electromagnetic diffraction-free beams,” J. Opt. Soc. Am. A 26, 2275–2281 (2009).
    [CrossRef]
  29. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).
  30. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge Univ. Press, 1985).
  31. S. K. Berberian, Introduction to Hilbert Space (Oxford Univ. Press, 1961).
  32. G. S. Agarwal, G. Gbur, and E. Wolf, “Coherence properties of sunlight,” Opt. Lett. 29, 459–461 (2004).
    [CrossRef] [PubMed]
  33. F. Gori, “Far-zone approximation for partially coherent sources,” Opt. Lett. 30, 2840–2842 (2005).
    [CrossRef] [PubMed]
  34. I. S. Gradshteyn and I. M. Ryzhik, in Table of Integrals, Series, and Products, 6th ed., A.Jeffrey and D.Zwillinger, eds. (Academic, 2000).
  35. Q. W. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
    [CrossRef]
  36. S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81, 597–600 (2005).
    [CrossRef]
  37. Q. W. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10, 324–331 (2002).
    [PubMed]

2009 (3)

2008 (3)

2007 (2)

M. Santarsiero, F. Gori, R. Borghi, and G. Guattari, “Vector-mode analysis of symmetric two-point sources,” J. Opt. A, Pure Appl. Opt. 9, 593–602 (2007).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).

2006 (2)

2005 (5)

P. Réfrégier and F. Goudail, “Invariant degrees of coherence of partially polarized light,” Opt. Express 13, 6051–6060 (2005).
[CrossRef] [PubMed]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (2005).
[CrossRef]

T. Shirai, “Polarization properties of a class of electromagnetic Gaussian Schell-model beams which have the same far-zone intensity distribution as a fully coherent laser beam,” Opt. Commun. 256, 197–209 (2005).
[CrossRef]

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81, 597–600 (2005).
[CrossRef]

F. Gori, “Far-zone approximation for partially coherent sources,” Opt. Lett. 30, 2840–2842 (2005).
[CrossRef] [PubMed]

2004 (4)

2003 (3)

2002 (1)

2001 (2)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1–9 (2001).
[CrossRef]

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, “Far field of beams generated by quasi-homogeneous sources passing through polarization gratings,” Opt. Commun. 195, 339–350 (2001).
[CrossRef]

2000 (2)

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert–Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291–1293 (2000).
[CrossRef]

I. S. Gradshteyn and I. M. Ryzhik, in Table of Integrals, Series, and Products, 6th ed., A.Jeffrey and D.Zwillinger, eds. (Academic, 2000).

1999 (2)

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “The irradiance of partially polarized beams in a scalar treatment,” Opt. Commun. 163, 159–163 (1999).
[CrossRef]

S. R. Seshadri, “Partially coherent Gaussian Schell-model electromagnetic beam,” J. Opt. Soc. Am. A 16, 1373–1380 (1999).
[CrossRef]

1998 (2)

F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 241–243 (1998).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarisation matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

1995 (1)

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

1994 (1)

1987 (2)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

F. Gori, G. Guattari, and C. Padovani, “Modal expansion of J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
[CrossRef]

1985 (1)

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge Univ. Press, 1985).

1961 (1)

S. K. Berberian, Introduction to Hilbert Space (Oxford Univ. Press, 1961).

Agarwal, G. S.

Berberian, S. K.

S. K. Berberian, Introduction to Hilbert Space (Oxford Univ. Press, 1961).

Borghi, R.

R. Borghi, F. Gori, and S. A. Ponomarenko, “On a class of electromagnetic diffraction-free beams,” J. Opt. Soc. Am. A 26, 2275–2281 (2009).
[CrossRef]

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33, 1857–1859 (2008).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, R. Borghi, and C. Li, “Partially correlated thin annular sources: the scalar case,” J. Opt. Soc. Am. A 25, 2826–2832 (2008).
[CrossRef]

M. Santarsiero, F. Gori, R. Borghi, and G. Guattari, “Vector-mode analysis of symmetric two-point sources,” J. Opt. A, Pure Appl. Opt. 9, 593–602 (2007).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, “Effects of coherence on the degree of polarization in Young interference pattern,” Opt. Lett. 31, 688–690 (2006).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, “Coherent-mode decomposition of partially polarized, partially coherent sources,” J. Opt. Soc. Am. A 20, 78–84 (2003).
[CrossRef]

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, “Far field of beams generated by quasi-homogeneous sources passing through polarization gratings,” Opt. Commun. 195, 339–350 (2001).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1–9 (2001).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert–Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291–1293 (2000).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “The irradiance of partially polarized beams in a scalar treatment,” Opt. Commun. 163, 159–163 (1999).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarisation matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Dorn, R.

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81, 597–600 (2005).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Friberg, A. T.

Gbur, G.

Gori, F.

R. Borghi, F. Gori, and S. A. Ponomarenko, “On a class of electromagnetic diffraction-free beams,” J. Opt. Soc. Am. A 26, 2275–2281 (2009).
[CrossRef]

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33, 1857–1859 (2008).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, R. Borghi, and C. Li, “Partially correlated thin annular sources: the scalar case,” J. Opt. Soc. Am. A 25, 2826–2832 (2008).
[CrossRef]

M. Santarsiero, F. Gori, R. Borghi, and G. Guattari, “Vector-mode analysis of symmetric two-point sources,” J. Opt. A, Pure Appl. Opt. 9, 593–602 (2007).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, “Effects of coherence on the degree of polarization in Young interference pattern,” Opt. Lett. 31, 688–690 (2006).
[CrossRef] [PubMed]

F. Gori, “Far-zone approximation for partially coherent sources,” Opt. Lett. 30, 2840–2842 (2005).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, “Coherent-mode decomposition of partially polarized, partially coherent sources,” J. Opt. Soc. Am. A 20, 78–84 (2003).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1–9 (2001).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert–Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291–1293 (2000).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “The irradiance of partially polarized beams in a scalar treatment,” Opt. Commun. 163, 159–163 (1999).
[CrossRef]

F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 241–243 (1998).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarisation matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Modal expansion of J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
[CrossRef]

Goudail, F.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, in Table of Integrals, Series, and Products, 6th ed., A.Jeffrey and D.Zwillinger, eds. (Academic, 2000).

Guattari, G.

M. Santarsiero, F. Gori, R. Borghi, and G. Guattari, “Vector-mode analysis of symmetric two-point sources,” J. Opt. A, Pure Appl. Opt. 9, 593–602 (2007).
[CrossRef]

F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, “Coherent-mode decomposition of partially polarized, partially coherent sources,” J. Opt. Soc. Am. A 20, 78–84 (2003).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “The irradiance of partially polarized beams in a scalar treatment,” Opt. Commun. 163, 159–163 (1999).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarisation matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Modal expansion of J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
[CrossRef]

Horn, R. A.

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge Univ. Press, 1985).

James, D. F. V.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10, 055001 (2008).
[CrossRef]

D. F. V. James, “Change of polarization of light beam on propagation in free-space,” J. Opt. Soc. Am. A 11, 1641–1643 (1994).
[CrossRef]

Johnson, C. R.

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge Univ. Press, 1985).

Korotkova, O.

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29, 1173–1175 (2004).
[CrossRef] [PubMed]

Leger, J. R.

Leuchs, G.

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81, 597–600 (2005).
[CrossRef]

Li, C.

Luis, A.

Mandel, L.

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

Martínez-Herrero, R.

R. Martínez-Herrero, G. Piquero, and P. Mejías, “Parametric characterization of the spatial structure of partially coherent and partially polarized beams,” J. Opt. A, Pure Appl. Opt. 6, S67–S71 (2004).
[CrossRef]

Mejías, P.

R. Martínez-Herrero, G. Piquero, and P. Mejías, “Parametric characterization of the spatial structure of partially coherent and partially polarized beams,” J. Opt. A, Pure Appl. Opt. 6, S67–S71 (2004).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Mondello, A.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1–9 (2001).
[CrossRef]

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, “Far field of beams generated by quasi-homogeneous sources passing through polarization gratings,” Opt. Commun. 195, 339–350 (2001).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Modal expansion of J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
[CrossRef]

Piquero, G.

R. Martínez-Herrero, G. Piquero, and P. Mejías, “Parametric characterization of the spatial structure of partially coherent and partially polarized beams,” J. Opt. A, Pure Appl. Opt. 6, S67–S71 (2004).
[CrossRef]

F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, “Coherent-mode decomposition of partially polarized, partially coherent sources,” J. Opt. Soc. Am. A 20, 78–84 (2003).
[CrossRef]

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, “Far field of beams generated by quasi-homogeneous sources passing through polarization gratings,” Opt. Commun. 195, 339–350 (2001).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1–9 (2001).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert–Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291–1293 (2000).
[CrossRef]

Ponomarenko, S. A.

Quabis, S.

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81, 597–600 (2005).
[CrossRef]

Réfrégier, P.

Rfrgier, P.

Roueff, A.

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (2005).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, in Table of Integrals, Series, and Products, 6th ed., A.Jeffrey and D.Zwillinger, eds. (Academic, 2000).

Salem, M.

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, and C. Li, “Partially correlated thin annular sources: the scalar case,” J. Opt. Soc. Am. A 25, 2826–2832 (2008).
[CrossRef]

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33, 1857–1859 (2008).
[CrossRef] [PubMed]

M. Santarsiero, F. Gori, R. Borghi, and G. Guattari, “Vector-mode analysis of symmetric two-point sources,” J. Opt. A, Pure Appl. Opt. 9, 593–602 (2007).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, “Effects of coherence on the degree of polarization in Young interference pattern,” Opt. Lett. 31, 688–690 (2006).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, “Coherent-mode decomposition of partially polarized, partially coherent sources,” J. Opt. Soc. Am. A 20, 78–84 (2003).
[CrossRef]

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, “Far field of beams generated by quasi-homogeneous sources passing through polarization gratings,” Opt. Commun. 195, 339–350 (2001).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1–9 (2001).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert–Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291–1293 (2000).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “The irradiance of partially polarized beams in a scalar treatment,” Opt. Commun. 163, 159–163 (1999).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarisation matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Seshadri, S. R.

Setälä, T.

Setl, T.

Shirai, T.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10, 055001 (2008).
[CrossRef]

T. Shirai, “Polarization properties of a class of electromagnetic Gaussian Schell-model beams which have the same far-zone intensity distribution as a fully coherent laser beam,” Opt. Commun. 256, 197–209 (2005).
[CrossRef]

Simon, R.

F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, “Coherent-mode decomposition of partially polarized, partially coherent sources,” J. Opt. Soc. Am. A 20, 78–84 (2003).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1–9 (2001).
[CrossRef]

Tervo, J.

Vicalvi, S.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarisation matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Volkov, S. N.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10, 055001 (2008).
[CrossRef]

Wolf, E.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10, 055001 (2008).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, “Effects of coherence on the degree of polarization in Young interference pattern,” Opt. Lett. 31, 688–690 (2006).
[CrossRef] [PubMed]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29, 1173–1175 (2004).
[CrossRef] [PubMed]

G. S. Agarwal, G. Gbur, and E. Wolf, “Coherence properties of sunlight,” Opt. Lett. 29, 459–461 (2004).
[CrossRef] [PubMed]

E. Wolf, “Unified theory of coherence and polarization of statistical electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

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

Zhan, Q. W.

Adv. Opt. Photon. (1)

Appl. Phys. B (1)

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81, 597–600 (2005).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (4)

M. Santarsiero, F. Gori, R. Borghi, and G. Guattari, “Vector-mode analysis of symmetric two-point sources,” J. Opt. A, Pure Appl. Opt. 9, 593–602 (2007).
[CrossRef]

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10, 055001 (2008).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1–9 (2001).
[CrossRef]

R. Martínez-Herrero, G. Piquero, and P. Mejías, “Parametric characterization of the spatial structure of partially coherent and partially polarized beams,” J. Opt. A, Pure Appl. Opt. 6, S67–S71 (2004).
[CrossRef]

J. Opt. Soc. Am. A (7)

Opt. Commun. (5)

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “The irradiance of partially polarized beams in a scalar treatment,” Opt. Commun. 163, 159–163 (1999).
[CrossRef]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (2005).
[CrossRef]

T. Shirai, “Polarization properties of a class of electromagnetic Gaussian Schell-model beams which have the same far-zone intensity distribution as a fully coherent laser beam,” Opt. Commun. 256, 197–209 (2005).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Modal expansion of J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
[CrossRef]

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, “Far field of beams generated by quasi-homogeneous sources passing through polarization gratings,” Opt. Commun. 195, 339–350 (2001).
[CrossRef]

Opt. Express (3)

Opt. Lett. (8)

Phys. Lett. A (1)

E. Wolf, “Unified theory of coherence and polarization of statistical electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Pure Appl. Opt. (1)

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarisation matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Other (5)

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

I. S. Gradshteyn and I. M. Ryzhik, in Table of Integrals, Series, and Products, 6th ed., A.Jeffrey and D.Zwillinger, eds. (Academic, 2000).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge Univ. Press, 1985).

S. K. Berberian, Introduction to Hilbert Space (Oxford Univ. Press, 1961).

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Figures (2)

Fig. 1
Fig. 1

Normalized irradiance distribution (dashed curve) and polarization degree (full curve) of the field emitted by the source described in Eq. (29).

Fig. 2
Fig. 2

Normalized irradiance distribution (dashed curve) and polarization degree (full curve) of the field emitted by the source described in Eq. (37).

Equations (53)

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J α β ( ρ 1 , ρ 2 , z ) = E α ( ρ 1 , z , t ) E β ( ρ 2 , z , t ) ,
J ̂ ( ρ 1 , ρ 2 , 0 ) = K δ ( ρ 1 a ) δ ( ρ 2 a ) J ̂ a ( φ 1 φ 2 ) ,
J ̂ a ( φ 1 φ 2 ) = n = γ ̂ n e i n ( φ 1 φ 2 ) ,
γ n , α α 0 ,     n     ( α = x , y ) .
Q = g ( φ 1 ) J ̂ a ( φ 1 φ 2 ) g ( φ 2 ) d φ 1 d φ 2 ,
g ( φ ) = n = η n   exp ( i n φ ) ,
n = η n γ ̂ n η n 0 ,
| γ n , x y | 2 γ n , x x γ n , y y ,     n .
γ ̂ n = i = 1 2 σ n ( i ) Φ n ( i ) Φ n ( i ) .
J ̂ a ( φ 1 φ 2 ) = n = + i = 1 2 λ n ( i ) Ψ n ( i ) ( φ 1 ) Ψ n ( i ) ( φ 2 ) ,
λ n ( i ) = 2 π σ n ( i ) ,
Ψ n ( i ) ( φ ) = 1 2 π Φ n ( i ) e i n φ .
Ψ n ( i ) ( φ ) Ψ m ( j ) ( φ ) d φ = δ i j δ n m ,
P ̂ n ( ρ , 0 ) = γ ̂ n ,
p n = | λ n ( 1 ) λ n ( 2 ) | λ n ( 1 ) + λ n ( 2 ) = | σ n ( 1 ) σ n ( 2 ) | σ n ( 1 ) + σ n ( 2 ) ,
μ eq ( φ 12 ) = Tr [ J ̂ a ( φ 12 ) ] Tr [ J ̂ a ( 0 ) ] .
μ em ( φ 12 ) = Tr [ J ̂ a ( φ 12 ) J ̂ a ( φ 12 ) ] Tr [ J ̂ a ( 0 ) ] .
γ ̂ n Φ n = σ n Φ n ,
σ n 2 T n σ n + D n = 0 ,
σ n ( 1 , 2 ) = T n 2 ( 1 ± 1 4 D n T n 2 ) ,
Φ n ( i ) = N n ( i ) [ 1 γ n , x x σ n ( i ) γ n , x y ] ,
N n ( i ) = ( 1 + | γ n , x x σ n ( i ) γ n , x y | 2 ) 1 / 2 .
Φ n ( 1 ) = [ 1 0 ] ,     Φ n ( 2 ) = [ 0 1 ] ,
J ̂ ( r 1 , r 2 , z ) = 1 λ 2 z 2 J ̂ ( ρ 1 , ρ 2 , 0 ) exp { i k 2 z [ ( r 1 ρ 1 ) 2 ( r 2 ρ 2 ) 2 ] } d 2 ρ 1 d 2 ρ 2 ,
J ̂ ( r 1 , r 2 , z ) = K a 2 λ 2 z 2 exp [ i k 2 z ( r 1 2 r 2 2 ) ] J ̂ a ( φ 1 φ 2 ) exp { i k a z [ r 1   cos ( ϑ 1 φ 1 ) r 2   cos ( ϑ 2 φ 2 ) ] } d φ 1 d φ 2 .
J ̂ ( r 1 , r 2 , z ) = i = 1 2 n = + λ n ( i ) Ψ n ( i ) ( ρ 1 , z ) Ψ n ( i ) ( ρ 2 , z ) ,
Ψ n ( i ) ( ρ , z ) = α z K 2 π J n ( α z r ) exp ( i k r 2 2 z ) Φ n ( i ) e i n ϑ     ( i = 1 , 2 ) ,
P ̂ ( r , z ) = K α z 2 n = + γ ̂ n J n 2 ( α z r ) ,
J ̂ a ( φ 12 ) = I 0 2 [ 1 0 0 e i φ 12 ] ,
γ ̂ 0 = I 0 2 [ 1 0 0 0 ] ,     γ ̂ 1 = I 0 2 [ 0 0 0 1 ] ,
P ̂ ( r , z ) = K I 0 α z 2 2 [ J 0 2 ( α z r ) 0 0 J 1 2 ( α z r ) ] ,
p ( r , z ) = | J 0 2 ( α z r ) J 1 2 ( α z r ) | J 0 2 ( α z r ) + J 1 2 ( α z r ) .
J ̂ a ( φ 12 ) = I 0 [ cos   φ 12 i β   sin   φ 12 sin   φ 12 i β   cos   φ 12 sin   φ 12 + i β   cos   φ 12 cos   φ 12 i β   sin   φ 12 ] ,
μ eq ( φ 12 ) = cos   φ 12 i β   sin   φ 12 ,
μ em ( φ 12 ) = 1 + β 2 2 ,
Ψ ± 1 ( φ ) = I 0 4 π [ 1 i ] e ± i φ .
J ̂ a ( φ 12 ) = I 0 [ tri ( φ 12 π ) tri ( φ 12 π 1 ) tri ( φ 12 π + 1 ) tri ( φ 12 π ) ] ,
tri ( t ) = { 1 | t | ( | t | 1 ) 0 ( | t | > 1 ) . }
γ ̂ n = I 0 2 sinc 2 ( n 2 ) [ 1 ( 1 ) n ( 1 ) n 1 ] ,
σ n = I 0 sinc 2 ( n 2 ) ,
Ψ n = 1 4 π [ 1 ( 1 ) n ] e i n φ .
P ̂ ( r , z ) = K I 0 α z 2 2 [ J 0 2 ( α z r ) + F ( α z r ) J 0 2 ( α z r ) F ( α z r ) J 0 2 ( α z r ) F ( α z r ) J 0 2 ( α z r ) + F ( α z r ) ] ,
F ( t ) = 8 π 2 n = 0 J 2 n + 1 2 ( t ) ( 2 n + 1 ) 2 ,
p ( r , z ) = | J 0 2 ( α z r ) F ( α z r ) | J 0 2 ( α z r ) + F ( α z r ) .
η = η ( φ ) .
η ( φ ) = φ .
E in = [ A x A y e i α ] ,
E out ( φ ) = [ cos   φ A x sin   φ A y e i α sin   φ A x + cos   φ A y e i α ] .
J ̂ a ( φ 12 ) = A 2 2 [ cos   φ 12 i ε   sin   α   sin   φ 12 sin   φ 12 i ε   sin   α   cos   φ 12 sin   φ 12 + i ε   sin   α   cos   φ 12 cos   φ 12 i ε   sin   α   sin   φ 12 ] ,
ε = 2 A x A y A 2 .
E x ( φ ) = A   rect ( φ π / 2 π ) ,
E x ( φ ) = A   rect ( φ + π / 2 π ) ,
rect ( t ) = { 1 ( | t | 1 / 2 ) 0 ( | t | > 1 / 2 ) . }

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