Abstract

A procedure for the synthesis of the most general electromagnetic Schell-model light source is proposed. It makes use of the generalized van Cittert–Zernike theorem to produce the electromagnetic source starting from a primary spatially incoherent source, characterized by a suitable position-dependent polarization matrix. By resorting to the spectral decomposition of the polarization matrix, it is shown how such an incoherent source can be synthesized by using a Mach–Zehnder interferometer, with suitable amplitude transmittances placed in its arms, fed by two mutually uncorrelated laser beams. Examples are given for the case of electromagnetic Gaussian Schell-model sources.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. G. Indebetouw, “Synthesis of polychromatic light sources with arbitrary degrees of coherence: some experiments,” J. Mod. Opt. 36, 251-259 (1989).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  26. O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353-364 (2005).
    [CrossRef]
  27. H. Roychowdhury, G. Agrawal, and E. Wolf, “Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber,” J. Opt. Soc. Am. A 23, 940-948 (2006).
    [CrossRef]
  28. 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]
  29. Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young's interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265, 63-72 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  32. 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]
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    [CrossRef]
  35. T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7, 232-237 (2005).
    [CrossRef]
  36. 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]
  37. F. Gori, M. Santarsiero, R. Borghi, and V. Ramìrez-Sànchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016-1021 (2008).
    [CrossRef]
  38. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 41-43 (1998).
    [CrossRef]
  39. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence polarization matrix,” Pure Appl. Opt. 7, 941-951 (1998).
    [CrossRef]
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    [CrossRef]

2008 (2)

2007 (2)

J. X. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E 75, 056610 (2007).
[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]

2006 (6)

Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young's interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265, 63-72 (2006).
[CrossRef]

R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901-183904 (2006).
[CrossRef] [PubMed]

M. Santarsiero and R. Borghi, “Measuring spatial coherence by using a reversed-wavefront Young interferometer,” Opt. Lett. 96, 183901-183904 (2006).

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]

H. Roychowdhury, G. Agrawal, and E. Wolf, “Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber,” J. Opt. Soc. Am. A 23, 940-948 (2006).
[CrossRef]

A. Luis, “Ray picture of polarization and coherence in a Young interferometer,” J. Opt. Soc. Am. A 23, 2855-2860 (2006).
[CrossRef]

2005 (5)

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7, 232-237 (2005).
[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 GSM beams which have the same far-zone intensity distribution as a fully coherent laser beam,” Opt. Commun. 256, 197-209 (2005).
[CrossRef]

H. Roychowdhury and E. Wolf, “Young's interference experiment with light of any state of coherence and polarization,” Opt. Commun. 252, 268-274 (2005).
[CrossRef]

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353-364 (2005).
[CrossRef]

2004 (2)

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. 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]

2003 (1)

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

2002 (1)

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9-16 (2002).
[CrossRef]

2001 (1)

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]

2000 (2)

S. R. Seshadri, “Polarization properties of partially coherent Gaussian Schell-model electromagnetic beams,” J. Appl. Phys. 87, 4084-4093 (2000).
[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]

1999 (1)

1998 (2)

F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 41-43 (1998).
[CrossRef]

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

1994 (2)

1993 (1)

1991 (1)

1989 (1)

G. Indebetouw, “Synthesis of polychromatic light sources with arbitrary degrees of coherence: some experiments,” J. Mod. Opt. 36, 251-259 (1989).
[CrossRef]

1986 (1)

1983 (1)

1982 (1)

R. Grella, “Synthesis of generalized Collett-Wolf sources,” J. Opt. 13, 127-131 (1982).
[CrossRef]

1979 (1)

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett-Wolf source,” Opt. Commun. 29, 256-260 (1979).
[CrossRef]

1978 (1)

1967 (1)

A. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,” IEEE Trans. Antennas Propag. 15, 187-188 (1967).
[CrossRef]

Agrawal, G.

Berberian, S. K.

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

Borghi, R.

F. Gori, M. Santarsiero, R. Borghi, and V. Ramìrez-Sànchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016-1021 (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]

M. Santarsiero and R. Borghi, “Measuring spatial coherence by using a reversed-wavefront Young interferometer,” Opt. Lett. 96, 183901-183904 (2006).

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]

R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901-183904 (2006).
[CrossRef] [PubMed]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9-16 (2002).
[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, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence polarization matrix,” Pure Appl. Opt. 7, 941-951 (1998).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics7th (expanded) ed. (Cambridge U. Press, 1999).

Bulabois, J.

Collett, E.

Courjon, D.

De Santis, P.

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Synthesis of partially coherent fields,” J. Opt. Soc. Am. A 3, 1258-1262 (1986).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett-Wolf source,” Opt. Commun. 29, 256-260 (1979).
[CrossRef]

Deschamps, J.

Dogariu, A.

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353-364 (2005).
[CrossRef]

Du, X. Y.

Friberg, A. T.

Goodman, J. W.

J. W. Goodman, “Synthetic-aperture optics,” in Progress in Optics, Vol. VIII, E.Wolf, ed. (Elsevier, 1970), pp.1-50.
[CrossRef]

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, and V. Ramìrez-Sànchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016-1021 (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]

R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901-183904 (2006).
[CrossRef] [PubMed]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9-16 (2002).
[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, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 41-43 (1998).
[CrossRef]

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

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Synthesis of partially coherent fields,” J. Opt. Soc. Am. A 3, 1258-1262 (1986).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett-Wolf source,” Opt. Commun. 29, 256-260 (1979).
[CrossRef]

Grella, R.

R. Grella, “Synthesis of generalized Collett-Wolf sources,” J. Opt. 13, 127-131 (1982).
[CrossRef]

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, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence polarization matrix,” Pure Appl. Opt. 7, 941-951 (1998).
[CrossRef]

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Synthesis of partially coherent fields,” J. Opt. Soc. Am. A 3, 1258-1262 (1986).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett-Wolf source,” Opt. Commun. 29, 256-260 (1979).
[CrossRef]

Indebetouw, G.

G. Indebetouw, “Synthesis of polychromatic light sources with arbitrary degrees of coherence: some experiments,” J. Mod. Opt. 36, 251-259 (1989).
[CrossRef]

James, D. F. V.

Korotkova, O.

J. X. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E 75, 056610 (2007).
[CrossRef]

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

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353-364 (2005).
[CrossRef]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7, 232-237 (2005).
[CrossRef]

Lee, H.

Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young's interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265, 63-72 (2006).
[CrossRef]

Li, Y.

Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young's interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265, 63-72 (2006).
[CrossRef]

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]

Mondello, A.

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9-16 (2002).
[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]

Mukunda, N.

Palma, C.

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Synthesis of partially coherent fields,” J. Opt. Soc. Am. A 3, 1258-1262 (1986).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett-Wolf source,” Opt. Commun. 29, 256-260 (1979).
[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]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9-16 (2002).
[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]

Pu, J. X.

J. X. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E 75, 056610 (2007).
[CrossRef]

Ramìrez-Sànchez, V.

Romanini, P.

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9-16 (2002).
[CrossRef]

Roychowdhury, H.

H. Roychowdhury, G. Agrawal, and E. Wolf, “Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber,” J. Opt. Soc. Am. A 23, 940-948 (2006).
[CrossRef]

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

H. Roychowdhury and E. Wolf, “Young's interference experiment with light of any state of coherence and polarization,” Opt. Commun. 252, 268-274 (2005).
[CrossRef]

Salem, M.

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353-364 (2005).
[CrossRef]

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, and V. Ramìrez-Sànchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016-1021 (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]

M. Santarsiero and R. Borghi, “Measuring spatial coherence by using a reversed-wavefront Young interferometer,” Opt. Lett. 96, 183901-183904 (2006).

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]

R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901-183904 (2006).
[CrossRef] [PubMed]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9-16 (2002).
[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, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence polarization matrix,” Pure Appl. Opt. 7, 941-951 (1998).
[CrossRef]

Schell, A.

A. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,” IEEE Trans. Antennas Propag. 15, 187-188 (1967).
[CrossRef]

Seshadri, S. R.

S. R. Seshadri, “Polarization properties of partially coherent Gaussian Schell-model electromagnetic beams,” J. Appl. Phys. 87, 4084-4093 (2000).
[CrossRef]

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

Setälä, T.

Shirai, T.

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

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7, 232-237 (2005).
[CrossRef]

Simon, R.

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. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 10, 95-109 (1993).
[CrossRef]

Tervo, J.

Tervonen, E.

Turunen, J.

Vasara, A.

Vicalvi, S.

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

Wolf, E.

J. X. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E 75, 056610 (2007).
[CrossRef]

H. Roychowdhury, G. Agrawal, and E. Wolf, “Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber,” J. Opt. Soc. Am. A 23, 940-948 (2006).
[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]

Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young's interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265, 63-72 (2006).
[CrossRef]

H. Roychowdhury and E. Wolf, “Young's interference experiment with light of any state of coherence and polarization,” Opt. Commun. 252, 268-274 (2005).
[CrossRef]

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353-364 (2005).
[CrossRef]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7, 232-237 (2005).
[CrossRef]

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

E. Collett and E. Wolf, “Is complete spatial coherence necessary for the generation of highly directional light beams?” Opt. Lett. 2, 27-29 (1978).
[CrossRef] [PubMed]

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

M. Born and E. Wolf, Principles of Optics7th (expanded) ed. (Cambridge U. Press, 1999).

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

Zhao, D. M.

Zhu, Y. B.

IEEE Trans. Antennas Propag. (1)

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[CrossRef]

J. Appl. Phys. (1)

S. R. Seshadri, “Polarization properties of partially coherent Gaussian Schell-model electromagnetic beams,” J. Appl. Phys. 87, 4084-4093 (2000).
[CrossRef]

J. Mod. Opt. (1)

G. Indebetouw, “Synthesis of polychromatic light sources with arbitrary degrees of coherence: some experiments,” J. Mod. Opt. 36, 251-259 (1989).
[CrossRef]

J. Opt. (1)

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[CrossRef]

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

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, 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]

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]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7, 232-237 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (10)

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]

A. T. Friberg, E. Tervonen, and J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 11, 1818-1826 (1994).
[CrossRef]

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

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Synthesis of partially coherent fields,” J. Opt. Soc. Am. A 3, 1258-1262 (1986).
[CrossRef]

J. Turunen, A. Vasara, and A. T. Friberg, “Propagation invariance and self-imaging in variable-coherence optics,” J. Opt. Soc. Am. A 8, 282-289 (1991).
[CrossRef]

R. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 10, 95-109 (1993).
[CrossRef]

H. Roychowdhury, G. Agrawal, and E. Wolf, “Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber,” J. Opt. Soc. Am. A 23, 940-948 (2006).
[CrossRef]

A. Luis, “Ray picture of polarization and coherence in a Young interferometer,” J. Opt. Soc. Am. A 23, 2855-2860 (2006).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and V. Ramìrez-Sànchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016-1021 (2008).
[CrossRef]

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]

Opt. Commun. (6)

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

Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young's interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265, 63-72 (2006).
[CrossRef]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9-16 (2002).
[CrossRef]

H. Roychowdhury and E. Wolf, “Young's interference experiment with light of any state of coherence and polarization,” Opt. Commun. 252, 268-274 (2005).
[CrossRef]

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

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett-Wolf source,” Opt. Commun. 29, 256-260 (1979).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

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. E (1)

J. X. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E 75, 056610 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901-183904 (2006).
[CrossRef] [PubMed]

Pure Appl. Opt. (1)

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

Waves Random Complex Media (1)

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353-364 (2005).
[CrossRef]

Other (5)

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

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

M. Born and E. Wolf, Principles of Optics7th (expanded) ed. (Cambridge U. Press, 1999).

J. W. Goodman, “Synthetic-aperture optics,” in Progress in Optics, Vol. VIII, E.Wolf, ed. (Elsevier, 1970), pp.1-50.
[CrossRef]

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

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Figures (3)

Fig. 1
Fig. 1

Fourier transforming optical system for the synthesis of electromagnetic Schell-model sources.

Fig. 2
Fig. 2

A MZI fed by two independent laser beams: l + (a) and l (b).

Fig. 3
Fig. 3

Transmission functions (solid curves, η l and τ + ; dashed curves, η u and τ ) to be used in the synthesis procedure for three different choices of the source parameters: (a) I x x = 1 , I y y = 0.8 , I x y = 0.4 , δ x x = 0.2 , δ y y = 0.1 , δ x y = 0.2 ; (b) I x x = 1 , I y y = 0.8 , I x y = 0 , δ x x = 0.2 , δ y y = 0.1 , δ x y = 0.2 ; (c) I x x = 1 , I y y = 1 , I x y = 0.1 , δ x x = 0.1 , δ y y = 0.1 , δ x y = 0.3 .

Equations (25)

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J α β ( r 1 , r 2 ) = E α ( r 1 , t ) E β * ( r 2 , t ) ; ( α , β = x , y ) ,
J α β ( r 1 , r 2 ) = s α ( r 1 ) s β ( r 2 ) j α β ( r 1 r 2 ) .
s α ( r ) = J α α ( r , r ) ,
j ̃ α α ( ν ) 0 ( α = x , y )
j y x ( r 1 r 2 ) = j x y * ( r 2 r 1 ) ,
j ̃ y x ( ν ) = j ̃ x y * ( ν ) .
j ̃ y x ( ν ) j ̃ x x ( ν ) j ̃ y y ( ν )
H α ( r ; u ) = t α ( r ) exp ( i 2 π λ f r u ) ,
J α β ( r 1 , r 2 ) = P α β ( u ) H α ( r 1 , u ) H β * ( r 2 , u ) d 2 u ,
P α β ( u ) = 1 λ 2 f 2 j ̃ α β ( u λ f ) ,
t α ( r ) = s α ( r ) .
P x x ( u ) P y y ( u ) P x y ( u ) 2
j ̃ x x ( u λ f ) j ̃ y y ( u λ f ) j ̃ x y ( u λ f ) 2 ,
P ̂ = μ + U + U + + μ U U .
μ ± = 1 2 [ ( P x x + P y y ) ± ( P x x P y y ) 2 + 4 P x y 2 ] ,
U + = 1 1 + η 2 [ η e i ϕ 1 ] ,
U = 1 1 + η 2 [ e i ϕ η ] ,
η = ( P x x P y y ) + ( P x x P y y ) 2 + 4 P x y 2 2 P x y ,
J α β ( r 1 , r 2 ) = I α β exp ( r 1 2 4 σ α 2 ) exp ( r 2 2 4 σ β 2 ) exp [ ( r 2 r 1 ) 2 2 δ α β 2 ] ,
I x x I y y δ x x 2 δ y y 2 exp [ 2 π 2 ( δ x x 2 + δ y y 2 ) λ 2 f 2 u 2 ] I x y 2 δ x y 4 exp ( 4 π 2 δ x y 2 λ 2 f 2 u 2 ) ,
δ x x 2 + δ y y 2 2 δ x y 2 δ x x δ y y I x x I y y I x y .
P α β ( u ) = 2 π I α β δ α β 2 λ 2 f 2 exp ( 2 π 2 δ α β 2 λ 2 f 2 u 2 ) ,
t α ( r ) = exp ( r 2 4 σ α 2 ) .
η = 1 ,
μ ± = P x x ± P x y ,

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