Abstract

A class of electromagnetic sources with nonuniformly distributed field correlations is introduced. The conditions on source parameters guaranteeing that the source generates a physical beam are derived. It is shown that the new sources are capable of producing beams with polarization properties that evolve on propagation in a manner much more complex compared to the well-known electromagnetic Gaussian Schell-model beams.

© 2012 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37, 2970–2972 (2012).
    [CrossRef]
  3. F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316(1987).
    [CrossRef]
  4. S. A. Ponomarenko, “A class of partially coherent beams carrying optical vortices,” J. Opt. Soc. Am. A 18, 150–156 (2001).
    [CrossRef]
  5. H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36, 4104–4106 (2011).
    [CrossRef]
  6. 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]
  7. H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (2005).
    [CrossRef]
  8. G. Wu, Q. Lou, J. Zhou, H. Guo, H. Zhao, and Z. Yuan, “Beam conditions for radiation by an electromagnetic J0-correlated Schell-model source,” Opt. Lett. 33, 2677–2679 (2008).
    [CrossRef]
  9. F. Gori, M. Santarsiero, R. Borghi, and V. R. Sanchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016–1021 (2008).
    [CrossRef]
  10. F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A Pure Appl. Opt. 11, 085706 (2009).
    [CrossRef]
  11. Z. Tong and O. Korotkova, “Non-uniformly correlated beams in uniformly correlated random media,” Opt. Lett. 37, 3240–3242 (2012).
    [CrossRef]
  12. O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
    [CrossRef]

2012 (2)

2011 (1)

2009 (1)

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A Pure Appl. Opt. 11, 085706 (2009).
[CrossRef]

2008 (2)

2005 (2)

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

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
[CrossRef]

2001 (2)

S. A. Ponomarenko, “A class of partially coherent beams carrying optical vortices,” J. Opt. Soc. Am. A 18, 150–156 (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]

1987 (1)

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

Borghi, R.

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

Gori, F.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A Pure Appl. Opt. 11, 085706 (2009).
[CrossRef]

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

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

Guattari, G.

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

Guo, H.

Korotkova, O.

Z. Tong and O. Korotkova, “Non-uniformly correlated beams in uniformly correlated random media,” Opt. Lett. 37, 3240–3242 (2012).
[CrossRef]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37, 2970–2972 (2012).
[CrossRef]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
[CrossRef]

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

Lajunen, H.

Lou, Q.

Mandel, L.

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

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]

Padovani, C.

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

Piquero, G.

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]

Ponomarenko, S. A.

Roychowdhury, H.

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

Saastamoinen, T.

Sahin, S.

Sanchez, V. R.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A Pure Appl. Opt. 11, 085706 (2009).
[CrossRef]

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

Santarsiero, M.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A Pure Appl. Opt. 11, 085706 (2009).
[CrossRef]

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

Shirai, T.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A Pure Appl. Opt. 11, 085706 (2009).
[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]

Tong, Z.

Wolf, E.

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
[CrossRef]

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

Wu, G.

Yuan, Z.

Zhao, H.

Zhou, J.

J. Opt. A Pure Appl. Opt. (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]

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A Pure Appl. Opt. 11, 085706 (2009).
[CrossRef]

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

Opt. Commun. (3)

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

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

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
[CrossRef]

Opt. Lett. (4)

Other (1)

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

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Figures (6)

Fig. 1.
Fig. 1.

Shift of the intensity center of the beam on propagation.

Fig. 2.
Fig. 2.

Spectral degree of polarization at the intensity center of the beam on propagation with Bxy=0.

Fig. 3.
Fig. 3.

Spectral degree of polarization along the z axis on propagation with Bxy=0.

Fig. 4.
Fig. 4.

Spectral degree of polarization at the intensity center of the beam on propagation with Bxy=0.2 and δxy=0.9σ0.

Fig. 5.
Fig. 5.

Spectral degree of polarization at the intensity center of the beam on propagation with Bxy=0.2 and x1=0.6σ0.

Fig. 6.
Fig. 6.

Distribution of the degree of polarization of the beam in transverse planes: (A) z=0m, (B) z=1m, (C) z=15m, (D) z=30m, (E) z=80m, and (F) z=100m.

Equations (19)

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W(0)(ρ1,ρ2;ω)=E(ρ1;ω)E(ρ2;ω),
Wαβ(0)(ρ1,ρ2)=pαβ(υ)Hα*(ρ1,υ)Hβ(ρ2,υ)dυ,(α,β=x,y),
pαβ(υ)=Bαβkδαβ22πexp[14k2δαβ4υ2],
Hα(ρ,υ)=Aαexp[ρ22σ02]exp[ik(ργα)2υ],Hβ(ρ,υ)=Aβexp[ρ22σ02]exp[ik(ργβ)2υ].
Wαβ(0)(ρ1,ρ2)=AαAβBαβexp[ρ12+ρ222σ02]×exp{[(ρ1γα)2(ρ2γβ)2]2δαβ4}.
Bxx=Byy=1,|Bxy|=|Byx|,ϕxy=ϕyx,andδxy=δyx.
pxx(υ)0,pyy(υ)0,andpxx(υ)pyy(υ)pxy(υ)pyx(υ)0
δxx2δyy2exp[k2υ24(δxx4+δyy4)]|Bxy|2δxy4exp[k2δxy4υ22].
δxx2δyy2|Bxy|2δxy4,
δxx4+δyy42δxy4.
δxx4+δyy424δxyδxxδyy|Bxy|.
S(0)(ρ)=TrW(0)(ρ,ρ)=(Ax2+Ay2)exp[ρ2σ02],
P(0)(ρ)=14DetW(0)(ρ,ρ)[TrW(0)(ρ,ρ)]2=(Ax2Ay2)2+4Ax2Ay2|Bxy|2μxy(0)2(ρ)Ax2+Ay2,
μxy(0)(ρ)=exp{[(ργx)2(ργy)2]2δxy4}.
Wαβ(r1,r2)=k24π2z2Wαβ(0)(ρ1,ρ2)×exp[ik(ρ1ρ1)2(ρ2ρ2)22z]d2ρ1d2ρ2.
Wαβ(r1,r2)=k24π2z2pαβ(υ)Hα*(ρ1,υ,z)Hβ(ρ2,υ,z)dυ,
Hα(ρ1,υ,z)=Hα(ρ1,υ)exp[ik2z(ρρ)2]d2ρ.
Hα*(ρ,υ,z)Hβ(ρ,υ,z)=AαAβ4π2z2k2σ02w2(z,υ)×exp[ik(γα2γβ2)υ]exp[k2σ02(γαγβ)2υ2]×exp{[ρυz(γα+γβ)+ikσ02υ(12υz)(γαγβ)]2w2(z,υ)},
w2(z,υ)=z2k2σ02+σ02(12υz)2

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