Abstract

A generalization of the classic Gaussian Schell-model source is considered for which the rms width of the beam σ and the rms width of the spectral degree of coherence δ are assumed to depend on wavelength. It is shown that the functional form σ(λ) and δ(λ) of such a source can affect the behavior of the spectral density, the degree of coherence, and the degree of polarization of the propagating beam.

© 2013 Optical Society of America

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References

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  1. J. A. Schell, IEEE Trans. Antennas Propag. 15, 187 (1967).
    [CrossRef]
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).
  3. R. Simon and N. Mukunda, J. Opt. Soc. Am. A 10, 95 (1993).
    [CrossRef]
  4. Y. Li and E. Wolf, Opt. Lett. 7, 256 (1982).
    [CrossRef]
  5. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
    [CrossRef]
  6. O. Korotkova and E. Shchepakina, Opt. Lett. 35, 3772 (2010).
    [CrossRef]
  7. S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
    [CrossRef]
  8. E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge University, 2007).
  9. H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
    [CrossRef]
  10. H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
    [CrossRef]
  11. Z. Tong and O. Korotkova, J. Opt. Soc. Am. A 29, 2154 (2012).
    [CrossRef]

2012

2011

2010

2009

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

2005

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

2001

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

1993

1982

1967

J. A. Schell, IEEE Trans. Antennas Propag. 15, 187 (1967).
[CrossRef]

Borghi, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Gori, F.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Korotkova, O.

Z. Tong and O. Korotkova, J. Opt. Soc. Am. A 29, 2154 (2012).
[CrossRef]

O. Korotkova and E. Shchepakina, Opt. Lett. 35, 3772 (2010).
[CrossRef]

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Lajunen, H.

Li, Y.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).

Mondello, A.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Mukunda, N.

Piquero, G.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Pu, J.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Saastamoinen, T.

Sahin, S.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

Santarsiero, M.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Schell, J. A.

J. A. Schell, IEEE Trans. Antennas Propag. 15, 187 (1967).
[CrossRef]

Shchepakina, E.

Simon, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

R. Simon and N. Mukunda, J. Opt. Soc. Am. A 10, 95 (1993).
[CrossRef]

Tong, Z.

Wolf, E.

Y. Li and E. Wolf, Opt. Lett. 7, 256 (1982).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).

E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge University, 2007).

Zhang, G.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

IEEE Trans. Antennas Propag.

J. A. Schell, IEEE Trans. Antennas Propag. 15, 187 (1967).
[CrossRef]

J. Opt. A

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Opt. Lett.

Other

E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge University, 2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).

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Figures (4)

Fig. 1.
Fig. 1.

Normalized spectral density SN=S(ρ,100;λ)/S(0,100;λ) versus ρ[m] on propagation in free space at z=100m: (a) λσ=0.5μm and λδ=0.4μm (solid curve), 0.45 μm (dashed curve), 0.5 μm (dotted curve); (b) λδ=0.5μm and λσ=0.4μm (solid curve), 0.45 μm (dashed curve), 0.5 μm (dotted curve).

Fig. 2.
Fig. 2.

Transverse degree of coherence [Eq. (8)] versus ρ[m]; λδ=0.5μm and λσ=0.4μm (solid curve), 0.45 μm (dashed curve), 0.5 μm (dotted curve).

Fig. 3.
Fig. 3.

Absolute value of the longitudinal spectral degree of coherence [Eq. (9)] as a function of (a) Δz=z2z1 and (b) z1; λδ=0.5μm and λσ=0.4μm (solid curve), 0.45 μm (dashed curve), 0.5 μm (dotted curve).

Fig. 4.
Fig. 4.

Degree of polarization [Eq. (13)] versus z[m]:λδ=0.4μm (solid curve), 0.45 μm (dashed curve), and 0.5 μm (dotted curve).

Equations (17)

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W(ρ1,0,ρ20;λ)=I(λ)exp[ρ12+ρ224σ2(λ)]exp[(ρ1ρ2)22δ2(λ)],
I(λ)=I0exp[(λλI)22ΛI2],σ(λ)=σ0exp[(λλσ)22Λσ2],δ(λ)=δ0exp[(λλδ)22Λδ2],
(2σ0)2exp[(λλσ)2Λσ2]+δ02exp[(λλδ)2Λδ2]2π2λ2.
W(ρ1,z1,ρ2,z2;λ)=I(λ)Δ2(z1,z2;λ)exp[(ρ1ρ2)22Δ2(z1,z2;λ)(14σ2(λ)+1δ2(λ))]×exp[(ρ1+ρ2)28σ2(λ)Δ2(z1,z2;λ)]exp[iπ(ρ12ρ22)λR(z1,z2;λ)]×exp[iλ(ρ1+ρ2)216Δ2(z1,z2;λ)(z2z1)πσ2(λ)(14σ2(λ)+1δ2(λ))],
Δ2(z1,z2;λ)=1+λ2z1z24π2σ2(λ)(14σ2(λ)+1δ2(λ))+iλz2z12π(12σ2(λ)+1δ2(λ)),
R(z1,z2;λ)=z1z2[1+4π2λ2z1z2(14σ2(λ)+1δ2(λ))1],
S(ρ,z;λ)=I(λ)Δ2(z,z;λ)exp[ρ22σ2(λ)Δ2(z,z;λ)],
μT(ρ/2,z,ρ/2,z;λ)=exp[ρ28σ2(λ)Δ2(z,z;λ)]×exp[ρ22Δ2(z,z;λ)(14σ2(λ)+1δ2(λ))],
μL(0,z1,0,z2;λ)=Δ2(z1,z1;λ)Δ2(z2,z2;λ)Δ2(z1,z2;λ).
Wij(ρ1,0,ρ2,0;λ)=Ii(λ)Ij(λ)Bij(λ)exp[ρ124σi2(λ)]exp[ρ224σj2(λ)]exp[(ρ1ρ2)22δij2(λ)],
max{δxx(λ),δyy(λ)}δxy(λ)min{δxx(λ)|Bxy(λ)|,δyy(λ)|Bxy(λ)|},
P(ρ,z;λ)=14DetW(ρ,z,ρ,z;λ)Tr2W(ρ,z,ρ,z;λ),
Wii(ρ1,0,ρ2,0;λ)=I(λ)exp[ρ12+ρ224σ2(λ)]×exp[(ρ1ρ2)22δii2(λ)],(i=x,y).
Wii(ρ,z,ρ,z;λ)=I(λ)Δii2(z,z;λ)exp[ρ22σ2(λ)Δii2(z,z;λ)].
P(0,z;λ)=|Δyy2(z,z;λ)Δxx2(z,z;λ)|Δxx2(z,z;λ)+Δyy2(z,z;λ),
Δii2(z,z;λ)=1+λ2z24π2σ2(λ)(14σ2(λ)+1δii2(λ)).
δii(λ)=δ0iiexp[(λλδii)22Λδii2],(i=x,y),

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