Abstract

We introduce a new class of partially coherent sources of Schell type with cosine-Gaussian spectral degree of coherence and confirm that such sources are physically genuine. Further, we derive the expression for the cross-spectral density function of a beam generated by the novel source propagating in free space and analyze the evolution of the spectral density and the spectral degree of coherence. It is shown that at sufficiently large distances from the source the degree of coherence of the propagating beam assumes Gaussian shape while the spectral density takes on the dark-hollow profile.

© 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)
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  3. F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
    [CrossRef]
  4. F. Gori, M. Santarsiero, and R. Borghi, Opt. Lett. 33, 1857 (2008).
    [CrossRef]
  5. S. Sahin and O. Korotkova, Opt. Lett. 37, 2970 (2012).
    [CrossRef]
  6. Z. Mei and O. Korotkova, Opt. Lett. 38, 91 (2013).
    [CrossRef]
  7. H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
    [CrossRef]
  8. H. T. Eyyuboğlu and Y. Baykal, Opt. Commun. 278, 17 (2007).
    [CrossRef]
  9. G. Zhou and X. Chu, Opt. Express 17, 10529 (2009).
    [CrossRef]
  10. H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, J. Opt. Soc. Am. A 24, 2891 (2007).
    [CrossRef]
  11. F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
    [CrossRef]
  12. M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, Opt. Commun. 288, 1 (2013).
    [CrossRef]
  13. O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
    [CrossRef]
  14. G. Gbur and T. D. Visser, Opt. Lett. 28, 1627 (2003).
    [CrossRef]

2013 (2)

Z. Mei and O. Korotkova, Opt. Lett. 38, 91 (2013).
[CrossRef]

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, Opt. Commun. 288, 1 (2013).
[CrossRef]

2012 (2)

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
[CrossRef]

S. Sahin and O. Korotkova, Opt. Lett. 37, 2970 (2012).
[CrossRef]

2011 (1)

2009 (1)

2008 (1)

2007 (3)

2003 (1)

1987 (1)

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

1967 (1)

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

Alavinejad, M.

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, Opt. Commun. 288, 1 (2013).
[CrossRef]

Avramov-Zamurovic, S.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
[CrossRef]

Baykal, Y.

Borghi, R.

Cai, Y.

Chu, X.

Eyyuboglu, H. T.

Gbur, G.

Ghafary, B.

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, Opt. Commun. 288, 1 (2013).
[CrossRef]

Gori, F.

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Hadilou, N.

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, Opt. Commun. 288, 1 (2013).
[CrossRef]

Korotkova, O.

Z. Mei and O. Korotkova, Opt. Lett. 38, 91 (2013).
[CrossRef]

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
[CrossRef]

S. Sahin and O. Korotkova, Opt. Lett. 37, 2970 (2012).
[CrossRef]

Lajunen, H.

Malek-Madani, R.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
[CrossRef]

Mandel, L.

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

Mei, Z.

Nelson, C.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

Schell, J. A.

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

Taherabadi, G.

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, Opt. Commun. 288, 1 (2013).
[CrossRef]

Visser, T. D.

Wolf, E.

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

Zhou, G.

IEEE Trans. Antennas Propag. (1)

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

J. Opt. Soc. Am. A (1)

Opt. Commun. (3)

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, Opt. Commun. 288, 1 (2013).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, Opt. Commun. 278, 17 (2007).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Proc. SPIE (1)

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
[CrossRef]

Other (1)

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

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Figures (4)

Fig. 1.
Fig. 1.

Degree of coherence profiles of the CGSM sources calculated from Eq. (8) for several values of n.

Fig. 2.
Fig. 2.

Evolution of the spectral density in the axial direction (left) and the transverse spectral density distribution at the selected propagation distances (right).

Fig. 3.
Fig. 3.

Transverse spectral density distribution of the CGSM beams for different values of parameter n at the plane z=1m.

Fig. 4.
Fig. 4.

Change in the degree of coherence of the CGSM beams versus (ρ2ρ1)/δ, (a) for different values of parameter n on the plane z=1m and (b) for several propagation distances with n=2.

Equations (18)

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f(ρ1)f(ρ2)W0(ρ1,ρ2)d2ρ1d2ρ20.
W0(ρ1,ρ2)=p(v)H0*(ρ1,v)H0(ρ2,v)d2v,
H0(ρ,v)=τ(ρ)exp(iv·ρ),
W0(ρ1,ρ2)=τ*(ρ1)τ(ρ2)p˜(ρ1ρ2),
p(v)=2πδ2cosh(n2πδv)exp(δ2v2+2n2π2),
τ(ρ)=exp(|ρ|24σ2).
W0(ρ1,ρ2)=exp(|ρ1|2+|ρ2|24σ2)μ(ρ2ρ1),
μ(ρ2ρ1)=cos[n2π(ρ2ρ1)δ]exp[|ρ2ρ1|22δ2].
W(ρ1,ρ2,z)=W˜0(f1,f2)exp[i(f1·ρ1+f2·ρ2]×exp[iz(f12f22)/(2k)]d2f1d2f2,
W˜0(f1,f2)=1(2π)4W0(ρ1,ρ2)×exp[i(f1·ρ1+f2·ρ2)d2ρ1d2ρ2.
W˜0(f1,f2)=σ28π2aexp[σ22(f1+f2)2116a(f1f2)2n2π2aδ2]cosh[n2π4aδ(f1f2)],
|W˜(0)(f,f)|0unlessf2k2.
14σ2+1δ22π2λ2.
W(ρ1,ρ2,z)=132aA(z)exp(n2π2aδ2)exp[(ρ1+ρ2)28σ2]{exp[γ+2A(z)]+exp[γ2A(z)]},
A(z)=116a+z28k2σ2,
γ±=i(ρ1ρ2)4z(ρ1+ρ2)8kσ2±n2π8aδ.
S(ρ,z)=W(ρ,ρ,z).
μ(ρ1,ρ2,z)=W(ρ1,ρ2,z)W(ρ1,ρ1,z)W(ρ2,ρ2,z).

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