Abstract

Planar, scalar, optical Schell-model, and quasi-homogeneous sources with correlations that are Fourier transforms of multi-Gaussian functions are introduced. It is demonstrated that far fields produced by these families of sources carry interesting characteristics, being flatlike with adjustable steepness of the edge. Beam conditions for such sources are also derived.

© 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. A. C. Schell, “The multiple plate antenna,” doctoral dissertation (MIT, 1961), Subsection 7.5.
  3. F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
    [CrossRef]
  4. S. A. Ponomarenko, J. Opt. Soc. Am. A 18, 150 (2001).
    [CrossRef]
  5. H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
    [CrossRef]
  6. F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
    [CrossRef]
  7. R. Martinez-Herrero, P. M. Mejias, and F. Gori, Opt. Lett. 34, 1399 (2009).
    [CrossRef]
  8. F. Gori, Opt. Commun. 107, 335 (1994).
    [CrossRef]
  9. S. Sahin, G. Gbur, and O. Korotkova, Opt. Lett. 36, 3957 (2011).
    [CrossRef]

2011 (2)

2009 (1)

2007 (1)

2001 (1)

1994 (1)

F. Gori, Opt. Commun. 107, 335 (1994).
[CrossRef]

1987 (1)

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

Gbur, G.

Gori, F.

Guattari, G.

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

Korotkova, O.

Lajunen, H.

Mandel, L.

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

Martinez-Herrero, R.

Mejias, P. M.

Padovani, C.

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

Ponomarenko, S. A.

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

Schell, A. C.

A. C. Schell, “The multiple plate antenna,” doctoral dissertation (MIT, 1961), Subsection 7.5.

Wolf, E.

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

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

Opt. Commun. (2)

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

F. Gori, Opt. Commun. 107, 335 (1994).
[CrossRef]

Opt. Lett. (4)

Other (2)

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

A. C. Schell, “The multiple plate antenna,” doctoral dissertation (MIT, 1961), Subsection 7.5.

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Figures (3)

Fig. 1.
Fig. 1.

Illustration of the degree of coherence calculated from Eq. (1) as a function of the nondimensional parameter |ρ2ρ1|/δ for several values of M: M=1 (solid curve); M=4 (dashed curve); M=10 (dotted curve), and M=40 (dotted–dashed curve).

Fig. 2.
Fig. 2.

Illustration of the function p calculated from Eq. (6) as a function of nondimensional parameter δ|υ| for the same values of M as in Fig. 1.

Fig. 3.
Fig. 3.

Far-field spectral density generated by a typical multi-Gaussian Schell-model source, calculated from Eq. (15), as a function of angle θ (in radians), for the same four values of M as in Fig. 1 and λ=632nm, σ=1mm, δ=0.1mm.

Equations (21)

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μ(ρ1,ρ2;ω)=1C0m=1M(Mm)(1)m1mexp[|ρ2ρ1|22mδ2],
W(0)(ρ1,ρ2)=S(ρ1)S(ρ2)μ(ρ2ρ1),
W(0)(ρ1,ρ2)=p(υ)H*(ρ1,υ)H(ρ2,υ)d2υ,
H(ρ,υ)=τ(ρ)exp[iυ·ρ],
W(0)(ρ1,ρ2)=τ*(ρ1)τ(ρ2)p˜[(ρ1ρ2)],
p(υ)=δ2C0m=1M(1)m1(Mm)exp[mδ2|υ|22],
p(υ)=δ2C0m=1M(Mm)(x)m=δ2C0[1(1x)M],
τ(ρ)=exp[|ρ|2/(4σ2)].
W(0)(ρ1,ρ2)=1C0exp[|ρ1|2+|ρ2|24σ2]×m=1M(1)m1m(Mm)exp[|ρ2ρ1|22mδ2],
W()(r1s1,r2s2)=(2πk)2cosθ1cosθ2×W˜(0)(ks1,ks2)exp[ik(r2r1)]r1r2,
W˜(0)(f1,f2)=1(2π)4W(0)(ρ1,ρ2)×exp[i(f1·ρ1+f2·ρ2)]d2ρ1d2ρ2
W()(r1,r2)=1C0k2cosθ1cosθ2exp[ik(r2r1)]r1r2×m=1M(1)m1m(Mm)1(am2bm2)×exp[k2(αms12+αms222βms1·s2)],
am=12(12σ2+1mδ2),bm=12mδ2,
αm=am4(am2bm2),βm=bm4(am2bm2).
S()(r)=k2cos2θC0|r|2×m=1M(1)m1m(Mm)exp[2k2s2(αmβm)](am2bm2).
exp[2k2s2θ2(αmβm)]0
2k2(αmβm)1,
14σ2+1m1δ22π2λ2,m=1,,M.
14σ2+1δ22π2λ2.
W(0)(ρ1,ρ2)S(ρ1+ρ22)μ(ρ1ρ2)S(ρ1+ρ22)p˜[ρ1ρ2],
S()(r)=1|r|2(2πk)2cos2θF˜(0)μ˜(ks).

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