Abstract

Two classes of scalar, stochastic sources are introduced, each capable of producing far fields with intensities forming rings. Although the Bessel–Gaussian and the Laguerre–Gaussian Schell-model sources are described by two different math models, the behavior of their degrees of coherence and, hence, the shapes of their far fields are qualitatively similar. The new beams are of importance for optical methods of particle manipulation.

© 2013 Optical Society of America

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References

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  1. M. Duocastella and C. B. Arnold, Laser Photon. Rev. 6, 607 (2012).
    [CrossRef]
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).
  3. S. Sahin and O. Korotkova, Opt. Lett. 37, 2970 (2012).
    [CrossRef]
  4. F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
    [CrossRef]
  5. F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
    [CrossRef]
  6. M. A. Bandres and J. C. Gutierres-Vega, Opt. Lett. 33, 177 (2008).
    [CrossRef]
  7. O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
    [CrossRef]

2012 (3)

M. Duocastella and C. B. Arnold, Laser Photon. Rev. 6, 607 (2012).
[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]

2008 (1)

2007 (1)

1987 (1)

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

Arnold, C. B.

M. Duocastella and C. B. Arnold, Laser Photon. Rev. 6, 607 (2012).
[CrossRef]

Avramov-Zamurovic, S.

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

Bandres, M. A.

Duocastella, M.

M. Duocastella and C. B. Arnold, Laser Photon. Rev. 6, 607 (2012).
[CrossRef]

Gori, F.

F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
[CrossRef]

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

Guattari, G.

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

Gutierres-Vega, J. C.

Korotkova, O.

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

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

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, 1995).

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]

Sahin, S.

Santarsiero, M.

Wolf, E.

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

Laser Photon. Rev. (1)

M. Duocastella and C. B. Arnold, Laser Photon. Rev. 6, 607 (2012).
[CrossRef]

Opt. Commun. (1)

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

Opt. Lett. (3)

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, 1995).

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Figures (4)

Fig. 1.
Fig. 1.

Degree of coherence. (a) BGSM and (b) LGSM sources.

Fig. 2.
Fig. 2.

Far-zone spectral density of the BGSM beam for several values of β. (a) β=0. (b) β=2.5. (c) β=20.

Fig. 3.
Fig. 3.

Far-field spectral density of the LGSM beam for several values of n. (a) n=0. (b) n=1. (c) n=30.

Fig. 4.
Fig. 4.

Simulated phase screens for the LC SLM based generation of the sources. Left GSM γφ2=3. Middle BGSM with γφ2=44.44, β=5. Right LGSM, γφ2=44.44, n=6.

Equations (18)

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W(0)(ρ1,ρ2)=p(v)H*(ρ1,v)H(ρ2,v)dv,
H(ρ,v)=τ(ρ)exp(2πiv·ρ),
W(0)(ρ1,ρ2)=τ*(ρ1)τ(ρ2)p˜(ρ1ρ2),
p(v)=(i)np(v)exp(inθ),
W(0)(ρ1,ρ2)=2πexp(in|φ12|)τ*(ρ1)τ(ρ2)×0p(v)Jn[2πv|ρ1ρ2|]vdv,
Q(f)=W(0)(ρ1,ρ2)f*(ρ1)f(ρ2)d2ρ1d2ρ2=2π0p(v)|τ(ρ)f(ρ)d2ρ|2vdv.
p(v)=2πδ2I0(2πβδv)exp(β2/22π2δ2v2),
μ(0)(ρ1ρ2)=J0(β|ρ1ρ2|δ)exp(|ρ1ρ2|22δ2),
W(0)(ρ1,ρ2)=exp(|ρ1|2+|ρ2|24σ2|ρ1ρ2|22δ2)J0(β|ρ1ρ2|δ).
W()(r1,r2)=(2πk)2cosθ1cosθ2W˜(0)(ks1,ks2)×exp[ik(r2r1)]r2r1,
W˜(0)(f1,f2)=1(2π)4W(0)(ρ1,ρ2)×exp[i(f1·ρ1+f2·ρ2)d2ρ1d2ρ2,
W˜(0)(f1,f2)=2σ2(4π)2aI0[β4aδ|f1f2|]exp(β24aδ2)×exp(σ22|f1+f2|2)exp(116a|f1f2|2),
S()(r)=k2σ22ar2cos2θI0[βk2aδs]exp(β24aδ2k24as2).
p(v)=(π2n+1δ2n+22n+1/n!)v2nexp(2π2δ2v2),
μ(0)(ρ1,ρ2)=Ln(|ρ1ρ2|22δ2)exp(|ρ1ρ2|22δ2).
W(0)(ρ1,ρ2)=exp(|ρ1|2+|ρ2|24σ2|ρ1ρ2|22δ2)Ln(|ρ1ρ2|22δ2),
W˜(0)(f1,f2)=σ2(2a1/δ2)n(2π)2(2a)n+1Ln[σ2|f1f2|24aδ2]×exp(σ22|f1+f2|2)exp(116a|f1f2|2),
S()(r)=(kσcosθ)2(2a1/δ2)n(2a)n+1|r|2Ln[k2σ2s2aδ2]exp(k2s24a).

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