Abstract

Cosine-Gaussian-correlated Schell-model sources whose degree of coherence (DOC) is of circular symmetry have been introduced just recently [Opt. Lett. 38, 2578 (2013)]. In this Letter, we propose a model for a source whose DOC is the superposition of two 1D cosine-Gaussian-correlated Schell-model sources, i.e., possesses rectangular symmetry. The novel model sources and beams they generate are termed rectangular cosine-Gaussian Schell-model (RCGSM). The RCGSM beam exhibits unique features on propagation, e.g., its intensity in the far field (or in the focal plane) displays a four-beamlet array profile, being qualitatively different from the ring-shaped profile of the CGSM beam whose DOC is of circular symmetry. Furthermore, we have carried out experimental generation of the proposed beam and measured its focusing properties. Our experimental results are consistent with the theoretical predictions.

© 2014 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, eds., Optical Coherence and Quantum Optics (Cambridge, 1995).
  2. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  3. F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
    [CrossRef]
  4. F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
    [CrossRef]
  5. L. Waller, G. Situ, and J. W. Fleisher, Nat. Photonics 6, 474 (2012).
    [CrossRef]
  6. H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
    [CrossRef]
  7. Z. Tong and O. Korotkova, Opt. Lett. 37, 3240 (2012).
    [CrossRef]
  8. Z. Tong and O. Korotkova, J. Opt. Soc. Am. A 29, 2154 (2012).
    [CrossRef]
  9. Y. Gu and G. Gbur, Opt. Lett. 38, 1395 (2013).
    [CrossRef]
  10. S. Sahin and O. Korotkova, Opt. Lett. 37, 2970 (2012).
    [CrossRef]
  11. O. Korotkova, S. Sahin, and E. Shchepakina, J. Opt. Soc. Am. A 29, 2159 (2012).
    [CrossRef]
  12. S. Du, Y. Yuan, C. Liang, and Y. Cai, Opt. Laser Technol. 50, 14 (2013).
    [CrossRef]
  13. Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
    [CrossRef]
  14. Z. Mei and O. Korotkova, Opt. Lett. 38, 2578 (2013).
    [CrossRef]
  15. Z. Mei, E. Schchepakina, and O. Korotkova, Opt. Express 21, 17512 (2013).
    [CrossRef]
  16. Z. Mei and O. Korotkova, Opt. Lett. 38, 91 (2013).
    [CrossRef]
  17. F. Wang, X. Liu, Y. Yuan, and Y. Cai, Opt. Lett. 38, 1814 (2013).
    [CrossRef]
  18. Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).
  19. P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
    [CrossRef]
  20. S. A. Collins, J. Opt. Soc. Am. 60, 1168 (1970).
    [CrossRef]
  21. Q. Lin and Y. Cai, Opt. Lett. 27, 216 (2002).
    [CrossRef]

2014 (1)

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).

2013 (7)

2012 (5)

2011 (1)

2009 (1)

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

2007 (1)

2002 (1)

1979 (1)

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

1970 (1)

Cai, Y.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).

F. Wang, X. Liu, Y. Yuan, and Y. Cai, Opt. Lett. 38, 1814 (2013).
[CrossRef]

S. Du, Y. Yuan, C. Liang, and Y. Cai, Opt. Laser Technol. 50, 14 (2013).
[CrossRef]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

Q. Lin and Y. Cai, Opt. Lett. 27, 216 (2002).
[CrossRef]

Chen, Y.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

Collins, S. A.

De Santis, P.

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Du, S.

S. Du, Y. Yuan, C. Liang, and Y. Cai, Opt. Laser Technol. 50, 14 (2013).
[CrossRef]

Eyyuboglu, H. T.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

Fleisher, J. W.

L. Waller, G. Situ, and J. W. Fleisher, Nat. Photonics 6, 474 (2012).
[CrossRef]

Gbur, G.

Gori, F.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

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

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Gu, Y.

Guattari, G.

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Korotkova, O.

Lajunen, H.

Liang, C.

S. Du, Y. Yuan, C. Liang, and Y. Cai, Opt. Laser Technol. 50, 14 (2013).
[CrossRef]

Lin, Q.

Liu, L.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).

Liu, X.

F. Wang, X. Liu, Y. Yuan, and Y. Cai, Opt. Lett. 38, 1814 (2013).
[CrossRef]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

Mei, Z.

Palma, C.

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Qu, J.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

Saastamoinen, T.

Sahin, S.

Sanchez, V. R.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

Santarsiero, M.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

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

Schchepakina, E.

Shchepakina, E.

Shirai, T.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

Situ, G.

L. Waller, G. Situ, and J. W. Fleisher, Nat. Photonics 6, 474 (2012).
[CrossRef]

Tong, Z.

Waller, L.

L. Waller, G. Situ, and J. W. Fleisher, Nat. Photonics 6, 474 (2012).
[CrossRef]

Wang, F.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).

F. Wang, X. Liu, Y. Yuan, and Y. Cai, Opt. Lett. 38, 1814 (2013).
[CrossRef]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

Wolf, E.

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

Yuan, Y.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

S. Du, Y. Yuan, C. Liang, and Y. Cai, Opt. Laser Technol. 50, 14 (2013).
[CrossRef]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, Opt. Lett. 38, 1814 (2013).
[CrossRef]

Zhao, C.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).

J. Opt. A (1)

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nat. Photonics (1)

L. Waller, G. Situ, and J. W. Fleisher, Nat. Photonics 6, 474 (2012).
[CrossRef]

Opt. Commun. (2)

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

S. Du, Y. Yuan, C. Liang, and Y. Cai, Opt. Laser Technol. 50, 14 (2013).
[CrossRef]

Opt. Lett. (9)

Phys. Rev. A (1)

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).

Other (2)

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

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

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Figures (5)

Fig. 1.
Fig. 1.

Density plot of the square of the modulus of the DOC of the RCGSM beam for different values of the beam order n with δx=δy=0.1mm.

Fig. 2.
Fig. 2.

Experimental setup for generating a RCGSM beam, measuring the square of the modulus of its DOC and its focused intensity. LS, Nd:YAG laser; SLM, spatial light modulator; CA, circular aperture; RGGD, rotating ground-disk; L1, L2, L3, thin lenses; GAF, Gaussian amplitude filter; BS, beam splitter; CCD, charge-coupled device; BPA, beam profile analyzer; PC1, PC2, personal computers.

Fig. 3.
Fig. 3.

Phase gratings for generating cosh-Gaussian beams with (a) n=1 and (b) n=2.

Fig. 4.
Fig. 4.

Experimental results of the square of the modulus of the DOC of the generated RCGSM beam for two values of the beam order n and the corresponding cross line (dotted curve, y1=0). The solid line denotes the theoretical fit of the experimental results.

Fig. 5.
Fig. 5.

Experimental results of the intensity distribution and the corresponding cross line (dotted curve) of the generated RCGSM beam for two values of the beam order n at the source plane and at two propagation distances after passing through the thin lens, L3. The solid line denotes the theoretical results calculated by Eq. (12).

Equations (18)

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J0(r1,r2)=C0exp[r12+r224σ02]γ(r1,r2),
γ(r1,r2)=exp[(r2r1)22δ2]cos[n2π(r2r1)δ].
γ(r1,r2)=γx(x1,x2)γy(y1,y2)=cos[n2π(x2x1)δx]exp[(x2x1)22δx2]×cos[n2π(y2y1)δy]exp[(y2y1)22δy2],
J0(r1,r2)=I(v)H*(r1,v)H(r2,v)d2v,
J0(r1,r2)=Ji(v1,v2)H*(r1,v1)H(r2,v2)d2v1d2v2,
Ji(v1,v2)=I(v1)I(v2)δ(v1v2).
H(r,v)=iλfT(r)exp[iπλf(v22r·v)],
I(v)=cosh(2n2πvx/ωx)cosh(2n2πvy/ωy)×exp(2vx2/ωx22vy2/ωy2),
T(r)=exp(r2/4σ02),
J(ρ1,ρ2)=k24π2B2exp[ik2B(Ar122r1·ρ1+Dρ12)]×J0(r1,r2)exp[ik2B(Ar222r2·ρ2+Dρ22)]d2r1d2r2,
J(ρ1,ρ2)=C0J(ρ1x,ρ2x)J(ρ1y,ρ2y),
J(ρ1α,ρ2α)=1Δαexp[2πn2B22k2δα2σ02Δα2ikρsαρdαRα]×exp[ρsα22σ02Δα2ρdα22Ωα2Δα2]×cosh[2πnBρsαkδασ02Δα2i2πnAρdαδαΔα2],(α=x,y)
ρsα=(ρ1α+ρ2α)/2,ρdα=ρ2αρ1α,Ωα2=(14σ02+1δα2),Δα=A2+(Bkσ0Ωα)2,Rα=BD+ABD2(Bkσ0Ωα)2+ABCD,(α=x,y).
g(2)(r1,r2)=I(r1,t)I(r2,t)I(r1,t)I(r2,t),
g(2)(r1,r2)=1+|γ(r1,r2)|2.
|γ(r1,r2=0)|2=1Mm=1MI(m)(x1,y1)I(m)(0,0)I¯(x1,y1)I¯(0,0)1,
I¯(x1,y1)=m=1MI(m)(x1,y1)/M,I¯(0,0)=m=1MI(m)(0,0)/M.
A=1z/f3,B=f3,C=1/f3,D=0.

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