Abstract

We established an experimental setup for generating partially coherent beams with different complex degrees of coherence, and we report experimental generation of an elliptical Gaussian Schell-model (GSM) beam and a Laguerre-GSM beam for the first time. It has been demonstrated experimentally that an elliptical GSM beam and a Laguerre-GSM beam produce an elliptical beam spot and a dark hollow beam spot in the focal plane (or in the far field), respectively, which agrees with theoretical predictions. Our results are useful for beam shaping and particle trapping.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Mandel and E. Wolf, eds., Optical Coherence and Quantum Optics (Cambridge, 1995), pp. 428–429.
  2. F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
    [CrossRef]
  3. F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
    [CrossRef]
  4. H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
    [CrossRef]
  5. H. Lajunen and T. Saastamoinen, Opt. Express 21, 190 (2013).
    [CrossRef]
  6. Z. Tong and O. Korotkova, Opt. Lett. 37, 3240 (2012).
    [CrossRef]
  7. Z. Tong and O. Korotkova, J. Opt. Soc. Am. A 29, 2154 (2012).
    [CrossRef]
  8. Z. Mei, Z. Tong, and O. Korotkova, Opt. Express 20, 26458 (2012).
    [CrossRef]
  9. S. Sahin and O. Korotkova, Opt. Lett. 37, 2970 (2012).
    [CrossRef]
  10. O. Korotkova, S. Sahin, and E. Shchepakina, J. Opt. Soc. Am. A 29, 2159 (2012).
    [CrossRef]
  11. Z. Mei and O. Korotkova, Opt. Lett. 38, 91 (2013).
    [CrossRef]
  12. P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
    [CrossRef]
  13. W. Löffler, A. Aiello, and J. P. Woerdman, Phys. Rev. Lett. 109, 213901 (2012).
    [CrossRef]
  14. Y. Cai, X. Lu, and Q. Lin, Opt. Lett. 28, 1084 (2003).
    [CrossRef]

2013

2012

2011

2009

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

2007

2003

1979

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

Aiello, A.

W. Löffler, A. Aiello, and J. P. Woerdman, Phys. Rev. Lett. 109, 213901 (2012).
[CrossRef]

Cai, Y.

De Santis, P.

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

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]

Guattari, G.

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

Korotkova, O.

Lajunen, H.

Lin, Q.

Löffler, W.

W. Löffler, A. Aiello, and J. P. Woerdman, Phys. Rev. Lett. 109, 213901 (2012).
[CrossRef]

Lu, X.

Mei, Z.

Palma, C.

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

Shchepakina, E.

Shirai, T.

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

Tong, Z.

Woerdman, J. P.

W. Löffler, A. Aiello, and J. P. Woerdman, Phys. Rev. Lett. 109, 213901 (2012).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Schematic for generating partially coherent beams with different CDOCs from an incoherent source.

Fig. 2.
Fig. 2.

Experimental setup for generating partially coherent beams with different CDOCs and measuring the CDOC and the focused intensity. LS, He–Ne laser; SLM, spatial light modulator; CA, circular aperture; RGGD, rotating ground-glass disk; L1, L2, L3, thin lenses; GAF, Gaussian amplitude filter; BS1, BS2, beam splitters; CC, coincidence circuit; BPA, beam profile analyzer; D1, D2, single photon detectors; PC1, PC2, personal computers.

Fig. 3.
Fig. 3.

(a) Phase grating for generating the EGB. (b) Phase grating for generating the DHB with n=1.

Fig. 4.
Fig. 4.

Experimental results of (a) the intensity and (b), (c) the square of the modulus of the CDOC of the generated elliptical GSM beam just after the GAF. The solid line denotes the theoretical fit of the experimental results.

Fig. 5.
Fig. 5.

Experimental results of (a) the intensity and (b) the square of the modulus of the CDOC of the generated Laguerre-GSM beam with n=1 just after the GAF. The solid line denotes the theoretical fit of the experimental results.

Fig. 6.
Fig. 6.

Experimental results of the intensities of (a) the generated elliptical GSM beam and (b) the generated Laguerre-GSM beam with n=1 in the focal plane.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

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)].
J0(r1,r2)=exp[(r12+r22)/4σ02]γ[(r1r2)/λf],
γ[(r2r1)/λf]=1λ2f2I(v)exp[i2πv·(r2r1)λf]d2v.
I(v)=exp[2vx2/ωx2+2vy2/ωy2],
J0(r1,r2)=C0exp[r12+r224σ02(x1x2)22δx2(y1y2)22δy2],
I(v)=(v2/ω02)nexp(2v2/ω02),
J0(r1,r2)=C1exp[r12+r224σ02(r1r2)22δ02]Ln0[(r1r2)22δ02],
g(2)(r1,r2,τ)=I(r1,t)I(r2,t+τ)I(r1,t)I(r2,t+τ),
g(2)(r1,r2,0)=1+|γ(r1,r2)|2.
γ(r1,r2)=J0(r1,r2)J0(r1,r1)J0(r2,r2),
If(ρx,ρy)=4σ02C0ωfxωfyexp[2ρx2ωfx22ρy2ωfy2],
I(ρ)=4C1σ04f12nk2n(ωf2σ02)n+1exp(2ρ2ωf2)Ln0(8σ02ρ2δ02ωf2),

Metrics