Abstract

We carry out an experimental study of the effect of spatial coherence on the beam wander and the deformation of a Gaussian Schell-model (GSM) beam propagating through thermally induced turbulence. It is demonstrated that a GSM beam with lower coherence indeed experiences smaller beam wander and deformation than that with higher coherence. Our experimental results are explained by the beam wander theory of partially coherent beam reasonably, and will be useful in free-space optical communications.

© 2014 Optical Society of America

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References

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  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.
  2. L. C. Andrews and R. L. Phillips, Laser Beam Propagation in the Turbulent Atmosphere (SPIE, 2005).
  3. A. I. Kon and V. I. Tatarskii, Radiophys. Quantum Electron. 15, 1187 (1972).
    [CrossRef]
  4. V. A. Banakh, V. M. Buldakov, and V. L. Mironov, Opt. Spektrosk. 54, 1054 (1983).
  5. V. A. Banakh and V. M. Buldakov, Opt. Spektrosk. 55, 707 (1983).
  6. V. A. Banakh and A. V. Falits, Atmos. Oceanic Opt. 26, 455 (2013).
    [CrossRef]
  7. J. C. Ricklin and F. M. Davidson, J. Opt. Soc. Am. A 19, 1794 (2002).
    [CrossRef]
  8. Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
    [CrossRef]
  9. F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, Opt. Lett. 37, 184 (2012).
    [CrossRef]
  10. O. Koorotkova, Opt. Commun. 281, 2342 (2008).
    [CrossRef]
  11. F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, Appl. Phys. Lett. 103, 091102 (2013).
    [CrossRef]
  12. F. Wang and Y. Cai, Opt. Express 18, 24661 (2010).
    [CrossRef]
  13. Y. Gu, O. Koorotkova, and G. Gbur, Opt. Lett. 34, 2261 (2009).
    [CrossRef]
  14. Y. Gu and G. Gbur, Opt. Lett. 35, 3456 (2010).
    [CrossRef]
  15. Y. Gu and G. Gbur, Opt. Lett. 37, 1553 (2012).
    [CrossRef]
  16. Y. Gu and G. Gbur, Opt. Lett. 38, 1395 (2013).
    [CrossRef]
  17. X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, Opt. Lett. 38, 5323 (2013).
    [CrossRef]
  18. J. Recolons, L. C. Andrews, and R. L. Phillips, Opt. Eng. 46, 086002 (2007).
    [CrossRef]
  19. H. T. Eyyuboğlu and C. Z. Çil, Appl. Phys. B 93, 595 (2008).
    [CrossRef]
  20. S. Yu, Z. Chen, T. Wang, G. Wu, H. Guo, and W. Gu, Appl. Opt. 51, 7581 (2012).
    [CrossRef]
  21. X. Xiao and D. G. Voelz, Opt. Eng. 51, 026001 (2012).
    [CrossRef]
  22. G. P. Berman, A. A. Chumak, and V. N. Gorshkov, Phys. Rev. E 76, 056606 (2007).
    [CrossRef]
  23. D. G. Pérez and G. Funes, Opt. Express 20, 27766 (2012).
    [CrossRef]
  24. W. Wen and X. Chu, J. Opt. Soc. Am. A 31, 685 (2014).
    [CrossRef]
  25. C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, Appl. Phys. B 95, 763 (2009).
    [CrossRef]
  26. P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
    [CrossRef]
  27. F. Wang and Y. Cai, J. Opt. Soc. Am. A 24, 1937 (2007).
    [CrossRef]
  28. L. Mandel and E. Wolf, eds., Optical Coherence and Quantum Optics (Cambridge University, 1995).
  29. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
    [CrossRef]

2014

2013

V. A. Banakh and A. V. Falits, Atmos. Oceanic Opt. 26, 455 (2013).
[CrossRef]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

Y. Gu and G. Gbur, Opt. Lett. 38, 1395 (2013).
[CrossRef]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, Opt. Lett. 38, 5323 (2013).
[CrossRef]

2012

2010

2009

Y. Gu, O. Koorotkova, and G. Gbur, Opt. Lett. 34, 2261 (2009).
[CrossRef]

C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, Appl. Phys. B 95, 763 (2009).
[CrossRef]

2008

H. T. Eyyuboğlu and C. Z. Çil, Appl. Phys. B 93, 595 (2008).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef]

O. Koorotkova, Opt. Commun. 281, 2342 (2008).
[CrossRef]

2007

G. P. Berman, A. A. Chumak, and V. N. Gorshkov, Phys. Rev. E 76, 056606 (2007).
[CrossRef]

J. Recolons, L. C. Andrews, and R. L. Phillips, Opt. Eng. 46, 086002 (2007).
[CrossRef]

F. Wang and Y. Cai, J. Opt. Soc. Am. A 24, 1937 (2007).
[CrossRef]

2006

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

2002

1983

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, Opt. Spektrosk. 54, 1054 (1983).

V. A. Banakh and V. M. Buldakov, Opt. Spektrosk. 55, 707 (1983).

1979

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

1972

A. I. Kon and V. I. Tatarskii, Radiophys. Quantum Electron. 15, 1187 (1972).
[CrossRef]

Andrews, L. C.

J. Recolons, L. C. Andrews, and R. L. Phillips, Opt. Eng. 46, 086002 (2007).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation in the Turbulent Atmosphere (SPIE, 2005).

Banakh, V. A.

V. A. Banakh and A. V. Falits, Atmos. Oceanic Opt. 26, 455 (2013).
[CrossRef]

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, Opt. Spektrosk. 54, 1054 (1983).

V. A. Banakh and V. M. Buldakov, Opt. Spektrosk. 55, 707 (1983).

Baykal, Y.

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, Opt. Lett. 37, 184 (2012).
[CrossRef]

C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, Appl. Phys. B 95, 763 (2009).
[CrossRef]

Berman, G. P.

G. P. Berman, A. A. Chumak, and V. N. Gorshkov, Phys. Rev. E 76, 056606 (2007).
[CrossRef]

Broky, J.

Buldakov, V. M.

V. A. Banakh and V. M. Buldakov, Opt. Spektrosk. 55, 707 (1983).

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, Opt. Spektrosk. 54, 1054 (1983).

Cai, Y.

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, Opt. Lett. 38, 5323 (2013).
[CrossRef]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, Opt. Lett. 37, 184 (2012).
[CrossRef]

F. Wang and Y. Cai, Opt. Express 18, 24661 (2010).
[CrossRef]

C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, Appl. Phys. B 95, 763 (2009).
[CrossRef]

F. Wang and Y. Cai, J. Opt. Soc. Am. A 24, 1937 (2007).
[CrossRef]

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

Chen, Z.

Christodoulides, D. N.

Chu, X.

Chumak, A. A.

G. P. Berman, A. A. Chumak, and V. N. Gorshkov, Phys. Rev. E 76, 056606 (2007).
[CrossRef]

Çil, C. Z.

C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, Appl. Phys. B 95, 763 (2009).
[CrossRef]

H. T. Eyyuboğlu and C. Z. Çil, Appl. Phys. B 93, 595 (2008).
[CrossRef]

Davidson, F. M.

De Santis, P.

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

Dogariu, A.

Eyyuboglu, H. T.

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, Opt. Lett. 37, 184 (2012).
[CrossRef]

C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, Appl. Phys. B 95, 763 (2009).
[CrossRef]

H. T. Eyyuboğlu and C. Z. Çil, Appl. Phys. B 93, 595 (2008).
[CrossRef]

Falits, A. V.

V. A. Banakh and A. V. Falits, Atmos. Oceanic Opt. 26, 455 (2013).
[CrossRef]

Funes, G.

Gbur, G.

Gori, F.

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

Gorshkov, V. N.

G. P. Berman, A. A. Chumak, and V. N. Gorshkov, Phys. Rev. E 76, 056606 (2007).
[CrossRef]

Gu, W.

Gu, Y.

Guattari, G.

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

Guo, H.

He, S.

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.

Kon, A. I.

A. I. Kon and V. I. Tatarskii, Radiophys. Quantum Electron. 15, 1187 (1972).
[CrossRef]

Koorotkova, O.

Liu, L.

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, Opt. Lett. 38, 5323 (2013).
[CrossRef]

Liu, X.

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, Opt. Lett. 38, 5323 (2013).
[CrossRef]

Mironov, V. L.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, Opt. Spektrosk. 54, 1054 (1983).

Palma, C.

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

Pérez, D. G.

Phillips, R. L.

J. Recolons, L. C. Andrews, and R. L. Phillips, Opt. Eng. 46, 086002 (2007).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation in the Turbulent Atmosphere (SPIE, 2005).

Recolons, J.

J. Recolons, L. C. Andrews, and R. L. Phillips, Opt. Eng. 46, 086002 (2007).
[CrossRef]

Ricklin, J. C.

Shen, Y.

Siviloglou, G. A.

Tatarskii, V. I.

A. I. Kon and V. I. Tatarskii, Radiophys. Quantum Electron. 15, 1187 (1972).
[CrossRef]

Voelz, D. G.

X. Xiao and D. G. Voelz, Opt. Eng. 51, 026001 (2012).
[CrossRef]

Wang, F.

Wang, T.

Wen, W.

Wu, G.

Xiao, X.

X. Xiao and D. G. Voelz, Opt. Eng. 51, 026001 (2012).
[CrossRef]

Yu, S.

Yuan, Y.

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

Appl. Opt.

Appl. Phys. B

C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, Appl. Phys. B 95, 763 (2009).
[CrossRef]

H. T. Eyyuboğlu and C. Z. Çil, Appl. Phys. B 93, 595 (2008).
[CrossRef]

Appl. Phys. Lett.

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

Atmos. Oceanic Opt.

V. A. Banakh and A. V. Falits, Atmos. Oceanic Opt. 26, 455 (2013).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

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

O. Koorotkova, Opt. Commun. 281, 2342 (2008).
[CrossRef]

Opt. Eng.

J. Recolons, L. C. Andrews, and R. L. Phillips, Opt. Eng. 46, 086002 (2007).
[CrossRef]

X. Xiao and D. G. Voelz, Opt. Eng. 51, 026001 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spektrosk.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, Opt. Spektrosk. 54, 1054 (1983).

V. A. Banakh and V. M. Buldakov, Opt. Spektrosk. 55, 707 (1983).

Phys. Rev. E

G. P. Berman, A. A. Chumak, and V. N. Gorshkov, Phys. Rev. E 76, 056606 (2007).
[CrossRef]

Radiophys. Quantum Electron.

A. I. Kon and V. I. Tatarskii, Radiophys. Quantum Electron. 15, 1187 (1972).
[CrossRef]

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation in the Turbulent Atmosphere (SPIE, 2005).

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

Supplementary Material (2)

» Media 1: AVI (3967 KB)     
» Media 2: AVI (3668 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup for generating a GSM beam, measuring its spatial coherence width, and measuring the beam wander of the generated beam passing through thermally induced turbulence. RGGD, rotating ground-glass disk; L1, L2, L3, L4, thin lenses; GAF, Gaussian amplitude filter; BS1, BS2, beam splitters; D1, D2, single photon detectors; EEC, electronic coincidence circuit; BPA, beam profile analyzer; PC, personal computer.

Fig. 2.
Fig. 2.

Experimental results of the intensity distribution of the generated GSM beam just behind the GAF and the corresponding cross line (dotted curve) for different values of the beam width. The solid curve is a result of the Gaussian fit.

Fig. 3.
Fig. 3.

Experimental results of the RMS of the centroid of the generated GSM beam in the receiver plane versus ω0 for two different values of σg (a) σg and (b) σg=0.084mm. The solid line denotes the theoretical prediction.

Fig. 4.
Fig. 4.

Experimental results of the RMS of the centroid of the generated GSM beam in the receiver plane versus (a) the coherence length σg, and (b) the temperature of the hot plate for different values of the coherence width σg.

Fig. 5.
Fig. 5.

Experimental results of the instantaneous beam profile of the generated GSM beam in the receiver plane for two different values of σg. (a) and (b) σg=0.45mm [Media 1]; (c) and (d) σg=1.05mm [Media 2].

Equations (14)

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

Γ(r1,r2)=exp[r12+r22ω02(r1r2)22σg2],
xn=iuiIn(ui,vi)/iIn(ui,vi),
yn=iviIn(ui,vi)/iIn(ui,vi).
rc21/2=(n=1N(xnx¯)2+(yny¯)2N)1/2,
x¯=1Nn=1Nxn,y¯=1Nn=1Nyn.
rc21/2=2.69Cnzω01/6[0z(1l/z)2GP(l)1/6dl]1/2,
Gp(l)=ω2(l)/ω02,
ω(l)=ω01+(1+ω02σg2)l2zR2.
rc21/2=2.69Cnω01/6z3/2×[4833(1+P(σg))5/6+5(8P(σg)3)2F1(1/6,1/2,3/2,P(σg))40P(σg)]1/2,
P(σg)=(1+ω02σg2)z2zR2,
F21(1/6,1/2,3/2,P(σg))1P(σg)18.
rc21/23.52Cnω01/6z3/2.
F21(1/6,1/2,3/2,P(σg))1.5P(σg)1/6.
rc21/21.97k1/6Cnz4/3σg1/6.

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