Abstract

Recent results show that partially coherent beams (PCB) can be conveniently generated in a multimode fiber and modulated with data at gigabit per second rates, which makes them attractive for free-space optical communication through turbulent atmosphere. An important feature of these realistic beams in contrast to model ones is the presence of residual coherence between pairs of points spatially separated by more than a few coherence radii on the beam aperture. In the present work we experimentally study the influence of this residual coherence on the scintillation of a partially coherent beam in a laboratory turbulence. It is shown that the total scintillation can be considered as a combination of scintillations of the coherent and incoherent parts of the full beam. When residual coherence is large the scintillation is mostly due to speckle motion on the detector. In the opposite case, the scintillation index settles at a low value pertaining to "ideal" homogeneous PCB.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).
  2. Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
    [Crossref]
  3. A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).
  4. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
    [Crossref]
  5. G. Gbur, “Partially coherent beam propagation in atmospheric turbulence,” J. Opt. Soc. Am. A 31, 2038–2045 (2014).
    [Crossref]
  6. H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, and M. Nakatsuka, “Partially coherent light generated by using single and multimode optical fibers in a high-power Nd:glass laser system,” Appl. Phys. Lett. 63, 580–582 (1993).
    [Crossref]
  7. A. Efimov, “Lateral-sheering, delay-dithering Mach-Zehnder interferometer for spatial coherence measurement,” Opt. Lett. 38, 4522–4525 (2013).
    [Crossref] [PubMed]
  8. A. Efimov, “Spatial coherence at the output of multimode optical fibers,” Opt. Express 22, 15577–15588 (2014).
    [Crossref] [PubMed]
  9. A. Efimov, “Scintillations of a partially coherent beam in a laboratory turbulence: Experiment and comparison to theory,” Proc. SPIE 9354, 935404 (2015).
    [Crossref]
  10. A. Efimov, “Gigabit per second modulation and transmission of a partially coherent beam through laboratory turbulence,” Proc. SPIE 9739, 97390L (2016).
  11. Q. Wang and M. K. Giles, “Coherence reduction using optical fibers,” Proc. SPIE 5892, 58920N (2005).
    [Crossref]
  12. X. Xiao and D. Voelz, “Analysis and simulation of a fiber bundle method for creating a partially spatially coherent beam,” Appl. Opt. 52, 5794 (2013).
    [Crossref] [PubMed]
  13. W. M. Bruno, R. Mangual, and R. F. Zampolin, “Diode laser spatial diversity transmitter,” Proc. SPIE 1044, 187–194 (1989).
    [Crossref]
  14. I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, and A. K. Majumdar, “Scintillation reduction using multiple transmitters,” Proc. SPIE 2990, 102–113 (1997).
    [Crossref]
  15. A. Efimov, K. Velizhanin, and G. Gelikonov, “Simultaneous scintillation measurements of coherent and partially coherent beams in an open atmosphere experiment,” Proc. SPIE 8971, 897105 (2014).
    [Crossref]
  16. A. Efimov, “Coherence and speckle contrast at the output of a stationary multimode optical fiber,” Opt. Lett. 43, 4767–4770 (2018).
    [Crossref] [PubMed]
  17. A. Efimov, “Different measures of speckle and coherence at the output of a multimode optical fiber,” J. Opt. Soc. Am. A 36, 1–11 (2019).
    [Crossref]
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    [Crossref]
  20. G. A. Pasmanik and V. G. Sidorovich, “Interrelation between the coherence properties and the space-time structure of light beams,” Radiophys. Quantum Electron. 23, 809–814 (1980).
    [Crossref]
  21. A. Starikov, “Effective number of degrees of freedom of partially coherent sources,” J. Opt. Soc. Am. 72, 1538–1544 (1982).
    [Crossref]
  22. N. V. Karelin and A. M. Lazaruk, “Space-time duality and average number of terms in mode decomposition of pulse fields,” Radiophys. Quantum Electron. 40, 603–608 (1997).
    [Crossref]
  23. A. Efimov, “Simple model for spatial coherence of light at the output of a multimode fiber,” J. Lightwave Tech., http://www.doi.org/10.1109/JLT.2019.2915788 (posted 10 May 2019, in press).
  24. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
    [Crossref]
  25. J. W. Goodman, Speckle Phenomena in Optics Theory and Applications (Viva Books, 2008).
  26. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
    [Crossref]
  27. V. S. R. Gudimetla, J. F. Holmes, M. E. Fossey, and P. A. Pincus, “Covariance of the received intensity of a partially coherent laser speckle pattern in the turbulent atmosphere,” Appl. Opt. 31, 1286–1293 (1992).
    [Crossref] [PubMed]
  28. J. F. Holmes and V. S. R. Gudimetla, “Variance of intensity for a discrete-spectrum, polychromatic speckle field after propagation through the turbulent atmosphere,” JOSA 71, 1176–1179 (1981).
    [Crossref]
  29. P. A. Pincus, M. E. Fossey, J. F. Holmes, and J. R. Kerr, “Speckle propagation through turbulence: Experimental,” JOSA 68, 760–762 (1978).
    [Crossref]
  30. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Nauka, 1961).
  31. A. Efimov, “Intuitive model for the scintillations of a partially coherent beam,” Opt. Express 22, 32353–32360 (2014).
    [Crossref]
  32. R. Dandliker, A. Bertholds, and F. Maystre, “How modal noise in multimode fibers depends on source spectrum and fiber dispersion,” IEEE J. Lightwave Tech. 3, 7–12 (1974).
    [Crossref]

2019 (1)

2018 (1)

2016 (1)

A. Efimov, “Gigabit per second modulation and transmission of a partially coherent beam through laboratory turbulence,” Proc. SPIE 9739, 97390L (2016).

2015 (2)

A. Efimov, “Scintillations of a partially coherent beam in a laboratory turbulence: Experiment and comparison to theory,” Proc. SPIE 9354, 935404 (2015).
[Crossref]

K. Blomstedt, T. Setälä, and A. Friberg, “Effective degree of coherence: A second look,” J. Opt. Soc. Am. A 32, 718–732 (2015).
[Crossref]

2014 (4)

2013 (2)

2005 (1)

Q. Wang and M. K. Giles, “Coherence reduction using optical fibers,” Proc. SPIE 5892, 58920N (2005).
[Crossref]

2002 (1)

1997 (2)

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, and A. K. Majumdar, “Scintillation reduction using multiple transmitters,” Proc. SPIE 2990, 102–113 (1997).
[Crossref]

N. V. Karelin and A. M. Lazaruk, “Space-time duality and average number of terms in mode decomposition of pulse fields,” Radiophys. Quantum Electron. 40, 603–608 (1997).
[Crossref]

1993 (1)

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, and M. Nakatsuka, “Partially coherent light generated by using single and multimode optical fibers in a high-power Nd:glass laser system,” Appl. Phys. Lett. 63, 580–582 (1993).
[Crossref]

1992 (1)

1989 (1)

W. M. Bruno, R. Mangual, and R. F. Zampolin, “Diode laser spatial diversity transmitter,” Proc. SPIE 1044, 187–194 (1989).
[Crossref]

1983 (2)

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
[Crossref]

1982 (1)

1981 (1)

J. F. Holmes and V. S. R. Gudimetla, “Variance of intensity for a discrete-spectrum, polychromatic speckle field after propagation through the turbulent atmosphere,” JOSA 71, 1176–1179 (1981).
[Crossref]

1980 (1)

G. A. Pasmanik and V. G. Sidorovich, “Interrelation between the coherence properties and the space-time structure of light beams,” Radiophys. Quantum Electron. 23, 809–814 (1980).
[Crossref]

1978 (1)

P. A. Pincus, M. E. Fossey, J. F. Holmes, and J. R. Kerr, “Speckle propagation through turbulence: Experimental,” JOSA 68, 760–762 (1978).
[Crossref]

1974 (1)

R. Dandliker, A. Bertholds, and F. Maystre, “How modal noise in multimode fibers depends on source spectrum and fiber dispersion,” IEEE J. Lightwave Tech. 3, 7–12 (1974).
[Crossref]

Adhikari, P.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, and A. K. Majumdar, “Scintillation reduction using multiple transmitters,” Proc. SPIE 2990, 102–113 (1997).
[Crossref]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
[Crossref]

Banakh, V. A.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

Baykal, Y.

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
[Crossref]

Bertholds, A.

R. Dandliker, A. Bertholds, and F. Maystre, “How modal noise in multimode fibers depends on source spectrum and fiber dispersion,” IEEE J. Lightwave Tech. 3, 7–12 (1974).
[Crossref]

Blomstedt, K.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Bruno, W. M.

W. M. Bruno, R. Mangual, and R. F. Zampolin, “Diode laser spatial diversity transmitter,” Proc. SPIE 1044, 187–194 (1989).
[Crossref]

Buldakov, V. M.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

Dandliker, R.

R. Dandliker, A. Bertholds, and F. Maystre, “How modal noise in multimode fibers depends on source spectrum and fiber dispersion,” IEEE J. Lightwave Tech. 3, 7–12 (1974).
[Crossref]

Efimov, A.

A. Efimov, “Different measures of speckle and coherence at the output of a multimode optical fiber,” J. Opt. Soc. Am. A 36, 1–11 (2019).
[Crossref]

A. Efimov, “Coherence and speckle contrast at the output of a stationary multimode optical fiber,” Opt. Lett. 43, 4767–4770 (2018).
[Crossref] [PubMed]

A. Efimov, “Gigabit per second modulation and transmission of a partially coherent beam through laboratory turbulence,” Proc. SPIE 9739, 97390L (2016).

A. Efimov, “Scintillations of a partially coherent beam in a laboratory turbulence: Experiment and comparison to theory,” Proc. SPIE 9354, 935404 (2015).
[Crossref]

A. Efimov, K. Velizhanin, and G. Gelikonov, “Simultaneous scintillation measurements of coherent and partially coherent beams in an open atmosphere experiment,” Proc. SPIE 8971, 897105 (2014).
[Crossref]

A. Efimov, “Intuitive model for the scintillations of a partially coherent beam,” Opt. Express 22, 32353–32360 (2014).
[Crossref]

A. Efimov, “Spatial coherence at the output of multimode optical fibers,” Opt. Express 22, 15577–15588 (2014).
[Crossref] [PubMed]

A. Efimov, “Lateral-sheering, delay-dithering Mach-Zehnder interferometer for spatial coherence measurement,” Opt. Lett. 38, 4522–4525 (2013).
[Crossref] [PubMed]

Fossey, M. E.

Friberg, A.

Gbur, G.

Gelikonov, G.

A. Efimov, K. Velizhanin, and G. Gelikonov, “Simultaneous scintillation measurements of coherent and partially coherent beams in an open atmosphere experiment,” Proc. SPIE 8971, 897105 (2014).
[Crossref]

Giles, M. K.

Q. Wang and M. K. Giles, “Coherence reduction using optical fibers,” Proc. SPIE 5892, 58920N (2005).
[Crossref]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics Theory and Applications (Viva Books, 2008).

Gudimetla, V. S. R.

V. S. R. Gudimetla, J. F. Holmes, M. E. Fossey, and P. A. Pincus, “Covariance of the received intensity of a partially coherent laser speckle pattern in the turbulent atmosphere,” Appl. Opt. 31, 1286–1293 (1992).
[Crossref] [PubMed]

J. F. Holmes and V. S. R. Gudimetla, “Variance of intensity for a discrete-spectrum, polychromatic speckle field after propagation through the turbulent atmosphere,” JOSA 71, 1176–1179 (1981).
[Crossref]

Gurvich, A. S.

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

Hakakha, H.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, and A. K. Majumdar, “Scintillation reduction using multiple transmitters,” Proc. SPIE 2990, 102–113 (1997).
[Crossref]

Holmes, J. F.

V. S. R. Gudimetla, J. F. Holmes, M. E. Fossey, and P. A. Pincus, “Covariance of the received intensity of a partially coherent laser speckle pattern in the turbulent atmosphere,” Appl. Opt. 31, 1286–1293 (1992).
[Crossref] [PubMed]

J. F. Holmes and V. S. R. Gudimetla, “Variance of intensity for a discrete-spectrum, polychromatic speckle field after propagation through the turbulent atmosphere,” JOSA 71, 1176–1179 (1981).
[Crossref]

P. A. Pincus, M. E. Fossey, J. F. Holmes, and J. R. Kerr, “Speckle propagation through turbulence: Experimental,” JOSA 68, 760–762 (1978).
[Crossref]

Kanabe, T.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, and M. Nakatsuka, “Partially coherent light generated by using single and multimode optical fibers in a high-power Nd:glass laser system,” Appl. Phys. Lett. 63, 580–582 (1993).
[Crossref]

Karelin, N. V.

N. V. Karelin and A. M. Lazaruk, “Space-time duality and average number of terms in mode decomposition of pulse fields,” Radiophys. Quantum Electron. 40, 603–608 (1997).
[Crossref]

Kerr, J. R.

P. A. Pincus, M. E. Fossey, J. F. Holmes, and J. R. Kerr, “Speckle propagation through turbulence: Experimental,” JOSA 68, 760–762 (1978).
[Crossref]

Khmelevtsov, S. S.

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

Kim, I. I.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, and A. K. Majumdar, “Scintillation reduction using multiple transmitters,” Proc. SPIE 2990, 102–113 (1997).
[Crossref]

Kon, A. I.

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

Korevaar, E.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, and A. K. Majumdar, “Scintillation reduction using multiple transmitters,” Proc. SPIE 2990, 102–113 (1997).
[Crossref]

Kutay, M. A.

Lazaruk, A. M.

N. V. Karelin and A. M. Lazaruk, “Space-time duality and average number of terms in mode decomposition of pulse fields,” Radiophys. Quantum Electron. 40, 603–608 (1997).
[Crossref]

Majumdar, A. K.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, and A. K. Majumdar, “Scintillation reduction using multiple transmitters,” Proc. SPIE 2990, 102–113 (1997).
[Crossref]

Mandel, L.

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

Mangual, R.

W. M. Bruno, R. Mangual, and R. F. Zampolin, “Diode laser spatial diversity transmitter,” Proc. SPIE 1044, 187–194 (1989).
[Crossref]

Maystre, F.

R. Dandliker, A. Bertholds, and F. Maystre, “How modal noise in multimode fibers depends on source spectrum and fiber dispersion,” IEEE J. Lightwave Tech. 3, 7–12 (1974).
[Crossref]

Mironov, V. L.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

Miyanaga, N.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, and M. Nakatsuka, “Partially coherent light generated by using single and multimode optical fibers in a high-power Nd:glass laser system,” Appl. Phys. Lett. 63, 580–582 (1993).
[Crossref]

Nakano, H.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, and M. Nakatsuka, “Partially coherent light generated by using single and multimode optical fibers in a high-power Nd:glass laser system,” Appl. Phys. Lett. 63, 580–582 (1993).
[Crossref]

Nakatsuka, M.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, and M. Nakatsuka, “Partially coherent light generated by using single and multimode optical fibers in a high-power Nd:glass laser system,” Appl. Phys. Lett. 63, 580–582 (1993).
[Crossref]

Ozaktas, H. M.

Pasmanik, G. A.

G. A. Pasmanik and V. G. Sidorovich, “Interrelation between the coherence properties and the space-time structure of light beams,” Radiophys. Quantum Electron. 23, 809–814 (1980).
[Crossref]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
[Crossref]

Pincus, P. A.

Plonus, M. A.

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
[Crossref]

Setälä, T.

Sidorovich, V. G.

G. A. Pasmanik and V. G. Sidorovich, “Interrelation between the coherence properties and the space-time structure of light beams,” Radiophys. Quantum Electron. 23, 809–814 (1980).
[Crossref]

Starikov, A.

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Nauka, 1961).

Tsubakimoto, K.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, and M. Nakatsuka, “Partially coherent light generated by using single and multimode optical fibers in a high-power Nd:glass laser system,” Appl. Phys. Lett. 63, 580–582 (1993).
[Crossref]

Velizhanin, K.

A. Efimov, K. Velizhanin, and G. Gelikonov, “Simultaneous scintillation measurements of coherent and partially coherent beams in an open atmosphere experiment,” Proc. SPIE 8971, 897105 (2014).
[Crossref]

Voelz, D.

Wang, Q.

Q. Wang and M. K. Giles, “Coherence reduction using optical fibers,” Proc. SPIE 5892, 58920N (2005).
[Crossref]

Wang, S. J.

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
[Crossref]

Wolf, E.

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

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Xiao, X.

Yagi, K.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, and M. Nakatsuka, “Partially coherent light generated by using single and multimode optical fibers in a high-power Nd:glass laser system,” Appl. Phys. Lett. 63, 580–582 (1993).
[Crossref]

Yuksel, S.

Zampolin, R. F.

W. M. Bruno, R. Mangual, and R. F. Zampolin, “Diode laser spatial diversity transmitter,” Proc. SPIE 1044, 187–194 (1989).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, and M. Nakatsuka, “Partially coherent light generated by using single and multimode optical fibers in a high-power Nd:glass laser system,” Appl. Phys. Lett. 63, 580–582 (1993).
[Crossref]

IEEE J. Lightwave Tech. (1)

R. Dandliker, A. Bertholds, and F. Maystre, “How modal noise in multimode fibers depends on source spectrum and fiber dispersion,” IEEE J. Lightwave Tech. 3, 7–12 (1974).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

JOSA (2)

J. F. Holmes and V. S. R. Gudimetla, “Variance of intensity for a discrete-spectrum, polychromatic speckle field after propagation through the turbulent atmosphere,” JOSA 71, 1176–1179 (1981).
[Crossref]

P. A. Pincus, M. E. Fossey, J. F. Holmes, and J. R. Kerr, “Speckle propagation through turbulence: Experimental,” JOSA 68, 760–762 (1978).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Opt. Spectrosc. (1)

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

Proc. SPIE (6)

A. Efimov, “Scintillations of a partially coherent beam in a laboratory turbulence: Experiment and comparison to theory,” Proc. SPIE 9354, 935404 (2015).
[Crossref]

A. Efimov, “Gigabit per second modulation and transmission of a partially coherent beam through laboratory turbulence,” Proc. SPIE 9739, 97390L (2016).

Q. Wang and M. K. Giles, “Coherence reduction using optical fibers,” Proc. SPIE 5892, 58920N (2005).
[Crossref]

W. M. Bruno, R. Mangual, and R. F. Zampolin, “Diode laser spatial diversity transmitter,” Proc. SPIE 1044, 187–194 (1989).
[Crossref]

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, and A. K. Majumdar, “Scintillation reduction using multiple transmitters,” Proc. SPIE 2990, 102–113 (1997).
[Crossref]

A. Efimov, K. Velizhanin, and G. Gelikonov, “Simultaneous scintillation measurements of coherent and partially coherent beams in an open atmosphere experiment,” Proc. SPIE 8971, 897105 (2014).
[Crossref]

Radio Sci. (1)

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
[Crossref]

Radiophys. Quantum Electron. (2)

G. A. Pasmanik and V. G. Sidorovich, “Interrelation between the coherence properties and the space-time structure of light beams,” Radiophys. Quantum Electron. 23, 809–814 (1980).
[Crossref]

N. V. Karelin and A. M. Lazaruk, “Space-time duality and average number of terms in mode decomposition of pulse fields,” Radiophys. Quantum Electron. 40, 603–608 (1997).
[Crossref]

Other (7)

A. Efimov, “Simple model for spatial coherence of light at the output of a multimode fiber,” J. Lightwave Tech., http://www.doi.org/10.1109/JLT.2019.2915788 (posted 10 May 2019, in press).

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

J. W. Goodman, Speckle Phenomena in Optics Theory and Applications (Viva Books, 2008).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Nauka, 1961).

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Interferometrically measured average modulus of the complex degree of coherence as a function of image shear Δr (spatial displacement between two images produced by the interferometer) of the output face of the fiber. Three color curves correspond to three different source bandwidths. Black dashed curve is the often used model 2|J1 (k0 NAΔr)/(k0 NAΔr)|, where J1 is the Bessel function of the first kind. Speckle pattern images of the fiber end face are shown on the right for each of the three curves in the main plot with speckle contrast values indicated.
Fig. 2
Fig. 2 Schematic of the experimental setup: SLD – superluminescent diode, SML – single-mode laser, EDFA – erbium-dopped fiber amplifier, MMF – PCB-generating multimode fiber, OSA – optical spectrum analyzer, MS – mode scrambler, FM – flipper mirror, DET – fiber-coupled InGaAs detector, CCD – InGaAs charge-coupled device, DAQ – data acquisition system. All fiber pigtails are single-mode.
Fig. 3
Fig. 3 Left: Speckle contrast as a function of optical source bandwidth at the output of a 105-micron diameter core MMF, 2-meters in length. Right: Dependence of the scintillation index of a PCB in a laboratory turbulence on the FBT speckle contrast. The experimental data (symbols) is fitted by Eq. (1) (red curve).
Fig. 4
Fig. 4 Scintillation index of the full beam as a function of coherent-to-PCB power ratio ξ (a) and average residual coherence γRC (b) for various values of the scintillation index of the “ideal” PCB SI2 in turbulence (solid black curves). From top to bottom curve the SI2 values are 0.1, 0.05, 0.03, 0.01, 0.005, and 0.003. Colored symbols represent SI = 1.1 SI2 values with vertical lines shown to help read the solution values from the horizontal axis in each plot.

Equations (1)

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S I = ξ 2 S I 1 + S I 2 + 2 δ ξ ( ξ + 1 ) 2 = γ RC 2 S I 1 + ( γ R C , m a x γ RC ) 2 S I 2 + 2 γ RC ( γ R C , m a x γ RC ) δ γ R C , m a x 2 ,

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