Abstract

A class of random sources producing far fields self-splitting intensity profiles with variable spacing between the x and y directions is introduced. The beam conditions for ensuring the sources to generate a beam are derived. Based on the derived analytical expression, the evolution behavior of the beams produced by these families of sources in free space and turbulence atmospheric are explored and comparatively analyzed. By changing the modulation parameters n and m, the degree of coherence of Gaussian Schell-model source in the x and y directions are modulated respectively, and then the number of splitting beams and the spacing between splitting beams can be adjusted. It is illustrated that the self-splitting intensity profile is stable when beams propagate in free space, but they eventually transformed into a Gaussian profiles when it passes at sufficiently large distances from its source through the turbulent atmosphere.

© 2014 Optical Society of America

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    [CrossRef]
  4. Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
    [CrossRef]
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  6. A. Suryanto, E. Van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258(2), 264–274 (2006).
    [CrossRef]
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    [CrossRef]
  13. H. Lajunen, T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. Z. Tong, O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A 29(10), 2154–2158 (2012).
    [CrossRef] [PubMed]
  16. Z. Mei, Z. Tong, O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 20(24), 26458–26463 (2012).
    [CrossRef] [PubMed]
  17. Z. Mei, O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013).
    [CrossRef] [PubMed]
  18. Z. Mei, O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
    [CrossRef] [PubMed]
  19. Z. Mei, “Light sources generating self-focusing beams of variable focal length,” Opt. Lett. 39(2), 347–350 (2014).
    [CrossRef] [PubMed]
  20. O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014).
    [CrossRef] [PubMed]
  21. C. Liang, F. Wang, X. Liu, Y. Cai, O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
    [CrossRef] [PubMed]
  22. J. Pu, O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009).
    [CrossRef]
  23. X. Du, D. Zhao, O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express 15(25), 16909–16915 (2007).
    [CrossRef] [PubMed]
  24. I. Toselli, L. C. Andrews, R. L. Phillips, V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
    [CrossRef]
  25. G. Zhou, X. Chu, “Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere,” Opt. Express 17(13), 10529–10534 (2009).
    [CrossRef] [PubMed]
  26. E. Shchepakina, O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18(10), 10650–10658 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  29. O. Korotkova, E. Shchepakina, “Color changes in stochastic light fields propagating in non-Kolmogorov turbulence,” Opt. Lett. 35(22), 3772–3774 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  32. Z. Mei, O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
    [CrossRef] [PubMed]
  33. F. Gori, M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007).
    [CrossRef] [PubMed]

2014 (3)

2013 (5)

2012 (5)

2011 (2)

2010 (5)

A. Zilberman, E. Golbraikh, N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[CrossRef]

E. Shchepakina, O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18(10), 10650–10658 (2010).
[CrossRef] [PubMed]

O. Korotkova, E. Shchepakina, “Color changes in stochastic light fields propagating in non-Kolmogorov turbulence,” Opt. Lett. 35(22), 3772–3774 (2010).
[CrossRef] [PubMed]

F. Wang, Y. Cai, “Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18(24), 24661–24672 (2010).
[CrossRef] [PubMed]

2009 (2)

G. Zhou, X. Chu, “Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere,” Opt. Express 17(13), 10529–10534 (2009).
[CrossRef] [PubMed]

J. Pu, O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009).
[CrossRef]

2008 (1)

I. Toselli, L. C. Andrews, R. L. Phillips, V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[CrossRef]

2007 (2)

2006 (1)

A. Suryanto, E. Van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258(2), 264–274 (2006).
[CrossRef]

2000 (1)

D. Cassettari, B. Hessmo, R. Folman, T. Maier, J. Schmiedmayer, “Beam splitter for guided atoms,” Phys. Rev. Lett. 85(26), 5483–5487 (2000).
[CrossRef] [PubMed]

1998 (1)

1997 (1)

J. P. Torres, L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29(7), 757–776 (1997).
[CrossRef]

1996 (1)

V. Tikhonenko, J. Christou, B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

1986 (1)

1982 (1)

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[CrossRef]

Ashkin, A.

Bjorkholm, J. E.

Buryak, A. V.

Cai, Y.

Cassettari, D.

D. Cassettari, B. Hessmo, R. Folman, T. Maier, J. Schmiedmayer, “Beam splitter for guided atoms,” Phys. Rev. Lett. 85(26), 5483–5487 (2000).
[CrossRef] [PubMed]

Christou, J.

V. Tikhonenko, J. Christou, B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

Chu, S.

Chu, X.

Du, X.

Duelk, M.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[CrossRef]

Dziedzic, J. M.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[CrossRef]

Folman, R.

D. Cassettari, B. Hessmo, R. Folman, T. Maier, J. Schmiedmayer, “Beam splitter for guided atoms,” Phys. Rev. Lett. 85(26), 5483–5487 (2000).
[CrossRef] [PubMed]

Golbraikh, E.

A. Zilberman, E. Golbraikh, N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010).
[CrossRef]

Gori, F.

Halevi, P.

Hamamoto, K.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[CrossRef]

Hessmo, B.

D. Cassettari, B. Hessmo, R. Folman, T. Maier, J. Schmiedmayer, “Beam splitter for guided atoms,” Phys. Rev. Lett. 85(26), 5483–5487 (2000).
[CrossRef] [PubMed]

Hinokuma, Y.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[CrossRef]

Ji, X.

Kopeika, N. S.

A. Zilberman, E. Golbraikh, N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010).
[CrossRef]

Korotkova, O.

C. Liang, F. Wang, X. Liu, Y. Cai, O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[CrossRef] [PubMed]

O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014).
[CrossRef] [PubMed]

Z. Mei, O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013).
[CrossRef] [PubMed]

Z. Mei, E. Shchepakina, O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express 21(15), 17512–17519 (2013).
[CrossRef] [PubMed]

Z. Mei, O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
[CrossRef] [PubMed]

Z. Mei, O. Korotkova, E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[CrossRef]

Z. Mei, O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[CrossRef] [PubMed]

Z. Mei, Z. Tong, O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 20(24), 26458–26463 (2012).
[CrossRef] [PubMed]

Z. Tong, O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[CrossRef] [PubMed]

Z. Tong, O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A 29(10), 2154–2158 (2012).
[CrossRef] [PubMed]

S. Sahin, O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
[CrossRef] [PubMed]

E. Shchepakina, O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18(10), 10650–10658 (2010).
[CrossRef] [PubMed]

O. Korotkova, E. Shchepakina, “Color changes in stochastic light fields propagating in non-Kolmogorov turbulence,” Opt. Lett. 35(22), 3772–3774 (2010).
[CrossRef] [PubMed]

J. Pu, O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009).
[CrossRef]

X. Du, D. Zhao, O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express 15(25), 16909–16915 (2007).
[CrossRef] [PubMed]

Lajunen, H.

Li, X.

Liang, C.

Liu, X.

Luther-Davies, B.

V. Tikhonenko, J. Christou, B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

Maier, T.

D. Cassettari, B. Hessmo, R. Folman, T. Maier, J. Schmiedmayer, “Beam splitter for guided atoms,” Phys. Rev. Lett. 85(26), 5483–5487 (2000).
[CrossRef] [PubMed]

Mei, Z.

Minato, T.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[CrossRef]

Mitchell, D. J.

Mukai, K.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[CrossRef]

Navaretti, P.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[CrossRef]

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[CrossRef]

Pu, J.

J. Pu, O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009).
[CrossRef]

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

Schmiedmayer, J.

D. Cassettari, B. Hessmo, R. Folman, T. Maier, J. Schmiedmayer, “Beam splitter for guided atoms,” Phys. Rev. Lett. 85(26), 5483–5487 (2000).
[CrossRef] [PubMed]

Shchepakina, E.

Snyder, A. W.

Suryanto, A.

A. Suryanto, E. Van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258(2), 264–274 (2006).
[CrossRef]

Tikhonenko, V.

V. Tikhonenko, J. Christou, B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

Tong, Z.

Torner, L.

J. P. Torres, L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29(7), 757–776 (1997).
[CrossRef]

Torres, J. P.

J. P. Torres, L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29(7), 757–776 (1997).
[CrossRef]

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[CrossRef]

Van Groesen, E.

A. Suryanto, E. Van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258(2), 264–274 (2006).
[CrossRef]

Velez, C.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[CrossRef]

Wang, F.

Zang, Z.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[CrossRef]

Zhao, D.

Zhou, G.

Zilberman, A.

A. Zilberman, E. Golbraikh, N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[CrossRef]

J. Opt. (1)

Z. Mei, O. Korotkova, E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[CrossRef]

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

Opt. Commun. (3)

A. Suryanto, E. Van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258(2), 264–274 (2006).
[CrossRef]

A. Zilberman, E. Golbraikh, N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010).
[CrossRef]

J. Pu, O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009).
[CrossRef]

Opt. Eng. (1)

I. Toselli, L. C. Andrews, R. L. Phillips, V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[CrossRef]

Opt. Express (7)

Opt. Lett. (13)

O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014).
[CrossRef] [PubMed]

Z. Mei, “Light sources generating self-focusing beams of variable focal length,” Opt. Lett. 39(2), 347–350 (2014).
[CrossRef] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[CrossRef] [PubMed]

Z. Mei, O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013).
[CrossRef] [PubMed]

Z. Mei, O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[CrossRef] [PubMed]

H. Lajunen, T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
[CrossRef] [PubMed]

S. Sahin, O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
[CrossRef] [PubMed]

Z. Tong, O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[CrossRef] [PubMed]

O. Korotkova, E. Shchepakina, “Color changes in stochastic light fields propagating in non-Kolmogorov turbulence,” Opt. Lett. 35(22), 3772–3774 (2010).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007).
[CrossRef] [PubMed]

P. Halevi, “Beam splitting by a plane-parallel absorptive slab,” Opt. Lett. 7(10), 469–470 (1982).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986).
[CrossRef] [PubMed]

A. W. Snyder, A. V. Buryak, D. J. Mitchell, “Beam splitting on weak illumination,” Opt. Lett. 23(1), 4–6 (1998).
[CrossRef] [PubMed]

Opt. Quantum Electron. (1)

J. P. Torres, L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29(7), 757–776 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

D. Cassettari, B. Hessmo, R. Folman, T. Maier, J. Schmiedmayer, “Beam splitter for guided atoms,” Phys. Rev. Lett. 85(26), 5483–5487 (2000).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

Other (1)

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

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Figures (5)

Fig. 1
Fig. 1

Absolute value of the degree of coherence calculated from Eq. (5) for several values of n and m.

Fig. 2
Fig. 2

Evolution of the spectral density of an OCGSM beam with n = 5 and m = 5 propagating in free space. (a) z = 0; (b) z = 40m; (c) z = 70m; (d) z = 200m.

Fig. 3
Fig. 3

Spectral density of the OCGSM beams with parameters as in Fig. 1 at the plane z = 5km.

Fig. 4
Fig. 4

Comparison of the spectral density of an OCGSM beam with n = 5 and m = 5 propagating in free space and atmosphere turbulence with α = 3.667 and C ˜ n 2 = 10 12 m 3 α .

Fig. 5
Fig. 5

Changes in spectral density of an OCGSM beam with n = 5 and m = 5 for different parameters α and C ˜ n 2 at the plane z = 5km in the non-Kolmogorov turbulence.

Tables (1)

Tables Icon

Table 1 Values of all calculated parameters in this paper

Equations (27)

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W (0) ( x 1 , y 1 , x 2 , y 2 )= [ S (0) ( x 1 , y 1 ) S (0) ( x 2 , y 2 )] 1/2 μ (0) ( x 1 x 2 , y 1 y 2 ),
W (0) ( x 1 , y 1 , x 2 , y 2 )= p( v x , v y ) H 0 ( x 1 , y 1 , v x , v y ) H 0 ( x 2 , y 2 , v x , v y )d v x d v y ,
H 0 ( x , y , v x , v y )=τ( x , y )exp[i2π( v x x v y y )],
W (0) ( x 1 , y 1 , x 2 , y 2 )= τ ( x 1 , y 1 )τ( x 2 , y 2 ) p ˜ x ( x 1 x 2 ) p ˜ y ( y 1 y 2 ),
μ ( 0 ) ( x 1 x 2 , y 1 y 2 ) = cos [ n 2 π ( x 2 x 1 ) δ x ] exp [ ( x 2 x 1 ) 2 2 δ x 2 ] × cos [ m 2 π ( y 2 y 1 ) δ y ] exp [ ( y 2 y 1 ) 2 2 δ y 2 ] ,
p( v x , v y )=2π δ x δ y cosh[n (2π) 3/2 δ x v x ]cosh[m (2π) 3/2 δ y v y ] ×exp[2 π 2 ( δ x v x + δ y v y )( n 2 + m 2 )π].
τ( x , y )=exp( x 2 + y 2 4 σ 2 ),
W (0) ( x 1 , y 1 , x 2 , y 2 )=exp( x 1 2 + x 2 2 4 σ x 2 y 1 2 + y 2 2 4 σ y 2 )cos[ n 2π ( x 2 x 1 ) δ x ] ×exp[ ( x 2 x 1 ) 2 2 δ x 2 ]cos[ m 2π ( y 2 y 1 ) δ y ]exp[ ( y 2 y 1 ) 2 2 δ y 2 ].
W () ( r 1 s 1 , r 2 s 2 )= ( 2πk ) 2 cos θ 1 cos θ 2 W ˜ (0) (k s 1 ,k s 2 ) exp[ik( r 2 r 1 )] r 1 r 2 ,
W ˜ (0) ( f 1 , f 2 )= ( 1 2π ) 4 W (0) ( ρ 1 , ρ 2 ) exp[i( f 1 ρ 1 + f 2 ρ 2 ) d 2 ρ 1 d 2 ρ 2 ,
W () ( r 1 s 1 , r 2 s 2 )= k 2 σ x σ y 2 a x a y cos θ 1 cos θ 2 exp[ik( r 2 r 1 )] r 1 r 2 ×cosh[ n 2π 4 a x δ x k( s 1x + s 2x ) ]cosh[ m 2π 4 a y δ y k( s 1y + s 2y ) ] ×exp[ k 2 σ x 2 2 ( s 1x s 2x ) 2 k 2 16 a x ( s 1x + s 2x ) 2 n 2 π 2 a x δ x 2 ] ×exp[ k 2 σ y 2 2 ( s 1y s 2y ) 2 k 2 16 a y ( s 1y + s 2y ) 2 m 2 π 2 a y δ y 2 ],
S () (rs)= k 2 σ x σ y 2 r 2 a x a y cos 2 θexp[ n 2 π 2 a x δ x 2 m 2 π 2 a y δ y 2 ] ×cosh( n 2π 2 a x δ x k s x )cosh( m 2π 2 a y δ y k s y )exp( k 2 s x 2 4 a x )exp( k 2 s y 2 4 a y ).
exp( k 2 s x 2 4 a x )0 and exp( k 2 s y 2 4 a y )0.
1 4 σ x 2 + 1 δ x 2 << 2 π 2 λ 2 and 1 4 σ y 2 + 1 δ y 2 << 2 π 2 λ 2 .
W( x 1 , x 2 , y 1 , y 2 ,z)= ( k 2πz ) 2 d x 1 d x 2 d y 1 d y 2 W (0) ( x 1 , y 1 , x 2 , y 2 ) ×exp{ ik 2z [ ( x 1 x 1 ) 2 + ( y 1 y 1 ) 2 ( x 2 x 2 ) 2 ( y 2 y 2 ) 2 ] } × exp[ ϕ ( x 1 , y 1 , x 1 , y 1 ,z)+ϕ( x 2 , y 2 , x 2 , y 2 ,z)] M ,
exp[ ϕ ( x 1 , y 1 , x 1 , y 1 ,z)+ϕ( x 2 , y 2 , x 2 , y 2 ,z)] M =exp{ ( π 2 k 2 z/3) × [ ( x 1 x 2 ) 2 + ( y 1 y 2 ) 2 +( x 1 x 2 )( x 1 x 2 )+( y 1 y 2 ) ×( y 1 y 2 ) + ( x 1 x 2 ) 2 + ( y 1 y 2 ) 2 ] 0 κ 3 Φ n (κ)dκ },
Φ n (κ)=A(α) C ˜ n 2 exp[( κ 2 / κ m 2 )]/ ( κ 2 + κ 0 2 ) α/2 , 0κ<, 3<α<4,
c(α)= [Γ(5 α 2 )A(α) 2π 3 ] 1/(α5) ,
A(α)=Γ(α1) cos(απ/2) 4 π 2 ,
0 κ 3 Φ n (κ)dκ = A(α) 2(α2) C ˜ n 2 [ κ m 2α βexp( κ 0 2 κ m 2 )Γ(2 α 2 , κ 0 2 κ m 2 )2 κ 0 4α ],
W( x 1 , x 2 , y 1 , y 2 ,z)= k 2 σ x σ y 4 z 2 Δ x (z) Δ y (z) exp[ ik 2z ( x 1 2 + y 1 2 x 2 2 y 2 2 ) ] ×exp[ ( x 1 x 2 ) 2 R x (z) ( y 1 y 2 ) 2 R y (z) ][ exp( γ x+ 2 Δ x (z) )+exp( γ x 2 Δ x (z) ) ] ×[ exp( γ y+ 2 Δ y (z) )+exp( γ y 2 Δ y (z) ) ],
1 R α (z) = k 2 σ α 2 2 z 2 + k 2 π 2 z 3 0 κ 3 Φ n (κ)dκ, α=x,y
Δ α (z)= 1 8 σ α 2 + 1 2 δ α 2 + 1 R α (z) , α=x,y
γ α± =( 3 k 2 σ α 2 4 z 2 1 2 R α (z) )( α 1 α 2 )+ ik 4z ( α 1 + α 2 )± in 2π 2 δ α , α=x,y.
R α (z)=2 z 2 /( k 2 σ α 2 ).
S(x,y,z)=W(x,x,y,y,z) = k 2 σ x σ y 4 z 2 Δ x (z) Δ y (z) [ exp( γ x+ 2 Δ x (z) )+exp( γ x 2 Δ x (z) ) ] ×[ exp( γ y+ 2 Δ y (z) )+exp( γ y 2 Δ y (z) ) ],
γ α± = ikα 4z ± in 2π 2 δ α , α=x,y.

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