Abstract

Elegant Hermite-Gaussian correlated Schell-model (EHGCSM) beam was introduced in theory and generated in experiment just recently [Phys. Rev. A 91, 013823 (2015)]. In this paper, we study the propagation properties of an EHGCSM beam in turbulent atmosphere with the help of the extended Huygens-Fresnel integral. Analytical expressions for the cross-spectral density and the propagation factors of an EHGCSM beam propagating in turbulent atmosphere are derived. The statistical properties, such as the spectral intensity, the spectral degree of coherence and the propagation factors, of an EHGCSM beam in Kolmogorov and non-Kolmogorov turbulence are illustrated numerically. It is found that an EHGCSM beam exhibits splitting and combing properties in turbulent atmosphere, and an EHGCSM beam with large mode orders is less affected by turbulence than an EHGCSM beam with small mode orders or a Gaussian Schell-model beam or a Gaussian beam, which will be useful in free-space optical communications.

© 2015 Optical Society of America

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References

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2015 (2)

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

F. Wang, X. Liu, and Y. Cai, “Propagation of partially coherent beam in turbulent atmosphere: a review (Invited review),” Prog. Electromagnetics Res. 150, 123–143 (2015).
[Crossref]

2014 (12)

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39(11), 3336–3339 (2014).
[Crossref] [PubMed]

G. Gbur, “Partially coherent beam propagation in atmospheric turbulence [Invited],” J. Opt. Soc. Am. A 31(9), 2038–2045 (2014).
[PubMed]

L. Lu, X. Ji, and Y. Baykal, “Wave structure function and spatial coherence radius of plane and spherical waves propagating through oceanic turbulence,” Opt. Express 22(22), 27112–27122 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [Invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, “Difference of cross-spectral densities,” Opt. Lett. 39(7), 1713–1716 (2014).
[Crossref] [PubMed]

F. Gori and M. Santarsiero, “Difference of two Gaussian Schell-model cross-spectral densities,” Opt. Lett. 39(9), 2731–2734 (2014).
[Crossref] [PubMed]

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).
[Crossref]

2013 (7)

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103(9), 091102 (2013).
[Crossref]

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

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

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

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

2012 (3)

2011 (2)

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

Y. Cai, “Generation of various partially coherent beams and their propagation properties in turbulent atmosphere: a review,” Proc. SPIE 7924, 792402 (2011).
[Crossref]

2010 (4)

2009 (3)

2008 (2)

Y. Dan and B. Zhang, “Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere,” Opt. Express 16(20), 15563–15575 (2008).
[Crossref] [PubMed]

O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. 281(9), 2342–2348 (2008).
[Crossref]

2007 (2)

1999 (1)

1993 (1)

R. Martínez -Herrero, P. M. Mejías, and H. Weber, “On the different definitions of laser beam moments,” Opt. Quantum Electron. 25, 423–428 (1993).
[Crossref]

1991 (1)

F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82(3-4), 197–203 (1991).
[Crossref]

Avramov-Zamurovic, S.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).
[Crossref]

Baykal, Y.

Borghi, R.

Cai, Y.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

F. Wang, X. Liu, and Y. Cai, “Propagation of partially coherent beam in turbulent atmosphere: a review (Invited review),” Prog. Electromagnetics Res. 150, 123–143 (2015).
[Crossref]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39(11), 3336–3339 (2014).
[Crossref] [PubMed]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [Invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103(9), 091102 (2013).
[Crossref]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Y. Cai, “Generation of various partially coherent beams and their propagation properties in turbulent atmosphere: a review,” Proc. SPIE 7924, 792402 (2011).
[Crossref]

Y. Cai and F. Wang, “Tensor method for treating the propagation of scalar and electromagnetic Gaussian Schell-model beams: a review,” Open Opt. J. 4(1), 1–20 (2010).
[Crossref]

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

Chen, Y.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [Invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Cheng, W.

Cincotti, G.

Dan, Y.

de Sande, J. C. G.

Du, S.

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Eyyuboglu, H. T.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Gbur, G.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).
[Crossref]

G. Gbur, “Partially coherent beam propagation in atmospheric turbulence [Invited],” J. Opt. Soc. Am. A 31(9), 2038–2045 (2014).
[PubMed]

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
[Crossref] [PubMed]

Gori, F.

Gu, J.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

Gu, Y.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).
[Crossref]

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
[Crossref] [PubMed]

Gutiérrez-Vega, J. C.

Haus, J. W.

Ji, X.

Korotkova, O.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).
[Crossref]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

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

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

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

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

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).
[Crossref] [PubMed]

E. Shchepakina and 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, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. 281(9), 2342–2348 (2008).
[Crossref]

Lajunen, H.

Liang, C.

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Liu, L.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103(9), 091102 (2013).
[Crossref]

Liu, X.

F. Wang, X. Liu, and Y. Cai, “Propagation of partially coherent beam in turbulent atmosphere: a review (Invited review),” Prog. Electromagnetics Res. 150, 123–143 (2015).
[Crossref]

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39(11), 3336–3339 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103(9), 091102 (2013).
[Crossref]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Liu, Z.

Lu, L.

Ma, Y.

Malek-Madani, R.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).
[Crossref]

Martínez -Herrero, R.

R. Martínez -Herrero, P. M. Mejías, and H. Weber, “On the different definitions of laser beam moments,” Opt. Quantum Electron. 25, 423–428 (1993).
[Crossref]

Martínez-Herrero, R.

Mei, Z.

Mejías, P. M.

R. Martínez-Herrero, P. M. Mejías, and F. Gori, “Genuine cross-spectral densities and pseudo-modal expansions,” Opt. Lett. 34(9), 1399–1401 (2009).
[Crossref] [PubMed]

R. Martínez -Herrero, P. M. Mejías, and H. Weber, “On the different definitions of laser beam moments,” Opt. Quantum Electron. 25, 423–428 (1993).
[Crossref]

Nelson, C.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).
[Crossref]

Noriega-Manez, R. J.

Piquero, G.

Qu, J.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Ramírez-Sánchez, V.

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

Shchepakina, E.

Shirai, T.

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

Sona, A.

F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82(3-4), 197–203 (1991).
[Crossref]

Tong, Z.

Vahimaa, P.

Wang, F.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

F. Wang, X. Liu, and Y. Cai, “Propagation of partially coherent beam in turbulent atmosphere: a review (Invited review),” Prog. Electromagnetics Res. 150, 123–143 (2015).
[Crossref]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39(11), 3336–3339 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [Invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103(9), 091102 (2013).
[Crossref]

Y. Cai and F. Wang, “Tensor method for treating the propagation of scalar and electromagnetic Gaussian Schell-model beams: a review,” Open Opt. J. 4(1), 1–20 (2010).
[Crossref]

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

Wang, X.

Weber, H.

R. Martínez -Herrero, P. M. Mejías, and H. Weber, “On the different definitions of laser beam moments,” Opt. Quantum Electron. 25, 423–428 (1993).
[Crossref]

Wei, C.

Yuan, Y.

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103(9), 091102 (2013).
[Crossref]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Zhan, Q.

Zhang, B.

Zhao, C.

Zhao, H.

Zhou, P.

Appl. Phys. Lett. (1)

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103(9), 091102 (2013).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

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

Open Opt. J. (1)

Y. Cai and F. Wang, “Tensor method for treating the propagation of scalar and electromagnetic Gaussian Schell-model beams: a review,” Open Opt. J. 4(1), 1–20 (2010).
[Crossref]

Opt. Commun. (3)

O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. 281(9), 2342–2348 (2008).
[Crossref]

F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82(3-4), 197–203 (1991).
[Crossref]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Opt. Express (10)

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

W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express 17(20), 17829–17836 (2009).
[Crossref] [PubMed]

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

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

L. Lu, X. Ji, and Y. Baykal, “Wave structure function and spatial coherence radius of plane and spherical waves propagating through oceanic turbulence,” Opt. Express 22(22), 27112–27122 (2014).
[Crossref] [PubMed]

R. J. Noriega-Manez and J. C. Gutiérrez-Vega, “Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere,” Opt. Express 15(25), 16328–16341 (2007).
[Crossref] [PubMed]

Y. Dan and B. Zhang, “Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere,” Opt. Express 16(20), 15563–15575 (2008).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Opt. Lett. (13)

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39(11), 3336–3339 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

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

R. Martínez-Herrero, P. M. Mejías, and F. Gori, “Genuine cross-spectral densities and pseudo-modal expansions,” Opt. Lett. 34(9), 1399–1401 (2009).
[Crossref] [PubMed]

M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, “Difference of cross-spectral densities,” Opt. Lett. 39(7), 1713–1716 (2014).
[Crossref] [PubMed]

F. Gori and M. Santarsiero, “Difference of two Gaussian Schell-model cross-spectral densities,” Opt. Lett. 39(9), 2731–2734 (2014).
[Crossref] [PubMed]

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

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

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

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

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
[Crossref] [PubMed]

P. Zhou, Y. Ma, X. Wang, H. Zhao, and Z. Liu, “Average spreading of a Gaussian beam array in non-Kolmogorov turbulence,” Opt. Lett. 35(7), 1043–1045 (2010).
[Crossref] [PubMed]

Opt. Quantum Electron. (1)

R. Martínez -Herrero, P. M. Mejías, and H. Weber, “On the different definitions of laser beam moments,” Opt. Quantum Electron. 25, 423–428 (1993).
[Crossref]

Phys. Rev. A (2)

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

Proc. SPIE (2)

Y. Cai, “Generation of various partially coherent beams and their propagation properties in turbulent atmosphere: a review,” Proc. SPIE 7924, 792402 (2011).
[Crossref]

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).
[Crossref]

Prog. Electromagnetics Res. (1)

F. Wang, X. Liu, and Y. Cai, “Propagation of partially coherent beam in turbulent atmosphere: a review (Invited review),” Prog. Electromagnetics Res. 150, 123–143 (2015).
[Crossref]

Other (5)

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, Washington, 2001).

Y. Cai, F. Wang, C. Zhao, S. Zhu, G. Wu, and Y. Dong, “Partially coherent vector beams: from theory to experiment,” in Vectorial Optical Fields: Fundamentals and Applications, Q. Zhen, ed. (World Scientific, 2013), Chap. 7, pp. 221–273.

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

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

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE 1224, 2C14 (1990).

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Figures (8)

Fig. 1
Fig. 1 3D-normalized spectral intensity distribution S( ρ,z )/S ( ρ,z ) max of an EHGCSM beam at several propagation distances in Kolmogorov turbulence with m = n = 5 and α=11/3 .
Fig. 2
Fig. 2 3D-normalized spectral intensity distribution S( ρ,z )/S ( ρ,z ) max of an EHGCSM beam at several propagation distances in non-Kolmogorov turbulence with m = n = 5 and α=3.1 .
Fig. 3
Fig. 3 3D-normalized spectral intensity distribution S( ρ,z )/S ( ρ,z ) max of an EHGCSM beam at several propagation distances in free space with m = n = 5 and α=11/3 .
Fig. 4
Fig. 4 Ratio of the spectral intensity in the optical axis ( ρ=0 ) to the maximum intensity in the transverse plane of an EHGCSM beam versus the propagation distance z in Kolmogorov ( α=11/3 ) or non-Kolmogorov turbulence ( α=3.1 ) for different values of the mode orders m and n .
Fig. 5
Fig. 5 Density plot of the modulus of the spectral degree of coherence and the corresponding cross line of an EHGCSM beam at several propagation distances in free space ( C ˜ n 2 =0 ) for different values of the mode orders m and n.
Fig. 6
Fig. 6 Density plot of the modulus of the spectral degree of coherence and the corresponding cross line of an EHGCSM beam at several propagation distances in Kolmogorov turbulence ( α=11/3 ) for different values of the mode orders m and n.
Fig. 7
Fig. 7 Density plot of the modulus of the spectral degree of coherence and the corresponding cross line of an EHGCSM beam at several propagation distances in non-Kolmogorov turbulence ( α=3.1 ) for different values of the mode orders m and n.
Fig. 8
Fig. 8 Normalized propagation factors of an EHGCSM beam versus the propagation distance z in Kolmogorov ( α=11/3 ) or non-Kolmogorov turbulence ( α=3.1 ) for different values of the mode orders m and n . The dark line denotes the corresponding result of a Gaussian beam.

Equations (40)

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W ( 0 ) ( r 1 , r 2 ,0 )= G 0 exp( r 1 2 + r 2 2 4 σ 0 2 )μ( r 2 r 1 ),
μ( r 2 r 1 )= H 2m [ ( x 2 x 1 )/ 2 δ 0x ] H 2m ( 0 ) H 2n [ ( y 2 y 1 )/ 2 δ 0y ] H 2n ( 0 ) exp[ ( x 2 x 1 ) 2 2 δ 0x 2 ( y 2 y 1 ) 2 2 δ 0y 2 ],
W( ρ 1 , ρ 2 ,z )= 1 λ 2 z 2 W ( 0 ) ( r 1 , r 2 ,0 ) ×exp[ ik 2z ( r 1 ρ 1 ) 2 + ik 2z ( r 2 ρ 2 ) 2 ] × exp[ Ψ( r 1 , ρ 1 )+ Ψ ( r 2 , ρ 2 ) ] d 2 r 1 d 2 r 2 ,
exp[ Ψ( r 1 , ρ 1 )+ Ψ ( r 2 , ρ 2 ) ] =exp{ ( π 2 k 2 z 3 )[ ( ρ 1 ρ 2 ) 2 +( ρ 1 ρ 2 )( r 1 r 2 )+ ( r 1 r 2 ) 2 ] 0 κ 3 Φ n ( κ ) dκ },
T= 0 κ 3 Φ n ( κ ) dκ.
T= A(α) 2(α2) C ˜ n 2 [ β κ m 2α exp( κ 0 2 / κ m 2 ) Γ 1 (2α/2, κ 0 2 / κ m 2 )2 κ 0 4α ], 3<α<4,
A(α)= 1 4 π 2 Γ(α1)cos( απ 2 ), c(α)= [ 2πA(α) 3 Γ( 5 α 2 ) ] 1/(α5) .
ik z ρ 1 = ik z ρ 1 π 2 k 2 zT 3 ( ρ 1 ρ 2 ), ik z ρ 2 = ik z ρ 2 π 2 k 2 zT 3 ( ρ 1 ρ 2 ),
A( ρ 1 , ρ 2 )=exp[ ik 2z ( ρ 1 2 ρ 2 2 ) π 2 k 2 zT 3 ( ρ 1 ρ 2 ) 2 ],
W( ρ 1 , ρ 2 ,z )= G 0 λ 2 z 2 A( ρ 1 , ρ 2 ) H 2m [ ( x 2 x 1 )/ 2 δ 0x ] H 2m ( 0 ) H 2n [ ( y 2 y 1 )/ 2 δ 0y ] H 2n ( 0 ) ×exp[ ( x 2 x 1 ) 2 2 δ 0x 2 ( y 2 y 1 ) 2 2 δ 0y 2 ]exp [ ( ik 2z 1 4 σ 0 2 ) r 1 2 +( ik 2z 1 4 σ 0 2 ) r 2 2 + ik z ( r 1 ρ 1 r 2 ρ 2 ) π 2 k 2 zT 3 ( r 1 r 2 ) 2 ] d 2 r 1 d 2 r 2 .
r s = r 1 + r 2 2 , x s = x 1 + x 2 2 , y s = y 1 + y 2 2 , r d = r 1 r 2 , x d = x 1 x 2 , y d = y 1 y 2 , ρ s = ρ 1 + ρ 2 2 , ρ sx = ρ 1x + ρ 2x 2 , ρ sy = ρ 1y + ρ 2y 2 , ρ d = ρ 1 ρ 2 , ρ dx = ρ 1x ρ 2x , ρ dy = ρ 1y ρ 2y ,
W( ρ 1 , ρ 2 ,z )= 4 G 0 σ 0 2 π 2 δ 0x δ 0y H 2m ( 0 ) H 2n ( 0 ) ab λ 2 z 2 ( 1 1 a ) m ( 1 1 b ) n H 2m [ c 2a ( 1 1 a ) 1/2 ] × H 2n [ d 2b ( 1 1 b ) 1/2 ]exp[ c 2 4a + d 2 4b ik z ( ρ sx ρ dx + ρ sy ρ dy )( 2 π 2 k 2 zT 3 + σ 0 2 k 2 2 z 2 )( ρ dx 2 + ρ dy 2 ) ],
a=2 δ 0x 2 ( 1 8 σ 0 2 + π 2 k 2 zT 3 + 1 2 δ 0x 2 + k 2 σ 0 2 2 z 2 ), b=2 δ 0y 2 ( 1 8 σ 0 2 + π 2 k 2 zT 3 + 1 2 δ 0y 2 + k 2 σ 0 2 2 z 2 ), c= 2 δ 0x ( ik ρ sx z + k 2 σ 0 2 ρ dx z 2 ), d= 2 δ 0y ( ik ρ sy z + k 2 σ 0 2 ρ dy z 2 ).
δ( s )= 1 2π exp( isx ) dx,
f( x ) δ n (x)dx = ( 1 ) n f ( n ) ( 0 ),( n=0,1,2 ),
exp( s 2 x 2 ±qx)dx= π s exp( q 2 4 s 2 ),
+ exp[ ( xy ) 2 2m ] H n ( x )dx= 2πm ( 12m ) n/2 H n [ y ( 12m ) 1/2 ].
S( ρ,z )=W( ρ 1 , ρ 2 ,z ).
μ( ρ 1 , ρ 2 ,z )= W( ρ 1 , ρ 2 ,z ) W( ρ 1 , ρ 1 ,z )W( ρ 2 , ρ 2 ,z ) .
ρ s = ρ 1 + ρ 2 2 , ρ d = ρ 1 ρ 2 ,
W( ρ s , ρ d ,z )= ( k 2πz ) 2 W ( 0 ) ( r s , r d ,0 ) ×exp[ ik z ( ρ s r s )( ρ d r d )H( ρ d , r d ,z ) ] d 2 r s d 2 r d ,
W ( 0 ) ( r s , r d ,0 )= W ( 0 ) ( r 1 , r 2 ,0 )= W ( 0 ) ( r s + r d 2 , r s r d 2 ,0 ),
H( ρ d , r d ,z )=4 π 2 k 2 z 0 1 dξ 0 [ 1 J 0 ( κ| r d ξ+( 1ξ ) ρ d | ) ] Φ n ( κ )κdκ,
W( ρ s , ρ d ,z )= ( 1 2π ) 2 W (0) ( r s , ρ d + z k κ d ,0 ) ×exp[ i ρ s κ d +i r s κ d H( ρ d , ρ d + z k κ d ,z ) ] d 2 r s d 2 κ d ,
H( ρ d , ρ d + z k κ d ,z )= π 2 k 2 z 3 ( 3 ρ d 2 +3 z k ρ d κ+ z 2 k 2 κ d 2 )T.
W( r s , ρ d + z k κ d ,0 )= G 0 H 2m ( 0 ) H 2n ( 0 ) exp[ r s 2 2 σ 0 2 1 8 σ 0 2 ( ρ d + z κ d k ) 2 ] × H 2m [ 1 2 δ 0x ( ρ dx + z k κ dx ) ] H 2n [ 1 2 δ 0y ( ρ dy + z k κ dy ) ] ×exp[ 1 2 δ 0x 2 ( ρ dx + z k κ dx ) 2 ]exp[ 1 2 δ 0y 2 ( ρ dy + z k κ dy ) 2 ].
h( ρ s ,θ,z )= ( k 2π ) 2 W( ρ s , ρ d ,z ) exp( ikθ ρ d ) d 2 ρ d ,
h( ρ s ,θ,z )=h( ρ sx , θ x ,z )h( ρ sy , θ y ,z ),
h( ρ sj , θ j ,z )= 2π G 0 σ 0 2 k 4 π 2 H 2l ( 0 ) H 2l [ 1 2 δ 0x ( ρ dx + z k κ dx ) ] ×exp( a x ρ dx 2 b x κ dx 2 c x ρ dx κ dx i ρ sx κ dx ik θ x ρ dx )d κ dx d ρ dx ,(j=x,yl=m,n),
a j = 1 2 δ 0j 2 + 1 8 σ 0 2 + π 2 k 2 zT, b j = z 2 2 k 2 δ 0j 2 + z 2 8 k 2 σ 0 2 + σ 0 2 2 + π 2 z 3 T 3 , c j = z k δ 0j 2 + z 4k σ 0 2 + π 2 z 2 kT, ( j=x,y ).
x n1 y n2 θ x m1 θ y m2 = 1 P x n1 y n2 θ x m1 θ y m2 h( ρ s ,θ,z ) d 2 ρ s d 2 θ,
P= h( ρ s ,θ,z ) d 2 ρ s d 2 θ.
ρ j 2 = 2π G 0 σ 0 2 P j H 2l ( 0 ) [ 2 z 2 ( 1 ) l1 ( 2l )! δ 0j 2 k 2 ( l1 )! 2 b j ( 1 ) l ( 2l )! l! ],
θ j 2 = 2π G 0 σ 0 2 P j H 2l ( 0 ) [ 2 ( 1 ) l1 ( 2l )! δ 0j 2 k 2 ( l1 )! 2 a j k 2 ( 1 ) l ( 2l )! l! ],
ρ j θ j = 2π G 0 σ 0 2 P j H 2l ( 0 ) [ 2z ( 1 ) l1 ( 2l )! δ 0j 2 k 2 ( l1 )! c j k ( 1 ) l ( 2l )! l! ],
P j = ( 1 ) l ( 2l )! 2π G 0 σ 0 2 l! H 2l ( 0 ) ,( j=x,y,l=m,n ).
M 2 ( z )=k ( ρ 2 θ 2 ρθ 2 ) 1/2 .
M x 2 ( z )=2k ( ρ x 2 θ x 2 ρ x θ x 2 ) 1/2 , M y 2 ( z )=2k ( ρ y 2 θ y 2 ρ y θ y 2 ) 1/2 ,
M j 2 (z)=2{ [ z 2 δ 0j 2 k 2 ( 2l+1 )+ z 2 4 k 2 σ 0 2 + σ 0 2 + 2 π 2 z 3 T 3 ][ 1 δ 0j 2 ( 2l+1 )+ 1 4 σ 0 2 +2 π 2 k 2 zT ] [ z k δ 0j 2 ( 2l+1 )+ z 4k σ 0 2 + π 2 z 2 kT ] 2 } 1/2 ,( j=x,y,l=m,n ).
M j 2 (z)= [ 4 σ 0 2 δ 0j 2 ( 2l+1 )+1 ] 1/2 = { 4 σ 0 2 δ 0j 2 [ 1 4l(2l1) H 2l2 ( 0 ) H 2l ( 0 ) ]+1 } 1/2 ,( j=x,y,l=m,n ).

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