Abstract

The effects of anisotropic, non-Kolmogorov turbulence on propagating stochastic electromagnetic beam-like fields are discussed for the first time. The atmosphere of interest can be found above the boundary layer, at high (more than 2 km above the ground) altitudes where the energy distribution among the turbulent eddies might not satisfy the classic assumption represented by the famous 11/3 Kolmogorov’s power law, and the anisotropy in the direction orthogonal to the Earth surface is possibly present. Our analysis focuses on the classic electromagnetic Gaussian Schell-model beams but can either be readily reduced to scalar and/or coherent beams or generalized to other beam classes. In particular, we explore the effects of the anisotropic parameter on the spectral density, the spectral degree of coherence and on the spectral degree of polarization of the beam.

© 2014 Optical Society of America

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2014 (3)

2013 (4)

2012 (3)

2011 (2)

2010 (4)

2009 (4)

F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17(25), 22366–22379 (2009).
[Crossref] [PubMed]

D. T. Kyrazis, F. D. Eaton, D. G. Black, W. T. Black, and R. A. Black, “The balloon ring: a high-performance, low-cost instrumentation platform for measuring atmospheric turbulence profiles,” Proc. SPIE 7463, 3–4 (2009).
[Crossref]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[Crossref]

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

2008 (4)

2007 (3)

W. Lu, L. Liu, J. Sun, Q. Yang, and Y. Zhu, “Change in the degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 271(1), 1–8 (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free-space laser beam propagation in non-Kolmogorov turbulence,” Proc. SPIE 6751, 65510E (2007).
[Crossref]

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

2006 (1)

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui space Surveillance Site (MSSS),” Proc. SPIE 6304, 6304U (2006).

2005 (2)

L. Biferale and I. Procaccia, “Anisotropy in turbulent flows and in turbulent transport,” Phys. Rep. 414(2-3), 43–164 (2005).
[Crossref]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (2005).
[Crossref]

1999 (2)

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

M. S. Belen’kii, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[Crossref]

1998 (1)

F. D. Eaton and G. D. Nastrom, “Preliminary estimates of the vertical profiles of inner and outer scales from White Sands Missile Range,” Radio Sci. 33(4), 895–903 (1998).
[Crossref]

1997 (1)

A. S. Gurvich and V. Kan, “Radio wave fluctuations in satellite–atmosphere–satellite links: estimates from stellar scintillation observations and their comparison with experimental data,” Atmos. Oceanic Phys. 33, 284–292 (1997).

1996 (1)

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1-3), 113–121 (1996).
[Crossref]

1995 (2)

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE 2375, 6–16 (1995).
[Crossref]

1994 (3)

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of ‘sheets’ in the atmospheric temperature Field,” J. Atmos. Sci. 51(2), 237–248 (1994).
[Crossref]

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularity,” Waves Rand. Compl. Media 4(3), 297–306 (1994).
[Crossref]

1992 (1)

G. M. Grechko, A. S. Gurvich, V. Kan, S. V. Kireev, and S. A. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

1970 (1)

1960 (1)

L. R. Tsvang, “Measurements of the spectrum of temperature fluctuations in the free atmosphere,” Izvestiya Akademii Nauk SSSR, Geofizicheskaya 1, 1117–1120 (1960).

Agrawal, B.

Andrews, L. C.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

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

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free-space laser beam propagation in non-Kolmogorov turbulence,” Proc. SPIE 6751, 65510E (2007).
[Crossref]

Barchers, J. D.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Beland, R. R.

R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE 2375, 6–16 (1995).
[Crossref]

Belen’kii, M. S.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui space Surveillance Site (MSSS),” Proc. SPIE 6304, 6304U (2006).

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

M. S. Belen’kii, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[Crossref]

Biferale, L.

L. Biferale and I. Procaccia, “Anisotropy in turbulent flows and in turbulent transport,” Phys. Rep. 414(2-3), 43–164 (2005).
[Crossref]

Bishop, K. P.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Black, D. G.

D. T. Kyrazis, F. D. Eaton, D. G. Black, W. T. Black, and R. A. Black, “The balloon ring: a high-performance, low-cost instrumentation platform for measuring atmospheric turbulence profiles,” Proc. SPIE 7463, 3–4 (2009).
[Crossref]

Black, R. A.

D. T. Kyrazis, F. D. Eaton, D. G. Black, W. T. Black, and R. A. Black, “The balloon ring: a high-performance, low-cost instrumentation platform for measuring atmospheric turbulence profiles,” Proc. SPIE 7463, 3–4 (2009).
[Crossref]

Black, W. T.

D. T. Kyrazis, F. D. Eaton, D. G. Black, W. T. Black, and R. A. Black, “The balloon ring: a high-performance, low-cost instrumentation platform for measuring atmospheric turbulence profiles,” Proc. SPIE 7463, 3–4 (2009).
[Crossref]

Borghi, R.

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33(16), 1857–1859 (2008).
[Crossref] [PubMed]

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1-3), 113–121 (1996).
[Crossref]

Brown, J. M.

M. S. Belen’kii, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[Crossref]

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Cai, Y.

C. Yan, F. Wang, and Y. Cai, “Propagation of a twist Gaussian–Schell model beam in non-Kolmogorov turbulence,” Opt. Commun. 324, 108–113 (2014).
[Crossref]

F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17(25), 22366–22379 (2009).
[Crossref] [PubMed]

Cincotti, G.

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1-3), 113–121 (1996).
[Crossref]

Conan, J. M.

Consortini, A.

Crabbs, R.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

Crochet, M.

F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of ‘sheets’ in the atmospheric temperature Field,” J. Atmos. Sci. 51(2), 237–248 (1994).
[Crossref]

Cuellar, E.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui space Surveillance Site (MSSS),” Proc. SPIE 6304, 6304U (2006).

Dalaudier, F.

Du, W.

L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, “Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(2), 451–462 (2010).
[Crossref] [PubMed]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[Crossref]

Eaton, F. D.

D. T. Kyrazis, F. D. Eaton, D. G. Black, W. T. Black, and R. A. Black, “The balloon ring: a high-performance, low-cost instrumentation platform for measuring atmospheric turbulence profiles,” Proc. SPIE 7463, 3–4 (2009).
[Crossref]

F. D. Eaton and G. D. Nastrom, “Preliminary estimates of the vertical profiles of inner and outer scales from White Sands Missile Range,” Radio Sci. 33(4), 895–903 (1998).
[Crossref]

Ferrero, V.

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

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free-space laser beam propagation in non-Kolmogorov turbulence,” Proc. SPIE 6751, 65510E (2007).
[Crossref]

Fugate, R. Q.

M. S. Belen’kii, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[Crossref]

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Golbraikh, E.

Gori, F.

Grechko, G. M.

G. M. Grechko, A. S. Gurvich, V. Kan, S. V. Kireev, and S. A. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Guo, H.

Gurvich, A. S.

A. S. Gurvich and V. Kan, “Radio wave fluctuations in satellite–atmosphere–satellite links: estimates from stellar scintillation observations and their comparison with experimental data,” Atmos. Oceanic Phys. 33, 284–292 (1997).

G. M. Grechko, A. S. Gurvich, V. Kan, S. V. Kireev, and S. A. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Han, Q.

Hughes, K. A.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui space Surveillance Site (MSSS),” Proc. SPIE 6304, 6304U (2006).

Jiang, Y.

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[Crossref]

Kan, V.

A. S. Gurvich and V. Kan, “Radio wave fluctuations in satellite–atmosphere–satellite links: estimates from stellar scintillation observations and their comparison with experimental data,” Atmos. Oceanic Phys. 33, 284–292 (1997).

G. M. Grechko, A. S. Gurvich, V. Kan, S. V. Kireev, and S. A. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Karis, S. J.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

M. S. Belen’kii, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[Crossref]

Keating, D. D. B.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Kireev, S. V.

G. M. Grechko, A. S. Gurvich, V. Kan, S. V. Kireev, and S. A. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Kon, A. I.

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularity,” Waves Rand. Compl. Media 4(3), 297–306 (1994).
[Crossref]

Kopeika, N. S.

Korotkova, O.

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

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

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

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

Z. S. Tong and O. Korotkova, “Non-uniformly 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]

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

O. Korotkova and E. Shchepakina, “Color changes in stochastic light fields propagating in non-Kolmogorov turbulence,” Opt. Lett. 35(22), 3772–3774 (2010).
[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, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17(25), 22366–22379 (2009).
[Crossref] [PubMed]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (2005).
[Crossref]

Kyrazis, D. T.

D. T. Kyrazis, F. D. Eaton, D. G. Black, W. T. Black, and R. A. Black, “The balloon ring: a high-performance, low-cost instrumentation platform for measuring atmospheric turbulence profiles,” Proc. SPIE 7463, 3–4 (2009).
[Crossref]

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Lajunen, H.

Leclerc, T.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

Liu, L.

W. Lu, L. Liu, J. Sun, Q. Yang, and Y. Zhu, “Change in the degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 271(1), 1–8 (2007).
[Crossref]

Lu, W.

W. Lu, L. Liu, J. Sun, Q. Yang, and Y. Zhu, “Change in the degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 271(1), 1–8 (2007).
[Crossref]

Luo, B.

Ma, J.

L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, “Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(2), 451–462 (2010).
[Crossref] [PubMed]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[Crossref]

Mei, Z. R.

Michau, V.

Nastrom, G. D.

F. D. Eaton and G. D. Nastrom, “Preliminary estimates of the vertical profiles of inner and outer scales from White Sands Missile Range,” Radio Sci. 33(4), 895–903 (1998).
[Crossref]

Osmon, C. L.

M. S. Belen’kii, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[Crossref]

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Palma, C.

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1-3), 113–121 (1996).
[Crossref]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

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

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free-space laser beam propagation in non-Kolmogorov turbulence,” Proc. SPIE 6751, 65510E (2007).
[Crossref]

Preble, A. J.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Procaccia, I.

L. Biferale and I. Procaccia, “Anisotropy in turbulent flows and in turbulent transport,” Phys. Rep. 414(2-3), 43–164 (2005).
[Crossref]

Renard, J. B.

Restaino, S.

Robert, C.

Roggemann, M. C.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Ronchi, L.

Rye, V. A.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui space Surveillance Site (MSSS),” Proc. SPIE 6304, 6304U (2006).

Saastamoinen, T.

Sahin, S.

Sanchez, V. R.

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

Santarsiero, M.

Savchenko, S. A.

G. M. Grechko, A. S. Gurvich, V. Kan, S. V. Kireev, and S. A. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Schchepakina, E.

Shchepakina, E.

Shirai, T.

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

Sidi, C.

F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of ‘sheets’ in the atmospheric temperature Field,” J. Atmos. Sci. 51(2), 237–248 (1994).
[Crossref]

Stefanutti, L.

Stribling, B. E.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Sun, J.

W. Lu, L. Liu, J. Sun, Q. Yang, and Y. Zhu, “Change in the degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 271(1), 1–8 (2007).
[Crossref]

Tan, L.

L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, “Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(2), 451–462 (2010).
[Crossref] [PubMed]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[Crossref]

Tong, Z. S.

Toselli, I.

I. Toselli, “Introducing the concept of anisotropy at different scales for modeling optical turbulence,” J. Opt. Soc. Am. A 31(8), 1868–1875 (2014).
[Crossref] [PubMed]

I. Toselli, B. Agrawal, and S. Restaino, “Light propagation through anisotropic turbulence,” J. Opt. Soc. Am. A 28(3), 483–488 (2011).
[Crossref] [PubMed]

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

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free-space laser beam propagation in non-Kolmogorov turbulence,” Proc. SPIE 6751, 65510E (2007).
[Crossref]

Tsvang, L. R.

L. R. Tsvang, “Measurements of the spectrum of temperature fluctuations in the free atmosphere,” Izvestiya Akademii Nauk SSSR, Geofizicheskaya 1, 1117–1120 (1960).

Vernin, J.

F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of ‘sheets’ in the atmospheric temperature Field,” J. Atmos. Sci. 51(2), 237–248 (1994).
[Crossref]

Wang, F.

C. Yan, F. Wang, and Y. Cai, “Propagation of a twist Gaussian–Schell model beam in non-Kolmogorov turbulence,” Opt. Commun. 324, 108–113 (2014).
[Crossref]

F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17(25), 22366–22379 (2009).
[Crossref] [PubMed]

Welsh, B. M.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Wissler, J.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Wolf, E.

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (2005).
[Crossref]

Wu, G.

Xie, W.

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[Crossref]

Yan, C.

C. Yan, F. Wang, and Y. Cai, “Propagation of a twist Gaussian–Schell model beam in non-Kolmogorov turbulence,” Opt. Commun. 324, 108–113 (2014).
[Crossref]

Yang, Q.

W. Lu, L. Liu, J. Sun, Q. Yang, and Y. Zhu, “Change in the degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 271(1), 1–8 (2007).
[Crossref]

Yu, S.

Zhu, Y.

W. Lu, L. Liu, J. Sun, Q. Yang, and Y. Zhu, “Change in the degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 271(1), 1–8 (2007).
[Crossref]

Zilberman, A.

Adv. Space Res. (1)

G. M. Grechko, A. S. Gurvich, V. Kan, S. V. Kireev, and S. A. Savchenko, “Anisotropy of spatial structures in the middle atmosphere,” Adv. Space Res. 12(10), 169–175 (1992).
[Crossref]

Appl. Opt. (2)

Atmos. Oceanic Phys. (1)

A. S. Gurvich and V. Kan, “Radio wave fluctuations in satellite–atmosphere–satellite links: estimates from stellar scintillation observations and their comparison with experimental data,” Atmos. Oceanic Phys. 33, 284–292 (1997).

Izvestiya Akademii Nauk SSSR, Geofizicheskaya (1)

L. R. Tsvang, “Measurements of the spectrum of temperature fluctuations in the free atmosphere,” Izvestiya Akademii Nauk SSSR, Geofizicheskaya 1, 1117–1120 (1960).

J. Atmos. Sci. (1)

F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of ‘sheets’ in the atmospheric temperature Field,” J. Atmos. Sci. 51(2), 237–248 (1994).
[Crossref]

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

F. Gori, V. R. Sanchez, 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)

Opt. Commun. (5)

W. Lu, L. Liu, J. Sun, Q. Yang, and Y. Zhu, “Change in the degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 271(1), 1–8 (2007).
[Crossref]

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1-3), 113–121 (1996).
[Crossref]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (2005).
[Crossref]

C. Yan, F. Wang, and Y. Cai, “Propagation of a twist Gaussian–Schell model beam in non-Kolmogorov turbulence,” Opt. Commun. 324, 108–113 (2014).
[Crossref]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[Crossref]

Opt. Eng. (1)

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

Opt. Express (4)

Opt. Lett. (10)

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

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

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

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

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

G. Wu, H. Guo, S. Yu, and B. Luo, “Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence,” Opt. Lett. 35(5), 715–717 (2010).
[Crossref] [PubMed]

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33(16), 1857–1859 (2008).
[Crossref] [PubMed]

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

Phys. Rep. (1)

L. Biferale and I. Procaccia, “Anisotropy in turbulent flows and in turbulent transport,” Phys. Rep. 414(2-3), 43–164 (2005).
[Crossref]

Proc. SPIE (9)

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

M. S. Belen’kii, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[Crossref]

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE 2375, 6–16 (1995).
[Crossref]

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

D. T. Kyrazis, F. D. Eaton, D. G. Black, W. T. Black, and R. A. Black, “The balloon ring: a high-performance, low-cost instrumentation platform for measuring atmospheric turbulence profiles,” Proc. SPIE 7463, 3–4 (2009).
[Crossref]

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui space Surveillance Site (MSSS),” Proc. SPIE 6304, 6304U (2006).

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free-space laser beam propagation in non-Kolmogorov turbulence,” Proc. SPIE 6751, 65510E (2007).
[Crossref]

Radio Sci. (1)

F. D. Eaton and G. D. Nastrom, “Preliminary estimates of the vertical profiles of inner and outer scales from White Sands Missile Range,” Radio Sci. 33(4), 895–903 (1998).
[Crossref]

Waves Rand. Compl. Media (1)

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularity,” Waves Rand. Compl. Media 4(3), 297–306 (1994).
[Crossref]

Other (6)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

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

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

L. C. Andrews and R. L. Phillips, Laser Beam Propagation in Random Media, 2nd ed. (SPIE 2005).
[Crossref]

O. Korotkova, Propagation of Partially Coherent Beams in Turbulent Atmosphere (WDM, 2009).

O. Korotkova, Random Beams: Theory and Applications (CRC, 2013).

Cited By

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Figures (8)

Fig. 1
Fig. 1 The normalized on-axis spectral density S N of a fully coherent EMGSM beam ( r=0 ): (a) as a function of distance z with different ς and α=3.5 ; (b) as a function of α and ς at z=30km .
Fig. 2
Fig. 2 The beam width of a fully coherent EMGSM source for r=0 : (a) as a function of distance z with different ς, (b) as a function of α and ς at z=30km .
Fig. 3
Fig. 3 The spectral degree of coherence η of fully coherent EMGSM source, (a) as a function of distance z with different ς for r=0 , (b) as a function of α and ς at z=30km (c) as a function of the width r d and ς at z=30km .
Fig. 4
Fig. 4 The normalized spectral density S N of a typical partially coherent EMGSM beam for r=0 , (a) as a function of distance z with different ς, (b) as a function of α and ς at z=30km .
Fig. 5
Fig. 5 The r.m.s. beam width of a partially coherent EMGSM beam for r=0 : (a) σ x and (c) σ y as a function of distance z with different ς, (b) σ x and (d) σ y as a function of α and ς at far field z=30km .
Fig. 6
Fig. 6 The spectral degree of coherenceη, (a) as a function of distance z with different ς for r=0 , (b) as a function of α and ς at z=30km (c) as a function of ς and the width r at z=30km .
Fig. 7
Fig. 7 The degree of polarization P of a partially coherent EMGSM beam for r=0 , (a) as a function of distance z with different ς, (b) as a function of α and ς at z=30km .
Fig. 8
Fig. 8 The evolution of polarization ellipse propagating at anisotropic turbulence with different ς for r=0 , (a) degree of polarization as a function of distance z with different ς; (b) polarization angle, (c) the degree of ellipticity, (d) polarization ellipse in the far field, z=30km . Other beam parameters are δ xy =0.015m , B xy =0.2 e iπ/6 .

Equations (20)

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

Φ n ( κ,α )=A( α ) C ˜ n 2 ζ 2 ( ζ 2 κ xy 2 + κ z 2 + κ 0 2 ) α 2 exp( ζ 2 κ xy 2 + κ z 2 κ m 2 ),κ>0,3<α<5,
C( α )= { πA( α )Γ( 3 2 α 2 )( 3α 3 ) } 1 α5 ,3<α<5,
A( α )= Γ( α1 ) 4 π 2 cos( α π 2 ),3<α<5,
W ij ( r 1 , r 2 ;ω )= ( k 2πz ) 2 W ij 0 ( r 1 0 , r 2 0 ;ω )K( r 1 0 , r 2 0 , r 1 , r 2 ;ω ) d 2 r 1 0 d 2 r 2 0 ,(i,j=x,y),
K( r 1 0 , r 2 0 , r 1 , r 2 ;ω )=exp[ ik ( r 1 r 1 0 ) 2 ( r 2 r 2 0 ) 2 2z ] ×exp{ π 2 k 2 z 3 [ ( r 1 r 2 ) 2 +( r 1 r 2 )( r 1 0 r 2 0 )+ ( r 1 0 r 2 0 ) 2 ] 0 κ 3 Φ n ( κ )dκ }.
C ˜ ¯ n 2 = 1 H h 0 h 0 H C ˜ n 2 ( h ) dh
C ˜ n 2 ( h )=0.00594 ( v pw 27 ) 2 ( 10 5 h ) 10 exp( h 1000 )+2.7× 10 16 exp( h 1500 )+ C ˜ n 2 exp( h 100 ),
I= 0 κ 3 Φ n ( κ ) dκ= ζ 2 0 κ 3 A( α ) C ˜ ¯ n 2 ( ζ 2 κ 2 + κ 0 2 ) α 2 exp( ζ 2 κ 2 κ m 2 )dκ = ζ 2α 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 ].
I= 0 κ 3 Φ n ( κ ) dκ= ζ 2 0 κ 3 A( α ) C ˜ ¯ n 2 [ ζ 2 ( κ 2 + κ 0 2 ζ 2 ) ] α 2 exp( ζ 2 κ 2 κ m 2 )dκ = ζ 2α 0 κ 3 A( α ) C ˜ ¯ n 2 ( κ 2 + κ ˜ 0 2 ) α 2 exp( κ 2 κ ˜ m 2 )dκ = ζ 2α 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 ij 0 ( r 1 0 , r 2 0 ;ω )= B ij I i I j exp[ ( r 1 0 ) 2 + ( r 2 0 ) 2 4 σ 2 ]exp[ ( r 1 0 r 2 0 ) 2 2 δ ij 2 ],(i,j=x,y),
W ij ( r 1 , r 2 ;ω )= B ij I i I j Δ ij 2 ( z ) exp[ ( r 1 + r 2 ) 2 8 σ 2 Δ ij 2 ( z ) ]exp[ ik( r 2 2 r 1 2 ) 2 R ij ( z ) ] ×exp{ [ 1 2 Δ ij 2 ( z ) ( 1 4 σ 2 + 1 δ ij 2 )+ 1 3 π 2 k 2 zI( 1+ 2 Δ ij 2 ( z ) ) π 4 k 2 z 4 I 2 18 σ 2 Δ ij 2 ( z ) ] ( r 1 r 2 ) 2 },
Δ ij 2 ( z )=1+ z 2 k 2 σ 2 ( 1 4 σ 2 + 1 δ ij 2 )+ 2 π 2 z 3 I 3 σ 2 , R ij ( z )= σ 2 Δ ij 2 ( z )z σ 2 Δ ij 2 ( z )+ ( π 2 z 3 I σ 2 ) /3 .
S( r;ω )=TrW( r,r;ω ),
η( r 1 , r 2 ;ω )= TrW( r 1 , r 2 ;ω ) S( r 1 ;ω ) S( r 2 ;ω ) ,
P( r;ω )= 1 4DetW( r,r;ω ) [ TrW( r,r;ω ) ] 2 = 1 4( W xx W yy W xy 2 ) ( W xx + W yy ) 2 ,
θ( r;ω )= 1 2 arctan[ 2Re W xy ( r,r;ω ) W xx ( r,r;ω ) W yy ( r,r;ω ) ],( π/2<θπ/2 )
ε( r;ω )= A minor ( r;ω )/ A major ( r;ω ),
A major 2 ( r;ω )= ( ( W xx W yy ) 2 +4 | W xy | 2 + ( W xx W yy ) 2 +4 [ Re( W xy ) ] 2 ) /2 ,
A minor 2 ( r;ω )= ( ( W xx W yy ) 2 +4 | W xy | 2 ( W xx W yy ) 2 +4 [ Re( W xy ) ] 2 ) /2 .
σ ij 2 ( z )= σ 2 Δ ij 2 ( z ),(i,j=x,y).

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