Abstract

Two different methodologies for generating an electromagnetic Gaussian-Schell model source are discussed. One approach uses a sequence of random phase screens at the source plane and the other uses a sequence of random complex transmittance screens. The relationships between the screen parameters and the desired electromagnetic Gaussian-Schell model source parameters are derived. The approaches are verified by comparing numerical simulation results with published theory. This work enables one to design an electromagnetic Gaussian-Schell model source with pre-defined characteristics for wave optics simulations or laboratory experiments.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  3. S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18(12), 12587–12598 (2010).
    [Crossref] [PubMed]
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    [Crossref]
  5. Y. Zhu, D. Zhao, and X. Du, “Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere,” Opt. Express 16(22), 18437–18442 (2008).
    [Crossref] [PubMed]
  6. O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
    [Crossref]
  7. M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
    [Crossref]
  8. O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. 281(9), 2342–2348 (2008).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  15. F. Gori, M. Santarsiero, R. Borghi, and V. Ramirez-Sanchez, “Realizability condition for electromagnetic Schell-model souces,” J. Opt. Soc. Am. A 25(5), 1016–1021 (2008).
    [Crossref]
  16. A. S. Ostrovsky, G. Martínez-Niconoff, V. Arrizón, P. Martínez-Vara, M. A. Olvera-Santamaría, and C. Rickenstorff-Parrao, “Modulation of coherence and polarization using liquid crystal spatial light modulators,” Opt. Express 17(7), 5257–5264 (2009).
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  17. X. Xiao and D. Voelz, “Wave optics simulation of partially coherent and partially polarized beam propagation in turbulence,” Proc. SPIE 7464, 74640T (2009).
    [Crossref]
  18. G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208(1-3), 9–16 (2002).
    [Crossref]
  19. F. Wang, G. Wu, X. Liu, S. Zhu, and Y. Cai, “Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source,” Opt. Lett. 36(14), 2722–2724 (2011).
    [Crossref] [PubMed]
  20. T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
    [Crossref]
  21. A. S. Ostrovsky, G. Rodríguez-Zurita, C. Meneses-Fabián, M. A. Olvera-Santamaría, and C. Rickenstorff-Parrao, “Experimental generating the partially coherent and partially polarized electromagnetic source,” Opt. Express 18(12), 12864–12871 (2010).
    [Crossref] [PubMed]
  22. P. Meemon, M. Salem, K. S. Lee, M. Chopra, and J. P. Rolland, “Determination of the coherency matrix of a broadband stochastic electromagnetic light beam,” J. Mod. Opt. 55(17), 2765–2776 (2008).
    [Crossref]
  23. S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “Polarization-induced reduction in scintillation of optical beams propagating in simulated turbulent atmospheric channels,” Waves Complex Random Media. in press.
  24. S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “The dependence of the intensity PDF of a random beam propagating in the maritime atmosphere on source coherence,” Waves Complex Random Media 24(1), 69–82 (2014).
    [Crossref]
  25. J. W. Goodman, Statistical Optics (Wiley, 2000).
  26. Boulder Nonlinear Systems, Inc., Spatial Light Modulators—XY Series (Retrieved November 13, 2014 from http://www.meadowlark.com/store/data_sheet/Datasheet_XYseries_SLM.pdf ).
  27. S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283(22), 4512–4518 (2010).
    [Crossref]

2014 (2)

J. C. G. de Sande, G. Piquero, M. Santarsiero, and F. Gori, “Partially coherent electromagnetic beams propagating through double-wedge depolarizers,” J. Opt. 16(3), 035708 (2014).
[Crossref]

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “The dependence of the intensity PDF of a random beam propagating in the maritime atmosphere on source coherence,” Waves Complex Random Media 24(1), 69–82 (2014).
[Crossref]

2011 (1)

2010 (3)

2009 (2)

2008 (4)

Y. Zhu, D. Zhao, and X. Du, “Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere,” Opt. Express 16(22), 18437–18442 (2008).
[Crossref] [PubMed]

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

P. Meemon, M. Salem, K. S. Lee, M. Chopra, and J. P. Rolland, “Determination of the coherency matrix of a broadband stochastic electromagnetic light beam,” J. Mod. Opt. 55(17), 2765–2776 (2008).
[Crossref]

F. Gori, M. Santarsiero, R. Borghi, and V. Ramirez-Sanchez, “Realizability condition for electromagnetic Schell-model souces,” J. Opt. Soc. Am. A 25(5), 1016–1021 (2008).
[Crossref]

2005 (2)

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

2004 (4)

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29(11), 1173–1175 (2004).
[Crossref] [PubMed]

J. Tervo, T. Setälä, and A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space-frequency domain,” J. Opt. Soc. Am. A 21(11), 2205–2215 (2004).
[Crossref] [PubMed]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[Crossref]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

2002 (1)

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208(1-3), 9–16 (2002).
[Crossref]

2001 (1)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

1998 (1)

1994 (1)

Arrizón, V.

Avramov-Zamurovic, S.

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “The dependence of the intensity PDF of a random beam propagating in the maritime atmosphere on source coherence,” Waves Complex Random Media 24(1), 69–82 (2014).
[Crossref]

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “Polarization-induced reduction in scintillation of optical beams propagating in simulated turbulent atmospheric channels,” Waves Complex Random Media. in press.

Borghi, R.

F. Gori, M. Santarsiero, R. Borghi, and V. Ramirez-Sanchez, “Realizability condition for electromagnetic Schell-model souces,” J. Opt. Soc. Am. A 25(5), 1016–1021 (2008).
[Crossref]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208(1-3), 9–16 (2002).
[Crossref]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Cai, Y.

Chopra, M.

P. Meemon, M. Salem, K. S. Lee, M. Chopra, and J. P. Rolland, “Determination of the coherency matrix of a broadband stochastic electromagnetic light beam,” J. Mod. Opt. 55(17), 2765–2776 (2008).
[Crossref]

de Sande, J. C. G.

J. C. G. de Sande, G. Piquero, M. Santarsiero, and F. Gori, “Partially coherent electromagnetic beams propagating through double-wedge depolarizers,” J. Opt. 16(3), 035708 (2014).
[Crossref]

Dogariu, A.

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

Du, X.

Friberg, A. T.

Gori, F.

J. C. G. de Sande, G. Piquero, M. Santarsiero, and F. Gori, “Partially coherent electromagnetic beams propagating through double-wedge depolarizers,” J. Opt. 16(3), 035708 (2014).
[Crossref]

F. Gori, M. Santarsiero, R. Borghi, and V. Ramirez-Sanchez, “Realizability condition for electromagnetic Schell-model souces,” J. Opt. Soc. Am. A 25(5), 1016–1021 (2008).
[Crossref]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208(1-3), 9–16 (2002).
[Crossref]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23(4), 241–243 (1998).
[Crossref] [PubMed]

James, D. F.

Korotkova, O.

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “The dependence of the intensity PDF of a random beam propagating in the maritime atmosphere on source coherence,” Waves Complex Random Media 24(1), 69–82 (2014).
[Crossref]

S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283(22), 4512–4518 (2010).
[Crossref]

S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18(12), 12587–12598 (2010).
[Crossref] [PubMed]

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

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29(11), 1173–1175 (2004).
[Crossref] [PubMed]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[Crossref]

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “Polarization-induced reduction in scintillation of optical beams propagating in simulated turbulent atmospheric channels,” Waves Complex Random Media. in press.

Lee, K. S.

P. Meemon, M. Salem, K. S. Lee, M. Chopra, and J. P. Rolland, “Determination of the coherency matrix of a broadband stochastic electromagnetic light beam,” J. Mod. Opt. 55(17), 2765–2776 (2008).
[Crossref]

Liu, X.

Malek-Madani, R.

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “The dependence of the intensity PDF of a random beam propagating in the maritime atmosphere on source coherence,” Waves Complex Random Media 24(1), 69–82 (2014).
[Crossref]

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “Polarization-induced reduction in scintillation of optical beams propagating in simulated turbulent atmospheric channels,” Waves Complex Random Media. in press.

Martínez-Niconoff, G.

Martínez-Vara, P.

Meemon, P.

P. Meemon, M. Salem, K. S. Lee, M. Chopra, and J. P. Rolland, “Determination of the coherency matrix of a broadband stochastic electromagnetic light beam,” J. Mod. Opt. 55(17), 2765–2776 (2008).
[Crossref]

Meneses-Fabián, C.

Mondello, A.

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208(1-3), 9–16 (2002).
[Crossref]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Nelson, C.

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “The dependence of the intensity PDF of a random beam propagating in the maritime atmosphere on source coherence,” Waves Complex Random Media 24(1), 69–82 (2014).
[Crossref]

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “Polarization-induced reduction in scintillation of optical beams propagating in simulated turbulent atmospheric channels,” Waves Complex Random Media. in press.

Olvera-Santamaría, M. A.

Ostrovsky, A. S.

Piquero, G.

J. C. G. de Sande, G. Piquero, M. Santarsiero, and F. Gori, “Partially coherent electromagnetic beams propagating through double-wedge depolarizers,” J. Opt. 16(3), 035708 (2014).
[Crossref]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208(1-3), 9–16 (2002).
[Crossref]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Ramirez-Sanchez, V.

Rickenstorff-Parrao, C.

Rodríguez-Zurita, G.

Rolland, J. P.

P. Meemon, M. Salem, K. S. Lee, M. Chopra, and J. P. Rolland, “Determination of the coherency matrix of a broadband stochastic electromagnetic light beam,” J. Mod. Opt. 55(17), 2765–2776 (2008).
[Crossref]

Romanini, P.

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208(1-3), 9–16 (2002).
[Crossref]

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

Sahin, S.

S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283(22), 4512–4518 (2010).
[Crossref]

Salem, M.

P. Meemon, M. Salem, K. S. Lee, M. Chopra, and J. P. Rolland, “Determination of the coherency matrix of a broadband stochastic electromagnetic light beam,” J. Mod. Opt. 55(17), 2765–2776 (2008).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29(11), 1173–1175 (2004).
[Crossref] [PubMed]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[Crossref]

Santarsiero, M.

J. C. G. de Sande, G. Piquero, M. Santarsiero, and F. Gori, “Partially coherent electromagnetic beams propagating through double-wedge depolarizers,” J. Opt. 16(3), 035708 (2014).
[Crossref]

F. Gori, M. Santarsiero, R. Borghi, and V. Ramirez-Sanchez, “Realizability condition for electromagnetic Schell-model souces,” J. Opt. Soc. Am. A 25(5), 1016–1021 (2008).
[Crossref]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208(1-3), 9–16 (2002).
[Crossref]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Setälä, T.

Shirai, T.

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

Simon, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Tervo, J.

Tong, Z.

S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283(22), 4512–4518 (2010).
[Crossref]

Voelz, D.

X. Xiao and D. Voelz, “Wave optics simulation of partially coherent and partially polarized beam propagation in turbulence,” Proc. SPIE 7464, 74640T (2009).
[Crossref]

Wang, F.

Wolf, E.

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29(11), 1173–1175 (2004).
[Crossref] [PubMed]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[Crossref]

Wu, G.

Xiao, X.

X. Xiao and D. Voelz, “Wave optics simulation of partially coherent and partially polarized beam propagation in turbulence,” Proc. SPIE 7464, 74640T (2009).
[Crossref]

Zhao, D.

Zhu, S.

Zhu, Y.

J. Mod. Opt. (1)

P. Meemon, M. Salem, K. S. Lee, M. Chopra, and J. P. Rolland, “Determination of the coherency matrix of a broadband stochastic electromagnetic light beam,” J. Mod. Opt. 55(17), 2765–2776 (2008).
[Crossref]

J. Opt. (1)

J. C. G. de Sande, G. Piquero, M. Santarsiero, and F. Gori, “Partially coherent electromagnetic beams propagating through double-wedge depolarizers,” J. Opt. 16(3), 035708 (2014).
[Crossref]

J. Opt. A, Pure Appl. Opt. (2)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

J. Opt. Soc. Am. A (3)

Opt. Commun. (5)

S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283(22), 4512–4518 (2010).
[Crossref]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208(1-3), 9–16 (2002).
[Crossref]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[Crossref]

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

Opt. Express (4)

Opt. Lett. (3)

Proc. SPIE (1)

X. Xiao and D. Voelz, “Wave optics simulation of partially coherent and partially polarized beam propagation in turbulence,” Proc. SPIE 7464, 74640T (2009).
[Crossref]

Waves Complex Random Media (1)

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “The dependence of the intensity PDF of a random beam propagating in the maritime atmosphere on source coherence,” Waves Complex Random Media 24(1), 69–82 (2014).
[Crossref]

Waves Random Media (1)

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

Other (5)

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

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

J. W. Goodman, Statistical Optics (Wiley, 2000).

Boulder Nonlinear Systems, Inc., Spatial Light Modulators—XY Series (Retrieved November 13, 2014 from http://www.meadowlark.com/store/data_sheet/Datasheet_XYseries_SLM.pdf ).

S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, and O. Korotkova, “Polarization-induced reduction in scintillation of optical beams propagating in simulated turbulent atmospheric channels,” Waves Complex Random Media. in press.

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Figures (3)

Fig. 1
Fig. 1 Proposed experimental schematic for generating EGSM sources. The acronyms used in the figure are beam expander (BE), half-wave plate (HWP), polarizing beamsplitter (PBS), lens systems (LS), spatial light modulator (SLM), Gaussian amplitude filter (GAF), and variable retarder (VR). The polarization state of the light passing through the system is denoted by two-sided arrows (representing horizontal polarization) and circles (representing vertical polarization). When both are present, the light is in a general polarization state, i.e., polarized, partially polarized, or unpolarized.
Fig. 2
Fig. 2 Case I PS and CS simulation results versus theory. The rows are S 0 , S 1 , S 2 , S 3 , and η, respectively, while the columns are the PS, CS, and theory results, respectively. Each row of images is on the same color scale specified by the color bar in each row.
Fig. 3
Fig. 3 Case II PS and CS simulation results versus theory. The rows are S 0 , S 1 , S 2 , S 3 , and η, respectively, while the columns are the PS, CS, and theory results, respectively. Each row of images is on the same color scale specified by the color bar in each row.

Tables (1)

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Table 1 EGSM Source Parameters

Equations (39)

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W αβ ( ρ 1 , ρ 2 ,0;ω )= S α ( ρ 1 ;ω ) S β ( ρ 2 ;ω ) μ αβ ( | ρ 1 ρ 2 |;ω ) S α ( ρ;ω )= A α 2 exp( ρ 2 2 σ α 2 ) μ αβ ( | ρ 1 ρ 2 |;ω )= B αβ exp( | ρ 1 ρ 2 | 2 2 δ αβ 2 ),
B αβ =1α=β | B αβ |1αβ B αβ = B βα * δ αβ = δ βα 1 4 σ α 2 + 1 δ αα 2 2 π 2 λ 2 .
δ xx 2 + δ yy 2 2 δ xy δ xx δ yy | B xy |
E( ρ,0 )= x ^ E x ( ρ )+ y ^ E y ( ρ ) E α ( ρ )= C α exp( ρ 2 4 σ α 2 )exp[ j ϕ α ( ρ ) ],
E( ρ 1 ,0 ) E * ( ρ 2 ,0 ) =W( ρ 1 , ρ 2 ,0 )=[ E x ( ρ 1 ,0 ) E x * ( ρ 2 ,0 ) E x ( ρ 1 ,0 ) E y * ( ρ 2 ,0 ) E y ( ρ 1 ,0 ) E x * ( ρ 2 ,0 ) E y ( ρ 1 ,0 ) E y * ( ρ 2 ,0 ) ] E α ( ρ 1 ,0 ) E β * ( ρ 2 ,0 ) = C α C β * exp[ ( ρ 1 2 4 σ α 2 + ρ 2 2 4 σ β 2 ) ] exp[ j ϕ α ( ρ 1 ) ]exp[ j ϕ β ( ρ 2 ) ] .
exp[ j ϕ α1 ]exp[ j ϕ β2 ] =exp{ 1 2 ( σ ϕ α 2 + σ ϕ β 2 )[ 1 2 σ ϕ α σ ϕ β σ ϕ α 2 + σ ϕ β 2 ρ ϕ α ϕ β γ ϕ α ϕ β ( | ρ 1 ρ 2 |; ϕ α ϕ β ) ] },
γ ϕ α ϕ β ( | ρ 1 ρ 2 |; ϕ α ϕ β )=exp( | ρ 1 ρ 2 | 2 ϕ α ϕ β 2 ).
E α1 E β2 * C α C β * exp[ ( ρ 1 2 4 σ α 2 + ρ 2 2 4 σ β 2 ) ]exp[ 1 2 ( σ ϕ α 2 2 ρ ϕ α ϕ β σ ϕ α σ ϕ β + σ ϕ β 2 ) ] exp[ | ρ 1 ρ 2 | 2 ϕ α ϕ β 2 / σ ϕ α σ ϕ β ρ ϕ α ϕ β ].
δ xx = 1 2 ϕ x ϕ x σ ϕ x A x =| C x | δ yy = 1 2 ϕ y ϕ y σ ϕ y A y =| C y | δ xy = 1 2 ϕ x ϕ y σ ϕ x σ ϕ y ρ ϕ x ϕ y | B xy |=exp[ 1 2 ( σ ϕ x 2 2 ρ ϕ x ϕ y σ ϕ x σ ϕ y + σ ϕ y 2 ) ] B xy = θ x θ y .
E α ( ρ )= C α exp( ρ 2 4 σ α 2 ) T α ( ρ ),
E α1 E β2 * = C α C β * exp[ ( ρ 1 2 4 σ α 2 + ρ 2 2 4 σ β 2 ) ] T α1 T β2 * .
T α1 T β2 * = σ T α σ T β ρ T α T β γ T α T β ( | ρ 1 ρ 2 |; T α T β ),
γ T α T β ( | ρ 1 ρ 2 |; T α T β )=exp( | ρ 1 ρ 2 | 2 T α T β 2 ).
E α1 E β2 * = C α C β * σ T α σ T β ρ T α T β exp[ ( ρ 1 2 4 σ α 2 + ρ 2 2 4 σ β 2 ) ]exp[ | ρ 1 ρ 2 | 2 T α T β 2 ].
δ xx = T x T x 2 A x = σ T x | C x | δ yy = T y T y 2 A y = σ T y | C y | δ xy = T x T y 2 | B xy |= ρ T x T y B xy = θ x θ y .
ϕ ˜ ( f x , f y )= ϕ( x,y )exp( j2π f x x )exp( j2π f y y )dxdy ϕ( x,y )= ϕ ˜ ( f x , f y )exp( j2π f x x )exp( j2π f y y )d f x d f y .
ϕ x ( x,y ) = ϕ y ( x,y ) = ϕ α ( x,y ) =0 ϕ α ( x 1 , y 1 ) ϕ α * ( x 2 , y 2 ) = σ ϕ α 2 exp( | ρ 1 ρ 2 | 2 ϕ α ϕ α 2 ).
ϕ α ( x,y )=Re[ m,n φ αmn exp( j2π m L x ) exp( j2π n L y ) ] = m,n φ αmn r cos[ 2π L ( mx+ny ) ] m,n φ αmn i sin[ 2π L ( mx+ny ) ] ,
ϕ α ( x 1 , y 1 ) ϕ α * ( x 2 , y 2 ) = m,n p,q φ αmn r φ αpq r cos[ 2π L ( m x 1 +n y 1 p x 2 q y 2 ) ] .
φ αmn r φ αpq r = φ αmn i φ αpq i = Φ ϕ α ϕ α ( m L , n L ) δ mp δ nq 1 L 2 ( φ αmn r ) 2 = ( φ αmn i ) 2 = Φ ϕ α ϕ α ( m L , n L ) 1 L 2 ,
ϕ α [ i,j ]=Re [ m,n r α [ m,n ] σ ϕ α π ϕ α ϕ α NΔ exp{ π 2 ϕ α ϕ α 2 2 [ ( m NΔ ) 2 + ( n NΔ ) 2 ] } exp( j 2π N mi )exp( j 2π N nj ) ],
ϕ x [ i,j ] ϕ y [ k,l ] = m,n p,q σ ϕ x π ϕ x ϕ x NΔ exp{ π 2 ϕ x ϕ x 2 2 [ ( m NΔ ) 2 + ( n NΔ ) 2 ] } σ ϕ y π ϕ y ϕ y NΔ exp{ π 2 ϕ y ϕ y 2 2 [ ( p NΔ ) 2 + ( q NΔ ) 2 ] } { r x r [ m,n ]cos( 2π N ( mi+nj ) ) r x i [ m,n ]sin( 2π N ( mi+nj ) ) } { r y r [ p,q ]cos( 2π N ( pk+ql ) ) r y i [ p,q ]sin( 2π N ( pk+ql ) ) } ,
r x r [ m,n ] r y r [ p,q ] = r x i [ m,n ] r y i [ p,q ] =Γ δ mp δ nq r x r [ m,n ] r y i [ p,q ] = r x i [ m,n ] r y r [ p,q ] =0,
ϕ x [ i,j ] ϕ y [ k,l ] = m,n σ ϕ x σ ϕ y π ϕ x ϕ x ϕ y ϕ y ( NΔ ) 2 Γ 2 exp{ π 2 ( ϕ x ϕ x 2 + ϕ y ϕ y 2 2 )[ ( m NΔ ) 2 + ( n NΔ ) 2 ] } { exp( j 2π N m( ik ) )exp( j 2π N n( jl ) )+exp( j 2π N m( ik ) )exp( j 2π N n( jl ) ) }.
ϕ x [ i,j ] ϕ y [ k,l ] = m,n σ ϕ x σ ϕ y π( Γ ϕ x ϕ x ϕ y ϕ y ) exp{ π 2 ( ϕ x ϕ x 2 + ϕ y ϕ y 2 2 )[ ( m NΔ ) 2 + ( n NΔ ) 2 ] } exp( j 2π N m( ik ) )exp( j 2π N n( jl ) ) 1 ( NΔ ) 2 .
Φ ϕ x ϕ y ( f x , f y )= σ ϕ x σ ϕ y π ρ ϕ x ϕ y ϕ x ϕ y 2 exp[ π 2 ϕ x ϕ y 2 ( f x 2 + f y 2 ) ],
ϕ x ϕ y = Γ ϕ x ϕ x ϕ y ϕ y ρ ϕ x ϕ y = ϕ x ϕ x 2 + ϕ y ϕ y 2 2 Γ= ρ ϕ x ϕ y ( ϕ x ϕ x 2 + ϕ y ϕ y 2 ) 2 ϕ x ϕ x ϕ y ϕ y .
δ xx = 1 2 ϕ x ϕ x σ ϕ x δ yy = 1 2 ϕ y ϕ y σ ϕ y δ xy = 1 2 ϕ x ϕ x 2 + ϕ y ϕ y 2 4Γ σ ϕ x σ ϕ y ϕ x ϕ x ϕ y ϕ y | B xy |=exp[ 1 2 ( σ ϕ x 2 4Γ σ ϕ x σ ϕ y ϕ x ϕ x ϕ y ϕ y ϕ x ϕ x 2 + ϕ y ϕ y 2 + σ ϕ y 2 ) ].
T x ( x,y ) = T y ( x,y ) = T α ( x,y ) =0 T α ( x 1 , y 1 ) T α * ( x 2 , y 2 ) = σ T α 2 exp( | ρ 1 ρ 2 | 2 T α T α 2 ).
T α ( x,y )= m,n T αmn exp( j2π m L x ) exp( j2π n L y ),
T α ( x 1 , y 1 ) T α * ( x 2 , y 2 ) = m,n p,q T αmn T αpq * exp[ j 2π L ( m x 1 p x 2 ) ] exp[ j 2π L ( n y 1 q y 2 ) ] .
T αmn T αpq * = Φ T α T α ( m L , n L ) δ mp δ nq 1 L 2 | T αmn | 2 = Φ T α T α ( m L , n L ) 1 L 2 ,
T α [ i,j ]= m,n r α [ m,n ] σ T α π/2 T α T α NΔ exp{ π 2 T α T α 2 2 [ ( m NΔ ) 2 + ( n NΔ ) 2 ] } exp( j 2π N mi )exp( j 2π N nj ),
T x [ i,j ] T y * [ k,l ] = m,n σ T x σ T y π T x T x T y T y Γ exp{ π 2 ( T x T x 2 + T y T y 2 2 )[ ( m NΔ ) 2 + ( n NΔ ) 2 ] } exp[ j 2π N m( ik ) ]exp[ j 2π N n( jl ) ] 1 ( NΔ ) 2 .
Φ T x T y ( f x , f y )= σ T x σ T y π ρ T x T y T x T y 2 exp[ π 2 T x T y 2 ( f x 2 + f y 2 ) ],
T x T y = Γ T x T x T y T y ρ T x T y = T x T x 2 + T y T y 2 2 Γ= ρ T x T y ( T x T x 2 + T y T y 2 ) 2 T x T x T y T y .
δ xx = T x T x 2 δ yy = T y T y 2 δ xy = 1 2 T x T x 2 + T y T y 2 2 | B xy |= 2Γ T x T x T y T y T x T x 2 + T y T y 2 .
argmin x ( δ xx desired δ xx ( x ) 1 ) 2 + ( δ yy desired δ yy ( x ) 1 ) 2 + ( δ xy desired δ xy ( x ) 1 ) 2 + ( | B xy desired | | B xy ( x ) | 1 ) 2 ,
S 0 ( ρ )= W xx ( ρ,ρ )+ W yy ( ρ,ρ ) S 1 ( ρ )= W xx ( ρ,ρ ) W yy ( ρ,ρ ) S 2 ( ρ )= W xy ( ρ,ρ )+ W yx ( ρ,ρ ) S 3 ( ρ )=j[ W yx ( ρ,ρ ) W xy ( ρ,ρ ) ] η( ρ 1 , ρ 2 )=η( x 1 , y 1 , x 2 , y 2 )= TrW( ρ 1 , ρ 2 ) TrW( ρ 1 , ρ 1 ) TrW( ρ 2 , ρ 2 ) ,

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