Abstract

When propagating in free space, the transversal distribution of the degree of polarization of an anisotropic electromagnetic Gaussian–Schell model (AEGSM) beam will generally undergo a complex evolution process. We find that this transversal distribution of the degree of polarization of an AEGSM beam can be controlled by exploiting the partial correlation properties of the source. The main research of our paper falls into two parts. First, the concept of analogical propagation of the transversal distribution of the degree of polarization is proposed, and the condition for an AEGSM beam having an analogical propagation is obtained. When an AEGSM beam is on analogical propagation, the distribution of the degree of polarization on any cross section of the beam is always similar to that on the source plane, except that the size of the distribution pattern will expand continuously as the propagation distance increases. Second, the far-field transversal distribution of the degree of polarization is considered, and the condition for the far-field transversal polarization distribution of an AEGSM beam to be always of circularly symmetric shape, no matter how complicated it is on the source, is obtained. Our research is expected to find applications in areas that make use of the polarization properties of random electromagnetic beams.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. F. Gori, M. Santarsiero, R. Borghi, and V. Ramirez-Sanchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016–1021 (2008).
    [CrossRef]
  4. F. Gori, V. Ramirez-Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11, 085706 (2009).
    [CrossRef]
  5. H. Wang, X. Wang, A. Zeng, and K. Yang, “Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation,” J. Opt. A, Pure Appl. Opt. 9, 1053–1056 (2007).
    [CrossRef]
  6. X. Du, D. Zhao, and O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express 15, 16909–16915 (2007).
    [CrossRef]
  7. O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
    [CrossRef]
  8. M. Salem, “Can two planar sources with the same sets of Stokes parameters generate beams with different degrees of polarization?” Opt. Lett. 31, 3025–3027 (2006).
    [CrossRef]
  9. H. Wang, X. Wang, A. Zeng, and K. Yang, “Effects of coherence on anisotropic electromagnetic Gaussian-Schell model beams on propagation,” Opt. Lett. 32, 2215–2217 (2007).
    [CrossRef]
  10. M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33, 1180–1182 (2008).
    [CrossRef]
  11. Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B 96, 499–507 (2009).
    [CrossRef]
  12. M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Complex Media 14, 513–523 (2004).
  13. 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, 225–230 (2004).
    [CrossRef]
  14. O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).
    [CrossRef]
  15. H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Changes in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
    [CrossRef]
  16. Y. Li and E. Wolf, “Radiation from anisotropic Gaussian Schell-model sources,” Opt. Lett. 7, 256–258 (1982).
    [CrossRef]
  17. F. Gori and G. Guattari, “A new type of optical fields,” Opt. Commun. 48, 7–12 (1983).
    [CrossRef]
  18. R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  22. Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian–Schell model beams,” Opt. Lett. 27, 216–218 (2002).
    [CrossRef]
  23. Y. Cai and S. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. 89, 041117 (2006).
    [CrossRef]
  24. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
    [CrossRef]
  25. E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: spectra and cross spectra of steady-state sources,” J. Opt. Soc. Am. 72, 343–351 (1982).
    [CrossRef]
  26. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  27. F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32, 3531–3537 (2007).
    [CrossRef]
  28. X. Du and D. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17, 4257–4262 (2009).
    [CrossRef]

2009 (3)

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

Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B 96, 499–507 (2009).
[CrossRef]

X. Du and D. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17, 4257–4262 (2009).
[CrossRef]

2008 (2)

2007 (4)

2006 (2)

Y. Cai and S. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

M. Salem, “Can two planar sources with the same sets of Stokes parameters generate beams with different degrees of polarization?” Opt. Lett. 31, 3025–3027 (2006).
[CrossRef]

2005 (4)

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

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).
[CrossRef]

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Changes in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
[CrossRef]

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

2004 (2)

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

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, 225–230 (2004).
[CrossRef]

2003 (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

2002 (1)

1999 (1)

1998 (1)

1995 (1)

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

1994 (1)

1986 (1)

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).

1985 (1)

R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
[CrossRef]

1983 (1)

F. Gori and G. Guattari, “A new type of optical fields,” Opt. Commun. 48, 7–12 (1983).
[CrossRef]

1982 (2)

Borghi, R.

Cai, Y.

Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B 96, 499–507 (2009).
[CrossRef]

Y. Cai and S. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian–Schell model beams,” Opt. Lett. 27, 216–218 (2002).
[CrossRef]

De Santis, P.

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).

Dogariu, A.

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).
[CrossRef]

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

Du, X.

Gori, F.

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

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

F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32, 3531–3537 (2007).
[CrossRef]

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).

F. Gori and G. Guattari, “A new type of optical fields,” Opt. Commun. 48, 7–12 (1983).
[CrossRef]

Guattari, G.

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).

F. Gori and G. Guattari, “A new type of optical fields,” Opt. Commun. 48, 7–12 (1983).
[CrossRef]

He, S.

Y. Cai and S. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

James, D. F. V.

Korotkova, O.

Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B 96, 499–507 (2009).
[CrossRef]

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

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

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (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, 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 Complex Media 14, 513–523 (2004).

Li, Y.

Lin, Q.

Mandel, L.

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

Mukunda, N.

Palma, C.

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).

Ponomarenko, S. A.

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Changes in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
[CrossRef]

Ramirez-Sanchez, V.

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

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

Roychowdhury, H.

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Changes in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
[CrossRef]

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

Salem, M.

M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33, 1180–1182 (2008).
[CrossRef]

M. Salem, “Can two planar sources with the same sets of Stokes parameters generate beams with different degrees of polarization?” Opt. Lett. 31, 3025–3027 (2006).
[CrossRef]

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).
[CrossRef]

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

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, 225–230 (2004).
[CrossRef]

Santarsiero, M.

Shirai, T.

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

Simon, R.

Sudarshan, E. C. G.

R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
[CrossRef]

Wang, H.

H. Wang, X. Wang, A. Zeng, and K. Yang, “Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation,” J. Opt. A, Pure Appl. Opt. 9, 1053–1056 (2007).
[CrossRef]

H. Wang, X. Wang, A. Zeng, and K. Yang, “Effects of coherence on anisotropic electromagnetic Gaussian-Schell model beams on propagation,” Opt. Lett. 32, 2215–2217 (2007).
[CrossRef]

Wang, X.

H. Wang, X. Wang, A. Zeng, and K. Yang, “Effects of coherence on anisotropic electromagnetic Gaussian-Schell model beams on propagation,” Opt. Lett. 32, 2215–2217 (2007).
[CrossRef]

H. Wang, X. Wang, A. Zeng, and K. Yang, “Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation,” J. Opt. A, Pure Appl. Opt. 9, 1053–1056 (2007).
[CrossRef]

Wolf, E.

M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33, 1180–1182 (2008).
[CrossRef]

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

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).
[CrossRef]

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Changes in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (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, 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 Complex Media 14, 513–523 (2004).

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

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

E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: spectra and cross spectra of steady-state sources,” J. Opt. Soc. Am. 72, 343–351 (1982).
[CrossRef]

Y. Li and E. Wolf, “Radiation from anisotropic Gaussian Schell-model sources,” Opt. Lett. 7, 256–258 (1982).
[CrossRef]

Yang, K.

H. Wang, X. Wang, A. Zeng, and K. Yang, “Effects of coherence on anisotropic electromagnetic Gaussian-Schell model beams on propagation,” Opt. Lett. 32, 2215–2217 (2007).
[CrossRef]

H. Wang, X. Wang, A. Zeng, and K. Yang, “Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation,” J. Opt. A, Pure Appl. Opt. 9, 1053–1056 (2007).
[CrossRef]

Zeng, A.

H. Wang, X. Wang, A. Zeng, and K. Yang, “Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation,” J. Opt. A, Pure Appl. Opt. 9, 1053–1056 (2007).
[CrossRef]

H. Wang, X. Wang, A. Zeng, and K. Yang, “Effects of coherence on anisotropic electromagnetic Gaussian-Schell model beams on propagation,” Opt. Lett. 32, 2215–2217 (2007).
[CrossRef]

Zhao, D.

Appl. Phys. B (1)

Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B 96, 499–507 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Cai and S. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

J. Mod. Opt. (1)

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Changes in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
[CrossRef]

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

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

H. Wang, X. Wang, A. Zeng, and K. Yang, “Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation,” J. Opt. A, Pure Appl. Opt. 9, 1053–1056 (2007).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Acta (1)

P. De Santis, F. Gori, G. Guattari, and C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).

Opt. Commun. (4)

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

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

F. Gori and G. Guattari, “A new type of optical fields,” Opt. Commun. 48, 7–12 (1983).
[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, 225–230 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (6)

Phys. Lett. A (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

Phys. Rev. A (1)

R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
[CrossRef]

Waves Random Complex Media (2)

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).
[CrossRef]

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

Other (1)

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

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