Abstract

Analytic expression is derived for the cross-spectral density matrix of a stochastic electromagnetic beam truncated by a slit aperture and passing through the turbulent atmosphere. The new formula can be used in study of the modulation in the spectral degree of polarization of the electromagnetic Gaussian Schell-model beam on propagation. We find that the spectral degree of polarization in the output plane can be directly controlled by the width of the slit aperture. The effect of polarization shaping is also illustrated by numerical examples.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Wolf, "Unified theory of coherence and polarization of random electromagnetic beams," Phys. Lett. A 312, 263-267 (2003).
    [CrossRef]
  2. E. Wolf, "Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation," Opt. Lett. 28, 1078-1080 (2003).
    [CrossRef] [PubMed]
  3. 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]
  4. H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, "Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere," J. Mod. Opt. 52, 1611-1618 (2005).
    [CrossRef]
  5. O. Korotkova and E. Wolf, "Beam criterion for atmospheric propagation," Opt. Lett. 32, 2137-2139 (2007).
    [CrossRef] [PubMed]
  6. Q1. Z. Chen and J. Pu, "Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere," J. Opt. A 9, 1123-1130 (2007).
    [CrossRef]
  7. 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] [PubMed]
  8. Y. Zhu, D. Zhao, and X. Du, "Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere," Opt. Express 16, 18437-18442 (2008).
    [CrossRef] [PubMed]
  9. X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B 87, 547-552 (2007).
    [CrossRef]
  10. X. Ji and G. Ji, "Effect of turbulence on the beam quality of apertured partially coherent beams," J. Opt. Soc. Am. A 25, 1246-1252 (2008).
    [CrossRef]
  11. A. A. Tovar, "Propagation of flat-topped multi-Gaussian laser beams," J. Opt. Soc. Am. A 18, 1897-1904 (2001).
    [CrossRef]

2008 (2)

2007 (4)

Q1. Z. Chen and J. Pu, "Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere," J. Opt. A 9, 1123-1130 (2007).
[CrossRef]

X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B 87, 547-552 (2007).
[CrossRef]

O. Korotkova and E. Wolf, "Beam criterion for atmospheric propagation," Opt. Lett. 32, 2137-2139 (2007).
[CrossRef] [PubMed]

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] [PubMed]

2005 (1)

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

2004 (1)

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 (2)

2001 (1)

Chen, Z.

Q1. Z. Chen and J. Pu, "Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere," J. Opt. A 9, 1123-1130 (2007).
[CrossRef]

Chu, X.

X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B 87, 547-552 (2007).
[CrossRef]

Du, X.

Ji, G.

Ji, X.

Korotkova, O.

Ni, Y.

X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B 87, 547-552 (2007).
[CrossRef]

Ponomarenko, S. A.

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

Pu, J.

Q1. Z. Chen and J. Pu, "Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere," J. Opt. A 9, 1123-1130 (2007).
[CrossRef]

Roychowdhury, H.

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

Salem, M.

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]

Tovar, A. A.

Wolf, E.

O. Korotkova and E. Wolf, "Beam criterion for atmospheric propagation," Opt. Lett. 32, 2137-2139 (2007).
[CrossRef] [PubMed]

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, "Change 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]

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

E. Wolf, "Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation," Opt. Lett. 28, 1078-1080 (2003).
[CrossRef] [PubMed]

Zhao, D.

Zhou, G.

X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B 87, 547-552 (2007).
[CrossRef]

Zhu, Y.

Appl. Phys. B (1)

X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B 87, 547-552 (2007).
[CrossRef]

J. Mod. Opt. (1)

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

J. Opt. A (1)

Q1. Z. Chen and J. Pu, "Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere," J. Opt. A 9, 1123-1130 (2007).
[CrossRef]

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

Opt. Commun. (1)

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. (2)

Phys. Lett. A (1)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Illustrating the notation.

Fig. 2.
Fig. 2.

Three-dimensional distribution and corresponding gray-scale projection of the slit aperture function expressed by Eq. (2) with αx = 10 mm and N = 10.

Fig. 3.
Fig. 3.

Changes in the spectral degree of polarization along the z-axis of the stochastic electromagnetic beam truncated by the same slit aperture with αx = 10 mm and passing through the turbulent atmosphere with different C 2 n . The source is assumed to be Gaussian Schell-model source with: λ = 632.8 nm, Ax = 2, Ay = 1, Bxy = 0.2exp(/3), σx = 10 mm, σy = 20 mm, δxx = δyy = 2 mm and δxy = δyx = 3 mm.

Fig. 4.
Fig. 4.

Changes in the spectral degree of polarization along the z-axis of the stochastic electromagnetic beam truncated by slit apertures with different αx and passing through the turbulent atmosphere with C 2 n = 10-14 m-2/3. The parameters of the source are the same as Fig. 3.

Fig. 5.
Fig. 5.

Three-dimensional distributions of the spectral degree of polarization and corresponding gray-scale projections of the stochastic electromagnetic beam truncated by slit apertures with (a) αx = 50 mm, (b) αx =10 mm , (c) αx = 1 mm, and passing through the turbulent atmosphere with C 2 n = 10-14 m-2/3. The propagation distance z = 1 km and the parameters of the source are the same as Fig. 3.

Equations (18)

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

A px ( x 1 ) = n 1 = N N exp [ ( x 1 / β x n 1 ) 2 ] n 1 = N N exp ( n 1 2 ) , and A py ( y 1 ) = 1 ,
A p ( ρ 1 ) = A px ( x 1 ) A py ( y 1 ) = n 1 = N N exp [ ik 2 ( ρ 1 T I 2 ρ 1 2 ρ 1 T I 1 n 1 + n 1 T I 0 n 1 ) ] n 1 = N N exp ( n 1 T n 1 ) ,
I 0 = [ 2 ik 0 0 0 ] , I 1 = [ 2 ik β x 0 0 0 ] , I 2 = [ 2 ik β x 2 0 0 0 ] ,
W ij ( ρ 12 , z , ω ) = k 2 4 π 2 [ Det ( B ̅ ) ] 1 / 2 A ̅ p ( ρ 12 ) W ij ( 0 ) ( ρ 12 , ω )
× exp [ ik 2 ( ρ 12 T B ̅ 1 ρ 12 2 ρ 12 T B ̅ 1 ρ 12 + ρ 12 T B ̅ 1 ρ 12 ) ] ,
× exp [ ik 2 ( ρ 12 T P ̅ ρ 12 ρ 12 T P ̅ ρ 12 + ρ 12 T P ̅ ρ 12 ) ] d 4 ρ 12
B ̅ = [ z I 0 0 z I ] , P ̅ = 2 ik ρ 0 2 [ I I I I ] ,
A ̅ p ( ρ 12 ) = n 1 = N N n 2 = N N exp [ ik 2 ( ρ 12 T I ̅ 2 ρ 12 2 ρ 12 I ̅ 1 n 12 + n 12 T I ̅ 0 n 12 ) ] n 1 = N N n 2 = N N exp ( n 12 T n 12 ) ,
I ̅ 0 = [ I 0 0 0 I 0 ] , I ̅ 1 = [ I 1 0 0 I 1 ] , I ̅ 2 = [ I 2 0 0 I 2 ] ,
W ij ( 0 ) ( ρ 12 , ω ) = A i A j B ij exp ( ik 2 ρ 12 T M ij 1 ρ 12 ) ,
M ij 1 = [ i k ( 1 2 σ i 2 + 1 δ ij 2 ) I i k 1 δ ij 2 I i k 1 δ ij 2 I i k ( 1 2 σ j 2 + 1 δ ij 2 ) I ] .
W ij ( ρ 12 , z , ω ) = A i A j B ij [ Det ( BI ̅ 2 + B ̅ M ij 1 + I ̅ + BP ̅ ) ] 1 / 2 n 1 = N N n 2 = N N exp ( n 12 T n 12 )
× exp { ik 2 ρ 12 T [ ( B ̅ 1 + P ̅ ) ( B ̅ 1 1 2 P ̅ ) T ( I ̅ 2 + M ij 1 + B ̅ 1 + P ̅ ) 1 ( B ̅ 1 1 2 P ̅ ) ] ρ 12 }
× n 1 = N N n 2 = N N exp [ ik ρ 12 T ( B ̅ −1 1 2 P ̅ ) T ( I ̅ 2 + M ij 1 + B ̅ 1 + P ̅ ) 1 I ̅ 1 n 12 ]
× exp { ik 2 n 12 T [ I ̅ 0 I ̅ 1 T ( I ̅ 2 + M ij 1 + B ̅ 1 + P ̅ ) 1 I ̅ 1 ] n 12 } ,
W ij ( ρ 12 , z , ω ) = A i A j B ij [ Det ( B ̅ M ij 1 + I ̅ + BP ̅ ) ] 1 / 2
× exp { ik 2 ρ 12 T [ ( B ̅ 1 + P ̅ ) ( B ̅ 1 1 2 P ̅ ) T ( M ij 1 + B ̅ 1 + P ̅ ) 1 ( B ̅ 1 1 2 P ̅ ) ] ρ 12 } .
P ( ρ 12 , z , ω ) = 1 4 Det W ( ρ 12 , z , ω ) [ Tr W ( ρ 12 , z , ω ) ] 2 .

Metrics