Abstract

The propagation of a class of partially polarized beams though atmospheric turbulence is treated using the coherent-modes-decomposition approach. This approach allows specifying the properties of sources generating radiation with a narrow polarization distribution that could be employed in active polarimetric remote sensing applications.

© 2006 Optical Society of America

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References

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  1. D. F. V. James, "Change of polarization of light beams on propagation in free space," J. Opt. Soc. Am. A 11, 1641-1643 (1994).
    [CrossRef]
  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, 1-9 (2001).
    [CrossRef]
  3. E. Wolf, "Unified theory of coherence and polarization of random electromagnetic beams," Phys. Lett. A 312, 263-267 (2003).
    [CrossRef]
  4. 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]
  5. O. Korotkova, M. Salem, and E. Wolf, "The far-zone behavior of the degree of polarization of partially coherent beams propagating through atmospheric turbulence," Opt. Commun. 233, 225-230 (2004).
    [CrossRef]
  6. M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, "Polarization changes in partially coherent electromagnetic beam propagating through the turbulent atmosphere," Waves Random Complex Media 14, 513-523 (2004).
  7. C. Schwartz and A. Dogariu, "Mode coupling approach to beam propagation in atmospheric turbulence," J. Opt. Soc. Am. A 23, 329-338 (2005).
    [CrossRef]
  8. E. Wolf, "New theory of partial coherence in space-frequency domain. Part I: spectra and cross-spectra of steady-state sources," J. Opt. Soc. Am. 72, 343-351 (1982).
    [CrossRef]
  9. E. Wolf, "New theory of partial coherence in space-frequency domain. Part II: steady-state fields and higher-order correlations," J. Opt. Soc. Am. A 3, 76-85 (1986).
    [CrossRef]
  10. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Section 4.7, pp. 213-223.
  11. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).
  12. E. Collett, Polarized Light Fundamentals and Applications (Marcel Dekker, 1993).
  13. F. Gori, M. Santarsiero, R. Simon, G. Piquero, Riccardo Borghi, and G. Guattari,"Coherent-mode decomposition of partially polarized, partially coherent sources," J. Opt. Soc. Am. A 20, 78-84 (2003).
    [CrossRef]
  14. G. Piqueroa, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, "Synthesis of partially polarized Gaussian Schell-model sources," Opt. Commun. 208, 9-16 (2002).
    [CrossRef]
  15. T. Shirai, O. Korotkova, and E. Wolf, "A method of generating electromagnetic Gaussian Schell-model beams," J. Opt. A Pure Appl. Opt. 7, 232-237 (2005).
    [CrossRef]

2005 (2)

C. Schwartz and A. Dogariu, "Mode coupling approach to beam propagation in atmospheric turbulence," J. Opt. Soc. Am. A 23, 329-338 (2005).
[CrossRef]

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

2004 (2)

O. Korotkova, M. Salem, and E. Wolf, "The far-zone behavior of the degree of polarization of partially coherent 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 beam propagating through the turbulent atmosphere," Waves Random Complex Media 14, 513-523 (2004).

2003 (3)

2002 (1)

G. Piqueroa, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, "Synthesis of partially polarized Gaussian Schell-model sources," Opt. Commun. 208, 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, 1-9 (2001).
[CrossRef]

1998 (1)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

1995 (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Section 4.7, pp. 213-223.

1994 (1)

1993 (1)

E. Collett, Polarized Light Fundamentals and Applications (Marcel Dekker, 1993).

1986 (1)

1982 (1)

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

Borghi, R.

G. Piqueroa, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, "Synthesis of partially polarized Gaussian Schell-model sources," Opt. Commun. 208, 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, 1-9 (2001).
[CrossRef]

Borghi, Riccardo

Collett, E.

E. Collett, Polarized Light Fundamentals and Applications (Marcel Dekker, 1993).

Dogariu, A.

C. Schwartz and A. Dogariu, "Mode coupling approach to beam propagation in atmospheric turbulence," J. Opt. Soc. Am. A 23, 329-338 (2005).
[CrossRef]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, "Polarization changes in partially coherent electromagnetic beam propagating through the turbulent atmosphere," Waves Random Complex Media 14, 513-523 (2004).

Gori, F.

F. Gori, M. Santarsiero, R. Simon, G. Piquero, Riccardo Borghi, and G. Guattari,"Coherent-mode decomposition of partially polarized, partially coherent sources," J. Opt. Soc. Am. A 20, 78-84 (2003).
[CrossRef]

G. Piqueroa, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, "Synthesis of partially polarized Gaussian Schell-model sources," Opt. Commun. 208, 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, 1-9 (2001).
[CrossRef]

Guattari, G.

James, D. F. V.

Korotkova, O.

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

O. Korotkova, M. Salem, and E. Wolf, "The far-zone behavior of the degree of polarization of partially coherent 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 beam propagating through the turbulent atmosphere," Waves Random Complex Media 14, 513-523 (2004).

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Section 4.7, pp. 213-223.

Mondello, A.

G. Piqueroa, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, "Synthesis of partially polarized Gaussian Schell-model sources," Opt. Commun. 208, 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, 1-9 (2001).
[CrossRef]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

Piquero, G.

F. Gori, M. Santarsiero, R. Simon, G. Piquero, Riccardo Borghi, and G. Guattari,"Coherent-mode decomposition of partially polarized, partially coherent sources," J. Opt. Soc. Am. A 20, 78-84 (2003).
[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, 1-9 (2001).
[CrossRef]

Piqueroa, G.

G. Piqueroa, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, "Synthesis of partially polarized Gaussian Schell-model sources," Opt. Commun. 208, 9-16 (2002).
[CrossRef]

Romanini, P.

G. Piqueroa, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, "Synthesis of partially polarized Gaussian Schell-model sources," Opt. Commun. 208, 9-16 (2002).
[CrossRef]

Salem, M.

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, "Polarization changes in partially coherent electromagnetic beam propagating through the 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 partially coherent beams propagating through atmospheric turbulence," Opt. Commun. 233, 225-230 (2004).
[CrossRef]

Santarsiero, M.

F. Gori, M. Santarsiero, R. Simon, G. Piquero, Riccardo Borghi, and G. Guattari,"Coherent-mode decomposition of partially polarized, partially coherent sources," J. Opt. Soc. Am. A 20, 78-84 (2003).
[CrossRef]

G. Piqueroa, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, "Synthesis of partially polarized Gaussian Schell-model sources," Opt. Commun. 208, 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, 1-9 (2001).
[CrossRef]

Schwartz, C.

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, 232-237 (2005).
[CrossRef]

Simon, R.

F. Gori, M. Santarsiero, R. Simon, G. Piquero, Riccardo Borghi, and G. Guattari,"Coherent-mode decomposition of partially polarized, partially coherent sources," J. Opt. Soc. Am. A 20, 78-84 (2003).
[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, 1-9 (2001).
[CrossRef]

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, 232-237 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, "The far-zone behavior of the degree of polarization of partially coherent 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 beam propagating through the 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]

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]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Section 4.7, pp. 213-223.

E. Wolf, "New theory of partial coherence in space-frequency domain. Part II: steady-state fields and higher-order correlations," J. Opt. Soc. Am. A 3, 76-85 (1986).
[CrossRef]

E. Wolf, "New theory of partial coherence in space-frequency domain. Part I: spectra and cross-spectra of steady-state sources," J. Opt. Soc. Am. 72, 343-351 (1982).
[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, 1-9 (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, 232-237 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (2)

G. Piqueroa, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, "Synthesis of partially polarized Gaussian Schell-model sources," Opt. Commun. 208, 9-16 (2002).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, "The far-zone behavior of the degree of polarization of partially coherent beams propagating through atmospheric turbulence," Opt. Commun. 233, 225-230 (2004).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

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

Waves Random Complex Media (1)

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, "Polarization changes in partially coherent electromagnetic beam propagating through the turbulent atmosphere," Waves Random Complex Media 14, 513-523 (2004).

Other (3)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Section 4.7, pp. 213-223.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

E. Collett, Polarized Light Fundamentals and Applications (Marcel Dekker, 1993).

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Figures (2)

Fig. 1
Fig. 1

Comparison of the Q polarization distribution from the polarized source (solid curve), a Gaussian beam in turbulence (dashed curve), and a Gaussian beam in free space (dotted curve). All the distributions were calculated for a range of 1000 m and are normalized to the respective axial value.

Fig. 2
Fig. 2

Comparison of the Q parameter distribution from the polarized source (solid curve), a Gaussian beam in turbulence (dashed curve), and a Gaussian beam in free space (dotted curve). All the distributions were calculated for a range of 2000 m and are normalized to the respective axial value.

Equations (8)

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W ( r 1 , r 2 , ω ) = E * ( r 1 , ω ) E ( r 2 , ω ) ,
W ( ρ 1 , ρ 2 , 0 , ω ) = λ l ( ω ) ϕ l * ( ρ 1 , ω ) ϕ l ( ρ 2 l , ω ) ,
λ ( z , ω ) = [ I + d ( z , ω ) ] λ ( 0 , ω ) ,
d n l ( z , ω ) = ψ n * ( ρ 1 , z , ω ) ψ n ( ρ 2 , z , ω ) ψ l * ( ρ 1 , z , ω ) ψ l ( ρ 2 , z , ω ) × { 1 exp [ 1 2 D Φ ( ρ 1 , ρ 2 , ω ) ] } d 2 ρ 1 d 2 ρ 2 .
S ( r ) = { I ( r ) , Q ( r ) , U ( r ) , V ( r ) } ,
I ( r ) = I 0 ( r ) = I 0 ( r ) + I 90 ( r ) ,
Q ( r ) = I 0 ( r ) I 90 ( r ) ; U ( r ) = I 45 ( r ) I 135 ( r ) ; V ( r ) = I R ( r ) I L ( r ) .
λ Q ( 0 , ω ) = [ I + d ( z , ω ) ] 1 λ Q ( z , ω ) ,

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