Abstract

Electromagnetic random beams with non-uniform source correlations have been recently shown to develop, on propagation in free space, the regions in transverse cross-sections where the degree and the state of polarization can significantly differ from those beyond that region. The size of the region and the values of polarimetric properties in it can be fully controlled from the source plane. In this paper the influence of a random isotropic medium on such beams is shown to suppress the effect in several ways, in particular by shifting the location of the region back to the axis.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett.36(20), 4104–4106 (2011).
    [CrossRef] [PubMed]
  2. F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt.11(8), 085706 (2009).
    [CrossRef]
  3. Z. Tong and O. Korotkova, “Non-uniformly correlated light beams in uniformly correlated media,” Opt. Lett.37(15), 3240–3242 (2012).
    [CrossRef] [PubMed]
  4. Z. Tong and O. Korotkova, “Electromagnetic non-uniformly correlated beams,” J. Opt. Soc. Am. A. in press).
  5. E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express18(10), 10650–10658 (2010).
    [CrossRef] [PubMed]
  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. Express15(25), 16909–16915 (2007).
    [CrossRef] [PubMed]
  7. 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]

2012 (1)

2011 (1)

2010 (1)

2009 (1)

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

2008 (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]

2007 (1)

Andrews, L. C.

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]

Du, X.

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]

Gori, F.

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

Korotkova, O.

Lajunen, H.

Phillips, R. L.

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]

Ramírez-Sánchez, V.

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

Saastamoinen, T.

Santarsiero, M.

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

Shchepakina, E.

Shirai, T.

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

Tong, Z.

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

Z. Tong and O. Korotkova, “Electromagnetic non-uniformly correlated beams,” J. Opt. Soc. Am. A. in press).

Toselli, I.

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]

Zhao, D.

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

F. Gori, V. Ramírez-Sánchez, 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 (1)

Z. Tong and O. Korotkova, “Electromagnetic non-uniformly correlated beams,” J. Opt. Soc. Am. A. in press).

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 (2)

Opt. Lett. (2)

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 (7)

Fig. 1
Fig. 1

The transverse distribution of the beam’s spectral density at the plane z = 30 m for α = 3.67, (a) γx = (0.8σ0,0), γy = (0.9σ0,0) and (b) γx = (0.8σ0,0), γy = (−0.9σ0,0); (c) and (d) are same as (a) and (b) but for z = 1 km.

Fig. 2
Fig. 2

There-dimensional transverse distributions of the beam’s spectral density at the plane z = 30 m and corresponding contour graphs for different parameters γx and γy, α = 3.67, δxx = 0.8σ0 and δyy = 0.9σ0 except for (f) δxx = δyy = 0.9σ0.

Fig. 3
Fig. 3

As Fig. 2 but at the plane z = 1 km.

Fig. 4
Fig. 4

The shift of the intensity center of the beam through non-Kolmogorov turbulence as a function of propagation distance z (a) for different α and (b) for α=3.67 and different C ˜ n 2 .

Fig. 5
Fig. 5

The spectral degree of polarization at the intensity center of the beam with |Bxy| = 0.2 through non-Kolmogorov turbulence as a function of propagation distance z. (a) for different α with δxy = 0.9σ0; (b) for different δxy with α = 3.67.

Fig. 6
Fig. 6

There-dimensional transverse distributions of the degree of polarization of the beam at z = 30m with γx = (0.8σ0,-0.7σ0) and γy = (0.9σ0,-0.6σ0). (a) α = 3.05; (b) α = 3.67; (c) free space.

Fig. 7
Fig. 7

As Fig. 6 but at the plane z = 1 km.

Equations (14)

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

W αβ (0) ( ρ 1 , ρ 2 ,ω)= A α A β B αβ exp( ρ 1 2 + ρ 2 2 2 σ 0 2 )exp{ [ ( ρ 1 γ α ) 2 ( ρ 2 γ β ) 2 ] 2 δ αβ 4 },
W αβ (0) ( ρ 1 , ρ 2 )= p αβ H α ( ρ 1 ,v) H β ( ρ 2 ,v) d 2 v,
p αβ (v)= B αβ k δ αβ 2 /(2 π )exp[ k 2 δ αβ 4 v 2 /4 ],
H j ( ρ ,v)= A j exp[ ρ 2 /(2 σ 0 2 ) ]exp[ ik ( ρ γ j ) 2 v ], (j=α,β).
W αβ ( ρ 1 , ρ 2 ,z,ω)= (k/2πz) 2 d 2 ρ 1 d 2 ρ 2 W αβ (0) ( ρ 1 , ρ 2 ,ω) ×exp{ ik[ ( ρ 1 ρ 1 ) 2 ( ρ 2 ρ 2 ) 2 ]/2z } exp[ ϕ ( ρ 1 , ρ 1 ,z,ω)+ϕ( ρ 2 , ρ 2 ,z,ω)] M .
exp[ ϕ ( ρ 1 , ρ 1 ,z,ω)+ϕ( ρ 2 , ρ 2 ,z,ω)] M = exp{ ( π 2 k 2 z/3)[ ( ρ 1 ρ 2 ) 2 +( ρ 1 ρ 2 )( ρ 1 ρ 2 )+ ( ρ 1 ρ 2 ) 2 ] 0 κ 3 Φ(κ)dκ },
W αβ ( ρ 1 , ρ 2 ,z,ω )=[ k 2 /(4 π 2 z 2 )] p αβ (v) H α ( ρ 1 ,v,z) H β ( ρ 2 ,v,z)dv ,
H α ( ρ 1 ,v,z) H β ( ρ 2 ,v,z)= d 2 ρ 1 d 2 ρ 2 H α ( ρ 1 ,v) H β ( ρ 2 ,v)exp{ ik[ ( ρ 1 ρ 1 ) 2 ( ρ 2 ρ 2 ) 2 ]/2z } ×exp{ ( π 2 k 2 z/3)[ ( ρ 1 ρ 2 ) 2 +( ρ 1 ρ 2 )( ρ 1 ρ 2 )+ ( ρ 1 ρ 2 ) 2 ] 0 κ 3 Φ(κ)dκ }.
H α ( ρ 1 ,v,z) H β ( ρ 2 ,v,z)=[4 π 2 z 2 σ 0 2 A α A β / k 2 w 2 (z,v)] ×exp[ 2ik Γ αβ + Γ αβ v ikut 2 k 2 σ 0 2 ( Γ αβ v t 2z ) 2 π 2 k 2 z t 2 3 0 κ 3 Φ(κ)dκ ] ×exp{ [ u2 Γ αβ + zv+ik σ 0 2 (12zv)( Γ αβ v t 2z )+ i π 2 k z 2 t 3 0 κ 3 Φ(κ)dκ ] 2 / w 2 (z,v) },
w 2 (z,v)= σ 0 2 (12zv) 2 + z 2 /( k 2 σ 0 2 )+(4 π 2 z 3 /3) 0 κ 3 Φ(κ)dκ .
S(ρ,z)=Tr W (ρ,z),
P(ρ,z)= 14Det W (ρ,z)/ [Tr W (ρ,z)] 2 ,
Φ α (κ)=A(α) C ˜ n 2 exp[( κ 2 / κ m 2 )]/ ( κ 2 + κ 0 2 ) α/2 , 0κ<, 3<α<5,
0 κ 2 Φ(κ)dκ = 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 ],

Metrics