Abstract

Analytical formulas are derived for the average irradiance and the degree of polarization of a radially or azimuthally polarized doughnut beam (PDB) propagating in a turbulent atmosphere by adopting a beam coherence-polarization matrix. It is found that the radial or azimuthal polarization structure of a radially or azimuthally PDB will be destroyed (i.e., a radially or azimuthally PDB is depolarized and becomes a partially polarized beam) and the doughnut beam spot becomes a circularly Gaussian beam spot during propagation in a turbulent atmosphere. The propagation properties are closely related to the parameters of the beam and the structure constant of the atmospheric turbulence.

© 2008 Optical Society of America

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2008 (1)

M. Alavinejad, B. Ghafary, and F. D. Kashani, "Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere," Opt. Lasers Eng. 46, 1-5 (2008).
[CrossRef]

2007 (7)

2006 (4)

2004 (2)

2003 (3)

2002 (1)

2001 (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Z. Bomzon, V. Kleiner and E. Hasman, "Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings," Appl. Phys. Lett. 79, 1587-1589 (2001).
[CrossRef]

2000 (3)

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

B. Sick, B. Hecht, and L. Novotny, "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

1998 (2)

1979 (1)

1978 (1)

1972 (1)

1970 (1)

T. L. Ho, "Coherence degration of Gaussian beams in a turbulent atmosphere," J. Opt. Soc. Am 60, 667-673 (1970).
[CrossRef]

Alavinejad, M.

M. Alavinejad, B. Ghafary, and F. D. Kashani, "Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere," Opt. Lasers Eng. 46, 1-5 (2008).
[CrossRef]

Baykal, Y.

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Blit, S.

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Bomzon, Z.

Z. Bomzon, V. Kleiner and E. Hasman, "Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings," Appl. Phys. Lett. 79, 1587-1589 (2001).
[CrossRef]

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

Cai, Y.

Chen, Y.

Chen, Z.

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

Chu, X.

Davidson, F. M.

Davidson, N.

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Deng, D.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper Focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Duan, K.

Eyyubo??lu, H. T.

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Ghafary, B.

M. Alavinejad, B. Ghafary, and F. D. Kashani, "Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere," Opt. Lasers Eng. 46, 1-5 (2008).
[CrossRef]

Gori, F.

Gutierrez-Vega, J. C.

Hasman, E.

Z. Bomzon, V. Kleiner and E. Hasman, "Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings," Appl. Phys. Lett. 79, 1587-1589 (2001).
[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]

Y. Cai and S. He, "Average intensity and spreading of an elliptical Gaussian beam propagating in a turbulent atmosphere," Opt. Lett. 31, 568-570 (2006).
[CrossRef] [PubMed]

Hecht, B.

B. Sick, B. Hecht, and L. Novotny, "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
[CrossRef] [PubMed]

Ho, T. L.

T. L. Ho, "Coherence degration of Gaussian beams in a turbulent atmosphere," J. Opt. Soc. Am 60, 667-673 (1970).
[CrossRef]

Kashani, F. D.

M. Alavinejad, B. Ghafary, and F. D. Kashani, "Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere," Opt. Lasers Eng. 46, 1-5 (2008).
[CrossRef]

Kleiner, V.

Z. Bomzon, V. Kleiner and E. Hasman, "Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings," Appl. Phys. Lett. 79, 1587-1589 (2001).
[CrossRef]

Leader, J. C.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper Focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Li, J.

Lin, Q.

Lu, B.

Lu, X.

Musha, M.

Noriega-Manez, R. J.

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

B. Sick, B. Hecht, and L. Novotny, "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
[CrossRef] [PubMed]

Oron, R.

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Plonus, M. A.

Pu, J.

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

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper Focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Ricklin, J. C.

Sheppard, C. J. R.

Shirakawa, A.

Sick, B.

B. Sick, B. Hecht, and L. Novotny, "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
[CrossRef] [PubMed]

Tervo, J.

Tovar, A. A.

Ueda, K. I.

Wang, S. C. H.

Yew, E. Y. S.

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

Yura, H. T.

Zhan, Q.

Zhong, L. X.

Appl. Opt. (1)

Appl. Phys. B (1)

H. T. Eyyubo�?lu, Y. Baykal, and Y. Cai, "Degree of polarization for partially coherent general beams in turbulent atmosphere," Appl. Phys. B 89, 91-97 (2007).
[CrossRef]

Appl. Phys. Lett. (3)

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]

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Z. Bomzon, V. Kleiner and E. Hasman, "Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings," Appl. Phys. Lett. 79, 1587-1589 (2001).
[CrossRef]

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

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

J. Opt. Soc. Am (1)

T. L. Ho, "Coherence degration of Gaussian beams in a turbulent atmosphere," J. Opt. Soc. Am 60, 667-673 (1970).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

J. Opt. Soc. Am. B (1)

Opt. Express (4)

Opt. Lasers Eng. (1)

M. Alavinejad, B. Ghafary, and F. D. Kashani, "Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere," Opt. Lasers Eng. 46, 1-5 (2008).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. Lett. (3)

R. Dorn, S. Quabis, and G. Leuchs, "Sharper Focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

B. Sick, B. Hecht, and L. Novotny, "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
[CrossRef] [PubMed]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Other (1)

A. Ishimaru, Wave Propagation and Scattering in Random Media, Vol. 2 (Academic Press, New York, 1978).

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Figures (6)

Fig. 1.
Fig. 1.

Propagation geometry of a radially or azimuthally PDB in a turbulent atmosphere

Fig. 2.
Fig. 2.

Cross line (y=0) of the normalized irradiance distribution I(x,0,z)/I(x,0,0)max of a radially PDB at several propagation distances in a turbulent atmosphere for two different values of structure constant C 2 n

Fig. 3.
Fig. 3.

Normalized 3D-irradiance distribution max I(x,y,z)/I(x,0,0)max of a radially PDB and the corresponding contour graph at several propagation distances in a turbulent atmosphere with w 0=2cm and C 2 n =3×10-15 m -2/3

Fig. 4.
Fig. 4.

Normalized on-axis irradiance distribution I(0,0,z)/I(x,0,0)max of a radially PDB along z in a turbulent atmosphere for different values of W 0 and C 2 n

Fig. 5.
Fig. 5.

Degree of polarization P(x, y, z) of a radially PDB and the corresponding cross line (y=0) at several propagation distance with w 0=2cm and C 2 n =10-15 m -2/3

Fig. 6.
Fig. 6.

Cross line (y=0) the degree of polarization P(x,0,z) of a radially PDB at z=15km in a turbulent atmosphere for different values of W 0 and C 2 n

Equations (16)

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E r ( x , y ) = E 1 e x + E 2 e y = E 0 [ x w 0 exp ( r 2 w 0 2 ) e x + y w 0 exp ( r 2 w 0 2 ) e y ] ,
E θ ( x , y ) = E 0 [ y w 0 exp ( r 2 w 0 2 ) e x + x w 0 exp ( r 2 w 0 2 ) e y ] .
Γ ̂ ( r 1 , r 2 , z ) = ( Γ 11 ( r 1 , r 2 , z ) Γ 12 ( r 1 , r 2 , z ) Γ 21 ( r 1 , r 2 , z ) Γ 22 ( r 1 , r 2 , z ) ) ,
Γ α β ( r 1 , r 2 , z ) = E α ( r 1 , r 2 , z ) E β * ( r 1 , r 2 , z ) , ( α , β = 1 , 2 )
I ( r , z ) = Γ 11 ( r , r , z ) + Γ 22 ( r , r , z ) ,
P ( r , z ) = 1 4 det [ Γ ̂ ( r , r , z ) ] { Tr [ Γ ̂ ( r , r , z ) ] } 2 ,
Γ ̂ r ( r 1 , r 2 , 0 ) = E 0 2 w 0 2 exp ( r 1 2 + r 2 2 w 0 2 ) ( x 1 x 2 x 1 y 2 y 1 x 2 y 1 y 2 ) ,
Γ ̂ θ ( r 1 , r 2 , 0 ) = E 0 2 w 0 2 exp ( r 1 2 + r 2 2 w 0 2 ) ( y 1 y 2 x 2 y 1 x 1 y 2 x 1 x 2 ) .
Γ α β ( r , r , z ) = k 2 4 π 2 z 2 Γ α β ( r 1 , r 2 , 0 ) exp [ ik 2 z ( r 1 r ) 2 + ik 2 z ( r 2 r ) 2 ]
× exp [ 1 ρ 0 2 ( r 1 r 2 ) 2 ] d r 1 d r 2 ,
Γ r 11 ( r , r , z ) = E 0 2 2 k 2 ρ 0 4 w 0 6 z 2 A 1 2 [ 1 ρ 0 2 + k 2 ρ 0 2 ( k 2 w 0 4 + 4 z 2 ) 2 z 2 A 1 x 2 ] exp [ 2 k 2 ρ 0 2 w 0 2 A 1 r 2 ] ,
Γ r 12 ( r , r , z ) = Γ r 21 ( r , r , z ) = E 0 2 k 4 ρ 0 6 w 0 6 ( k 2 w 0 4 + 4 z 2 ) xy A 1 3 exp [ 2 k 2 ρ 0 2 w 0 2 A 1 r 2 ] ,
Γ r 22 ( r , r , z ) = E 0 2 2 k 2 ρ 0 4 w 0 6 z 2 A 1 2 [ 1 ρ 0 2 + k 2 ρ 0 2 ( k 2 w 0 4 + 4 z 2 ) 2 z 2 A 1 y 2 ] exp [ 2 k 2 ρ 0 2 w 0 2 A 1 r 2 ] ,
Γ θ 11 ( r , z ) = Γ r 22 ( r , z ) , Γ θ 22 ( r , z ) = Γ r 11 ( r , z ) , Γ θ 12 ( r , z ) = Γ θ 21 ( r , z ) = Γ r 12 ( r , z ) .
I r ( r , z ) = Γ r 11 ( r , z ) cos 2 ϕ + Γ r 22 ( r , z ) sin 2 ϕ + Γ r 12 ( r , z ) sin 2 ϕ ,
I θ ( r , z ) = Γ θ 11 ( r , z ) cos 2 ϕ + Γ θ 22 ( r , z ) sin 2 ϕ + Γ θ 12 ( r , z ) sin 2 ϕ .

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