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)

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]

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]

2000 (3)

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

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]

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

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]

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]

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]

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]

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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