Abstract

This is the first in a series of papers demonstrating that photons with orbital angular momentum can be created in optical waves propagating through distributed turbulence. The scope of this first paper is much narrower. Here, we demonstrate that atmospheric turbulence can impart non-trivial angular momentum to beams and that this non-trivial angular momentum is highly localized. Furthermore, creation of this angular momentum is a normal part of propagation through atmospheric turbulence.

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  2. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, USA, 1975), 2nd ed.
  3. R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (SPIE Press, Wa, USA, 2007), 2nd ed.
  4. D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed atmospheric turbulence,” Opt. Exp. (2011). Accepted for publication.
  5. I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes (Dover Publications, Inc., New York, USA, 1969), 1st ed. An english translation of the original work.
  6. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, WA, USA, 1998), 2nd ed.
  7. D. L. Fried, “Probability of getting a lucky short-exposure image through turbulence,” J. Opt. Soc. Am. 40, 1651–1658 (1977).
  8. M. Reed and B. Simon, Methods of Modern Mathematical Analysis, I: Functional Analysis (Academic Press, New York, USA, 1980), revised and enlarged ed.

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

1977 (1)

D. L. Fried, “Probability of getting a lucky short-exposure image through turbulence,” J. Opt. Soc. Am. 40, 1651–1658 (1977).

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, WA, USA, 1998), 2nd ed.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Fried, D. L.

D. L. Fried, “Probability of getting a lucky short-exposure image through turbulence,” J. Opt. Soc. Am. 40, 1651–1658 (1977).

Gikhman, I. I.

I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes (Dover Publications, Inc., New York, USA, 1969), 1st ed. An english translation of the original work.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, USA, 1975), 2nd ed.

Oesch, D. W.

D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed atmospheric turbulence,” Opt. Exp. (2011). Accepted for publication.

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, WA, USA, 1998), 2nd ed.

Reed, M.

M. Reed and B. Simon, Methods of Modern Mathematical Analysis, I: Functional Analysis (Academic Press, New York, USA, 1980), revised and enlarged ed.

Sanchez, D. J.

D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed atmospheric turbulence,” Opt. Exp. (2011). Accepted for publication.

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (SPIE Press, Wa, USA, 2007), 2nd ed.

Simon, B.

M. Reed and B. Simon, Methods of Modern Mathematical Analysis, I: Functional Analysis (Academic Press, New York, USA, 1980), revised and enlarged ed.

Skorokhod, A. V.

I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes (Dover Publications, Inc., New York, USA, 1969), 1st ed. An english translation of the original work.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

D. L. Fried, “Probability of getting a lucky short-exposure image through turbulence,” J. Opt. Soc. Am. 40, 1651–1658 (1977).

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Other (6)

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, USA, 1975), 2nd ed.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (SPIE Press, Wa, USA, 2007), 2nd ed.

D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed atmospheric turbulence,” Opt. Exp. (2011). Accepted for publication.

I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes (Dover Publications, Inc., New York, USA, 1969), 1st ed. An english translation of the original work.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, WA, USA, 1998), 2nd ed.

M. Reed and B. Simon, Methods of Modern Mathematical Analysis, I: Functional Analysis (Academic Press, New York, USA, 1980), revised and enlarged ed.

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Equations (18)

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2 E + k 2 n 2 E + 2 ( E ) log n = 0
z ^ E 0
z ^ ( E ) log n ( r ) = ( E ) log n ( r ) z
z ^ ( E log n ) 2 = ( [ z + 1 ] E ) ( log n + z log n ) 2
z ^ ( E log n ) 2 = ( 1 + k 2 ) [ d κ ( 1 + κ z 2 ) ( A ( r ) κ ) 2 f ( κ ) ]
k 2 n 2 E 2 = k 4 A 2 ( r ) ( d κ f ( κ ) ) 2 = k 4 A 2 ( r )
( E log n ) 2 k 2 n 2 E 2 = k 2 d κ κ z 2 ( A ( r ) κ ) 2 f ( κ ) k 4 A 2 ( r ) ( d κ f ( κ ) ) 2 = λ 2 2 π d κ κ z 2 ( e ^ κ ) 2 f ( κ )
( E log n ) 2 k 2 n 2 E 2 for κ large
( E log n ) 2 k 2 n 2 E 2 λ 2 d κ κ 4 ( κ 2 + κ o 2 ) 11 / 6 exp ( κ 2 κ i 2 )
n = 1 + n 0 + n 1
( i ) ( x , x ) 0 and ( x , x ) = 0 iff x = 0 ( ii ) ( x , y + z ) = ( x , x ) + ( x , z ) ( iii ) ( x , α y ) = α ( x , y ) ( iv ) ( x , y ) = ( y , x ) *
R ( x , y ) = M ( [ ξ ( y ) M ( ξ ( y ) ) ] [ ξ ( x ) M ( ξ ( x ) ) ] * )
R ( x , y ) = M ( [ y M ( y ) ] [ x M ( x ) ] * ) .
( i ) R ( x , x ) 0 and R ( x , x ) = 0 iff ξ ( x ) = constant ( ii ) R ( x , y ) = R * ( y , x ) ( iii ) | R ( x , y ) | 2 = R ( x , x ) R ( y , y ) ( ii ) n , x 1 , x n V and λ 1 , , λ n , j , k = 1 n R ( x j , x k ) λ j λ k * 0
R ( x , x ) = M ( x 2 ) > 0 R ( x , y + z ) = R ( x , y ) + R ( x , z ) R ( x , ay ) = a R ( x , y ) R ( x , y ) = ( R ( y , x ) ) *
R ( x , x ) = 0 x = 0 .
f ( κ ) = C κ 11 / 3
f ( κ ) = C ( κ 2 + κ o 2 ) 11 / 6 exp ( κ 2 κ i 2 )

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