Abstract

The evolution of Airy beam intensity distribution in turbulence is examined. Results show that the centroid position and skewness of an Airy beam are independent on turbulence. When the exponential truncation factor is small, an Airy beam has a long tail on the left side. When the exponential truncation factor is larger than 1, an Airy beam can be approximately expressed by an off-axis Gaussian beam. If the effect of turbulence is large enough, the Airy beam converges to a Gaussian distribution. However, the convergence is slower for a small exponential truncation factor than for a large one. That is, an Airy beam with a smaller exponential truncation factor exhibits more resilience against perturbations of turbulence than does a larger one.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
    [CrossRef]
  5. P. Saari and K. Reivelt, Phys. Rev. E 69, 036612 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  10. J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2010 (2)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise1, Nat. Photon. 4, 103 (2010).
[CrossRef]

Y. Gu and G. Gbur, Opt. Lett. 35, 3456 (2010).
[CrossRef] [PubMed]

2009 (2)

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

2008 (5)

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves: Theory and Applications (Wiley, 2008).
[CrossRef]

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

P. Saari, Opt. Express 16, 10303 (2008).
[CrossRef] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (1)

H. T. Eyyuboğlu, Y. Baykal, and E. Sermutlu, Opt. Commun. 265, 399 (2006).
[CrossRef]

2005 (1)

ISO Standard 11146 (International Organization for Standardization, 2005).

2004 (1)

P. Saari and K. Reivelt, Phys. Rev. E 69, 036612 (2004).
[CrossRef]

2002 (1)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

2000 (2)

R. N. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 2000).

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

1998 (1)

I. M. Besieris, M. Abdel-Rahman, A. Shaarawi, and A. Chatzipetros, Prog. Electromagn. Res. 19, 1 (1998).
[CrossRef]

1987 (1)

1979 (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Abdel-Rahman, M.

I. M. Besieris, M. Abdel-Rahman, A. Shaarawi, and A. Chatzipetros, Prog. Electromagn. Res. 19, 1 (1998).
[CrossRef]

Arie, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

Asorey, M.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

Baykal, Y.

H. T. Eyyuboğlu, Y. Baykal, and E. Sermutlu, Opt. Commun. 265, 399 (2006).
[CrossRef]

Berry, M. V.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Besieris, I. M.

I. M. Besieris and A. M. Shaarawi, Opt. Lett. 32, 2447 (2007).
[CrossRef] [PubMed]

I. M. Besieris, M. Abdel-Rahman, A. Shaarawi, and A. Chatzipetros, Prog. Electromagn. Res. 19, 1 (1998).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 2000).

Broky, J.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Chatzipetros, A.

I. M. Besieris, M. Abdel-Rahman, A. Shaarawi, and A. Chatzipetros, Prog. Electromagn. Res. 19, 1 (1998).
[CrossRef]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise1, Nat. Photon. 4, 103 (2010).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise1, Nat. Photon. 4, 103 (2010).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Dogariu, A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dolev, I.

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

Ellenbogen, T.

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Eyyuboglu, H. T.

H. T. Eyyuboğlu, Y. Baykal, and E. Sermutlu, Opt. Commun. 265, 399 (2006).
[CrossRef]

Facchi, P.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Fagerholm, J.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

Friberg, A. T.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Gbur, G.

Gu, Y.

Hanson, S. G.

Hernández-Figueroa, H. E.

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves: Theory and Applications (Wiley, 2008).
[CrossRef]

Man’ko, V. I.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Marmo, G.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

McGloin, D.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Melville, H.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Pascazio, S.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Recami, E.

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves: Theory and Applications (Wiley, 2008).
[CrossRef]

Reivelt, K.

P. Saari and K. Reivelt, Phys. Rev. E 69, 036612 (2004).
[CrossRef]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise1, Nat. Photon. 4, 103 (2010).
[CrossRef]

Saari, P.

P. Saari, Opt. Express 16, 10303 (2008).
[CrossRef] [PubMed]

P. Saari and K. Reivelt, Phys. Rev. E 69, 036612 (2004).
[CrossRef]

Salo, J.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

Salomaa, M. M.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

Sermutlu, E.

H. T. Eyyuboğlu, Y. Baykal, and E. Sermutlu, Opt. Commun. 265, 399 (2006).
[CrossRef]

Shaarawi, A.

I. M. Besieris, M. Abdel-Rahman, A. Shaarawi, and A. Chatzipetros, Prog. Electromagn. Res. 19, 1 (1998).
[CrossRef]

Shaarawi, A. M.

Sibbett, W.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Siviloglou, G. A.

Sudarshan, E. C. G.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Voloch-Bloch, N.

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Wise1, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise1, Nat. Photon. 4, 103 (2010).
[CrossRef]

Yura, H. T.

Zamboni-Rached, M.

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves: Theory and Applications (Wiley, 2008).
[CrossRef]

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Appl. Phys. Lett. (1)

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

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

Nat. Photon. (3)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise1, Nat. Photon. 4, 103 (2010).
[CrossRef]

Nature (1)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

H. T. Eyyuboğlu, Y. Baykal, and E. Sermutlu, Opt. Commun. 265, 399 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (1)

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Phys. Rev. E (2)

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

P. Saari and K. Reivelt, Phys. Rev. E 69, 036612 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Prog. Electromagn. Res. (1)

I. M. Besieris, M. Abdel-Rahman, A. Shaarawi, and A. Chatzipetros, Prog. Electromagn. Res. 19, 1 (1998).
[CrossRef]

Other (3)

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves: Theory and Applications (Wiley, 2008).
[CrossRef]

R. N. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 2000).

ISO Standard 11146 (International Organization for Standardization, 2005).

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Figures (3)

Fig. 1
Fig. 1

Evolution of normalized intensity (a) at the initial plane, (b) in free space where ξ = 2 , and (c) in turbulence where ξ = 2 and a = 0.19 .

Fig. 2
Fig. 2

Variation of kurtosis parameters where w 0 = 0.1 m and l 0 = 0.01 m , (a) with a at the initial plane, (b) with ξ in free space, and (c) with ξ in turbulence where a = 0.19 and λ = 3.8 × 10 6 m .

Fig. 3
Fig. 3

Evolution of the kurtosis parameters of an Airy beam with w 0 = 0.1 m and l 0 = 0.01 m , where (a)  ξ = 0.1 , (b)  ξ = 1 , and (c)  ξ = 2 .

Equations (20)

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u 0 ( R ) = Ai ( x 0 w 0 ) exp ( a x 0 w 0 ) Ai ( y 0 w 0 ) exp ( a y 0 w 0 ) ,
I ( r ) = ( k 2 π z ) 2 H ( ρ d ) M ( ρ d ) exp ( i k z r · ρ d ) d 2 ρ d ,
H ( ρ d ) = u 0 ( ρ + ρ d 2 ) u 0 * ( ρ ρ d 2 ) exp ( i k z ρ · ρ d ) d 2 ρ .
I ( r ) = F 1 [ H ( ω ) M ( z k ω ) ] ,
H ( ω ) = H 1 ( ω , z k ω ) ,
H 1 ( ω , ρ d ) = [ exp ( i 2 ω · ρ d ) u 0 ( ω ) ] * [ exp ( i 2 ω · ρ d ) u 0 * ( ω ) ] .
h ( ω x ) = w 0 4 π ( 2 a + i ω x w 0 ) exp [ ( 2 a + i ω x w 0 ) 3 12 ξ 2 w 0 2 ω x 2 4 ( 2 a + i ω x w 0 ) ] ,
P = H ( 0 ) = w 0 2 8 π a exp ( 4 a 3 3 ) .
μ j 1 j 2 = ( i ) j 1 j 2 H ( 0 ) j 1 + j 2 ω x j 1 ω y j 2 { H ( ω ) M ( z k ω ) } ω = 0 .
M ( ρ d ) = exp [ D ( ρ d ) / 2 ] .
D ( ρ d ) = 8 π 2 k 2 z 0 0 1 [ 1 J 0 ( κ ξ | ρ d | ) ] Φ ( κ ) κ d ξ d κ .
D ( ρ d ) = 2 t = 1 b t | ρ d | 2 t .
b t = 4 π 2 k 2 z ( 1 ) t 1 2 2 t ( t ! ) 2 ( 2 t + 1 ) 0 κ 2 t Φ ( κ ) κ d κ .
μ j 1 j 2 = ( i ) j 1 j 2 H ( 0 ) j 1 + j 2 ω x j 1 ω y j 2 { H ( ω ) exp [ t = 1 [ j 1 / 2 ] + [ j 2 / 2 ] b t ( z k ω ) 2 t ] } ω = 0 .
μ j = 1 P ( x x c ) j I ( x , y ) d x d y .
x c = ( a 2 1 / 4 a ) w 0 , μ 2 = ( 8 a 3 + 1 8 a 2 + ξ 2 4 a + 2 ξ 2 b 1 w 0 2 ) w 0 2 , μ 3 = ( 4 a 3 1 8 a 3 3 ξ 2 8 a 2 ) w 0 3 , μ 4 = { 3 ( 5 64 a 4 + 1 4 a + a 2 ) + 3 2 ξ 2 ( 1 + 5 8 a 3 + ξ 2 8 a 2 ) + ξ 2 w 0 2 [ 3 b 1 2 a 2 ( 1 + 8 a 3 + 2 a ξ 2 + 8 a 2 ξ 2 w 0 2 b 1 ) 24 ξ 2 w 0 2 b 2 ] } w 0 4 .
Φ ( κ ) = 0.033 C n 2 κ 11 / 3 exp ( κ 2 κ m 2 ) ,
b 1 = 0.71 r 0 5 / 3 κ m 1 / 3 , b 2 = 0.0045 r 0 5 / 3 κ m 7 / 3 ,
u ( x ) = Ai [ x w 0 ( ξ 2 ) 2 + i a ξ ] exp ( a x w 0 a ξ 2 2 ) .
u 0 ( x 0 ) Ai ( a 2 1 4 a ) exp ( a 3 1 4 ) exp [ ( x 0 x c ) 2 4 a w 0 2 ] .

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