Abstract

We demonstrate both theoretically and experimentally that optical Airy beams propagating in free space can perform ballistic dynamics akin to those of projectiles moving under the action of gravity. The parabolic trajectories of these beams as well as the motion of their center of gravity were observed in good agreement with theory. The possibility of circumventing an obstacle placed in the path of the Airy beam is discussed.

© 2008 Optical Society of America

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References

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  1. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  2. M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
    [CrossRef]
  3. D. M. Greenberger, Am. J. Phys. 48, 256 (1980).
    [CrossRef]
  4. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef] [PubMed]
  5. L. I. Schiff, Quantum Mechanics, 3rd ed. (McGraw-Hill, 1968).
  6. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  7. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, Opt. Lett. 25, 1493 (2000).
    [CrossRef]
  8. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, Opt. Lett. 29, 44 (2004).
    [CrossRef] [PubMed]
  9. I. M. Besieris and A. M. Shaarawi, Opt. Lett. 32, 2447 (2007).
    [CrossRef] [PubMed]
  10. D. N. Christodoulides and T. H. Coskun, Opt. Lett. 21, 1460 (1996).
    [CrossRef] [PubMed]
  11. W. T. Cathey and E. R. Dowski, Appl. Opt. 41, 6080 (2002).
    [CrossRef] [PubMed]

2007

2004

2002

2000

1996

1987

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

1980

D. M. Greenberger, Am. J. Phys. 48, 256 (1980).
[CrossRef]

1979

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

Am. J. Phys.

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

D. M. Greenberger, Am. J. Phys. 48, 256 (1980).
[CrossRef]

Appl. Opt.

Opt. Lett.

Phys. Rev. Lett.

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

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Other

L. I. Schiff, Quantum Mechanics, 3rd ed. (McGraw-Hill, 1968).

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Figures (5)

Fig. 1
Fig. 1

Ballistic dynamics of an ideal Airy beam ( a = 0 ) when (a) v = 2 , (b) v = 0 , and (c) v = + 2 . The circle in (a) represents an opaque obstacle.

Fig. 2
Fig. 2

Experimental setup. M, mirror; BE, beam expander; BS, beam splitter; L, lens; MO, microscope objective.

Fig. 3
Fig. 3

Input intensity profile of the Airy beam used for all launching angles for (a) experiment and (b) theory when x 0 = 59 μ m and a = 0.08 . The arrow C indicates the wavefunction’s center of gravity.

Fig. 4
Fig. 4

Airy beam ballistics for (A) θ = 1.33 mrad , (B) θ = 1.0 mrad , (C) θ = 0.5 mrad , (D) θ = + 0.17 mrad , and (E) θ = + 0.83 mrad

Fig. 5
Fig. 5

Motion of the beam’s center of gravity as a function of distance for the same parameters used in Fig. 4.

Equations (3)

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i ϕ ξ + 1 2 2 ϕ s 2 = 0 ,
ϕ ( s , ξ ) = Ai [ s ( ξ 2 ) 2 v ξ + i a ξ ] exp [ a s ( a ξ 2 2 ) a v ξ ] × exp [ i ( ( ξ 3 12 ) + ( ( a 2 v 2 + s ) ξ 2 ) + v s ( v ξ 2 2 ) ) ] .
s = v ξ + 4 a 3 1 4 a .

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