Abstract

We demonstrate the projectile motion of two-dimensional truncated Airy beams in a general ballistic trajectory with controllable range and height. We show that the peak beam intensity can be delivered to any desired location along the trajectory as well as repositioned to a given target after displacement due to propagation through disordered or turbulent media.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef] [PubMed]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
    [CrossRef] [PubMed]
  4. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
    [CrossRef] [PubMed]
  5. T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
    [CrossRef]
  6. J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
    [CrossRef]
  7. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
    [CrossRef] [PubMed]
  8. J. Li, W. Zang, and J. Tian, Opt. Express 18, 7300 (2010).
    [CrossRef] [PubMed]
  9. A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
    [CrossRef]
  10. I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
    [CrossRef]
  11. M. A. Bandres, Opt. Lett. 33, 1678 (2008).
    [CrossRef] [PubMed]
  12. J. A. Davis, M. J. Mitry, M. A. Bandres, and D. M. Cottrell, Opt. Express 16, 12866 (2008).
    [CrossRef] [PubMed]

2010 (2)

J. Li, W. Zang, and J. Tian, Opt. Express 18, 7300 (2010).
[CrossRef] [PubMed]

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

2009 (3)

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

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

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

2008 (5)

2007 (2)

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

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

Arie, A.

T. Ellenbogen, N. Voloch, 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]

Bandres, M. A.

Baumgartl, J.

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

Broky, J.

Chong, A.

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

Christodoulides, D. N.

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

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef] [PubMed]

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

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

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

Cottrell, D. M.

Davis, J. A.

Dholakia, K.

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

Dogariu, A.

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, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Ganany-Padowicz, A.

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

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Li, J.

Mazilu, M.

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

Mitry, M. J.

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Renninger, W.

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

Siviloglou, G. A.

Tian, J.

Voloch, N.

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

Voloch-Bloch, N.

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

Wise, F. W.

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

Zang, W.

Appl. Phys. Lett. (1)

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

Nat. Photon. (3)

T. Ellenbogen, N. Voloch, 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. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

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

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Schematic of input Gaussian beam, cubic phase mask, and Fourier lens used for generation of truncated Airy beam. (b) Location of mask (center denoted by open circle) and input beam (marked by dashed circle and center denoted by solid dot) in the Fourier plane. (c) Illustration of different trajectories obtained at different D g and D m when the peak beam intensity appears at maximum heights or ranges (marked by dots). The inset shows the Airy beam profile at the maximum height of the upper curve. The lower curve corresponds to normal excitation at D g = D m = 0 ; so its peak intensity is at the starting point ( z = 0 ). (d) Numerical simulations of beam propagation for two specific cases corresponding to the upper trajectory shown in (c).

Fig. 2
Fig. 2

Experimental demonstration of controlled trajectories (dashed curves) of truncated Airy beams under different excitation conditions. Snapshots of transverse intensity patterns are shown at marked positions. (a) Normal condition when peak beam intensity is at the starting point, corresponding to lower curve in Fig. 1c. (b), (d) Peak intensity goes to the maximum height with shifting of only the cubic phase mask. (c), (e) Peak intensity goes to the “point of fall” with additional shifting of the Gaussian beam.

Fig. 3
Fig. 3

Experimental demonstration of accelerating Airy beams with transverse uniform motion. (a) Relative positions of cubic phase mask and Gaussian beam in the Fourier plane. (b), (c) Experimental results of the trajectory and intensity pattern of the Airy beam obtained under different excitation conditions as depicted in (a).

Fig. 4
Fig. 4

(a) Schematic of Airy beam propagation through a disordered medium. The dashed (solid) curve depicts the trajectory in free space (disordered medium). (b) Intensity pattern of output Airy beam at z = 25 cm through air and (c) stirred salt–water mixture. (d) Restoration of the Airy beam peak intensity at the target after translating the phase mask and input Gaussian beam. (e) Typical output pattern of a Gaussian beam from the salt–water mixture. The white cross corresponds to the target point at ( 0 , 0 , 25 cm ) .

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

ϕ = C f ( s , ξ ) Ai [ s w m ξ ( ξ / 2 ) 2 + i α ( ξ 2 w g + 2 w m ) ] exp ( i w m s ) ,
C = exp ( α w g 2 α w m 2 + i 2 α 2 w m i 2 α 2 w g + 2 α w m w g ) ,
f ( s , ξ ) = exp [ α s + i s ξ / 2 + ( i w m 2 / 2 + i α 2 / 2 2 α w m + α w g ) ξ + ( α / 2 i w m / 2 ) ξ 2 i ξ 3 / 12 ] ,

Metrics