Abstract

We demonstrate an optical element for generation of accelerating Airy beams. The element is conveniently constructed by combination of positive and negative cylindrical lenses of matching radii of curvature. With proper choice of lens curvatures, the resulting surface profile closely follows a cubic polynomial. Passing a Gaussian beam through this element and performing optical Fourier transform yields beam profiles close to the Airy function. Our experiments demonstrate parabolic propagation, or acceleration, of the resulting focal spots.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  2. K. Dholakia, “Optics: against the spread of the light,” Nature 451, 413–413 (2008).
    [CrossRef] [PubMed]
  3. C. G. Durfee and H. M. Milchberg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71, 2409–2412 (1993).
    [CrossRef] [PubMed]
  4. S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun. 282, 129–134 (2008).
  5. G. Milne, G. D. M. Jeffries, and D. T. Chiu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101–261103 (2008).
    [CrossRef]
  6. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901–213904 (2007).
    [CrossRef]
  7. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
    [CrossRef] [PubMed]
  8. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
    [CrossRef] [PubMed]
  9. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
    [CrossRef]
  10. J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334–1336 (2009).
    [CrossRef] [PubMed]
  11. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beam,”Nat. Photonics 3, 395–398 (2009).
    [CrossRef]
  12. J. E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995).
    [CrossRef] [PubMed]
  13. W. T. Cathey and E. R. Dowski, “New paradigm for imaging systems,” Appl. Opt. 41, 6080–6092 (2002).
    [CrossRef] [PubMed]
  14. S. Akturk, “Method and device for generation of accelerating Airy beams,” Patent Application PCT/EP2010/054385, 31 March 2010 .

2009

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef] [PubMed]

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334–1336 (2009).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beam,”Nat. Photonics 3, 395–398 (2009).
[CrossRef]

2008

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
[CrossRef]

K. Dholakia, “Optics: against the spread of the light,” Nature 451, 413–413 (2008).
[CrossRef] [PubMed]

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun. 282, 129–134 (2008).

G. Milne, G. D. M. Jeffries, and D. T. Chiu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101–261103 (2008).
[CrossRef]

2007

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901–213904 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef] [PubMed]

2002

1995

1993

C. G. Durfee and H. M. Milchberg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71, 2409–2412 (1993).
[CrossRef] [PubMed]

1987

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Akturk, S.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun. 282, 129–134 (2008).

S. Akturk, “Method and device for generation of accelerating Airy beams,” Patent Application PCT/EP2010/054385, 31 March 2010 .

Arie, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beam,”Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Baumgartl, J.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334–1336 (2009).
[CrossRef] [PubMed]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901–213904 (2007).
[CrossRef]

Cathey, W. T.

Chiu, D. T.

G. Milne, G. D. M. Jeffries, and D. T. Chiu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101–261103 (2008).
[CrossRef]

Christodoulides, D. N.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901–213904 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef] [PubMed]

Couairon, A.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun. 282, 129–134 (2008).

Day, D.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334–1336 (2009).
[CrossRef] [PubMed]

Dholakia, K.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334–1336 (2009).
[CrossRef] [PubMed]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
[CrossRef]

K. Dholakia, “Optics: against the spread of the light,” Nature 451, 413–413 (2008).
[CrossRef] [PubMed]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901–213904 (2007).
[CrossRef]

Dowski, E. R.

Dowski, J. E. R.

Durfee, C. G.

C. G. Durfee and H. M. Milchberg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71, 2409–2412 (1993).
[CrossRef] [PubMed]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beam,”Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Franco, M.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun. 282, 129–134 (2008).

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beam,”Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Gu, M.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334–1336 (2009).
[CrossRef] [PubMed]

Hannappel, G. M.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334–1336 (2009).
[CrossRef] [PubMed]

Jeffries, G. D. M.

G. Milne, G. D. M. Jeffries, and D. T. Chiu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101–261103 (2008).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef] [PubMed]

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Milchberg, H. M.

C. G. Durfee and H. M. Milchberg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71, 2409–2412 (1993).
[CrossRef] [PubMed]

Milne, G.

G. Milne, G. D. M. Jeffries, and D. T. Chiu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101–261103 (2008).
[CrossRef]

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef] [PubMed]

Mysyrowicz, A.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun. 282, 129–134 (2008).

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef] [PubMed]

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901–213904 (2007).
[CrossRef]

Stevenson, D. J.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334–1336 (2009).
[CrossRef] [PubMed]

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beam,”Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Zhou, B.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun. 282, 129–134 (2008).

Appl. Opt.

Appl. Phys. Lett.

G. Milne, G. D. M. Jeffries, and D. T. Chiu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101–261103 (2008).
[CrossRef]

Lab Chip

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334–1336 (2009).
[CrossRef] [PubMed]

Nat. Photonics

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beam,”Nat. Photonics 3, 395–398 (2009).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
[CrossRef]

Nature

K. Dholakia, “Optics: against the spread of the light,” Nature 451, 413–413 (2008).
[CrossRef] [PubMed]

Opt. Commun.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun. 282, 129–134 (2008).

Opt. Lett.

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

C. G. Durfee and H. M. Milchberg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71, 2409–2412 (1993).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901–213904 (2007).
[CrossRef]

Science

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef] [PubMed]

Other

S. Akturk, “Method and device for generation of accelerating Airy beams,” Patent Application PCT/EP2010/054385, 31 March 2010 .

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 (3)

Fig. 1
Fig. 1

Left, construction of the optical element from cylindrical lenses. The drawing shows view from the side. Right, spatial phase introduced by the optical element used in the experiments (see below) and cubic polynomial fit.

Fig. 2
Fig. 2

(a) Measured intensity profile at the focal plane of the Fourier transform lens. (b) Calculated intensity profile. These profiles show that the main aberration in the measurements is in the form of an intensity peak next to the principal one, in the positive x direction. This aberration is caused by the finite thicknesses of the cylindrical lenses and corresponding diffraction effects in the contact region. (c) Measured positions of beam maxima along the propagation direction. These points closely fit to a parabola, as expected. The deviations mainly result from the pixel size ( 4.65 μ m ) of our CCD camera.

Fig. 3
Fig. 3

Theoretical (left) and experimental (right) two-dimensional transverse Airy–Gauss beam profiles. In these profiles, the cross section in either transverse direction yields Airy-function-squared, as shown in Fig. 2. The most intense spots can be identified as focal regions, and they move along a parabola (in both transverse directions) as the beam propagates.

Equations (6)

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

( n 1 ) k x 2 2 R = φ 3 x 3 at x = w 0 φ 3 = ( n 1 ) k 2 R w 0 ,
w 0 2 R λ 10 ,
E ( x ) exp [ x 2 w 0 2 i φ 3 x 3 ] .
E ( x ) A i ( x x 0 ) exp ( a x x 0 ) ,
x 0 = f ( 3 φ 3 ) 1 3 k ,
a = ( f k x 0 w 0 ) 2 .

Metrics