Abstract

We report on the experimental observation of abruptly autofocusing waves. This interesting family of wave packets has been realized by using a radially symmetric Airy intensity distribution. As demonstrated in our experiments, these waves can exhibit unusual features, such as the ability to autofocus by following a parabolic trajectory toward their focus.

© 2011 Optical Society of America

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References

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  1. N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, Opt. Express 16, 15733 (2008).
    [CrossRef] [PubMed]
  4. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
    [CrossRef]
  5. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, Appl. Opt. 38, 5004 (1999).
    [CrossRef]
  6. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
    [CrossRef] [PubMed]
  7. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
    [CrossRef]

2010 (3)

N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
[CrossRef] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

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

2009 (1)

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

2008 (1)

2007 (1)

1999 (1)

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Campos, J.

Chong, A.

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

Christodoulides, D. N.

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

N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
[CrossRef] [PubMed]

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

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

Cottrell, D. M.

Davis, J. A.

Di Trapani, P.

Efremidis, N. K.

Faccio, D.

Kolesik, M.

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

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, Opt. Express 16, 15733 (2008).
[CrossRef] [PubMed]

Moloney, J.

Moloney, J. V.

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

Moreno, I.

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Polynkin, P.

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

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, Opt. Express 16, 15733 (2008).
[CrossRef] [PubMed]

Renninger, W. H.

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

Roberts, A.

Siviloglou, G. A.

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

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

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Wise, F. W.

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

Yzuel, M. J.

Appl. Opt. (1)

Nat. Photon. (1)

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

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Science (1)

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

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Figures (6)

Fig. 1
Fig. 1

Experimental setup. FT, Fourier transform; f L , FT lens focal length; f Ai , effective focal length of the Airy ring.

Fig. 2
Fig. 2

(a) Radial profile of the phase mask. Inset, phase mask (b) Theoretical intensity at the FT plane (in the center is the zero order) (c) Experimental intensity profile of the generated Airy ring as captured by the CCD at z = 200 mm (zero order blocked).

Fig. 3
Fig. 3

Radially averaged intensity as a function of the propagation distance. Intensity values are normalized to the peak intensity at z = 0 .

Fig. 4
Fig. 4

(a) Intensity contrast as a function of the propagation distance: solid circles, experimental values; dashed curve and dashed–dotted curve, intensity contrast of equivalent Gaussian beams. (b) Radius of the ring Airy as a function of the propagation distance: open circles, experimental points; dashed curve, quadratic fit.

Fig. 5
Fig. 5

(a) Processing of a thick sample. Comparison of an Airy ring with a Gaussian beam of similar spot size. (b) Ablation crater in the back side of a 1 cm thick fused silica sample after illumination by an intense Airy ring beam.

Fig. 6
Fig. 6

Spatiotemporal isointensity surface profiles of autofocusing Airy ring wave packets for various tempo ral profiles. (a) Gaussian temporal profile; (b) Airy temporal profile; (c) two counteraccelerating Airy temporal profiles.

Equations (4)

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u o ( r , 0 ) = Ai ( r o r w ) exp [ a · ( r o r w ) ] ,
R ( z ) ( r o w ) 3.15 · 10 3 ( λ 2 / w 3 ) · z 2 ,
f Ai 17.9 ( w 2 / λ ) ( r o / w 1 ) .
R ( z ) R ( 0 ) ( 1 z 2 / f Ai 2 ) .

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