Abstract

Accelerated Airy beams have previously been generated using a cubic phase pattern that represents the Fourier transform of the Airy beam. The Fourier transform of this pattern is formed using a system length of 2f, where f is the focal length of the Fourier transform lens. In this work, we directly generate the Airy beam using a 32 phase pattern encoded onto an LCD. Experimental results show a deflection that depends on the square of the distance from the LCD and match theoretical predictions. However the system length is much shorter.

© 2009 Optical Society of America

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References

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  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. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
    [CrossRef]
  5. J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, Lab Chip 9, 1334 (2009).
    [CrossRef] [PubMed]
  6. J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, Appl. Opt. 48, 1 (2009).
    [CrossRef]
  7. M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
    [CrossRef]
  8. J. A. Davis, I. Moreno, and P. Tsai, Appl. Opt. 37, 937 (1998).
    [CrossRef]
  9. I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, Opt. Eng. 37, 3048 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]

2009 (2)

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, Lab Chip 9, 1334 (2009).
[CrossRef] [PubMed]

J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, Appl. Opt. 48, 1 (2009).
[CrossRef]

2008 (2)

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]

2002 (1)

1998 (2)

J. A. Davis, I. Moreno, and P. Tsai, Appl. Opt. 37, 937 (1998).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, Opt. Eng. 37, 3048 (1998).
[CrossRef]

1979 (1)

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

Allison, D. B.

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, Opt. Eng. 37, 3048 (1998).
[CrossRef]

Balazs, N. L.

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

Bandres, M. A.

Baumgartl, J.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, Lab Chip 9, 1334 (2009).
[CrossRef] [PubMed]

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

Berry, M. V.

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

Broky, J.

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

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

Christodoulides, D. N.

Cottrell, D. M.

Davis, J. A.

Day, D.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, Lab Chip 9, 1334 (2009).
[CrossRef] [PubMed]

Dholakia, K.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, Lab Chip 9, 1334 (2009).
[CrossRef] [PubMed]

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

D'Nelly, K. G.

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, Opt. Eng. 37, 3048 (1998).
[CrossRef]

Dogariu, A.

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

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

Gu, M.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, Lab Chip 9, 1334 (2009).
[CrossRef] [PubMed]

Hannappel, G. M.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, Lab Chip 9, 1334 (2009).
[CrossRef] [PubMed]

Marquez, A.

Mazilu, M.

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

McAuley, K. P.

Mitry, M. J.

Moreno, I.

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, Opt. Eng. 37, 3048 (1998).
[CrossRef]

J. A. Davis, I. Moreno, and P. Tsai, Appl. Opt. 37, 937 (1998).
[CrossRef]

Nicolas, J.

Ruiz, I.

Siviloglou, G. A.

Stevenson, D. J.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, Lab Chip 9, 1334 (2009).
[CrossRef] [PubMed]

Tsai, P.

Am. J. Phys. (1)

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

Appl. Opt. (3)

Lab Chip (1)

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, Lab Chip 9, 1334 (2009).
[CrossRef] [PubMed]

Nat. Photonics (1)

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

Opt. Eng. (1)

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, Opt. Eng. 37, 3048 (1998).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

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

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Figures (4)

Fig. 1
Fig. 1

Geometrical model for accelerating beams.

Fig. 2
Fig. 2

Phase patterns encoded onto an LCD for (a) 3 2 phase pattern, (b) lens with offset focal point.

Fig. 3
Fig. 3

Experimental results for Airy beams with values of a = { 0.00115 , 0.0013 , 0.00145 } mm 0.5 (columns) at distances (rows) of z = ( 500 , 1000 , 1500 mm ) . Each photo shows an area of 5 × 5 mm .

Fig. 4
Fig. 4

Deflection (in millimeters) versus propagation distance (in millimeters) from the LCD for Airy beams where a = { 0.000852 , 0.00112 , 0.00141 } mm 0.5 . Points show experimental data, and the lines show theoretical curves.

Equations (1)

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d δ d ζ = d x d z = 2 a x = 2 a ζ ,

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