Abstract

We investigate the finite power Airy beams generated by finite extent input beams such as a Gaussian beam, a uniform beam of finite extent, and an inverse Gaussian beam. Each has different propagation behavior: A finite Airy beam generated by a uniform input beam keeps its Airy profile much longer than the conventional finite Airy beam. Also, an inverse Gaussian beam generates a finite Airy beam with a good bent focusing in free space. In this paper, the analysis and experimental results of finite Airy beams are presented.

© 2013 Optical Society of America

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References

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  1. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
    [Crossref]
  2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
    [Crossref] [PubMed]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
    [Crossref] [PubMed]
  4. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
    [Crossref]
  5. D. N. Christodoulides, “Optical trapping: riding along an Airy beam,” Nat. Photonics 2(11), 652–653 (2008).
    [Crossref]
  6. Z. Zheng, B.-F. Zhang, H. Chen, J. Ding, and H.-T. Wang, “Optical trapping with focused Airy beams,” Appl. Opt. 50(1), 43–49 (2011).
    [Crossref] [PubMed]
  7. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
    [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(5924), 229–232 (2009).
    [Crossref] [PubMed]
  9. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
    [Crossref]
  10. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
    [Crossref]
  11. C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
    [Crossref] [PubMed]
  12. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
    [Crossref] [PubMed]
  13. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
    [Crossref] [PubMed]
  14. Y. Lim, S.-Y. Lee, K.-Y. Kim, J. Park, and B. Lee, “Negative refraction of Airy plasmons in a metal–insulator–metal waveguide,” IEEE Photon. Technol. Lett. 23(17), 1258–1260 (2011).
    [Crossref]
  15. D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. 24(16), 1440–1442 (2012).
    [Crossref]
  16. K.-Y. Kim, C.-Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19(3), 2286–2293 (2011).
    [Crossref] [PubMed]
  17. C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Bessel-like beam generation by superposing multiple Airy beams,” Opt. Express 19(8), 7356–7364 (2011).
    [Crossref] [PubMed]
  18. C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photon. J. 4(1), 174–180 (2012).
    [Crossref]
  19. J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
    [Crossref] [PubMed]
  20. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29(1), 44–46 (2004).
    [Crossref] [PubMed]
  21. Y. Jiang, K. Huang, and X. Lu, “Airy-related beam generated from flat-topped Gaussian beams,” J. Opt. Soc. Am. A 29(7), 1412–1416 (2012).
    [Crossref] [PubMed]
  22. S. Barwick, “Reduced side-lobe Airy beams,” Opt. Lett. 36(15), 2827–2829 (2011).
    [Crossref] [PubMed]
  23. J. D. Ring, C. J. Howls, and M. R. Dennis, “Incomplete Airy beams: finite energy from a sharp spectral cutoff,” Opt. Lett. 38(10), 1639–1641 (2013).
    [Crossref]
  24. J. Hahn, H. Kim, and B. Lee, “Optimization of the spatial light modulation with twisted nematic liquid crystals by a genetic algorithm,” Appl. Opt. 47(19), D87–D95 (2008).
    [Crossref] [PubMed]

2013 (1)

2012 (3)

Y. Jiang, K. Huang, and X. Lu, “Airy-related beam generated from flat-topped Gaussian beams,” J. Opt. Soc. Am. A 29(7), 1412–1416 (2012).
[Crossref] [PubMed]

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. 24(16), 1440–1442 (2012).
[Crossref]

C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photon. J. 4(1), 174–180 (2012).
[Crossref]

2011 (6)

2010 (3)

2009 (2)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

2008 (4)

2007 (2)

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 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(21), 213901 (2007).
[Crossref] [PubMed]

2004 (1)

1987 (1)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

1979 (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Arie, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Bandres, M. A.

Barwick, S.

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Berry, M. V.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Broky, J.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Chávez-Cerda, S.

Chen, H.

Choi, D.

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. 24(16), 1440–1442 (2012).
[Crossref]

C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
[Crossref] [PubMed]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

D. N. Christodoulides, “Optical trapping: riding along an Airy beam,” Nat. Photonics 2(11), 652–653 (2008).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref] [PubMed]

Dennis, M. R.

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Ding, J.

Dogariu, A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Durnin, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

Gutiérrez-Vega, J. C.

Hahn, J.

Howls, C. J.

Huang, K.

Hwang, C.-Y.

Janunts, N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

Jiang, Y.

Kim, H.

Kim, K.-Y.

C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photon. J. 4(1), 174–180 (2012).
[Crossref]

K.-Y. Kim, C.-Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19(3), 2286–2293 (2011).
[Crossref] [PubMed]

C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Bessel-like beam generation by superposing multiple Airy beams,” Opt. Express 19(8), 7356–7364 (2011).
[Crossref] [PubMed]

Y. Lim, S.-Y. Lee, K.-Y. Kim, J. Park, and B. Lee, “Negative refraction of Airy plasmons in a metal–insulator–metal waveguide,” IEEE Photon. Technol. Lett. 23(17), 1258–1260 (2011).
[Crossref]

C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
[Crossref] [PubMed]

Kivshar, Y. S.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

Klein, A. E.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

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(5924), 229–232 (2009).
[Crossref] [PubMed]

Lee, B.

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. 24(16), 1440–1442 (2012).
[Crossref]

C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photon. J. 4(1), 174–180 (2012).
[Crossref]

Y. Lim, S.-Y. Lee, K.-Y. Kim, J. Park, and B. Lee, “Negative refraction of Airy plasmons in a metal–insulator–metal waveguide,” IEEE Photon. Technol. Lett. 23(17), 1258–1260 (2011).
[Crossref]

C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Bessel-like beam generation by superposing multiple Airy beams,” Opt. Express 19(8), 7356–7364 (2011).
[Crossref] [PubMed]

K.-Y. Kim, C.-Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19(3), 2286–2293 (2011).
[Crossref] [PubMed]

C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
[Crossref] [PubMed]

J. Hahn, H. Kim, and B. Lee, “Optimization of the spatial light modulation with twisted nematic liquid crystals by a genetic algorithm,” Appl. Opt. 47(19), D87–D95 (2008).
[Crossref] [PubMed]

Lee, I.-M.

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. 24(16), 1440–1442 (2012).
[Crossref]

Lee, S.-Y.

Y. Lim, S.-Y. Lee, K.-Y. Kim, J. Park, and B. Lee, “Negative refraction of Airy plasmons in a metal–insulator–metal waveguide,” IEEE Photon. Technol. Lett. 23(17), 1258–1260 (2011).
[Crossref]

Lim, Y.

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. 24(16), 1440–1442 (2012).
[Crossref]

Y. Lim, S.-Y. Lee, K.-Y. Kim, J. Park, and B. Lee, “Negative refraction of Airy plasmons in a metal–insulator–metal waveguide,” IEEE Photon. Technol. Lett. 23(17), 1258–1260 (2011).
[Crossref]

Lu, X.

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Minovich, A.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

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(5924), 229–232 (2009).
[Crossref] [PubMed]

Neshev, D. N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

Park, J.

Y. Lim, S.-Y. Lee, K.-Y. Kim, J. Park, and B. Lee, “Negative refraction of Airy plasmons in a metal–insulator–metal waveguide,” IEEE Photon. Technol. Lett. 23(17), 1258–1260 (2011).
[Crossref]

Pertsch, T.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

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(5924), 229–232 (2009).
[Crossref] [PubMed]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Ring, J. D.

Roh, S.

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. 24(16), 1440–1442 (2012).
[Crossref]

Salandrino, A.

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(5924), 229–232 (2009).
[Crossref] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref] [PubMed]

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

Wang, H.-T.

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Zhang, B.-F.

Zheng, Z.

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Appl. Opt. (2)

IEEE Photon. J. (1)

C.-Y. Hwang, K.-Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photon. J. 4(1), 174–180 (2012).
[Crossref]

IEEE Photon. Technol. Lett. (2)

Y. Lim, S.-Y. Lee, K.-Y. Kim, J. Park, and B. Lee, “Negative refraction of Airy plasmons in a metal–insulator–metal waveguide,” IEEE Photon. Technol. Lett. 23(17), 1258–1260 (2011).
[Crossref]

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. 24(16), 1440–1442 (2012).
[Crossref]

J. Opt. Soc. Am. A (1)

Nat. Photonics (4)

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

D. N. Christodoulides, “Optical trapping: riding along an Airy beam,” Nat. Photonics 2(11), 652–653 (2008).
[Crossref]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. Lett. (3)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

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Figures (5)
Fig. 1
Fig. 1 Propagation dynamics of finite power Airy beams generated by (a) a Gaussian beam, (b) a uniform beam of finite extent, and (c) an inverse Gaussian beam. (d) Propagation dynamics of an ideal Airy beam.

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Fig. 2
Fig. 2 Cross-correlations of finite power Airy beams with the ideal Airy beam along the propagation direction: C1(z).

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Fig. 3
Fig. 3 Intensity distributions of (2 + 1)D finite power Airy beams. CASE I: (a) at z = 0 cm and (b) z = 15 cm. CASE II: (c) at z = 0 cm and (d) z = 15 cm. CASE III: (e) at z = 0 cm and (f) z = 15 cm.

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Fig. 4
Fig. 4 (a) Schematic diagram. M1 is a mirror, P1, P2 and P3 are polarizers, and L1 is a lens with f = 50 cm. (b) Experimental setup for the generation of finite power Airy beams.

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Fig. 5
Fig. 5 CCD images of finite power Airy beams. CASE I: (a) at z = 0 cm and (b) z = 15 cm. CASE II: (c) at z = 0 cm and (d) z = 15 cm. CASE III: (e) at z = 0 cm and (f) z = 15 cm.

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Equations (15)

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i ∂ ϕ ∂ ξ + 1 2 ∂ 2 ϕ ∂ s 2 = 0 ,
ϕ 0 ( s , ξ ) = A i ( s − ( ξ 2 ) 2 ) exp ( i ( s ξ 2 ) − i ( ξ 3 12 ) ) .
Φ 0 ( k ) = exp ( i k 3 3 ) .
ϕ 1 ( s , ξ = 0 ) = Ai ( s ) exp ( a s ) ,
Φ 1 ( k ) = exp ( − a k 2 ) exp ( i 3 ( k 3 − 3 a 2 k − i a 3 ) ) .
Φ 1 ( k ) = Π ( λ f 2 π l k ) exp ( − a k 2 ) exp ( i 3 ( k 3 − 3 a 2 k − i a 3 ) ) ,
ϕ 1 ( x , z ) = ∫ − ∞ ∞ Π ( λ f 2 π l k ) exp ( − a x 0 2 k 2 ) exp ( i 3 ( x 0 3 k 3 − 3 a 2 x 0 k − i a 3 ) − i z 2 k 0 k 2 ) exp ( + i k x ) d k ,
Φ 2 ( k ) = Π ( λ f 2 π l k ) exp ( i k 3 3 ) .
ϕ 2 ( x , z = 0 ) = sin c ( l λ f x ) * A i ( x x 0 ) ,
ϕ 2 ( x , z ) = ∫ − ∞ ∞ Π ( λ f 2 π l k ) exp ( i ( x 0 k ) 3 3 − i z 2 k 0 k 2 ) exp ( + i k x ) d k ,
ϕ 3 ( x , z ) = ∫ − ∞ ∞ Π ( λ f 2 π l k ) ( 1 − exp ( − a x 0 2 k 2 ) ) × exp ( i 3 ( x 0 3 k 3 − 3 a 2 x 0 k − i a 3 ) − i z 2 k 0 k 2 ) exp ( + i k x ) d k .
C 1 ( z ) = max ( ∫ − ∞ + ∞ | ϕ 0 * ( τ ) | 2 | ϕ i = 1 , 2 , 3 ( x + τ ) | 2 d τ ) .
ϕ 1 ( x , y , z ) = ∏ χ = x ,   y ∫ − ∞ ∞ Π ( λ f 2 π l χ k χ ) exp ( − a χ 0 2 k χ 2 ) × exp ( i 3 ( χ 0 3 k χ 3 − 3 a 2 χ 0 k χ − i a 3 ) − i z 2 k 0 k χ 2 ) exp ( + i k χ χ ) d k χ ,
ϕ 2 ( x , y , z ) = ∏ χ = x ,   y ∫ − ∞ ∞ Π ( λ f 2 π l χ k χ ) exp ( i ( χ 0 k χ ) 3 3 − i z 2 k 0 k χ 2 ) exp ( + i k χ χ ) d k χ ,
ϕ 3 ( x , y , z ) = ∏ χ = x ,   y ∫ − ∞ ∞ Π ( λ f 2 π l χ k χ ) ( 1 − exp ( − a χ 0 2 k χ 2 ) ) × exp ( i 3 ( χ 0 3 k χ 3 − 3 a 2 χ 0 k χ − i a 3 ) − i z 2 k 0 k χ 2 ) exp ( + i k χ χ ) d k χ ,

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