Abstract

We propose a way of generating Bessel-like non-diffracting beams based on the superposition of multiple Airy beams. We also demonstrate, through numerical simulations of the propagation dynamics of the Bessel-like beams, that these Bessel-like beams can be modified to show the feature of vortex power flow by controlling the initial positions of each single Airy beam.

© 2011 OSA

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  1. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
    [CrossRef]
  2. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
    [CrossRef]
  3. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
    [CrossRef] [PubMed]
  4. J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13(2), 79–80 (1988).
    [CrossRef] [PubMed]
  5. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
    [CrossRef]
  6. Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31(15), 2708–2713 (1992).
    [CrossRef] [PubMed]
  7. V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184(1-4), 105–112 (2000).
    [CrossRef]
  8. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
    [CrossRef]
  9. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
    [CrossRef]
  10. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000).
    [CrossRef]
  11. J. C. Gutiérrez-Vega and M. A. Bandres, “Helmholtz-Gauss waves,” J. Opt. Soc. Am. A 22(2), 289–298 (2005).
    [CrossRef]
  12. M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33(15), 1678–1680 (2008).
    [CrossRef] [PubMed]
  13. L. Vicari, “Truncation of non diffracting beams,” Opt. Commun. 70(4), 263–266 (1989).
    [CrossRef]
  14. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44(8), 592–597 (1954).
    [CrossRef]
  15. G. Scott and N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31(12), 2640–2643 (1992).
    [CrossRef]
  16. J. Turunen, A. Vasara, and A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27(19), 3959–3962 (1988).
    [CrossRef] [PubMed]
  17. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
    [CrossRef] [PubMed]
  18. D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28(8), 657–659 (2003).
    [CrossRef] [PubMed]
  19. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
    [CrossRef] [PubMed]
  20. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
    [CrossRef]
  21. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
    [CrossRef]
  22. M. A. Bandres, “Accelerating beams,” Opt. Lett. 34(24), 3791–3793 (2009).
    [CrossRef] [PubMed]
  23. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
    [CrossRef]
  24. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
    [CrossRef] [PubMed]
  25. 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]
  26. H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16(13), 9411–9416 (2008).
    [CrossRef] [PubMed]
  27. I. M. Besieris and A. M. Shaarawi, “A note on an accelerating finite energy Airy beam,” Opt. Lett. 32(16), 2447–2449 (2007).
    [CrossRef] [PubMed]
  28. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
    [CrossRef] [PubMed]
  29. Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35(13), 2260–2262 (2010).
    [CrossRef] [PubMed]
  30. 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]
  31. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
    [CrossRef]
  32. H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010).
    [CrossRef] [PubMed]
  33. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
    [CrossRef] [PubMed]
  34. K.-Y. Kim, C.-Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19(3), 2286–2293 (2011).
    [CrossRef] [PubMed]
  35. 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]
  36. C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
    [CrossRef] [PubMed]
  37. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
    [CrossRef] [PubMed]
  38. J. Baumgartl, T. Čižmár, M. Mazilu, V. C. Chan, A. E. Carruthers, B. A. Capron, W. McNeely, E. M. Wright, and K. Dholakia, “Optical path clearing and enhanced transmission through colloidal suspensions,” Opt. Express 18(16), 17130–17140 (2010).
    [CrossRef] [PubMed]
  39. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [CrossRef] [PubMed]

2011

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

M. A. Bandres, “Accelerating beams,” Opt. Lett. 34(24), 3791–3793 (2009).
[CrossRef] [PubMed]

2008

2007

2005

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[CrossRef]

J. C. Gutiérrez-Vega and M. A. Bandres, “Helmholtz-Gauss waves,” J. Opt. Soc. Am. A 22(2), 289–298 (2005).
[CrossRef]

2003

2002

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

2000

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[CrossRef]

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184(1-4), 105–112 (2000).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000).
[CrossRef]

1998

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[CrossRef]

1992

G. Scott and N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31(12), 2640–2643 (1992).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31(15), 2708–2713 (1992).
[CrossRef] [PubMed]

1989

L. Vicari, “Truncation of non diffracting beams,” Opt. Commun. 70(4), 263–266 (1989).
[CrossRef]

1988

1987

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

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[CrossRef]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
[CrossRef]

1979

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

1954

Alfano, R. R.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[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.

Baumgartl, J.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Berry, M. V.

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

Besieris, I. M.

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[CrossRef]

Broky, J.

Brown, D. L.

Capron, B. A.

Carruthers, A. E.

Chan, V. C.

Chávez-Cerda, S.

Chen, Z.

Cheng, H.

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[CrossRef]

Choi, D.

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.

Cižmár, T.

Dholakia, K.

J. Baumgartl, T. Čižmár, M. Mazilu, V. C. Chan, A. E. Carruthers, B. A. Capron, W. McNeely, E. M. Wright, and K. Dholakia, “Optical path clearing and enhanced transmission through colloidal suspensions,” Opt. Express 18(16), 17130–17140 (2010).
[CrossRef] [PubMed]

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

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[CrossRef]

D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28(8), 657–659 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[CrossRef]

Dogariu, A.

Durnin, J.

Eberly, J. H.

Efremidis, N. K.

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[CrossRef]

Friberg, A. T.

Garcés-Chávez, V.

D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28(8), 657–659 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[CrossRef]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[CrossRef]

Gutiérrez-Vega, J. C.

Hu, Y.

Huang, H.

Huang, S.

Hwang, C.-Y.

Iturbe-Castillo, M. D.

Jarutis, V.

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184(1-4), 105–112 (2000).
[CrossRef]

Kim, K.-Y.

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.

Lin, Y.

Lou, C.

Mazilu, M.

McArdle, N.

G. Scott and N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31(12), 2640–2643 (1992).
[CrossRef]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[CrossRef]

D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28(8), 657–659 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

McLeod, J. H.

McNeely, W.

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13(2), 79–80 (1988).
[CrossRef] [PubMed]

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

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[CrossRef]

Paškauskas, R.

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184(1-4), 105–112 (2000).
[CrossRef]

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]

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[CrossRef]

Salandrino, A.

Scott, G.

G. Scott and N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31(12), 2640–2643 (1992).
[CrossRef]

Seka, W.

Shaarawi, A. M.

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[CrossRef]

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]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[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]

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

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Stabinis, A.

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184(1-4), 105–112 (2000).
[CrossRef]

Sztul, H. I.

Tian, J.

Turunen, J.

Vasara, A.

Vicari, L.

L. Vicari, “Truncation of non diffracting beams,” Opt. Commun. 70(4), 263–266 (1989).
[CrossRef]

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[CrossRef]

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]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Wright, E. M.

Xu, J.

Zang, W.

Zhang, P.

Zhou, W.

Am. J. Phys.

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

Appl. Opt.

Contemp. Phys.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nat. Photonics

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[CrossRef]

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

Nature

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Opt. Commun.

L. Vicari, “Truncation of non diffracting beams,” Opt. Commun. 70(4), 263–266 (1989).
[CrossRef]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[CrossRef]

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184(1-4), 105–112 (2000).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[CrossRef]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[CrossRef]

Opt. Eng.

G. Scott and N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31(12), 2640–2643 (1992).
[CrossRef]

Opt. Express

Opt. Lett.

M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33(15), 1678–1680 (2008).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[CrossRef] [PubMed]

M. A. Bandres, “Accelerating beams,” Opt. Lett. 34(24), 3791–3793 (2009).
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Supplementary Material (2)

» Media 1: AVI (333 KB)     
» Media 2: AVI (811 KB)     

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Figures (5)

Fig. 1
Fig. 1

Calculated transverse intensity profiles of the zero-order Bessel-like beam ( d = 10 ) at (a) z = 0 μ m (Media 1), (b) z = 75 μ m ( ξ r = 6.35 ), and (c) z = 150 μ m ( ξ r = 12.7 ). The corresponding results for the first-order beam are shown in (d)–(f). In each figure, the intensity scale is normalized with respect to its corresponding initial distribution. (g) Radial intensity profiles of the zero-order Bessel-like beam (solid red line) shown in (c) and the ideal Bessel beam (dotted blue line). The transverse wave number of the ideal Bessel beam is suitably adjusted for the purpose of comparison. From (g), it is evident that in the far-field range, the transverse intensity pattern of the Bessel-like beam proposed here becomes similar to that of the Bessel beam.

Fig. 2
Fig. 2

Calculated normalized intensity profiles of (a) zero-order and (b) first-order Bessel-like beams in the y-z plane (x=0).

Fig. 3
Fig. 3

(a) Axial intensity variation of the zero-order Bessel-like beam. Radial intensity profiles of zero-order beam at (b) z = 75 μ m ( ξ r = 6.35 ) and (c) z = 150 μ m ( ξ r = 12.7 ). The corresponding results of the first-order beam are shown in (d) and (e).

Fig. 4
Fig. 4

Calculated transverse intensity profiles of the zero-order vortex Bessel-like beam at (a) z = 0 μm (Media 2), (b) z = 75 μ m ( ξ r = 6.35 ), and (c) z = 150 μ m ( ξ r = 12.7 ). The corresponding results of the first-order vortex Bessel-like beam are shown in (d)–(f). In each figure, the intensity scale is normalized with respect to its corresponding initial distribution.

Fig. 5
Fig. 5

Calculated transverse power flow S of (a) the zero-order and (b) the first-order beams at z = 150 μ m ( ξ r = 12.7 ). Background intensity plots are magnified versions of Figs. 4(c) and 4(f).

Equations (10)

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2 ϕ x 2 + 2 ϕ y 2 + i 2 k ϕ z = 0 ,
ϕ ( x , y , z ) = m = x , y u m ( s m , ξ m ) ,
u m ( s m , ξ m ) = A i [ s m + p ( ξ m ) ] exp [ q ( ξ m ) s m + r ( ξ m ) ] ,
p ( ξ m ) = 1 4 ξ m 2 + i a m ξ m + d m ,
q ( ξ m ) = i 1 2 ξ m + a m ,
r ( ξ m ) = i 1 12 ξ m 3 1 2 a m ξ m 2 + i 1 2 ( d m + a m 2 ) ξ m .
ϕ ( s x , s y , ξ r ) = A i [ s x cos θ + s y sin θ + p ( ξ r ) ] A i [ s x sin θ + s y cos θ + p ( ξ r ) ]                                 × exp [ q ( ξ r ) { s x ( cos θ sin θ ) + s y ( cos θ + sin θ ) } ] exp [ 2 r ( ξ r ) ] .
ϕ ( ρ , φ , ξ r ) = A i [ ρ cos ( θ φ ) + p ( ξ r ) ] A i [ ρ sin ( θ φ ) + p ( ξ r ) ]                               × exp [ q ( ξ r ) ρ { cos ( θ φ ) sin ( θ φ ) } ] exp [ 2 r ( ξ r ) ] ,
ψ ( ρ , ξ r ) = exp [ 2 r ( ξ r ) ] 0 2 π A ( ρ , ξ r , θ ) exp [ q ( ξ r ) ρ ( cos θ sin θ ) ] d θ ,
ψ ( ρ , ξ r ) = exp [ 2 r ( ξ r ) ] n = + A n ( ρ , ξ r ) 0 2 π exp [ i { n θ + ( 2 1 / 2 ρ ξ r ) sin θ } ] d θ .

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