Abstract

We demonstrate three-dimensional (3D) Airy-Laguerre-Gaussian localized wave packets in free space. An exact solution of the (3 + 1)D potential-free Schrödinger equation is obtained by using the method of separation of variables. Linear compressed wave pulses are constructed with the help of a superposition of two counter-accelerating finite energy Airy wave functions and the generalized Laguerre-Gaussian polynomials in cylindrical coordinates. Such wave packets do not accelerate and can retain their structure over several Rayleigh lengths during propagation. The generation, control, and manipulation of the linear but localized wave packets described here is affected by four parameters: the decay factor, the radial mode number, the azimuthal mode number and the modulation depth.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
  3. 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]
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  5. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
    [Crossref] [PubMed]
  6. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
    [Crossref]
  7. J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
    [Crossref] [PubMed]
  8. W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. 36(7), 1164–1166 (2011).
    [Crossref] [PubMed]
  9. 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]
  10. 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]
  11. 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]
  12. Y. Zhang, M. R. Belić, H. Zheng, H. Chen, C. Li, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express 22(6), 7160–7171 (2014).
    [Crossref] [PubMed]
  13. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
    [Crossref] [PubMed]
  14. W. P. Zhong, M. R. Belić, and T. Huang, “Three-dimensional finite-energy Airy self-accelerating parabolic-cylinder light bullets,” Phys. Rev. A 88(3), 033824 (2013).
    [Crossref]
  15. W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phys. 340(1), 171–178 (2014).
    [Crossref]
  16. 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]
  17. J. Fan, E. Parra, and H. M. Milchberg, “Resonant self-trapping and absorption of intense bessel beams,” Phys. Rev. Lett. 84(14), 3085–3088 (2000).
    [Crossref] [PubMed]
  18. M. Erdélyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for application in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
    [Crossref]
  19. M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6(2), 259–268 (2004).
    [Crossref]
  20. I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
    [Crossref]
  21. W. P. Zhong, M. R. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
    [Crossref]
  22. W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239(1-3), 129–135 (2004).
    [Crossref]
  23. J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
    [Crossref]
  24. S. Tao, X. C. Yuan, J. Lin, X. Peng, and H. Niu, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13(20), 7726–7731 (2005).
    [Crossref] [PubMed]
  25. M. R. Belić and W. P. Zhong, “Two-dimensional spatial solitons in highly nonlocal nonlinear media,” Eur. Phys. J. D 53(1), 97–106 (2009).
    [Crossref]
  26. W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373(2), 296–298 (2009).
    [Crossref]
  27. W. P. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 061801 (2007).
    [Crossref]
  28. W. P. Zhong and M. Belić, “Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media,” Phys. Rev. A 79(2), 023804 (2009).
    [Crossref]
  29. D. Zwillinger, Handbook of Differential Equations, 3rd ed. (Academic, 1997).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  33. M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101(12), 123904 (2008).
    [Crossref] [PubMed]

2014 (2)

2013 (1)

W. P. Zhong, M. R. Belić, and T. Huang, “Three-dimensional finite-energy Airy self-accelerating parabolic-cylinder light bullets,” Phys. Rev. A 88(3), 033824 (2013).
[Crossref]

2011 (2)

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. 36(7), 1164–1166 (2011).
[Crossref] [PubMed]

W. P. Zhong, M. R. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

2010 (2)

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]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

2009 (4)

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]

M. R. Belić and W. P. Zhong, “Two-dimensional spatial solitons in highly nonlocal nonlinear media,” Eur. Phys. J. D 53(1), 97–106 (2009).
[Crossref]

W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373(2), 296–298 (2009).
[Crossref]

W. P. Zhong and M. Belić, “Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media,” Phys. Rev. A 79(2), 023804 (2009).
[Crossref]

2008 (4)

2007 (3)

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]

W. P. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 061801 (2007).
[Crossref]

2005 (2)

S. Tao, X. C. Yuan, J. Lin, X. Peng, and H. Niu, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13(20), 7726–7731 (2005).
[Crossref] [PubMed]

A. S. Desyatnikov, D. N. Neshev, and Y. S. Kivshar, “Vortex solitons, soliton clusters, and vortex lattices,” Ukr. J. Phys. Opt. 6(2), 71–77 (2005).
[Crossref]

2004 (4)

W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239(1-3), 129–135 (2004).
[Crossref]

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[Crossref]

2002 (1)

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 (1)

J. Fan, E. Parra, and H. M. Milchberg, “Resonant self-trapping and absorption of intense bessel beams,” Phys. Rev. Lett. 84(14), 3085–3088 (2000).
[Crossref] [PubMed]

1997 (1)

M. Erdélyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for application in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

1992 (1)

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]

1987 (2)

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

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]

1966 (1)

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

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]

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]

Assanto, G.

W. P. Zhong, M. R. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

Balazs, N. L.

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

Basistiy, I. V.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[Crossref]

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]

Belic, M.

W. P. Zhong and M. Belić, “Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media,” Phys. Rev. A 79(2), 023804 (2009).
[Crossref]

W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373(2), 296–298 (2009).
[Crossref]

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101(12), 123904 (2008).
[Crossref] [PubMed]

Belic, M. R.

Y. Zhang, M. R. Belić, H. Zheng, H. Chen, C. Li, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express 22(6), 7160–7171 (2014).
[Crossref] [PubMed]

W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phys. 340(1), 171–178 (2014).
[Crossref]

W. P. Zhong, M. R. Belić, and T. Huang, “Three-dimensional finite-energy Airy self-accelerating parabolic-cylinder light bullets,” Phys. Rev. A 88(3), 033824 (2013).
[Crossref]

W. P. Zhong, M. R. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

M. R. Belić and W. P. Zhong, “Two-dimensional spatial solitons in highly nonlocal nonlinear media,” Eur. Phys. J. D 53(1), 97–106 (2009).
[Crossref]

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

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

Bor, Zs.

M. Erdélyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for application in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Broky, J.

Cavallaro, J. R.

M. Erdélyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for application in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Chen, G.

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101(12), 123904 (2008).
[Crossref] [PubMed]

Chen, H.

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.

Desyatnikov, A. S.

A. S. Desyatnikov, D. N. Neshev, and Y. S. Kivshar, “Vortex solitons, soliton clusters, and vortex lattices,” Ukr. J. Phys. Opt. 6(2), 71–77 (2005).
[Crossref]

Dholakia, K.

W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239(1-3), 129–135 (2004).
[Crossref]

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]

Dogariu, A.

Durnin, J.

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

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

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]

Erdélyi, M.

M. Erdélyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for application in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Fan, J.

J. Fan, E. Parra, and H. M. Milchberg, “Resonant self-trapping and absorption of intense bessel beams,” Phys. Rev. Lett. 84(14), 3085–3088 (2000).
[Crossref] [PubMed]

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]

Garcés-Chávez, V.

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]

Horvath, Z. L.

M. Erdélyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for application in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Huang, T.

W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phys. 340(1), 171–178 (2014).
[Crossref]

W. P. Zhong, M. R. Belić, and T. Huang, “Three-dimensional finite-energy Airy self-accelerating parabolic-cylinder light bullets,” Phys. Rev. A 88(3), 033824 (2013).
[Crossref]

W. P. Zhong, M. R. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

Kivshar, Y. S.

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. 36(7), 1164–1166 (2011).
[Crossref] [PubMed]

A. S. Desyatnikov, D. N. Neshev, and Y. S. Kivshar, “Vortex solitons, soliton clusters, and vortex lattices,” Ukr. J. Phys. Opt. 6(2), 71–77 (2005).
[Crossref]

Kogelnik, H.

Leach, J.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Lee, W. M.

W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239(1-3), 129–135 (2004).
[Crossref]

Li, C.

Li, T.

Li, Y.

Lin, J.

Liu, W.

Malomed, B. A.

W. P. Zhong, M. R. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

McGloin, D.

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]

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

Milchberg, H. M.

J. Fan, E. Parra, and H. M. Milchberg, “Resonant self-trapping and absorption of intense bessel beams,” Phys. Rev. Lett. 84(14), 3085–3088 (2000).
[Crossref] [PubMed]

Miroshnichenko, A. E.

Neshev, D. N.

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. 36(7), 1164–1166 (2011).
[Crossref] [PubMed]

A. S. Desyatnikov, D. N. Neshev, and Y. S. Kivshar, “Vortex solitons, soliton clusters, and vortex lattices,” Ukr. J. Phys. Opt. 6(2), 71–77 (2005).
[Crossref]

Niu, H.

Padgett, M. J.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Parra, E.

J. Fan, E. Parra, and H. M. Milchberg, “Resonant self-trapping and absorption of intense bessel beams,” Phys. Rev. Lett. 84(14), 3085–3088 (2000).
[Crossref] [PubMed]

Pas’ko, V. A.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[Crossref]

Peng, X.

Petrovic, N.

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101(12), 123904 (2008).
[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]

Shadrivov, I. V.

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]

Siviloglou, G. A.

Slyusar, V. V.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[Crossref]

Smayling, M. C.

M. Erdélyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for application in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Soskin, M. S.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[Crossref]

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]

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Szabo, G.

M. Erdélyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for application in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Tao, S.

Tittel, F. K.

M. Erdélyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for application in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Vasnetsov, M. V.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[Crossref]

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]

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]

Xie, R. H.

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101(12), 123904 (2008).
[Crossref] [PubMed]

Yao, E.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Yi, L.

W. P. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 061801 (2007).
[Crossref]

Yuan, X. C.

S. Tao, X. C. Yuan, J. Lin, X. Peng, and H. Niu, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13(20), 7726–7731 (2005).
[Crossref] [PubMed]

W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239(1-3), 129–135 (2004).
[Crossref]

Zhang, Y.

Zhang, Y. Q.

W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phys. 340(1), 171–178 (2014).
[Crossref]

Zheng, H.

Zhong, W. P.

W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phys. 340(1), 171–178 (2014).
[Crossref]

W. P. Zhong, M. R. Belić, and T. Huang, “Three-dimensional finite-energy Airy self-accelerating parabolic-cylinder light bullets,” Phys. Rev. A 88(3), 033824 (2013).
[Crossref]

W. P. Zhong, M. R. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

W. P. Zhong and M. Belić, “Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media,” Phys. Rev. A 79(2), 023804 (2009).
[Crossref]

M. R. Belić and W. P. Zhong, “Two-dimensional spatial solitons in highly nonlocal nonlinear media,” Eur. Phys. J. D 53(1), 97–106 (2009).
[Crossref]

W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373(2), 296–298 (2009).
[Crossref]

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101(12), 123904 (2008).
[Crossref] [PubMed]

W. P. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 061801 (2007).
[Crossref]

Am. J. Phys. (1)

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

Ann. Phys. (1)

W. P. Zhong, M. R. Belić, Y. Q. Zhang, and T. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phys. 340(1), 171–178 (2014).
[Crossref]

Appl. Opt. (1)

Eur. Phys. J. D (1)

M. R. Belić and W. P. Zhong, “Two-dimensional spatial solitons in highly nonlocal nonlinear media,” Eur. Phys. J. D 53(1), 97–106 (2009).
[Crossref]

J. Opt. A, Pure Appl. Opt. (2)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[Crossref]

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

J. Vac. Sci. Technol. B (1)

M. Erdélyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for application in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Nat. Photonics (2)

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]

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]

Nature (1)

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]

New J. Phys. (1)

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Opt. Commun. (1)

W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239(1-3), 129–135 (2004).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Phys. Lett. A (1)

W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373(2), 296–298 (2009).
[Crossref]

Phys. Rev. A (5)

W. P. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 061801 (2007).
[Crossref]

W. P. Zhong and M. Belić, “Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media,” Phys. Rev. A 79(2), 023804 (2009).
[Crossref]

W. P. Zhong, M. R. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[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]

W. P. Zhong, M. R. Belić, and T. Huang, “Three-dimensional finite-energy Airy self-accelerating parabolic-cylinder light bullets,” Phys. Rev. A 88(3), 033824 (2013).
[Crossref]

Phys. Rev. Lett. (5)

J. Fan, E. Parra, and H. M. Milchberg, “Resonant self-trapping and absorption of intense bessel beams,” Phys. Rev. Lett. 84(14), 3085–3088 (2000).
[Crossref] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

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

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101(12), 123904 (2008).
[Crossref] [PubMed]

Ukr. J. Phys. Opt. (1)

A. S. Desyatnikov, D. N. Neshev, and Y. S. Kivshar, “Vortex solitons, soliton clusters, and vortex lattices,” Ukr. J. Phys. Opt. 6(2), 71–77 (2005).
[Crossref]

Other (1)

D. Zwillinger, Handbook of Differential Equations, 3rd ed. (Academic, 1997).

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Figures (5)

Fig. 1
Fig. 1 (a) Accelerating finite-energy Airy beam with σ = 1 and I+ = |P+|2, along the positive t direction. (b) Accelerating finite-energy Airy beam with σ = −1 and I- = |P-|2, along the negative t direction. (c) Non-accelerating superposition of the two counter-accelerating beams. The left column: Intensity profiles at various distances. The right column: Contour-plots of the beam intensity distribution, as functions of the propagation distance. The parameters are: r0 = 100 μm, λ0 = 0.5 μm, and a = 0.15. Note that ζ = 5 when z = 63 cm.
Fig. 2
Fig. 2 Snapshots describing the evolution of a linear beam with zero-vorticity (m = 0) at ζ = 0 (the left column) and ζ = 3ζR (the right column) with n = 1 (top row), n = 2 (bottom row) and a = 0.15.
Fig. 3
Fig. 3 Vortex Airy-Laguerre-Gaussian beams. Setup is the same as in Fig. 2, except for n = 3 in the bottom row, m = 1, and a = 0.1.
Fig. 4
Fig. 4 Necklace Airy-Laguerre-Gaussian beams at ζ = 0 (the left column) and ζ = 3ζR (the right column). The parameters are (a) n = 0, m = 5 (top row); (b) n = 1, m = 3 (bottom row), and a = 0.2. Color is used for easier identification of different pulse clusters.
Fig. 5
Fig. 5 Comparison of the analytical solution with the numerical simulation for the parameters a = 0.15, n = 3. (a) The initial beam profile, (b) the analytical solution (6) at ζ = 3ζR, (c) the numerical simulation at ζ = 3ζR.

Equations (10)

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

i u ζ + 1 2 ( 2 u R 2 + 1 R u R + 1 R 2 2 u ϕ 2 + 2 u T 2 ) = 0
i P ζ + 1 2 2 P T 2 = 0
2 Φ ϕ 2 + m 2 Φ = 0
i V ζ + 1 2 ( 2 V R 2 + 1 R V R m 2 R 2 V ) = 0
P + ( ζ , T ) = Ai ( T ζ 2 4 + i a ζ ) e a T 1 4 a ζ 2 + i ( 1 24 ζ 3 + 1 2 a 2 ζ + 1 2 T ζ )
P ( ζ , T ) = Ai ( T ζ 2 4 + i a ζ ) e a T 1 4 a ζ 2 + i ( 1 24 ζ 3 + 1 2 a 2 ζ 1 2 T ζ )
P ( ζ , T ) = P + ( ζ , T ) + i P ( ζ , T )
Φ ( ϕ ) = cos ( m ϕ ) + i q sin ( m ϕ )
V ( ζ , R ) = n ! ( n + m ) ! w 0 w ( ζ ) [ 2 R w ( ζ ) ] m L n m [ 2 R 2 w 2 ( ζ ) ] e R 2 2 w 2 ( ζ ) + i [ ζ 2 ( ζ 2 + ζ R 2 ) R 2 ( 2 n m + 1 ) arctan ( ζ ζ R ) ]
u ( ζ , T , r , ϕ ) = V ( ζ , R ) ( P + ( ζ , T ) + i P ( ζ , T ) ) [ sin ( m ϕ ) + i q cos ( m ϕ ) ]

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