Abstract

The evolution of the three-dimensional (3D) self-accelerating Airy-Ince-Gaussian (AiIG) and Airy-Helical-Ince-Gaussian (AiHIG) light bullets is investigated by solving the (3+1)D linear spatiotemporal evolution equation of an optical field analytically. As far as we know, the numerical experimental demonstrations of the Ince-Gaussian (IG) and Helical-Ince-Gaussian (HIG) beams in various modes are first developed to study the evolution characteristics of the different 3D spatiotemporal light bullets. A conclusion can be drawn that the different photoelastics, pulse stacked, boundary, elliptical ring and physically separated in-line vortices can be achieved by adjusting the ellipticity, the evolution distance and the mode-number of light bullets.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
  2. M. A. Bandres and B. M. Rodrĺłguez-Lara, “Nondiffracting Accelerating Waves: Weber waves and parabolic momentum,” New J. Phys. 15(1), 13054–13062 (2012).
    [Crossref]
  3. M. A. Alonso and M. A. Bandres, “Spherical fields as nonparaxial accelerating waves,” Opt. Lett. 37(24), 5175–5177 (2012).
    [Crossref] [PubMed]
  4. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
    [Crossref]
  5. T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photon. 3(7), 395–398 (2009).
    [Crossref]
  6. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4(2), 103–106 (2010).
    [Crossref]
  7. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 1842–1844 (2010).
    [Crossref]
  8. P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 176–179 (2012).
    [Crossref]
  9. 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]
  10. C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 136–141 (2011).
    [Crossref]
  11. J. Broky, G. Siviloglou, A. Dogariu, and D. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
    [Crossref]
  12. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7(5), R53–R72 (2005).
    [Crossref]
  13. D. Mihalache, “Linear and nonlinear light bullets: recent theoretical and experimental studies,” Rom. J. Phys. 57(1–2), 352–371 (2012).
  14. H. Valtna-Lukner, P. Bowlan, M. Lõhmus, P. Piksarv, R. Trebino, and P. Saari, “Direct spatiotemporal measurements of accelerating ultrashort Bessel-type light bullets,” Opt. Express 17(17), 14948–14955 (2009).
    [Crossref] [PubMed]
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    [Crossref]
  16. 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), 2974–2981 (2013).
    [Crossref]
  17. W. P. Zhong, M. Belić, Y. Zhang, and T. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phys. 340(1), 171–178 (2014).
    [Crossref]
  18. W. P. Zhong, M. Belić, and Y. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
    [Crossref] [PubMed]
  19. W. P. Zhong, M. Belić, and Y. Zhang, “Self-decelerating Airy-Bessel light bullets,” J. Phys. B: At. Mol. Opt. Phys. 48(17), 175401 (2015).
    [Crossref]
  20. F. Deng and D. Deng, “Three-dimensional localized Airy-Hermite-Gaussian and Airy-Helical-Hermite-Gaussian wave packets in free space,” Opt. Express 24(5), 5478–5486 (2016).
    [Crossref]
  21. M. A. Bandres and J. C. Gutiĺęrrez-Vega, “Ince-Gaussian beams,” Opt. Lett. 29(2), 144–146 (2004).
    [Crossref] [PubMed]
  22. U. T. Schwarz, M. A. Bandres, and J. C. Gutiĺęrrezvega, “Observation of Ince-Gaussian modes in stable resonators,” Opt. Lett. 29(16), 1870–1872 (2004).
    [Crossref] [PubMed]
  23. U. T. Schwarz, M. A. Bandres, and J. C. Gutierrez-Vega, “Formation of Ince-Gaussian modes in a stable laser oscillator,” Proc. SPIE 5708, 124–131 (2005).
    [Crossref]
  24. M. A. Bandres and J. C. Gutiĺęrrez-Vega, “Ince-Gaussian series representation of the two-dimensional fractional Fourier transform,” Opt. Lett. 30(5), 540–542 (2005).
    [Crossref] [PubMed]
  25. D. Deng and Q. Guo, “Ince-Gaussian solitons in strongly nonlocal nonlinear media,” Opt. Lett. 32(21), 3206–3208 (2007).
    [Crossref] [PubMed]
  26. D. Deng and Q. Guo, “Ince-Gaussian beams in strongly nonlocal nonlinear media,” J. Phys. B: At. Mol. Opt. Phys. 41, 145401 (2008).
    [Crossref]
  27. D. Deng and Q. Guo, “Propagation of elliptic-Gaussian beams in strongly nonlocal nonlinear media,” Phys. Rev. E 84, 046604 (2011).
    [Crossref]
  28. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98(5), 053901 (2007).
    [Crossref] [PubMed]
  29. D. Deng, X. Zhao, Q. Guo, and S. Lan, “Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media,” J. Opt. Soc. Am. B 24(9), 2537–2544 (2007).
    [Crossref]
  30. D. Deng and Q. Guo, “Propagation of Laguerre Gaussian beams in nonlocal nonlinear media,” J. Opt. A: Pure Appl. Opt. 10(3), 206–210 (2008).
    [Crossref]
  31. N. K. Efremidis, “Airy trajectory engineering in dynamic linear index potentials,” Opt. Lett. 36(15), 3006–3008 (2011).
    [Crossref] [PubMed]
  32. F. M. Arscott, “Periodic differential equations. An introduction to Mathieu, Lamĺę, and Allied functions,” International 192(3), 137–160 (1964).
  33. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011).
    [Crossref] [PubMed]

2016 (1)

2015 (2)

W. P. Zhong, M. Belić, and Y. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
[Crossref] [PubMed]

W. P. Zhong, M. Belić, and Y. Zhang, “Self-decelerating Airy-Bessel light bullets,” J. Phys. B: At. Mol. Opt. Phys. 48(17), 175401 (2015).
[Crossref]

2014 (1)

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

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), 2974–2981 (2013).
[Crossref]

2012 (4)

M. A. Bandres and B. M. Rodrĺłguez-Lara, “Nondiffracting Accelerating Waves: Weber waves and parabolic momentum,” New J. Phys. 15(1), 13054–13062 (2012).
[Crossref]

D. Mihalache, “Linear and nonlinear light bullets: recent theoretical and experimental studies,” Rom. J. Phys. 57(1–2), 352–371 (2012).

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 176–179 (2012).
[Crossref]

M. A. Alonso and M. A. Bandres, “Spherical fields as nonparaxial accelerating waves,” Opt. Lett. 37(24), 5175–5177 (2012).
[Crossref] [PubMed]

2011 (4)

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011).
[Crossref] [PubMed]

N. K. Efremidis, “Airy trajectory engineering in dynamic linear index potentials,” Opt. Lett. 36(15), 3006–3008 (2011).
[Crossref] [PubMed]

D. Deng and Q. Guo, “Propagation of elliptic-Gaussian beams in strongly nonlocal nonlinear media,” Phys. Rev. E 84, 046604 (2011).
[Crossref]

C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 136–141 (2011).
[Crossref]

2010 (3)

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

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 1842–1844 (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), 5903–5911 (2010).
[Crossref]

2009 (2)

2008 (3)

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. Deng and Q. Guo, “Propagation of Laguerre Gaussian beams in nonlocal nonlinear media,” J. Opt. A: Pure Appl. Opt. 10(3), 206–210 (2008).
[Crossref]

D. Deng and Q. Guo, “Ince-Gaussian beams in strongly nonlocal nonlinear media,” J. Phys. B: At. Mol. Opt. Phys. 41, 145401 (2008).
[Crossref]

2007 (5)

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

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[Crossref] [PubMed]

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

D. Deng, X. Zhao, Q. Guo, and S. Lan, “Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media,” J. Opt. Soc. Am. B 24(9), 2537–2544 (2007).
[Crossref]

D. Deng and Q. Guo, “Ince-Gaussian solitons in strongly nonlocal nonlinear media,” Opt. Lett. 32(21), 3206–3208 (2007).
[Crossref] [PubMed]

2005 (3)

M. A. Bandres and J. C. Gutiĺęrrez-Vega, “Ince-Gaussian series representation of the two-dimensional fractional Fourier transform,” Opt. Lett. 30(5), 540–542 (2005).
[Crossref] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7(5), R53–R72 (2005).
[Crossref]

U. T. Schwarz, M. A. Bandres, and J. C. Gutierrez-Vega, “Formation of Ince-Gaussian modes in a stable laser oscillator,” Proc. SPIE 5708, 124–131 (2005).
[Crossref]

2004 (2)

1979 (1)

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

1964 (1)

F. M. Arscott, “Periodic differential equations. An introduction to Mathieu, Lamĺę, and Allied functions,” International 192(3), 137–160 (1964).

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), 5903–5911 (2010).
[Crossref]

Aleahmad, P.

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 176–179 (2012).
[Crossref]

Alonso, M. A.

Ament, C.

C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 136–141 (2011).
[Crossref]

Arie, A.

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

Arscott, F. M.

F. M. Arscott, “Periodic differential equations. An introduction to Mathieu, Lamĺę, and Allied functions,” International 192(3), 137–160 (1964).

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.

Belic, M.

W. P. Zhong, M. Belić, and Y. Zhang, “Self-decelerating Airy-Bessel light bullets,” J. Phys. B: At. Mol. Opt. Phys. 48(17), 175401 (2015).
[Crossref]

W. P. Zhong, M. Belić, and Y. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
[Crossref] [PubMed]

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

Belic, M. R.

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), 2974–2981 (2013).
[Crossref]

Berry, M. V.

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

Bowlan, P.

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]

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

Buccoliero, D.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[Crossref] [PubMed]

Chen, Z.

Chong, A.

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

Christodoulides, D.

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

Christodoulides, D. N.

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 176–179 (2012).
[Crossref]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011).
[Crossref] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 1842–1844 (2010).
[Crossref]

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

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

Deng, D.

F. Deng and D. Deng, “Three-dimensional localized Airy-Hermite-Gaussian and Airy-Helical-Hermite-Gaussian wave packets in free space,” Opt. Express 24(5), 5478–5486 (2016).
[Crossref]

D. Deng and Q. Guo, “Propagation of elliptic-Gaussian beams in strongly nonlocal nonlinear media,” Phys. Rev. E 84, 046604 (2011).
[Crossref]

D. Deng and Q. Guo, “Ince-Gaussian beams in strongly nonlocal nonlinear media,” J. Phys. B: At. Mol. Opt. Phys. 41, 145401 (2008).
[Crossref]

D. Deng and Q. Guo, “Propagation of Laguerre Gaussian beams in nonlocal nonlinear media,” J. Opt. A: Pure Appl. Opt. 10(3), 206–210 (2008).
[Crossref]

D. Deng, X. Zhao, Q. Guo, and S. Lan, “Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media,” J. Opt. Soc. Am. B 24(9), 2537–2544 (2007).
[Crossref]

D. Deng and Q. Guo, “Ince-Gaussian solitons in strongly nonlocal nonlinear media,” Opt. Lett. 32(21), 3206–3208 (2007).
[Crossref] [PubMed]

Deng, F.

Desyatnikov, A. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[Crossref] [PubMed]

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]

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

Efremidis, N. K.

Ellenbogen, T.

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

Ganany-Padowicz, A.

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

Guo, Q.

D. Deng and Q. Guo, “Propagation of elliptic-Gaussian beams in strongly nonlocal nonlinear media,” Phys. Rev. E 84, 046604 (2011).
[Crossref]

D. Deng and Q. Guo, “Ince-Gaussian beams in strongly nonlocal nonlinear media,” J. Phys. B: At. Mol. Opt. Phys. 41, 145401 (2008).
[Crossref]

D. Deng and Q. Guo, “Propagation of Laguerre Gaussian beams in nonlocal nonlinear media,” J. Opt. A: Pure Appl. Opt. 10(3), 206–210 (2008).
[Crossref]

D. Deng and Q. Guo, “Ince-Gaussian solitons in strongly nonlocal nonlinear media,” Opt. Lett. 32(21), 3206–3208 (2007).
[Crossref] [PubMed]

D. Deng, X. Zhao, Q. Guo, and S. Lan, “Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media,” J. Opt. Soc. Am. B 24(9), 2537–2544 (2007).
[Crossref]

Gutierrez-Vega, J. C.

U. T. Schwarz, M. A. Bandres, and J. C. Gutierrez-Vega, “Formation of Ince-Gaussian modes in a stable laser oscillator,” Proc. SPIE 5708, 124–131 (2005).
[Crossref]

Gutilerrezvega, J. C.

Gutilerrez-Vega, J. C.

Huang, T.

W. P. Zhong, M. Belić, Y. 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), 2974–2981 (2013).
[Crossref]

Kaminer, I.

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 176–179 (2012).
[Crossref]

Kivshar, Y. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[Crossref] [PubMed]

Krolikowski, W.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[Crossref] [PubMed]

Lan, S.

Lõhmus, M.

Malomed, B. A.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7(5), R53–R72 (2005).
[Crossref]

Mihalache, D.

D. Mihalache, “Linear and nonlinear light bullets: recent theoretical and experimental studies,” Rom. J. Phys. 57(1–2), 352–371 (2012).

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7(5), R53–R72 (2005).
[Crossref]

Mills, M. S.

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 176–179 (2012).
[Crossref]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011).
[Crossref] [PubMed]

Miri, M. A.

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 176–179 (2012).
[Crossref]

Moloney, J. V.

C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 136–141 (2011).
[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), 5903–5911 (2010).
[Crossref]

Piksarv, P.

Polynkin, P.

C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with femtosecond self-healing Airy pulses,” Phys. Rev. Lett. 107(24), 136–141 (2011).
[Crossref]

Prakash, J.

Renninger, W. H.

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Rodrllguez-Lara, B. M.

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Saari, P.

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U. T. Schwarz, M. A. Bandres, and J. C. Gutierrez-Vega, “Formation of Ince-Gaussian modes in a stable laser oscillator,” Proc. SPIE 5708, 124–131 (2005).
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U. T. Schwarz, M. A. Bandres, and J. C. Gutiĺęrrezvega, “Observation of Ince-Gaussian modes in stable resonators,” Opt. Lett. 29(16), 1870–1872 (2004).
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P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 176–179 (2012).
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Siviloglou, G.

J. Broky, G. Siviloglou, A. Dogariu, and D. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
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Siviloglou, G. A.

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), 5903–5911 (2010).
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Torner, L.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7(5), R53–R72 (2005).
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Trebino, R.

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), 5903–5911 (2010).
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Valtna-Lukner, H.

Voloch, N.

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

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7(5), R53–R72 (2005).
[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. Photon. 4(2), 103–106 (2010).
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W. P. Zhong, M. Belić, and Y. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
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W. P. Zhong, M. Belić, and Y. Zhang, “Self-decelerating Airy-Bessel light bullets,” J. Phys. B: At. Mol. Opt. Phys. 48(17), 175401 (2015).
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Zhang, Z.

Zhao, X.

Zhong, W. P.

W. P. Zhong, M. Belić, and Y. Zhang, “Self-decelerating Airy-Bessel light bullets,” J. Phys. B: At. Mol. Opt. Phys. 48(17), 175401 (2015).
[Crossref]

W. P. Zhong, M. Belić, and Y. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
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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), 2974–2981 (2013).
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W. P. Zhong, M. Belić, Y. Zhang, and T. Huang, “Accelerating Airy-Gauss-Kummer localized wave packets,” Ann. Phys. 340(1), 171–178 (2014).
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D. Deng and Q. Guo, “Propagation of Laguerre Gaussian beams in nonlocal nonlinear media,” J. Opt. A: Pure Appl. Opt. 10(3), 206–210 (2008).
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J. Opt. B (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7(5), R53–R72 (2005).
[Crossref]

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

J. Phys. B: At. Mol. Opt. Phys. (2)

W. P. Zhong, M. Belić, and Y. Zhang, “Self-decelerating Airy-Bessel light bullets,” J. Phys. B: At. Mol. Opt. Phys. 48(17), 175401 (2015).
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D. Deng and Q. Guo, “Ince-Gaussian beams in strongly nonlocal nonlinear media,” J. Phys. B: At. Mol. Opt. Phys. 41, 145401 (2008).
[Crossref]

Nat. Photon. (2)

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photon. 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. Photon. 4(2), 103–106 (2010).
[Crossref]

New J. Phys. (1)

M. A. Bandres and B. M. Rodrĺłguez-Lara, “Nondiffracting Accelerating Waves: Weber waves and parabolic momentum,” New J. Phys. 15(1), 13054–13062 (2012).
[Crossref]

Opt. Express (4)

Opt. Lett. (9)

Phys. Rev. A (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), 2974–2981 (2013).
[Crossref]

Phys. Rev. E (1)

D. Deng and Q. Guo, “Propagation of elliptic-Gaussian beams in strongly nonlocal nonlinear media,” Phys. Rev. E 84, 046604 (2011).
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D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Laguerre and Hermite soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98(5), 053901 (2007).
[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), 5903–5911 (2010).
[Crossref]

P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109(20), 176–179 (2012).
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[Crossref]

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

Proc. SPIE (1)

U. T. Schwarz, M. A. Bandres, and J. C. Gutierrez-Vega, “Formation of Ince-Gaussian modes in a stable laser oscillator,” Proc. SPIE 5708, 124–131 (2005).
[Crossref]

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D. Mihalache, “Linear and nonlinear light bullets: recent theoretical and experimental studies,” Rom. J. Phys. 57(1–2), 352–371 (2012).

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Figures (10)

Fig. 1
Fig. 1 Numerical experimental demonstrations of the even IG beams evolution for different parameters ε. (a1)–(c1) Numerical simulations of the intensity distributions of the even IG beams for ε → 0,2,∞, respectively; (a2)–(c2) numerical simulations of the phase distributions of the even IG beams for ε → 0,2,∞, respectively; (a3)–(c3) interference intensity of the initial generated beam and a plane wave for ε → 0,2,∞, respectively; (a4)–(c4) computer-generated hologram for ε → 0,2,∞, respectively; (a5)–(c5) numerical experimentally recorded the transverse intensity distributions of the even IG beams for ε → 0,2,∞, respectively. The other parameters are chosen as p = 3, m = 3, De = 2, Z = 0.
Fig. 2
Fig. 2 Numerical experimental demonstrations of the odd IG beams evolution for different parameters ε. The graphic arrangement and parameters are the same as those in figure 1 except for Do = 2.
Fig. 3
Fig. 3 Numerical experimental demonstrations of the HIG beams evolution for different parameters ε. The graphic arrangement and parameters are the same as those in figure 1 except for De = Do = 2.
Fig. 4
Fig. 4 Isosurface intensity plots of the self-accelerating even AiIG light bullets with p = m = 3, De = 2 at Z = 0 (the top row) and Z = 2 (the bottom row) with ε → 0 (the first column), ε = 2 (the second column), ε → ∞ (the third column).
Fig. 5
Fig. 5 Snapshots describing the evolution of the self-accelerating odd AiIG light bullets. All the parameters are the same as those in figure 4 except for Do = 2.
Fig. 6
Fig. 6 Snapshots describing the evolution of the self-accelerating AiHIG light bullets. All the parameters are the same as those in figure 4 except for De = Do = 2.
Fig. 7
Fig. 7 (a1)–(a3) Intensity distributions of the self-accelerating even AiIG light bullets with p = 2, m = 0 with ε → 0 (the first column), ε = 2 (the second column), ε → ∞ (the third column). (b1)–(b3) Intensity distributions of the self-accelerating even AiIG light bullets with p = 3, m = 1 with ε → 0 (the first column), ε = 2 (the second column), ε → ∞ (the third column). (c1)–(c5) Numerical experimental demonstrations of the even IG beams with p = 2, m = 0 and ε = 2. (d1)–(d3) Numerical experimental demonstrations of the even IG beams with p = 3, m = 1 and ε = 2. The other parameters are chosen as De = 2, Z = 0.
Fig. 8
Fig. 8 Intensity distributions of the self-accelerating odd AiIG light bullets with p = 3, m = 1, ε = 2, Do = 2 with Z = 0 (the first column), Z = 2 (the second column). (b1)–(b2) Intensity distributions of the self-accelerating odd AiIG light bullets with p = 4, m = 2, ε = 2, Do = 22 with Z = 0 (the first column), Z = 2 (the second column). (c1)–(c5) Numerical experimental demonstrations of the odd IG beams with p = 3, m = 1, Z = 0, ε = 2 and Do = 2. (d1)–(d3) Numerical experimental demonstrations of the odd IG beams with p = 4, m = 2, Z = 0, ε = 2 and Do = 2.
Fig. 9
Fig. 9 Numerical experimental demonstrations of the HIG beams evolution for different parameters ε. The graphic arrangement and parameters are the same as those in figure 1, except for p = 3, m = 1 and De = Do = 2.
Fig. 10
Fig. 10 Snapshots describing the evolution of the self-accelerating AiHIG light bullets. All the parameters are the same as those in figure 4, except for p = 3, m = 1 and De = Do = 2.

Equations (14)

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i Ψ Z + 1 2 ( 2 Ψ X 2 + 2 Ψ Y 2 + 2 Ψ T 2 ) = 0 ,
Ψ ( X , Y , Z , T ) = M ( ξ ) N ( J ) A ( Z , T ) e i Z 1 ( Z ) Ψ G ( X , Y , Z ) ,
i A ( Z , T ) Z + 1 2 2 A ( Z , T ) T 2 = 0 ,
( Z 2 + 1 ) d Z 1 d Z = 2 p ,
2 M ( ξ ) ξ 2 ε sinh 2 ξ M ( ξ ) ξ ( a p ε cosh 2 ξ ) M ( ξ ) = 0 ,
2 N ( J ) J 2 ε sin 2 J N ( J ) J + ( a p ε cos 2 J ) N ( J ) = 0 ,
A + ( Z , T ) = A i ( T Z 2 4 + i α Z ) e α T 1 2 α Z 2 + i ( 1 12 Z 3 + 1 2 α 2 Z + 1 2 T Z ) .
Z 1 ( Z ) = 2 p arctan Z .
I G p , m e ( X , Y , Z ) = M e ( ξ ) N e ( J ) e i Z 1 ( Z ) Ψ G ( X , Y , Z ) = D e w ( Z ) C p m ( i ξ , ε ) C p m ( J , ε ) e X 2 + Y 2 w 2 ( Z ) + i ( Z 2 δ 2 + Z ( X 2 + Y 2 ) w 2 ( Z ) ( 2 p + 1 ) arctan Z ) ,
I G p , m o ( X , Y , Z ) = M o ( ξ ) N o ( J ) e i Z 1 ( Z ) Ψ G ( X , Y , Z ) = D o w ( Z ) S p m ( i ξ , ε ) S p m ( J , ε ) e X 2 + Y 2 w 2 ( Z ) + i ( Z 2 δ 2 + Z ( X 2 + Y 2 ) w 2 ( Z ) ( 2 p + 1 ) arctan Z ) ,
Ψ + e ( X , Y , Z , T ) = M e ( ξ ) N e ( J ) A + ( Z , T ) e i Z 1 ( Z ) Ψ G ( X , Y , Z ) = D e w ( Z ) C p m ( i ξ , ε ) C p m ( J , ε ) e X 2 + Y 2 w 2 ( Z ) + i ( Z 2 δ 2 + Z ( X 2 + Y 2 ) w 2 ( Z ) ( 2 p + 1 ) arctan Z ) × A i ( T Z 2 4 + i α Z ) e α T 1 2 α Z 2 + i ( 1 12 Z 3 + 1 2 α 2 Z + 1 2 T Z ) ,
Ψ + o ( X , Y , Z , T ) = M o ( ξ ) N o ( J ) A + ( Z , T ) e i Z 1 ( Z ) Ψ G ( X , Y , Z ) = D o w ( Z ) S p m ( i ξ , ε ) S p m ( J , ε ) e X 2 + Y 2 w 2 ( Z ) + i ( Z 2 δ 2 + Z ( X 2 + Y 2 ) w 2 ( Z ) ( 2 p + 1 ) arctan Z ) × A i ( T Z 2 4 + i α Z ) e α T 1 2 α Z 2 + i ( 1 12 Z 3 + 1 2 α 2 Z + 1 2 T Z ) .
H I G p , m + ( X , Y , Z ) = I G p , m e ( X , Y , Z ) + i I G p , m o ( X , Y , Z ) = 1 w ( Z ) ( D e C p m ( i ξ , ε ) C p m ( J , ε ) + i D o S p m ( i ξ , ε ) S p m ( J , ε ) ) × e X 2 + Y 2 w 2 ( Z ) + i ( Z 2 δ 2 + Z ( X 2 + Y 2 ) w 2 ( Z ) ( 2 p + 1 ) arctan Z ) ,
Ψ + A i H I G ( X , Y , Z , T ) = Ψ + e ( X , Y , Z , T ) + i Ψ + o ( X , Y , Z , T ) = 1 w ( Z ) ( D e C p m ( i ξ , ε ) C p m ( J , ε ) + i D o S p m ( i ξ , ε ) S p m ( J , ε ) ) × e X 2 + Y 2 w 2 ( Z ) + i ( Z 2 δ 2 + Z ( X 2 + Y 2 ) w 2 ( Z ) ( 2 p + 1 ) arctan Z ) × A i ( T Z 2 4 + i α Z ) e α T 1 2 α Z 2 + i ( 1 12 Z 3 + 1 2 α 2 Z + 1 2 T Z ) .

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