Abstract

We study the behavior of Airy beams propagating from a nonlinear medium to a linear medium. We show that an Airy beam initially driven by a self-defocusing nonlinearity experiences anomalous diffraction and can maintain its shape in subsequent propagation, but its intensity pattern and acceleration cannot persist when driven by a self-focusing nonlinearity. The unusual behavior of Airy beams is examined from their energy flow as well as the Brillouin zone spectrum of self-induced chirped photonic lattices.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef] [PubMed]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  3. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
    [CrossRef] [PubMed]
  4. J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
    [CrossRef]
  5. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
    [CrossRef] [PubMed]
  6. A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
    [CrossRef]
  7. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
    [CrossRef] [PubMed]
  8. Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, Opt. Lett. 35, 2260 (2010).
    [CrossRef] [PubMed]
  9. T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
    [CrossRef]
  10. I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581(2010).
    [CrossRef] [PubMed]
  11. S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
    [CrossRef] [PubMed]
  12. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef] [PubMed]
  13. P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 35, 892 (2010).
    [CrossRef] [PubMed]
  14. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
    [CrossRef] [PubMed]
  15. M. I. Molina, Y. V. Kartashov, L. Torner, and Y. S. Kivshar, Opt. Lett. 32, 2668 (2007).
    [CrossRef] [PubMed]
  16. S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, Appl. Phys. B 99, 727 (2010).
    [CrossRef]
  17. C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, Phys. Rev. Lett. 98, 213903 (2007).
    [CrossRef] [PubMed]

2010 (6)

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, Appl. Phys. B 99, 727 (2010).
[CrossRef]

P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 35, 892 (2010).
[CrossRef] [PubMed]

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581(2010).
[CrossRef] [PubMed]

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, Opt. Lett. 35, 2260 (2010).
[CrossRef] [PubMed]

2009 (2)

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (5)

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

M. I. Molina, Y. V. Kartashov, L. Torner, and Y. S. Kivshar, Opt. Lett. 32, 2668 (2007).
[CrossRef] [PubMed]

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

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Arie, A.

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581(2010).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Baumgartl, J.

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

Bezryadina, A.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Broky, J.

Chen, Z.

P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 35, 892 (2010).
[CrossRef] [PubMed]

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, Opt. Lett. 35, 2260 (2010).
[CrossRef] [PubMed]

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Chong, A.

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

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

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef] [PubMed]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

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

Dholakia, K.

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

Dogariu, A.

Dolev, I.

Ellenbogen, T.

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581(2010).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Fleischer, J. W.

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

Gan, X.

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, Appl. Phys. B 99, 727 (2010).
[CrossRef]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Hu, Y.

Huang, S.

Jia, S.

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

Kartashov, Y. V.

Kivshar, Y. S.

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Lee, J.

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

Liu, S.

P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 35, 892 (2010).
[CrossRef] [PubMed]

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, Appl. Phys. B 99, 727 (2010).
[CrossRef]

Lou, C.

Makris, K. G.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Mazilu, M.

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

Molina, M. I.

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Renninger, W.

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

Siviloglou, G. A.

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

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

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef] [PubMed]

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

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

Stegeman, G. I.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Torner, L.

Voloch, N.

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Wang, X.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Wise, F. W.

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

Xiao, F.

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, Appl. Phys. B 99, 727 (2010).
[CrossRef]

Xu, J.

Yang, J.

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Zhang, P.

Zhao, J.

P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 35, 892 (2010).
[CrossRef] [PubMed]

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, Appl. Phys. B 99, 727 (2010).
[CrossRef]

Appl. Phys. B (1)

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, Appl. Phys. B 99, 727 (2010).
[CrossRef]

Nat. Photon. (3)

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

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. Lett. (5)

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

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

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Schematic of experimental setup. SLM, spatial light modulator; SBN, strontium–barium–niobate crystal; PC, personal computer; BS, beam splitter; L, Fourier transform lens. (b)–(d) Output intensity patterns of an Airy beam after 1 cm through crystal (first column) plus another 1 cm through air (second column) when (b) no nonlinearity, (c) self-focusing nonlinearity, and (d) self-defocusing nonlinearity are present. White dashed line marks the “head” position of the Airy beam at crystal output. The third column shows Fourier spectra of the Airy beam corresponding to the first column.

Fig. 2
Fig. 2

Numerical simulation of an Airy beam propagating under initial self-focusing nonlinearity. (a), (b) Transverse intensity patterns after (a) 1 cm through crystal plus (b) another 1 cm through air. (c) Fourier spectrum of the output Airy beam. (d) Side view of 2 cm propagation, where the dashed curve represents the trajectory of the Airy beam without initial nonlinearity. (e), (f) Calculated transverse energy flow around the main lobe corresponding to the square area shown in (a) and (b), respectively.

Fig. 3
Fig. 3

Numerical simulation of an Airy beam propagating under initial self-defocusing nonlinearity. Other description is the same as that for Fig. 2.

Fig. 4
Fig. 4

(a), (b) Plots of output intensity profiles along the y axis of an Airy beam as a function of the bias field after (a) 2 cm and (b) 3 cm of propagation, while the nonlinearity is on only for the first 1 cm . Positive (negative) values of E 0 correspond to self-focusing (self-defocusing) nonlinearity. (c) Transverse intensity pattern of a perfect Airy beam. (d) Zoom-in of nonuniform intensity pattern in the region marked by dashed square in (c). (e) Index lattice self-induced by the intensity pattern of (d) at E 0 = 4 × 10 4 V / m . (f) Brillouin zone spectrum of the induced lattice of (e).

Equations (1)

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

U z = i 2 k 0 n 0 ( 2 U x 2 + 2 U y 2 ) + i k 0 Δ n U ,

Metrics