Abstract

We demonstrate theoretically and experimentally that a finite Airy beam changes its trajectory while maintaining its acceleration in nonlinear photorefractive media. During this process, the spatial spectrum reshapes dramatically, leading to negative (or positive) spectral defects on the initial spectral distribution under a self-focusing (or defocusing) nonlinearity.

© 2012 Optical Society of America

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  1. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
    [CrossRef]
  4. Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, Opt. Lett. 35, 2260 (2010).
    [CrossRef]
  5. Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, Opt. Lett. 36, 3230 (2011).
    [CrossRef]
  6. S. Chávez-Cerda, U. Ruiz, V. Arrizón, and H. M. Moya-Cessa, Opt. Express 19, 16448 (2011).
    [CrossRef]
  7. E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
    [CrossRef]
  8. T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
    [CrossRef]
  9. S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
    [CrossRef]
  10. Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, Opt. Lett. 35, 3952 (2010).
    [CrossRef]
  11. R. Chen, C. Yin, X. Chu, and H. Wang, Phys. Rev. A 82, 043832 (2010).
    [CrossRef]
  12. I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
    [CrossRef]
  13. A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
    [CrossRef]
  14. I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
    [CrossRef]
  15. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
    [CrossRef]
  16. F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, Opt. Lett. 37, 1736 (2012).
    [CrossRef]
  17. P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).

2012 (3)

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, Opt. Lett. 37, 1736 (2012).
[CrossRef]

2011 (5)

S. Chávez-Cerda, U. Ruiz, V. Arrizón, and H. M. Moya-Cessa, Opt. Express 19, 16448 (2011).
[CrossRef]

Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, Opt. Lett. 36, 3230 (2011).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef]

2010 (4)

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

R. Chen, C. Yin, X. Chu, and H. Wang, Phys. Rev. A 82, 043832 (2010).
[CrossRef]

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

Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, Opt. Lett. 35, 3952 (2010).
[CrossRef]

2009 (1)

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

2008 (1)

2007 (2)

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]

Abdollahpour, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Arie, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

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

Arrizón, V.

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Broky, J.

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

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

Cannan, D.

Chávez-Cerda, S.

Chen, R.

R. Chen, C. Yin, X. Chu, and H. Wang, Phys. Rev. A 82, 043832 (2010).
[CrossRef]

Chen, Z.

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

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

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

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

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

Chu, X.

R. Chen, C. Yin, X. Chu, and H. Wang, Phys. Rev. A 82, 043832 (2010).
[CrossRef]

Couairon, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Courvoisier, F.

Dogariu, A.

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

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

Dolev, I.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

Dudley, J. M.

Ellenbogen, T.

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

Faccio, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[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]

Froehly, L.

Furfaro, L.

Ganany-Padowicz, A.

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

Giust, R.

Greenfield, E.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef]

Hu, Y.

Huang, S.

Jacquot, M.

Jia, S.

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

Kaminer, I.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

Lacourt, P. A.

Lee, J.

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

Li, T.

Liu, S.

Lotti, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Lou, C.

Mathis, A.

Morandotti, R.

Moya-Cessa, H. M.

Nemirovsky, J.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Panagiotopoulos, P.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Papazoglou, D. G.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Raz, O.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef]

Ruiz, U.

Salandrino, A.

Segev, M.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

Shapira, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[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]

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

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

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

Song, D.

Tzortzakis, S.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Voloch, N.

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

Walasik, W.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef]

Wang, H.

R. Chen, C. Yin, X. Chu, and H. Wang, Phys. Rev. A 82, 043832 (2010).
[CrossRef]

Xu, J.

Ye, Z.

Yin, C.

R. Chen, C. Yin, X. Chu, and H. Wang, Phys. Rev. A 82, 043832 (2010).
[CrossRef]

Zhang, P.

Zhang, X.

Zhao, J.

Nat. Photon. (1)

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

Opt. Express (1)

Opt. Lett. (7)

Phys. Rev. A (2)

R. Chen, C. Yin, X. Chu, and H. Wang, Phys. Rev. A 82, 043832 (2010).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Phys. Rev. Lett. (6)

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

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

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

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Linear (row 1) and nonlinear (rows 2 and 3) propagation of an Airy beam under different conditions. The panels from left to right correspond to different shifting ωm=0, 1, and 6 of the cubic phase mask, and from top to bottom to beam propagation under (a) linear, (b) nonlinear self-focusing, and (c) nonlinear self-defocusing conditions.

Fig. 2.
Fig. 2.

Spatial power spectra of Airy beams at ωm=6 during beam propagation under (a) linear, (b) nonlinear self-focusing, and (c) nonlinear self-defocusing conditions.

Fig. 3.
Fig. 3.

Nonlinear self-accelerating solutions under saturable nonlinearities. (a) and (d) Self-accelerating modes under self-focusing and -defocusing nonlinearities, respectively. (The red dashed curve corresponds to a linear infinite Airy beam). (b) and (e) Spectra corresponding to (a) and (d). (c) and (f) Spectral distribution during the nonlinear propagation of the self-accelerating modes in (a) and (d), respectively.

Fig. 4.
Fig. 4.

Experimental observations of Airy beams propagating in a biased photorefractive crystal. From top to bottom the panels correspond to beam propagation under (a) and (d) linear, (b) and (e) nonlinear self-focusing, and (c) and (f) nonlinear self-defocusing conditions. (a)–(c) and (d)–(f) correspond, respectively, to the cases in which the peak intensity is set at the middle (a)–(c) and at the output (d)–(f) of the crystal. (a2)–(f2) show the averaged spectral distributions of the outputs in (a1)–(f1). The downward pointing (red) arrows indicate the position of the spectral defects in k-space.

Equations (5)

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

Ψ/ξ=0.5i2Ψ/s2iγΨ/(1+|Ψ|2),
ϕ(s,ξ)=I0f(s,ξ)exp(αωm2+i2α2ωm)Ai[sωmξ(ξ/2)2+iα(ξ+2ωm)]exp(iωms),
f(s,ξ)=exp[αs+isξ/2+(iωm2/2+iα2/22αωm)ξ]×exp[(α/2iωm/2)ξ2iξ3/12],
Ψ/ξhξΨ/ς=0.5i2Ψ/ς2iγΨ/(1+|Ψ|2).
d2u/dς22hςu2γu/(1+u2)=0.

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