Abstract

We report on the existence of optical Bloch oscillations (OBOs) and Zener tunneling (ZT) of Airy beams in ionic-type photonic lattices with a refractive index ramp. Different from their counterparts in uniform lattices, Airy beams undergoing OBOs show an alternatively switched concave and convex trajectory as well as a periodical revival of input beam profiles. Moreover, the ionic-type photonic lattice established in photorefractive crystal exhibits a reconfigurable lattice structure, which provides a flexible way to tune the amplitude and period of the OBOs. Remarkably, it is demonstrated that the band gap of the lattice can be readily controlled by rotating the lattice inducing beam, which forces the ZT rate to follow two significant different decay curves amidst decreasing index gradient. Our results open up new possibilities for all-optical switching, routing and manipulation of Airy beams.

© 2016 Optical Society of America

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References

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  1. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
    [Crossref] [PubMed]
  2. 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]
  3. 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]
  4. E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
    [Crossref] [PubMed]
  5. L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
    [Crossref] [PubMed]
  6. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
    [Crossref] [PubMed]
  7. N. Gotte, T. Winkler, T. Meinl, T. Kusserow, B. Zielinski, C. Sarpe, A. Senftleben, H. Hillmer, and T. Baumert, “Temporal Airy pulses for controlled high aspect ratio nanomachining of dielectrics,” Optica 3(4), 389–395 (2016).
    [Crossref]
  8. 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]
  9. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
    [Crossref]
  10. P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
    [Crossref]
  11. T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
    [Crossref] [PubMed]
  12. S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
    [Crossref] [PubMed]
  13. Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
    [Crossref]
  14. Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35(13), 2260–2262 (2010).
    [Crossref] [PubMed]
  15. L. Froehly, F. Courvoisier, A. Mathis, M. Jacquot, L. Furfaro, R. Giust, P. A. Lacourt, and J. M. Dudley, “Arbitrary accelerating micron-scale caustic beams in two and three dimensions,” Opt. Express 19(17), 16455–16465 (2011).
    [Crossref] [PubMed]
  16. Y. Zhang, M. R. Belić, L. Zhang, W. Zhong, D. Zhu, R. Wang, and Y. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23(8), 10467–10480 (2015).
    [Crossref] [PubMed]
  17. Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, “Acceleration control of Airy beams with optically induced refractive-index gradient,” Opt. Lett. 36(16), 3230–3232 (2011).
    [Crossref] [PubMed]
  18. M. A. Bandres and J. C. Gutiérrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express 15(25), 16719–16728 (2007).
    [Crossref] [PubMed]
  19. 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]
  20. I. Dolev and A. Arie, “Three wave mixing of airy beams in a quadratic nonlinear photonic crystals,” Appl. Phys. Lett. 97(17), 171102 (2010).
    [Crossref]
  21. S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy Beams in photorefractive media,” Phys. Rev. Lett. 104(25), 253904 (2010).
    [Crossref] [PubMed]
  22. Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett. 37(15), 3201–3203 (2012).
    [Crossref] [PubMed]
  23. C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, Y. S. Kivshar, and W. Krolikowski, “Tunable positive and negative refraction in optically induced photonic lattices,” Opt. Lett. 30(17), 2293–2295 (2005).
    [Crossref] [PubMed]
  24. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
    [Crossref] [PubMed]
  25. D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
    [Crossref] [PubMed]
  26. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
    [Crossref]
  27. R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
    [Crossref]
  28. H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96(2), 023901 (2006).
    [Crossref] [PubMed]
  29. H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
    [Crossref] [PubMed]
  30. I. Garanovich, S. Longhi, A. Sukhorukov, and Y. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
    [Crossref]
  31. P. Zhang, S. Liu, C. Lou, F. Xiao, X. Wang, J. Zhao, J. Xu, and Z. Chen, “Incomplete Brillouin-zone spectra and controlled Bragg reflection with ionic-type photonic lattices,” Phys. Rev. A 81(4), 041801 (2010).
    [Crossref]
  32. P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, “Elliptical solitons in nonconventionally biased photorefractive crystals,” Opt. Express 15(2), 536–544 (2007).
    [Crossref] [PubMed]
  33. P. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B 39(4), 231–246 (1986).
    [Crossref]
  34. S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
    [Crossref]
  35. N. K. Efremidis, “Airy trajectory engineering in dynamic linear index potentials,” Opt. Lett. 36(15), 3006–3008 (2011).
    [Crossref] [PubMed]
  36. P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, “Elliptical discrete solitons supported by enhanced photorefractive anisotropy,” Opt. Express 16(6), 3865–3870 (2008).
    [Crossref] [PubMed]
  37. F. Xiao, B. Li, M. Wang, W. Zhu, P. Zhang, S. Liu, M. Premaratne, and J. Zhao, “Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient,” Opt. Express 22(19), 22763–22770 (2014).
    [Crossref] [PubMed]
  38. C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. Lond. A Math. Phys. Sci. 145(855), 523–529 (1934).
    [Crossref]

2016 (1)

2015 (1)

2014 (3)

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref] [PubMed]

F. Xiao, B. Li, M. Wang, W. Zhu, P. Zhang, S. Liu, M. Premaratne, and J. Zhao, “Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient,” Opt. Express 22(19), 22763–22770 (2014).
[Crossref] [PubMed]

2013 (2)

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

2012 (2)

I. Garanovich, S. Longhi, A. Sukhorukov, and Y. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett. 37(15), 3201–3203 (2012).
[Crossref] [PubMed]

2011 (6)

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

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[Crossref] [PubMed]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[Crossref] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[Crossref] [PubMed]

Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, “Acceleration control of Airy beams with optically induced refractive-index gradient,” Opt. Lett. 36(16), 3230–3232 (2011).
[Crossref] [PubMed]

L. Froehly, F. Courvoisier, A. Mathis, M. Jacquot, L. Furfaro, R. Giust, P. A. Lacourt, and J. M. Dudley, “Arbitrary accelerating micron-scale caustic beams in two and three dimensions,” Opt. Express 19(17), 16455–16465 (2011).
[Crossref] [PubMed]

2010 (6)

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35(13), 2260–2262 (2010).
[Crossref] [PubMed]

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]

P. Zhang, S. Liu, C. Lou, F. Xiao, X. Wang, J. Zhao, J. Xu, and Z. Chen, “Incomplete Brillouin-zone spectra and controlled Bragg reflection with ionic-type photonic lattices,” Phys. Rev. A 81(4), 041801 (2010).
[Crossref]

I. Dolev and A. Arie, “Three wave mixing of airy beams in a quadratic nonlinear photonic crystals,” Appl. Phys. Lett. 97(17), 171102 (2010).
[Crossref]

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy Beams in photorefractive media,” Phys. Rev. Lett. 104(25), 253904 (2010).
[Crossref] [PubMed]

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
[Crossref]

2009 (1)

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]

2008 (3)

2007 (4)

2006 (2)

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96(2), 023901 (2006).
[Crossref] [PubMed]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

2005 (1)

2001 (1)

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

1999 (2)

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
[Crossref]

1986 (1)

P. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B 39(4), 231–246 (1986).
[Crossref]

1934 (1)

C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. Lond. A Math. Phys. Sci. 145(855), 523–529 (1934).
[Crossref]

Aitchison, J.

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
[Crossref]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Arie, A.

I. Dolev and A. Arie, “Three wave mixing of airy beams in a quadratic nonlinear photonic crystals,” Appl. Phys. Lett. 97(17), 171102 (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]

Bandres, M. A.

Baumert, T.

Baumgartl, J.

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

Belic, M. R.

Boguslawski, M.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

Bongiovanni, D.

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
[Crossref]

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett. 37(15), 3201–3203 (2012).
[Crossref] [PubMed]

Bräuer, A.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96(2), 023901 (2006).
[Crossref] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

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]

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]

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. Photonics 4(2), 103–106 (2010).
[Crossref]

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[Crossref] [PubMed]

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]

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy Beams in photorefractive media,” Phys. Rev. Lett. 104(25), 253904 (2010).
[Crossref] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou 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]

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

Cižmár, T.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

Coll-Lladó, C.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

Courvoisier, F.

Dalgarno, H. I.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

Denz, C.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

Desyatnikov, A. S.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Dholakia, K.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

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

Diebel, F.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

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]

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]

Dolev, I.

I. Dolev and A. Arie, “Three wave mixing of airy beams in a quadratic nonlinear photonic crystals,” Appl. Phys. Lett. 97(17), 171102 (2010).
[Crossref]

Dudley, J. M.

Efremidis, N. K.

Eisenberg, H.

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
[Crossref]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

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]

Eugenieva, E. D.

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

Ferrier, D. E.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

Fleischer, J. W.

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy Beams in photorefractive media,” Phys. Rev. Lett. 104(25), 253904 (2010).
[Crossref] [PubMed]

Froehly, L.

Furfaro, L.

Gan, X.

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
[Crossref]

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]

Gao, Y.

Garanovich, I.

I. Garanovich, S. Longhi, A. Sukhorukov, and Y. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

Giust, R.

Gotte, N.

Greenfield, E.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[Crossref] [PubMed]

Gunn-Moore, F. J.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

Gutiérrez-Vega, J. C.

Hillmer, H.

Hu, Y.

Huang, S.

Jacquot, M.

Jia, S.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref] [PubMed]

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy Beams in photorefractive media,” Phys. Rev. Lett. 104(25), 253904 (2010).
[Crossref] [PubMed]

Kaminer, I.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[Crossref] [PubMed]

Kivshar, Y.

I. Garanovich, S. Longhi, A. Sukhorukov, and Y. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

Kivshar, Y. S.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, Y. S. Kivshar, and W. Krolikowski, “Tunable positive and negative refraction in optically induced photonic lattices,” Opt. Lett. 30(17), 2293–2295 (2005).
[Crossref] [PubMed]

Krolikowski, W.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, Y. S. Kivshar, and W. Krolikowski, “Tunable positive and negative refraction in optically induced photonic lattices,” Opt. Lett. 30(17), 2293–2295 (2005).
[Crossref] [PubMed]

Kusserow, T.

Lacourt, P. A.

Lederer, F.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96(2), 023901 (2006).
[Crossref] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

Lee, J.

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy Beams in photorefractive media,” Phys. Rev. Lett. 104(25), 253904 (2010).
[Crossref] [PubMed]

Li, B.

Li, L.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[Crossref] [PubMed]

Li, T.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[Crossref] [PubMed]

Liu, Q.

Liu, S.

F. Xiao, B. Li, M. Wang, W. Zhu, P. Zhang, S. Liu, M. Premaratne, and J. Zhao, “Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient,” Opt. Express 22(19), 22763–22770 (2014).
[Crossref] [PubMed]

Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, “Acceleration control of Airy beams with optically induced refractive-index gradient,” Opt. Lett. 36(16), 3230–3232 (2011).
[Crossref] [PubMed]

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
[Crossref]

P. Zhang, S. Liu, C. Lou, F. Xiao, X. Wang, J. Zhao, J. Xu, and Z. Chen, “Incomplete Brillouin-zone spectra and controlled Bragg reflection with ionic-type photonic lattices,” Phys. Rev. A 81(4), 041801 (2010).
[Crossref]

Longhi, S.

I. Garanovich, S. Longhi, A. Sukhorukov, and Y. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

Lou, C.

Mathis, A.

Mazilu, M.

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

Meinl, T.

Michaelis, D.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96(2), 023901 (2006).
[Crossref] [PubMed]

Morandotti, R.

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
[Crossref]

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett. 37(15), 3201–3203 (2012).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
[Crossref]

Neshev, D. N.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, Y. S. Kivshar, and W. Krolikowski, “Tunable positive and negative refraction in optically induced photonic lattices,” Opt. Lett. 30(17), 2293–2295 (2005).
[Crossref] [PubMed]

Nylk, J.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

Pertsch, T.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96(2), 023901 (2006).
[Crossref] [PubMed]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

Peschel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96(2), 023901 (2006).
[Crossref] [PubMed]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
[Crossref]

Premaratne, M.

Raz, O.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[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]

Rosberg, C. R.

Rose, P.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

Russell, P.

P. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B 39(4), 231–246 (1986).
[Crossref]

Sarpe, C.

Segev, M.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[Crossref] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[Crossref] [PubMed]

Senftleben, A.

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
[Crossref]

Siviloglou, G. A.

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy Beams in photorefractive media,” Phys. Rev. Lett. 104(25), 253904 (2010).
[Crossref] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou 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]

Song, D.

Streppel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96(2), 023901 (2006).
[Crossref] [PubMed]

Sukhorukov, A.

I. Garanovich, S. Longhi, A. Sukhorukov, and Y. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

Sukhorukov, A. A.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, Y. S. Kivshar, and W. Krolikowski, “Tunable positive and negative refraction in optically induced photonic lattices,” Opt. Lett. 30(17), 2293–2295 (2005).
[Crossref] [PubMed]

Sun, Z.

Tan, X.

Trompeter, H.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96(2), 023901 (2006).
[Crossref] [PubMed]

Vaughan, J. C.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref] [PubMed]

Vettenburg, T.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

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]

Walasik, W.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[Crossref] [PubMed]

Wang, M.

Wang, R.

Wang, S. M.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[Crossref] [PubMed]

Wang, X.

P. Zhang, S. Liu, C. Lou, F. Xiao, X. Wang, J. Zhao, J. Xu, and Z. Chen, “Incomplete Brillouin-zone spectra and controlled Bragg reflection with ionic-type photonic lattices,” Phys. Rev. A 81(4), 041801 (2010).
[Crossref]

Winkler, T.

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]

Xiao, F.

F. Xiao, B. Li, M. Wang, W. Zhu, P. Zhang, S. Liu, M. Premaratne, and J. Zhao, “Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient,” Opt. Express 22(19), 22763–22770 (2014).
[Crossref] [PubMed]

P. Zhang, S. Liu, C. Lou, F. Xiao, X. Wang, J. Zhao, J. Xu, and Z. Chen, “Incomplete Brillouin-zone spectra and controlled Bragg reflection with ionic-type photonic lattices,” Phys. Rev. A 81(4), 041801 (2010).
[Crossref]

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
[Crossref]

P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, “Elliptical discrete solitons supported by enhanced photorefractive anisotropy,” Opt. Express 16(6), 3865–3870 (2008).
[Crossref] [PubMed]

Xu, J.

Yang, D.

Ye, Z.

Zener, C.

C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. Lond. A Math. Phys. Sci. 145(855), 523–529 (1934).
[Crossref]

Zhang, C.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[Crossref] [PubMed]

Zhang, L.

Zhang, P.

F. Xiao, B. Li, M. Wang, W. Zhu, P. Zhang, S. Liu, M. Premaratne, and J. Zhao, “Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient,” Opt. Express 22(19), 22763–22770 (2014).
[Crossref] [PubMed]

Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, “Acceleration control of Airy beams with optically induced refractive-index gradient,” Opt. Lett. 36(16), 3230–3232 (2011).
[Crossref] [PubMed]

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
[Crossref]

P. Zhang, S. Liu, C. Lou, F. Xiao, X. Wang, J. Zhao, J. Xu, and Z. Chen, “Incomplete Brillouin-zone spectra and controlled Bragg reflection with ionic-type photonic lattices,” Phys. Rev. A 81(4), 041801 (2010).
[Crossref]

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35(13), 2260–2262 (2010).
[Crossref] [PubMed]

P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, “Elliptical discrete solitons supported by enhanced photorefractive anisotropy,” Opt. Express 16(6), 3865–3870 (2008).
[Crossref] [PubMed]

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, “Elliptical solitons in nonconventionally biased photorefractive crystals,” Opt. Express 15(2), 536–544 (2007).
[Crossref] [PubMed]

Zhang, Y.

Zhao, J.

Zhong, W.

Zhu, D.

Zhu, S. N.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[Crossref] [PubMed]

Zhu, W.

Zhuang, X.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref] [PubMed]

Zielinski, B.

Appl. Phys. B (2)

P. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B 39(4), 231–246 (1986).
[Crossref]

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
[Crossref]

Appl. Phys. Lett. (2)

I. Dolev and A. Arie, “Three wave mixing of airy beams in a quadratic nonlinear photonic crystals,” Appl. Phys. Lett. 97(17), 171102 (2010).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

Nat. Methods (1)

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

Nat. Photonics (4)

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref] [PubMed]

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

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]

Opt. Express (7)

M. A. Bandres and J. C. Gutiérrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express 15(25), 16719–16728 (2007).
[Crossref] [PubMed]

P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, “Elliptical discrete solitons supported by enhanced photorefractive anisotropy,” Opt. Express 16(6), 3865–3870 (2008).
[Crossref] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, “Elliptical solitons in nonconventionally biased photorefractive crystals,” Opt. Express 15(2), 536–544 (2007).
[Crossref] [PubMed]

L. Froehly, F. Courvoisier, A. Mathis, M. Jacquot, L. Furfaro, R. Giust, P. A. Lacourt, and J. M. Dudley, “Arbitrary accelerating micron-scale caustic beams in two and three dimensions,” Opt. Express 19(17), 16455–16465 (2011).
[Crossref] [PubMed]

F. Xiao, B. Li, M. Wang, W. Zhu, P. Zhang, S. Liu, M. Premaratne, and J. Zhao, “Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient,” Opt. Express 22(19), 22763–22770 (2014).
[Crossref] [PubMed]

Y. Zhang, M. R. Belić, L. Zhang, W. Zhong, D. Zhu, R. Wang, and Y. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23(8), 10467–10480 (2015).
[Crossref] [PubMed]

Opt. Lett. (6)

Optica (1)

Phys. Rep. (1)

I. Garanovich, S. Longhi, A. Sukhorukov, and Y. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

Phys. Rev. A (2)

P. Zhang, S. Liu, C. Lou, F. Xiao, X. Wang, J. Zhao, J. Xu, and Z. Chen, “Incomplete Brillouin-zone spectra and controlled Bragg reflection with ionic-type photonic lattices,” Phys. Rev. A 81(4), 041801 (2010).
[Crossref]

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
[Crossref]

Phys. Rev. Lett. (11)

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]

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[Crossref] [PubMed]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011).
[Crossref] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
[Crossref]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96(2), 023901 (2006).
[Crossref] [PubMed]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy Beams in photorefractive media,” Phys. Rev. Lett. 104(25), 253904 (2010).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. Lond. A Math. Phys. Sci. 145(855), 523–529 (1934).
[Crossref]

Supplementary Material (4)

NameDescription
» Visualization 1: AVI (2900 KB)      Optical Bloch oscillations of Airy beam in lattice 1
» Visualization 2: AVI (2268 KB)      Optical Bloch oscillations of Airy beam in lattice 2
» Visualization 3: AVI (2392 KB)      Zener tunneling of Airy beam in lattice 1
» Visualization 4: AVI (2419 KB)      Zener tunneling of Airy beam in lattice 2

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic view of optically induced ionic-type photonic lattices in photorefractive crystal under non-conventional biased condition. (b) and (c) are corresponding to the ionic-type photonic lattices induced by the lattice beams with the orientation of 0 (lattice 1) and π/4 (lattice 2) as regards to x axis, where the refractive index is in the unit of 10−4. (d) and (c) are the band diagrams of the lattices 1 and 2, respectively. The insets in (d) and (e) are their corresponding Brillouin zone spectra.

Fig. 2
Fig. 2

Propagations of an Airy beam in (a) lattice 1 and (b) lattice 2. (c) Intensity distribution of the input Airy beam. Here, the image has been magnified 2 times for clear identification. Outputs of the Airy beam when travelling through (d) lattice 1 and (e) lattice 2 with a distance of 100, where the scale bar in (d) is 40.

Fig. 3
Fig. 3

Optical Bloch oscillations of Airy beam in (1) lattice 1 (see Visualization 1) and (2) lattice 2 (see Visualization 2) with index gradient α = 0.008. (a)Trajectory of Airy beam at the longitudinal section. The solid arrows in (a) indicate the positions where Bragg reflection (BR) and total internal reflection (TIR) occur. The upper panels of (b)-(d) are the Airy beam intensity at the input and the sequent dashed-line labeled positions in (a). Here, the scale bar in (c1) is 80, the upper panels of (b1), (d1), (b2), (d2) and (c2) are magnified 4 and 2 times for clear identification, respectively. The lower panels of (b)-(d) are the corresponding Fourier spectra of the upper panels, where the solid lines indicate the boundaries of the first Brillouin zones, and the dashed-line arrows are the directions of the index gradients.

Fig. 4
Fig. 4

Zener tunneling rate Γ as a function of the inverse of the index grandniece 1/α. The red dots and yellow triangles are the numerically derived Γ in lattices 1 and 2, respectively. The blue and green solid curves corresponds to the theoretical predicted Γ in lattices 1 and 2, respectively.

Fig. 5
Fig. 5

Zener tunneling of Airy beam in (1) lattice 1 (see Visualization 3) and (2) lattice 2 (see Visualization 4) with index gradient α = 0.04. The upper panels of (b) and (c) are the Airy beam intensity at the sequent dashed-line labeled positions in (a). Here, the scale bar in (c1) is 50, (b2) and (c2) are magnified 2 times for clear identification. The lower panels of (b) and (c) are the corresponding Fourier spectra of upper panels, where the solid lines indicate the boundaries of the first Brillouin zones, and the dashed-line arrows are the directions of the index gradients.

Equations (6)

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Δ n 0 = 1 2 n e 3 γ 33 E 0 y φ ,
2 φ + φ ln ( 1 + I 0 ) = E 0 y ln ( 1 + I 0 ) .
Δ n = Δ n 0 + ( x cos ϕ + y cos ϕ ) ρ ,
i ζ ψ + 1 2 ( 2 ξ 2 + 2 η 2 ) ψ [ ξ φ + α ( x cos ϕ + y sin ϕ ) ] ψ = 0.
r ( z ) = 2 κ k 0 α cos ( Λ k 0 α z ) ,
Γ exp ( A Δ β / α ) ,

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