Abstract

We theoretically report the existence of optical Bloch oscillations (BO) of an Airy beam in a one-dimensional optically induced photonic lattice with a linear transverse index gradient. The Airy beam experiencing optical BO shows a more robust non-diffracting feature than its counterparts in free space or in a uniform photonic lattice. Interestingly, a periodical recurrence of Airy shape accompanied with constant alternation of its acceleration direction is also found during the BO. Furthermore, we demonstrate that the period and amplitude of BO of an Airy beam can be readily controlled over a wide range by varying the index gradient and/or the lattice period. Exploiting these features, we propose a scheme to rout an Airy beam to a predefined output channel without losing its characteristics by longitudinally modulating the transverse index gradient.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
  3. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2(11), 675–678 (2008).
    [Crossref]
  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]
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    [Crossref] [PubMed]
  6. 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]
  7. P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett. 36(16), 3191–3193 (2011).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  37. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
    [Crossref] [PubMed]
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    [Crossref]
  40. P. Zhang, R. Egger, and Z. Chen, “Optical induction of three-dimensional photonic lattices and enhancement of discrete diffraction,” Opt. Express 17(15), 13151–13156 (2009).
    [Crossref] [PubMed]
  41. J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22(3), 356–360 (2010).
    [Crossref] [PubMed]

2014 (5)

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. Photon. 8(4), 302–306 (2014).
[Crossref]

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

X. Qi, K. G. Makris, R. El-Ganainy, P. Zhang, J. Bai, D. N. Christodoulides, and Z. Chen, “Observation of accelerating Wannier-Stark beams in optically induced photonic lattices,” Opt. Lett. 39, 1065–1067 (2014).

K. Makris, I. Kaminer, R. El-Ganainy, N. Efremidis, Z. Chen, M. Segev, and D. Christodoulides, “Accelerating diffraction-free beams in photonic lattices,” Opt. Lett. 39(7), 2129–2132 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (1)

2011 (11)

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

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]

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett. 36(16), 3191–3193 (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]

R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express 19(24), 23706–23715 (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]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A 84(2), 023842 (2011).
[Crossref]

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]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (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]

2010 (5)

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. 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. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22(3), 356–360 (2010).
[Crossref] [PubMed]

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. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Geometric potential and transport in photonic topological crystals,” Phys. Rev. Lett. 104(15), 150403 (2010).
[Crossref] [PubMed]

2009 (2)

P. Zhang, R. Egger, and Z. Chen, “Optical induction of three-dimensional photonic lattices and enhancement of discrete diffraction,” Opt. Express 17(15), 13151–13156 (2009).
[Crossref] [PubMed]

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

2008 (1)

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

2007 (3)

2006 (1)

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]

2004 (1)

D. Witthaut, F. Keck, H. Korsch, and S. Mossmann, “Bloch oscillations in two-dimensional lattices,” New J. Phys. 6, 41 (2004).
[Crossref]

2002 (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[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]

1998 (1)

1995 (1)

L. I. Ivleva, N. V. Bogodaev, N. M. Polozkov, and V. V. Osiko, “Growth of SBN single crystals by Stepanov technique for photorefractive applications,” Opt. Mater. 4(2–3), 168–173 (1995).
[Crossref]

1986 (1)

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

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

Bai, J.

Bandres, M. A.

Baumgartl, J.

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

Bekenstein, R.

Bleckmann, F.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Block, A.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Bogodaev, N. V.

L. I. Ivleva, N. V. Bogodaev, N. M. Polozkov, and V. V. Osiko, “Growth of SBN single crystals by Stepanov technique for photorefractive applications,” Opt. Mater. 4(2–3), 168–173 (1995).
[Crossref]

Boguslawski, M.

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

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22(3), 356–360 (2010).
[Crossref] [PubMed]

Bongiovanni, D.

Bräuer, A.

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.

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

Chen, Z.

X. Qi, K. G. Makris, R. El-Ganainy, P. Zhang, J. Bai, D. N. Christodoulides, and Z. Chen, “Observation of accelerating Wannier-Stark beams in optically induced photonic lattices,” Opt. Lett. 39, 1065–1067 (2014).

K. Makris, I. Kaminer, R. El-Ganainy, N. Efremidis, Z. Chen, M. Segev, and D. Christodoulides, “Accelerating diffraction-free beams in photonic lattices,” Opt. Lett. 39(7), 2129–2132 (2014).
[Crossref] [PubMed]

K. Makris, I. Kaminer, R. El-Ganainy, N. Efremidis, Z. Chen, M. Segev, and D. Christodoulides, “Accelerating diffraction-free beams in photonic lattices,” Opt. Express 21, 8886–8896 (2013).
[Crossref] [PubMed]

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space,” Opt. Lett. 38(17), 3387–3389 (2013).
[Crossref] [PubMed]

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett. 36(16), 3191–3193 (2011).
[Crossref] [PubMed]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A 84(2), 023842 (2011).
[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]

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]

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, 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]

P. Zhang, R. Egger, and Z. Chen, “Optical induction of three-dimensional photonic lattices and enhancement of discrete diffraction,” Opt. Express 17(15), 13151–13156 (2009).
[Crossref] [PubMed]

Chremmos, I.

Christodoulides, D.

Christodoulides, D. N.

X. Qi, K. G. Makris, R. El-Ganainy, P. Zhang, J. Bai, D. N. Christodoulides, and Z. Chen, “Observation of accelerating Wannier-Stark beams in optically induced photonic lattices,” Opt. Lett. 39, 1065–1067 (2014).

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A 84(2), 023842 (2011).
[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]

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

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

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[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]

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]

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22(3), 356–360 (2010).
[Crossref] [PubMed]

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. Photon. 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.

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

Dreisow, F.

A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Geometric potential and transport in photonic topological crystals,” Phys. Rev. Lett. 104(15), 150403 (2010).
[Crossref] [PubMed]

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Efremidis, N. K.

Egger, R.

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]

El-Ganainy, R.

Ellenbogen, T.

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

Etrich, C.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[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]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Ganany-Padowicz, A.

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

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).
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Gutiérrez-Vega, J. C.

Heinrich, M.

A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Geometric potential and transport in photonic topological crystals,” Phys. Rev. Lett. 104(15), 150403 (2010).
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Hu, Y.

Huang, S.

Ivleva, L. I.

L. I. Ivleva, N. V. Bogodaev, N. M. Polozkov, and V. V. Osiko, “Growth of SBN single crystals by Stepanov technique for photorefractive applications,” Opt. Mater. 4(2–3), 168–173 (1995).
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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
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S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photon. 8(4), 302–306 (2014).
[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]

Joseph, J.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22(3), 356–360 (2010).
[Crossref] [PubMed]

Kaminer, I.

Keck, F.

D. Witthaut, F. Keck, H. Korsch, and S. Mossmann, “Bloch oscillations in two-dimensional lattices,” New J. Phys. 6, 41 (2004).
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A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Geometric potential and transport in photonic topological crystals,” Phys. Rev. Lett. 104(15), 150403 (2010).
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W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. 36(7), 1164–1166 (2011).
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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[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).
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Klein, A. E.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
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D. Witthaut, F. Keck, H. Korsch, and S. Mossmann, “Bloch oscillations in two-dimensional lattices,” New J. Phys. 6, 41 (2004).
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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]

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]

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]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23(21), 1701–1703 (1998).
[Crossref] [PubMed]

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]

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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).
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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).
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A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Linden, S.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
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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).
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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).
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Liu, Y.

Longhi, S.

A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Geometric potential and transport in photonic topological crystals,” Phys. Rev. Lett. 104(15), 150403 (2010).
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Lou, C.

Lu, C.

Makris, K.

Makris, K. G.

X. Qi, K. G. Makris, R. El-Ganainy, P. Zhang, J. Bai, D. N. Christodoulides, and Z. Chen, “Observation of accelerating Wannier-Stark beams in optically induced photonic lattices,” Opt. Lett. 39, 1065–1067 (2014).

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A 84(2), 023842 (2011).
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Mazilu, M.

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

Mills, M. S.

Minovich, A.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
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Miri, M. A.

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A 84(2), 023842 (2011).
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Morandotti, R.

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space,” Opt. Lett. 38(17), 3387–3389 (2013).
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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]

Mossmann, S.

D. Witthaut, F. Keck, H. Korsch, and S. Mossmann, “Bloch oscillations in two-dimensional lattices,” New J. Phys. 6, 41 (2004).
[Crossref]

Neshev, D. N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[Crossref] [PubMed]

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

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]

Nolte, S.

A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Geometric potential and transport in photonic topological crystals,” Phys. Rev. Lett. 104(15), 150403 (2010).
[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]

Osiko, V. V.

L. I. Ivleva, N. V. Bogodaev, N. M. Polozkov, and V. V. Osiko, “Growth of SBN single crystals by Stepanov technique for photorefractive applications,” Opt. Mater. 4(2–3), 168–173 (1995).
[Crossref]

Pertsch, T.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011).
[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]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23(21), 1701–1703 (1998).
[Crossref] [PubMed]

Peschel, U.

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]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23(21), 1701–1703 (1998).
[Crossref] [PubMed]

Polozkov, N. M.

L. I. Ivleva, N. V. Bogodaev, N. M. Polozkov, and V. V. Osiko, “Growth of SBN single crystals by Stepanov technique for photorefractive applications,” Opt. Mater. 4(2–3), 168–173 (1995).
[Crossref]

Prakash, J.

Qi, X.

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]

Rockstuhl, C.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Rose, P.

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

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22(3), 356–360 (2010).
[Crossref] [PubMed]

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

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Segev, M.

K. Makris, I. Kaminer, R. El-Ganainy, N. Efremidis, Z. Chen, M. Segev, and D. Christodoulides, “Accelerating diffraction-free beams in photonic lattices,” Opt. Lett. 39(7), 2129–2132 (2014).
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K. Makris, I. Kaminer, R. El-Ganainy, N. Efremidis, Z. Chen, M. Segev, and D. Christodoulides, “Accelerating diffraction-free beams in photonic lattices,” Opt. Express 21, 8886–8896 (2013).
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R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express 19(24), 23706–23715 (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]

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]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Shadrivov, I. V.

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.

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

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]

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

Soergel, E.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Song, D.

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]

Szameit, A.

A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Geometric potential and transport in photonic topological crystals,” Phys. Rev. Lett. 104(15), 150403 (2010).
[Crossref] [PubMed]

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]

Tünnermann, A.

A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Geometric potential and transport in photonic topological crystals,” Phys. Rev. Lett. 104(15), 150403 (2010).
[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. Photon. 8(4), 302–306 (2014).
[Crossref]

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. Photon. 3(7), 395–398 (2009).
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Figures (5)

Fig. 1
Fig. 1 (a) Schematic view of one-dimensional (1D) photonic lattice (left) with its index distribution (right). (b) Schematic view of 1D photonic lattice with an index gradient (left) and its index distribution (right). (c) The first two Bloch bands of the uniform 1D photonic lattice as shown in (a).
Fig. 2
Fig. 2 Propagation dynamics of Airy beam in (a) photonic lattice with a liner transverse index gradient, (b) free space, and (c) uniform photonic lattice. (d) Input intensity profile of Airy beam. (e)-(g) Cross-sections of light intensity at the dashed lines of (a)-(c), respectively.
Fig. 3
Fig. 3 Optical Bloch oscillations (BO) of Airy beam in 1D photonic lattices with index gradients (a) α = 0.006, (b) α = 0.01, and (c) α = 0.015 at Λ = 2. (d) BO period and (e) amplitude versus 1/α, where the red dots and solid lines are the simulation and fitting results, respectively.
Fig. 4
Fig. 4 BO of Airy beam in 1D photonic lattices with lattice periods (a) Λ = 2, (b) Λ = 3, and (c) Λ = 3.6 at α = 0.01. (d) BO period versus 1/Λ, where the red dots and solid line are the simulation and fitting results, respectively. (e) Dependence of oscillation amplitude (red dots) and coupling coefficient 2η (blue dots) on 1/Λ.
Fig. 5
Fig. 5 Controlling the beam path of Airy beam by longitudinally changing (a) the index gradient and (b) period of photonic lattice. The upper and lower panels of (a) are respectively for the index gradient modulations of α = 0.01 + 9.5 × 10−7ξ and α = 0.01-9.5 × 10−7ξ, while those of (b) are for the lattice period modulations of Λ = 2.9 + 1.8 × 10−4ξ and Λ = 2.9-1.8 × 10−4ξ, respectively. (c) Assigning the Airy beam to the desirable output channel by altering the index gradient variation along the propagation direction. The intensity profiles in (c) from top to bottom are respectively for the input beam, and the output beams at ξ = 800 after index gradient modulations of α = 0.01-9.7 × 10−7ξ, α = 0.015-1.5 × 10−6ξ, α = 0.007 + 1.6 × 10−6ξ and α = 0.005 + 2.4 × 10−6ξ.

Equations (6)

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Δ n = 1 2 n e 2 γ 33 E 0 I 0 1 + I 0 + ρ x .
k z = β + 2 η cos ( Λ k x ) .
v ( k x ) = k z k x = 2 η Λ sin ( Λ k x ) .
k x z = k 0 n = k 0 ρ ,
x ( z ) = v ( k x ) d z = 2 η k 0 ρ cos ( Λ k 0 ρ z ) ,
( ξ i 2 2 s 2 ) ψ = i ( I 0 1 + I 0 + α x ) ψ .

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