Abstract

Light beams undergoing optical Bloch oscillations (OBOs) in two-dimensional (2D) photonic lattices suffer from severe diffraction along the perpendicular direction to the oscillation plane. In this paper, we propose and demonstrate that such diffraction could be suppressed in hexagonal photonic lattices via sophisticated managements of the discrete diffraction. By positioning the Fourier spectrum of the beam to a special region in the Brillouin zone, the light driven by the OBO experiences normal and anomalous diffractions alternatively, leading to a non-diffracting propagation for a long distance. We show that non-diffracting OBOs can be implemented not only for Gaussian beam but also for other complex 2D beams including self-accelerating Airy beams and vortex beams. Our results provide novel insights into the diffraction or dispersion engineering of waves in periodic structures.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
  6. P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  8. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
    [Crossref] [PubMed]
  9. P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, “Tuning of Bloch modes, diffraction, and refraction by two-dimensional lattice reconfiguration,” Opt. Lett. 35(6), 892–894 (2010).
    [Crossref] [PubMed]
  10. S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices,” Opt. Lett. 37(12), 2184–2186 (2012).
    [Crossref] [PubMed]
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    [Crossref]
  12. D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
    [Crossref] [PubMed]
  13. D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  17. 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]
  18. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  23. 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]
  24. A. S. Desyatnikov, Y. S. Kivshar, V. S. Shchesnovich, S. B. Cavalcanti, and J. M. Hickmann, “Resonant Zener tunneling in two-dimensional periodic photonic lattices,” Opt. Lett. 32(4), 325–327 (2007).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  26. F. Xiao, W. Zhu, W. Shang, M. Wang, P. Zhang, S. Liu, M. Premaratne, and J. Zhao, “Optical Bloch oscillations and Zener tunneling of Airy beams in ionic-type photonic lattices,” Opt. Express 24(16), 18332–18339 (2016).
    [Crossref] [PubMed]

2016 (1)

2015 (3)

V. Paltoglou, Z. Chen, and N. K. Efremidis, “Composite multi-vortex diffraction-free beams and van-Hove singularities in honeycomb lattices,” Opt. Lett. 40(6), 1037–1040 (2015).
[Crossref] [PubMed]

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
[Crossref]

2014 (2)

2012 (3)

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices,” Opt. Lett. 37(12), 2184–2186 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Symmetry-breaking diffraction and dynamic self-trapping in optically induced hexagonal photonic lattices,” Appl. Phys. Lett. 100(6), 061907 (2012).
[Crossref]

2011 (1)

2010 (1)

2009 (1)

2008 (1)

S. Longhi, “Optical Bloch oscillations and Zener tunneling with nonclassical light,” Phys. Rev. Lett. 101(19), 193902 (2008).
[Crossref] [PubMed]

2007 (3)

2006 (2)

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]

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

2000 (2)

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. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
[Crossref]

1998 (1)

1987 (2)

J. Durnin, “Exact solutions for nondifracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651 (1987).
[Crossref]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Ablowitz, M.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

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]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
[Crossref]

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, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[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.

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]

Cannan, D.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

Cavalcanti, S. B.

Chávez-Cerda, S.

Chen, Z.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
[Crossref]

V. Paltoglou, Z. Chen, and N. K. Efremidis, “Composite multi-vortex diffraction-free beams and van-Hove singularities in honeycomb lattices,” Opt. Lett. 40(6), 1037–1040 (2015).
[Crossref] [PubMed]

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

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Symmetry-breaking diffraction and dynamic self-trapping in optically induced hexagonal photonic lattices,” Appl. Phys. Lett. 100(6), 061907 (2012).
[Crossref]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices,” Opt. Lett. 37(12), 2184–2186 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, “Tuning of Bloch modes, diffraction, and refraction by two-dimensional lattice reconfiguration,” Opt. Lett. 35(6), 892–894 (2010).
[Crossref] [PubMed]

Christodoulides, D. N.

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]

Desyatnikov, A. S.

A. S. Desyatnikov, Y. S. Kivshar, V. S. Shchesnovich, S. B. Cavalcanti, and J. M. Hickmann, “Resonant Zener tunneling in two-dimensional periodic photonic lattices,” Opt. Lett. 32(4), 325–327 (2007).
[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]

Dogariu, A.

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]

Durnin, J.

J. Durnin, “Exact solutions for nondifracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651 (1987).
[Crossref]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Efremidis, N. K.

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
[Crossref]

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

V. Paltoglou, Z. Chen, and N. K. Efremidis, “Composite multi-vortex diffraction-free beams and van-Hove singularities in honeycomb lattices,” Opt. Lett. 40(6), 1037–1040 (2015).
[Crossref] [PubMed]

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

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]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations,” Phys. Rev. Lett. 83(23), 4756–4759 (1999).
[Crossref]

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.

Gallardo, D.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
[Crossref]

Gan, X.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Symmetry-breaking diffraction and dynamic self-trapping in optically induced hexagonal photonic lattices,” Appl. Phys. Lett. 100(6), 061907 (2012).
[Crossref]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices,” Opt. Lett. 37(12), 2184–2186 (2012).
[Crossref] [PubMed]

Gutiérrez-Vega, J. C.

Hickmann, J. M.

Hu, Y.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices,” Opt. Lett. 37(12), 2184–2186 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Symmetry-breaking diffraction and dynamic self-trapping in optically induced hexagonal photonic lattices,” Appl. Phys. Lett. 100(6), 061907 (2012).
[Crossref]

Iturbe-Castillo, M. D.

Kaminer, I.

Kivshar, Y. S.

A. S. Desyatnikov, Y. S. Kivshar, V. S. Shchesnovich, S. B. Cavalcanti, and J. M. Hickmann, “Resonant Zener tunneling in two-dimensional periodic photonic lattices,” Opt. Lett. 32(4), 325–327 (2007).
[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]

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]

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, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[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]

Li, B.

Li, T.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

Liu, S.

F. Xiao, W. Zhu, W. Shang, M. Wang, P. Zhang, S. Liu, M. Premaratne, and J. Zhao, “Optical Bloch oscillations and Zener tunneling of Airy beams in ionic-type photonic lattices,” Opt. Express 24(16), 18332–18339 (2016).
[Crossref] [PubMed]

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
[Crossref]

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[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]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices,” Opt. Lett. 37(12), 2184–2186 (2012).
[Crossref] [PubMed]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Symmetry-breaking diffraction and dynamic self-trapping in optically induced hexagonal photonic lattices,” Appl. Phys. Lett. 100(6), 061907 (2012).
[Crossref]

P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, “Tuning of Bloch modes, diffraction, and refraction by two-dimensional lattice reconfiguration,” Opt. Lett. 35(6), 892–894 (2010).
[Crossref] [PubMed]

Longhi, S.

Lou, C.

Makris, K. G.

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

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.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (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. S. Aitchison, H. S. 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]

Paltoglou, V.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
[Crossref]

V. Paltoglou, Z. Chen, and N. K. Efremidis, “Composite multi-vortex diffraction-free beams and van-Hove singularities in honeycomb lattices,” Opt. Lett. 40(6), 1037–1040 (2015).
[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, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[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]

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, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. 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]

Premaratne, M.

Segev, M.

Shang, W.

Shchesnovich, V. S.

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. S. Aitchison, H. S. 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.

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]

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

Song, D.

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
[Crossref]

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices,” Opt. Lett. 37(12), 2184–2186 (2012).
[Crossref] [PubMed]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Symmetry-breaking diffraction and dynamic self-trapping in optically induced hexagonal photonic lattices,” Appl. Phys. Lett. 100(6), 061907 (2012).
[Crossref]

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. 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]

Tang, L.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
[Crossref]

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]

Wang, M.

Xiao, F.

Xu, J.

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
[Crossref]

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices,” Opt. Lett. 37(12), 2184–2186 (2012).
[Crossref] [PubMed]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Symmetry-breaking diffraction and dynamic self-trapping in optically induced hexagonal photonic lattices,” Appl. Phys. Lett. 100(6), 061907 (2012).
[Crossref]

P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, “Tuning of Bloch modes, diffraction, and refraction by two-dimensional lattice reconfiguration,” Opt. Lett. 35(6), 892–894 (2010).
[Crossref] [PubMed]

Yin, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

Zhang, P.

Zhang, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

Zhao, J.

Zhu, W.

Zhu, Y.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

2D Mater. (1)

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Zhao, J. Xu, N. K. Efremidis, and Z. Chen, “Controlled generation of pseudospin-mediated vortices in photonic graphene,” 2D Mater. 2(3), 034007 (2015).
[Crossref]

Appl. Phys. Lett. (1)

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Symmetry-breaking diffraction and dynamic self-trapping in optically induced hexagonal photonic lattices,” Appl. Phys. Lett. 100(6), 061907 (2012).
[Crossref]

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

Nat. Commun. (1)

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 6, 6272 (2015).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (10)

V. Paltoglou, Z. Chen, and N. K. Efremidis, “Composite multi-vortex diffraction-free beams and van-Hove singularities in honeycomb lattices,” Opt. Lett. 40(6), 1037–1040 (2015).
[Crossref] [PubMed]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000).
[Crossref] [PubMed]

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

A. S. Desyatnikov, Y. S. Kivshar, V. S. Shchesnovich, S. B. Cavalcanti, and J. M. Hickmann, “Resonant Zener tunneling in two-dimensional periodic photonic lattices,” Opt. Lett. 32(4), 325–327 (2007).
[Crossref] [PubMed]

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

S. Longhi, “Polychromatic optical Bloch oscillations,” Opt. Lett. 34(14), 2174–2176 (2009).
[Crossref] [PubMed]

P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, “Tuning of Bloch modes, diffraction, and refraction by two-dimensional lattice reconfiguration,” Opt. Lett. 35(6), 892–894 (2010).
[Crossref] [PubMed]

S. Longhi, “Photonic Bloch oscillations of correlated particles,” Opt. Lett. 36(16), 3248–3250 (2011).
[Crossref] [PubMed]

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, “Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices,” Opt. Lett. 37(12), 2184–2186 (2012).
[Crossref] [PubMed]

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

Phys. Rev. Lett. (10)

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. S. Aitchison, H. S. 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]

S. Longhi, “Optical Bloch oscillations and Zener tunneling with nonclassical light,” Phys. Rev. Lett. 101(19), 193902 (2008).
[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]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[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]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (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]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

Supplementary Material (2)

NameDescription
» Visualization 1: MP4 (3892 KB)      visualization 1
» Visualization 2: MP4 (3737 KB)      visualization 2

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic drawing of the optical Bloch oscillation (OBO) of a two-dimensional (2D) beam in a hexagonal photonic lattice (HPL) with an index gradient. (b) Reciprocal space and the 1st Brillouin zone of the HPL. (c) OBO of a 2D Gaussian beam in the HPL (see Visualization 1); Top: side view of propagation process in the y-z plane; Bottom: intensity distributions at different propagation distances.

Fig. 2
Fig. 2

Diffraction characteristics of a HPL. (a) 3D view of the 1st and 2nd transmission bands of the HPL. (b) Contour plot of the 1st band β(kx,ky) with the 1st Brillouin zone marked by a dotted hexagon. (c) Diffraction characteristics along the x-axis, where the dashed lines indicate locations with Dx = 0.

Fig. 3
Fig. 3

Non-diffracting OBO of a Gaussian beam. (a) Numerically simulated OBO of a tilted Gaussian beam in a HPL, where the translucent planes correspond to y = 0, z = 0, 100, 200, and 300, respectively. (b)-(e) Intensity cross-sections at different propagation distances, where the coordinates of the beam centers (marked by the crosses) are labeled. (f) Exciting geometry of the input beam and the HPL, and (g) the corresponding propagation process in the y-z plane (see Visualization 2).

Fig. 4
Fig. 4

Diffraction suppression of an Airy beam during the OBO in a HPL. (a) Input Airy beam and its spectrum, where the dashed hexagon marks the 1st Brillouin zone of the HPL. (b)-(d) Evolutions of the Airy beam in an uniform HPL, in a HPL with index gradient along the y-axis, and in a tilted HPL matching the diffraction suppression condition, respectively; the figures from left to right correspond to the propagation processes in the y-z plane and the output at z = 300, respectively. The crosses mark the initial beam positions, and the scales of (a1), (b2), (c2) and (d2) are the same.

Fig. 5
Fig. 5

Non-diffracting OBO of an Airy beam accelerating in the y-axis. (a) Input Airy beam and its spectrum. (b),(c) The OBOs of the Airy beam without and with imposing the condition of diffraction suppression, respectively; the figures from left to right correspond to the propagation processes in the y-z plane and the output at z = 300, respectively. The crosses marks the initial beam positions.

Fig. 6
Fig. 6

Non-diffracting OBO of a vortex beam. (a) Intensity and phase distributions of the input beam. (b),(c) The OBOs of a vortex beam without and with diffraction suppression in the x-axis, respectively; the figures from left to right correspond to the propagation processes in the y-z plane, the output intensity and phase distributions at z = 300. The crosses marks the initial beam positions, and the scales of (a), (b2) and (c2) are the same.

Equations (3)

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

B z i 2 ( 2 B x 2 + 2 B y 2 )=nB,
I l =A | n=1,2,3 exp ( ig k n r ) | 2 ,
Δn=γ I l 1+ I l +ρy,

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