Abstract

We study controllable self-shifting Bloch modes in anisotropic hexagonal photonic lattices. The shifting results from a deformed band structure due to deformation of the index distribution in each unit cell. By reconfiguration of the index profile of the unit cell, the direction in which the Bloch modes move can be controlled. Our theoretical predictions are experimentally demonstrated in hexagonal lattices optically induced in an anisotropic nonlinear crystal.

© 2012 Optical Society of America

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References

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef]
  2. A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
    [CrossRef]
  3. P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 35, 892 (2010).
    [CrossRef]
  4. O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
    [CrossRef]
  5. O. Bahat-Treidel, O. Peleg, and M. Segev, Opt. Lett. 33, 2251 (2008).
    [CrossRef]
  6. S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
    [CrossRef]
  7. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef]
  8. C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
    [CrossRef]
  9. X. Wang, Z. Chen, J. Wang, and J. Yang, Phys. Rev. Lett. 99, 243901 (2007).
    [CrossRef]
  10. B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
    [CrossRef]
  11. Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, and Z. Chen, Opt. Lett. 34, 3259 (2009).
    [CrossRef]
  12. P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, Opt. Express 16, 3865 (2008).
    [CrossRef]
  13. P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. B 95, 559 (2009).
    [CrossRef]
  14. P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, Opt. Express 15, 536 (2007).
  15. J. Zhao, P. Zhang, J. Zhou, D. Yang, D. Yang, and E. Li Chin, Phys. Lett. 20, 1748 (2003).
  16. P. Zhang, D. Yang, J. Zhao, K. Su, J. Zhou, B. Li, and D. Yang, Chin. Phys. Lett. 21, 1558 (2004).

2012 (1)

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

2010 (1)

2009 (2)

Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, and Z. Chen, Opt. Lett. 34, 3259 (2009).
[CrossRef]

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. B 95, 559 (2009).
[CrossRef]

2008 (3)

P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, Opt. Express 16, 3865 (2008).
[CrossRef]

O. Bahat-Treidel, O. Peleg, and M. Segev, Opt. Lett. 33, 2251 (2008).
[CrossRef]

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef]

2007 (3)

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef]

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

X. Wang, Z. Chen, J. Wang, and J. Yang, Phys. Rev. Lett. 99, 243901 (2007).
[CrossRef]

2004 (1)

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef]

2003 (3)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef]

J. Zhao, P. Zhang, J. Zhou, D. Yang, D. Yang, and E. Li Chin, Phys. Lett. 20, 1748 (2003).

Bahat-Treidel, O.

Bartal, G.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef]

Chen, Z.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

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

Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, and Z. Chen, Opt. Lett. 34, 3259 (2009).
[CrossRef]

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. B 95, 559 (2009).
[CrossRef]

P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, Opt. Express 16, 3865 (2008).
[CrossRef]

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

X. Wang, Z. Chen, J. Wang, and J. Yang, Phys. Rev. Lett. 99, 243901 (2007).
[CrossRef]

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, Opt. Express 15, 536 (2007).

Chin, E. Li

J. Zhao, P. Zhang, J. Zhou, D. Yang, D. Yang, and E. Li Chin, Phys. Lett. 20, 1748 (2003).

Christodoulides, D. N.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef]

Denz, C.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef]

Desyatnikov, A. S.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef]

Freedman, B.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef]

Gan, X.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

Gao, Y.

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. B 95, 559 (2009).
[CrossRef]

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, Opt. Express 15, 536 (2007).

Hu, Y.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, and Z. Chen, Opt. Lett. 34, 3259 (2009).
[CrossRef]

Kaiser, F.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef]

Kivshar, Y. S.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef]

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef]

Krolikowski, W.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef]

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef]

Li, B.

P. Zhang, D. Yang, J. Zhao, K. Su, J. Zhou, B. Li, and D. Yang, Chin. Phys. Lett. 21, 1558 (2004).

Liu, Q.

Liu, S.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

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

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. B 95, 559 (2009).
[CrossRef]

Lou, C.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

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

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. B 95, 559 (2009).
[CrossRef]

Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, and Z. Chen, Opt. Lett. 34, 3259 (2009).
[CrossRef]

P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, Opt. Express 16, 3865 (2008).
[CrossRef]

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

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, Opt. Express 15, 536 (2007).

Manela, O.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef]

Neshev, D.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef]

Neshev, D. N.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef]

Peleg, O.

O. Bahat-Treidel, O. Peleg, and M. Segev, Opt. Lett. 33, 2251 (2008).
[CrossRef]

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef]

Richter, T.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef]

Segev, M.

O. Bahat-Treidel, O. Peleg, and M. Segev, Opt. Lett. 33, 2251 (2008).
[CrossRef]

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef]

Song, D.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

Su, K.

P. Zhang, D. Yang, J. Zhao, K. Su, J. Zhou, B. Li, and D. Yang, Chin. Phys. Lett. 21, 1558 (2004).

Sukhorukov, A. A.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef]

Tan, X.

Terhalle, B.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef]

Wang, J.

X. Wang, Z. Chen, J. Wang, and J. Yang, Phys. Rev. Lett. 99, 243901 (2007).
[CrossRef]

Wang, X.

X. Wang, Z. Chen, J. Wang, and J. Yang, Phys. Rev. Lett. 99, 243901 (2007).
[CrossRef]

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

Xiao, F.

Xu, J.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

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

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. B 95, 559 (2009).
[CrossRef]

Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, and Z. Chen, Opt. Lett. 34, 3259 (2009).
[CrossRef]

P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, Opt. Express 16, 3865 (2008).
[CrossRef]

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

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, Opt. Express 15, 536 (2007).

Yang, D.

J. Zhao, P. Zhang, J. Zhou, D. Yang, D. Yang, and E. Li Chin, Phys. Lett. 20, 1748 (2003).

J. Zhao, P. Zhang, J. Zhou, D. Yang, D. Yang, and E. Li Chin, Phys. Lett. 20, 1748 (2003).

P. Zhang, D. Yang, J. Zhao, K. Su, J. Zhou, B. Li, and D. Yang, Chin. Phys. Lett. 21, 1558 (2004).

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, Opt. Express 15, 536 (2007).

P. Zhang, D. Yang, J. Zhao, K. Su, J. Zhou, B. Li, and D. Yang, Chin. Phys. Lett. 21, 1558 (2004).

Yang, J.

Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, and Z. Chen, Opt. Lett. 34, 3259 (2009).
[CrossRef]

X. Wang, Z. Chen, J. Wang, and J. Yang, Phys. Rev. Lett. 99, 243901 (2007).
[CrossRef]

Zhang, P.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

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

Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, and Z. Chen, Opt. Lett. 34, 3259 (2009).
[CrossRef]

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. B 95, 559 (2009).
[CrossRef]

P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, Opt. Express 16, 3865 (2008).
[CrossRef]

J. Zhao, P. Zhang, J. Zhou, D. Yang, D. Yang, and E. Li Chin, Phys. Lett. 20, 1748 (2003).

P. Zhang, D. Yang, J. Zhao, K. Su, J. Zhou, B. Li, and D. Yang, Chin. Phys. Lett. 21, 1558 (2004).

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, Opt. Express 15, 536 (2007).

Zhao, J.

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

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

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. B 95, 559 (2009).
[CrossRef]

P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, and Z. Chen, Opt. Express 16, 3865 (2008).
[CrossRef]

J. Zhao, P. Zhang, J. Zhou, D. Yang, D. Yang, and E. Li Chin, Phys. Lett. 20, 1748 (2003).

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, Opt. Express 15, 536 (2007).

P. Zhang, D. Yang, J. Zhao, K. Su, J. Zhou, B. Li, and D. Yang, Chin. Phys. Lett. 21, 1558 (2004).

Zhou, J.

J. Zhao, P. Zhang, J. Zhou, D. Yang, D. Yang, and E. Li Chin, Phys. Lett. 20, 1748 (2003).

P. Zhang, D. Yang, J. Zhao, K. Su, J. Zhou, B. Li, and D. Yang, Chin. Phys. Lett. 21, 1558 (2004).

Appl. Phys. B (1)

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. B 95, 559 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

S. Liu, Y. Hu, P. Zhang, X. Gan, C. Lou, D. Song, J. Zhao, J. Xu, and Z. Chen, Appl. Phys. Lett. 100, 061907 (2012).
[CrossRef]

Chin. Phys. Lett. (1)

P. Zhang, D. Yang, J. Zhao, K. Su, J. Zhou, B. Li, and D. Yang, Chin. Phys. Lett. 21, 1558 (2004).

Nature (2)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Lett. (1)

J. Zhao, P. Zhang, J. Zhou, D. Yang, D. Yang, and E. Li Chin, Phys. Lett. 20, 1748 (2003).

Phys. Rev. Lett. (5)

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef]

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef]

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

X. Wang, Z. Chen, J. Wang, and J. Yang, Phys. Rev. Lett. 99, 243901 (2007).
[CrossRef]

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Diffraction curves of the first band in (a) perfect and (b), (c) anisotropic hexagonal lattices. Left, lattice structures; middle, diffraction curves; right, local distributions of the first band around the M-point. Insets show the local diffraction curves around the M-point.

Fig. 2.
Fig. 2.

Bloch waves at the M-point corresponding to the lattice structures in Figs. 1(a)–1(c). Top, amplitude and phase distributions; bottom, transverse Poynting vectors of the Bloch waves.

Fig. 3.
Fig. 3.

(a) Geometry of a typical anisotropic hexagonal lattice. (b) Displacement and direction of the shifting of the Bloch wave versus θ. (c) Input beam modulated with the M-point Bloch wave with its spectrum inserted. (d)–(g) Propagation in lattices with θ=0°, 45°, 90°, and 135°, respectively, with the input sites indicated by plus signs.

Fig. 4.
Fig. 4.

Experimental observation of the self-shifting Bloch modes in light-induced hexagonal lattices. (a) Geometry of the bias condition. (b) Input profile (top) and linear output without lattice (bottom); the inset shows the k-space spectrum. (c)–(e) Output beam profiles (bottom) in the anisotropic hexagonal lattices (top) under different bias conditions; insets depict the corresponding calculated lattice index profiles.

Equations (1)

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(zi22)Ψ=iΔnlΨ,

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