Abstract

We demonstrate self-trapping of light by simultaneously compensating normal and anomalous (saddle-shaped) diffractions with self-focusing and self-defocusing hybrid nonlinearity in optically induced ionic-type photonic lattices. Innovative two-dimensional gap solitons, named “saddle solitons,” are established, whose phase and spectrum characteristics are different from all previously observed spatial solitons.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Lederer, G. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
    [CrossRef]
  2. J. Fleischer, M. Segev, N. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  3. H. Martin, E. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef] [PubMed]
  4. C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, Phys. Rev. Lett. 98, 213903 (2007).
    [CrossRef] [PubMed]
  5. J. Hudock, N. K. Efremidis, and D. N. Christodoulides, Opt. Lett. 29, 268 (2004).
    [CrossRef] [PubMed]
  6. X. Wang, Z. Chen, J. Wang, and J. Yang, Phys. Rev. Lett. 99, 243901 (2007).
    [CrossRef]
  7. J. Yang, B. A. Malomed, and D. J. Kaup, Phys. Rev. Lett. 83, 1958 (1999).
    [CrossRef]
  8. P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, Opt. Express 15, 536 (2007).
    [CrossRef] [PubMed]
  9. Y. Hu, C. Lou, S. Liu, P. Zhang, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 34, 1114 (2009).
    [CrossRef] [PubMed]
  10. P. Zhang, C. Lou, S. Liu, F. Xiao, J. Zhao, J. Xu, and Z. Chen, Opt. Photonics News 19(12), 25 (2008).
    [CrossRef]
  11. R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
    [CrossRef] [PubMed]
  12. G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
    [CrossRef] [PubMed]
  13. N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
    [CrossRef] [PubMed]

2009 (1)

2008 (2)

F. Lederer, G. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

P. Zhang, C. Lou, S. Liu, F. Xiao, J. Zhao, J. Xu, and Z. Chen, Opt. Photonics News 19(12), 25 (2008).
[CrossRef]

2007 (3)

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

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).
[CrossRef] [PubMed]

2006 (1)

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

2005 (1)

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

2004 (2)

H. Martin, E. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

J. Hudock, N. K. Efremidis, and D. N. Christodoulides, Opt. Lett. 29, 268 (2004).
[CrossRef] [PubMed]

2003 (2)

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

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

1999 (1)

J. Yang, B. A. Malomed, and D. J. Kaup, Phys. Rev. Lett. 83, 1958 (1999).
[CrossRef]

Assanto, G.

F. Lederer, G. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Bartal, G.

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

Buljan, H.

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

Chen, Z.

Y. Hu, C. Lou, S. Liu, P. Zhang, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 34, 1114 (2009).
[CrossRef] [PubMed]

P. Zhang, C. Lou, S. Liu, F. Xiao, J. Zhao, J. Xu, and Z. Chen, Opt. Photonics News 19(12), 25 (2008).
[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).
[CrossRef] [PubMed]

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

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

H. Martin, E. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

F. Lederer, G. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

J. Hudock, N. K. Efremidis, and D. N. Christodoulides, Opt. Lett. 29, 268 (2004).
[CrossRef] [PubMed]

H. Martin, E. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

Cohen, O.

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

Denz, C.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

Efremidis, N.

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

Efremidis, N. K.

J. Hudock, N. K. Efremidis, and D. N. Christodoulides, Opt. Lett. 29, 268 (2004).
[CrossRef] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

Eugenieva, E.

H. Martin, E. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Fischer, R.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

Fleischer, J.

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

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

Fleischer, J. W.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

Gao, Y.

Hu, Y.

Hudock, J.

J. Hudock, N. K. Efremidis, and D. N. Christodoulides, Opt. Lett. 29, 268 (2004).
[CrossRef] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

Kaup, D. J.

J. Yang, B. A. Malomed, and D. J. Kaup, Phys. Rev. Lett. 83, 1958 (1999).
[CrossRef]

Kivshar, Y. S.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

Krolikowski, W.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

Lederer, F.

F. Lederer, G. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Liu, Q.

Liu, S.

Y. Hu, C. Lou, S. Liu, P. Zhang, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 34, 1114 (2009).
[CrossRef] [PubMed]

P. Zhang, C. Lou, S. Liu, F. Xiao, J. Zhao, J. Xu, and Z. Chen, Opt. Photonics News 19(12), 25 (2008).
[CrossRef]

Lou, C.

Y. Hu, C. Lou, S. Liu, P. Zhang, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 34, 1114 (2009).
[CrossRef] [PubMed]

P. Zhang, C. Lou, S. Liu, F. Xiao, J. Zhao, J. Xu, and Z. Chen, Opt. Photonics News 19(12), 25 (2008).
[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).
[CrossRef] [PubMed]

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

Malomed, B. A.

J. Yang, B. A. Malomed, and D. J. Kaup, Phys. Rev. Lett. 83, 1958 (1999).
[CrossRef]

Manela, O.

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

Martin, H.

H. Martin, E. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Neshev, D. N.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

Segev, M.

F. Lederer, G. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

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

Silberberg, Y.

F. Lederer, G. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Stegeman, G.

F. Lederer, G. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Sukhorukov, A. A.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

Tan, X.

Träger, D.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

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, Z. Chen, and J. Yang, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Xiao, F.

P. Zhang, C. Lou, S. Liu, F. Xiao, J. Zhao, J. Xu, and Z. Chen, Opt. Photonics News 19(12), 25 (2008).
[CrossRef]

Xu, J.

Y. Hu, C. Lou, S. Liu, P. Zhang, J. Zhao, J. Xu, and Z. Chen, Opt. Lett. 34, 1114 (2009).
[CrossRef] [PubMed]

P. Zhang, C. Lou, S. Liu, F. Xiao, J. Zhao, J. Xu, and Z. Chen, Opt. Photonics News 19(12), 25 (2008).
[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).
[CrossRef] [PubMed]

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

Yang, D.

Yang, J.

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

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

J. Yang, B. A. Malomed, and D. J. Kaup, Phys. Rev. Lett. 83, 1958 (1999).
[CrossRef]

Zhang, P.

Zhao, J.

Nature (1)

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

Opt. Express (1)

Opt. Lett. (2)

Opt. Photonics News (1)

P. Zhang, C. Lou, S. Liu, F. Xiao, J. Zhao, J. Xu, and Z. Chen, Opt. Photonics News 19(12), 25 (2008).
[CrossRef]

Phys. Rep. (1)

F. Lederer, G. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Phys. Rev. Lett. (7)

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

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

J. Yang, B. A. Malomed, and D. J. Kaup, Phys. Rev. Lett. 83, 1958 (1999).
[CrossRef]

H. Martin, E. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Orientations of crystalline c axis, bias field, and square lattice-inducing beam; (b) refractive index distribution of the induced ionic-type lattice; (c) extended first Bloch band; (d) Existence curve of saddle solitons at V 0 = 0.94 ; (e)–(g) Intensity pattern (associated index change shown in insert), phase structure, and Fourier spectrum of the saddle soliton at the marked point in (d); (h), (i) evolution of intensity profiles along dashed lines in (e) for 10 cm propagation of the soliton solution. Added squares in (c) and (g) mark the boundary of the first Brillouin zone.

Fig. 2
Fig. 2

(a)–(d) Experimental and (e)–(j) numerical results of in-gap saddle soliton. The first row shows the (a) intensity pattern; (b), (c) interferograms with a tilted plane wave at two orthogonal directions; and (d) Fourier spectrum of the soliton. The second row shows corresponding numerical results. The third row shows evolution of intensity profiles along dashed lines in (e) for 3 cm propagation of the probe beam.

Fig. 3
Fig. 3

Numerical solutions for quasi-localized in-band saddle soliton at V 0 = 0.5 . Other description for Figs. 3a, 3b, 3c, 3d, 3e, 3f is the same as that for Figs. 1d, 1e, 1f, 1g, 1h, 1i.

Fig. 4
Fig. 4

(a)–(d) Experimental and (e)–(h) numerical results of in-band saddle soliton. Other description for Figs. 4a, 4b, 4c, 4d, 4e, 4f, 4g, 4h is the same as that for Figs. 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h.

Equations (3)

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

( z i 2 2 ) B ( r ) = i γ φ x B ( r ) ,
2 φ + φ ln ( 1 + I ) = y ln ( 1 + I ) ,
( β 1 2 2 ) b ( x , y ) = γ φ x b ( x , y ) .

Metrics