Abstract

We demonstrate theoretically and experimentally that the transverse instability of coherent soliton stripes can be greatly suppressed or totally eliminated when the soliton stripes propagate in a one-dimensional photonic lattice under self-defocusing nonlinearity.

© 2012 Optical Society of America

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  1. V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).
    [CrossRef]
  2. N. N. Akhmediev, V. I. Korneev, and R. F. Nabiev, Opt. Lett. 17, 393 (1992).
    [CrossRef]
  3. A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
    [CrossRef]
  4. Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
    [CrossRef]
  5. A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
    [CrossRef]
  6. A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 22, 868 (1997).
    [CrossRef]
  7. Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
    [CrossRef]
  8. S. P. Gorza, Ph. Emplit, and M. Haelterman, Opt. Lett. 31, 1280 (2006).
    [CrossRef]
  9. J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 2010).
  10. A. B. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, Opt. Lett. 19, 1186 (1994).
    [CrossRef]
  11. D. Neshev, A. A. Sukhorukov, Y. S. Kivshar, and W. Krolikowski, Opt. Lett. 29, 259 (2004).
    [CrossRef]
  12. C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
    [CrossRef]
  13. Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
    [CrossRef]
  14. Z. H. Musslimani and J. Yang, Opt. Lett. 26, 1981 (2001).
    [CrossRef]
  15. X. Wang, Z. Chen, J. Wang, and J. Yang, Phys. Rev. Lett. 99, 243901 (2007).
    [CrossRef]
  16. J. Yang, Phys. Rev. A. 84, 033840 (2011).
    [CrossRef]
  17. P. G. Kevrekidis, The Discrete Nonlinear Schrödinger Equation (Springer, 2009).

2011

J. Yang, Phys. Rev. A. 84, 033840 (2011).
[CrossRef]

2007

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

2006

2004

2001

2000

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef]

1999

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

1997

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 22, 868 (1997).
[CrossRef]

1996

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef]

1994

1992

1974

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).
[CrossRef]

Aceves, A. B.

Akhmediev, N. N.

Anastassiou, C.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef]

Buryak, A. V.

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 22, 868 (1997).
[CrossRef]

Chen, Z.

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

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef]

Christodoulides, D. N.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef]

Coskun, T. H.

De Angelis, C.

De Rossi, A.

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 22, 868 (1997).
[CrossRef]

Emplit, Ph.

Eugenieva, E. D.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef]

Gorza, S. P.

Haelterman, M.

Kevrekidis, P. G.

P. G. Kevrekidis, The Discrete Nonlinear Schrödinger Equation (Springer, 2009).

Kip, D.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef]

Kivshar, Y. S.

D. Neshev, A. A. Sukhorukov, Y. S. Kivshar, and W. Krolikowski, Opt. Lett. 29, 259 (2004).
[CrossRef]

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 22, 868 (1997).
[CrossRef]

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

Korneev, V. I.

Krolikowski, W.

Luther, G. G.

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
[CrossRef]

Musslimani, Z. H.

Z. H. Musslimani and J. Yang, Opt. Lett. 26, 1981 (2001).
[CrossRef]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

Nabiev, R. F.

Nepomnyashchy, A.

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

Neshev, D.

Pelinovsky, D. E.

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Rubenchik, A. M.

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
[CrossRef]

Segev, M.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef]

Soljacic, M.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef]

Sukhorukov, A. A.

Torres, J. P.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef]

Trillo, S.

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 22, 868 (1997).
[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]

Yang, J.

J. Yang, Phys. Rev. A. 84, 033840 (2011).
[CrossRef]

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

Z. H. Musslimani and J. Yang, Opt. Lett. 26, 1981 (2001).
[CrossRef]

J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 2010).

Zakharov, V. E.

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).
[CrossRef]

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
[CrossRef]

Europhys. Lett.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
[CrossRef]

Opt. Lett.

Phys. Rep.

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Phys. Rev. A.

J. Yang, Phys. Rev. A. 84, 033840 (2011).
[CrossRef]

Phys. Rev. E

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

Phys. Rev. Lett.

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

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef]

Sov. Phys. JETP

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).
[CrossRef]

Other

J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 2010).

P. G. Kevrekidis, The Discrete Nonlinear Schrödinger Equation (Springer, 2009).

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Figures (5)

Fig. 1.
Fig. 1.

(a) 1D lattice, (b) power curves of stripe solitons (dashed red indicates instability, solid blue indicates stability, and shaded regions are Bloch bands), (c) intensity profile of a stripe soliton in the first gap (at μ=4.5) under defocusing nonlinearity, (d) intensity profile of a stripe soliton in the semi-infinite gap (at μ=1) under focusing nonlinearity, (e), (f) stability spectra of stripe solitons in (c), (d), respectively.

Fig. 2.
Fig. 2.

The most unstable eigenvalue λmax versus μ for stripe solitons in the first gap under defocusing nonlinearity: (left) real part, (right) imaginary part.

Fig. 3.
Fig. 3.

(a) Initial intensity pattern of the stripe soliton in Fig. 1(c) under 2% perturbations, (b) output intensity of the perturbed soliton in (a) after nonlinear evolution of z=100 under defocusing nonlinearity, (c) output intensity of the perturbed soliton in Fig. 1(d) after nonlinear evolution of z=3 under focusing nonlinearity.

Fig. 4.
Fig. 4.

Experimental results. Upper row, first column, 1D lattice; lower row, first column, initial probe beam; upper row, results with lattice; lower row, results without lattice; second column, linear diffraction; third column, output with focusing nonlinearity; fourth column, output with defocusing nonlinearity. The bias field and crystalline c axis are along the vertical direction.

Fig. 5.
Fig. 5.

(a) Power curve of discrete stripe solitons under defocusing nonlinearity, (b), (c) real and imaginary parts of the most unstable eigenvalue λmax versus μ.

Equations (8)

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

iUz+Uxx+Uyy+n(x)U+σ|U|2U=0,
n(x)=6sin2x
U(x,y,z)=eiμz{u(x)+[v(x)+w(x)]eiky+λz+[v*(x)w*(x)]eiky+λ*z},
L0w=iλv,L1v=iλw,
L0=xx+n(x)+μk2+σu2,L1=xx+n(x)+μk2+3σu2,
U(x,y,z)=eiμ0z[ϵΨ(X,Y,Z)p(x)+ϵ2U2+],
iΨZ+DΨXX+ΨYY+σα|Ψ|2Ψ=0,
iUn,z+Un+12Un+Un1+Un,yy+σ|Un|2Un=0

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