Abstract

Different discrete soliton states in optical waveguide lattices are studied theoretically for the different external conditions such as the biased field, lattice spacing and the position of the input pulse. It is demonstrated that the discrete solitons can be formed in an appropriate biased field and exhibit different discrete properties in different biased field. The results also indicate that lattice spacing and the position of input pulse can affect apparently the discreteness of discrete solitons. If changing the ratio of the waist width of input beam to lattice period, the discrete solitons will be excited in more or less channels. In addition, the increase of lattice intensity almost does not affect the propagation behavior of soliton.

© 2007 Optical Society of America

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  1. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988).
    [CrossRef] [PubMed]
  2. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
    [CrossRef]
  3. D. N. Christodoulides, F. Lederer and Y. Siberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
    [CrossRef] [PubMed]
  4. D. Campbell, S. Flach and Y. S. Kivshar, "Localizing energy through nonlinearity and discreteness," Phys. Today,  57, 43-49 (2004).
    [CrossRef]
  5. R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Controlled switching of discrete solitons in waveguide arrays," Opt. Lett. 28, 1942-1944 (2003).
    [CrossRef] [PubMed]
  6. A. A. Sukhorukov and Y. S. Kivshar, "Soliton switching and Bloch-wave filtering in periodic photonic lattices," arXiv Physics/ 0412151 23, Dec 2004
  7. Y.-D. Wu, "New all-optical switch based on the spatial soliton repulsion," Opt. Express,  14, 4005-4012 (2006).
    [CrossRef] [PubMed]
  8. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, 2003).
  9. K. Staliunas and R. Herrero, "Nondiffractive propagation of light in photonic crystals," Phys. Rev. E 73, 016601 1-6 (2006).
    [CrossRef]
  10. F. Lederer and Y. Silberberg, "Discrete solitons," Opt. Photon. News 13,48-53 (2002).
    [CrossRef]
  11. T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. I. Stegeman, Y. Min, and W. Sohler, "Discrete Solitons in χ(2)-waveguide arrays," in Proc. Nonlinear Guided Waves and their Applications (Stresa, Italy, Sept. 2002), paper NLTuA1.
  12. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
    [CrossRef] [PubMed]
  13. F. Lederer, S. Damanyan, A. Kobyakov, Discrete solitons, in: Spatial Solitons, S. Trillo and W. Torruellas, eds., (Springer, Berlin 2001) pp. 269-276.
  14. T. J.  Alexander and Y. S.  Kivshar, "Soliton complexes and flat-top nonlinear modes in optical lattices," Appl. Phys. B 82, 203-206 (2006).
    [CrossRef]
  15. 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. 66, 046602, 1-5 (2002).
    [CrossRef]
  16. D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905, 1-4 (2004).
    [CrossRef]
  17. I. L. Garanovich, A. A. Sukhorukov and Y. S. Kivshar, "Soliton control in modulated optically-induced photonic lattices," Opt. Express 13, 5704-5710 (2005).
    [CrossRef] [PubMed]
  18. G. P. Agrawal, Nonlinear Fiber Optics (London, U.K, Academic, 1989), Ch. 2 and Ch. 4.
  19. Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, "Spatial soliton switching in quasicontinuous optical arrays," Opt. Lett. 29, 766-768 (2004).
    [CrossRef] [PubMed]

2006

Y.-D. Wu, "New all-optical switch based on the spatial soliton repulsion," Opt. Express,  14, 4005-4012 (2006).
[CrossRef] [PubMed]

K. Staliunas and R. Herrero, "Nondiffractive propagation of light in photonic crystals," Phys. Rev. E 73, 016601 1-6 (2006).
[CrossRef]

T. J.  Alexander and Y. S.  Kivshar, "Soliton complexes and flat-top nonlinear modes in optical lattices," Appl. Phys. B 82, 203-206 (2006).
[CrossRef]

2005

2004

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, "Spatial soliton switching in quasicontinuous optical arrays," Opt. Lett. 29, 766-768 (2004).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905, 1-4 (2004).
[CrossRef]

D. Campbell, S. Flach and Y. S. Kivshar, "Localizing energy through nonlinearity and discreteness," Phys. Today,  57, 43-49 (2004).
[CrossRef]

2003

R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Controlled switching of discrete solitons in waveguide arrays," Opt. Lett. 28, 1942-1944 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer and Y. Siberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

2002

F. Lederer and Y. Silberberg, "Discrete solitons," Opt. Photon. News 13,48-53 (2002).
[CrossRef]

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. 66, 046602, 1-5 (2002).
[CrossRef]

1998

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

1988

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Alexander, T. J.

T. J.  Alexander and Y. S.  Kivshar, "Soliton complexes and flat-top nonlinear modes in optical lattices," Appl. Phys. B 82, 203-206 (2006).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Campbell, D.

D. Campbell, S. Flach and Y. S. Kivshar, "Localizing energy through nonlinearity and discreteness," Phys. Today,  57, 43-49 (2004).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides, F. Lederer and Y. Siberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[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. 66, 046602, 1-5 (2002).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988).
[CrossRef] [PubMed]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[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. 66, 046602, 1-5 (2002).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Flach, S.

D. Campbell, S. Flach and Y. S. Kivshar, "Localizing energy through nonlinearity and discreteness," Phys. Today,  57, 43-49 (2004).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[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. 66, 046602, 1-5 (2002).
[CrossRef]

Garanovich, I. L.

Hanna, B.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905, 1-4 (2004).
[CrossRef]

Herrero, R.

K. Staliunas and R. Herrero, "Nondiffractive propagation of light in photonic crystals," Phys. Rev. E 73, 016601 1-6 (2006).
[CrossRef]

Joseph, R. I.

Kartashov, Y. V.

Kivshar, Y. S.

T. J.  Alexander and Y. S.  Kivshar, "Soliton complexes and flat-top nonlinear modes in optical lattices," Appl. Phys. B 82, 203-206 (2006).
[CrossRef]

I. L. Garanovich, A. A. Sukhorukov and Y. S. Kivshar, "Soliton control in modulated optically-induced photonic lattices," Opt. Express 13, 5704-5710 (2005).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905, 1-4 (2004).
[CrossRef]

D. Campbell, S. Flach and Y. S. Kivshar, "Localizing energy through nonlinearity and discreteness," Phys. Today,  57, 43-49 (2004).
[CrossRef]

R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Controlled switching of discrete solitons in waveguide arrays," Opt. Lett. 28, 1942-1944 (2003).
[CrossRef] [PubMed]

Krolikowski, W.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905, 1-4 (2004).
[CrossRef]

Lederer, F.

D. N. Christodoulides, F. Lederer and Y. Siberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

F. Lederer and Y. Silberberg, "Discrete solitons," Opt. Photon. News 13,48-53 (2002).
[CrossRef]

Molina, M. I.

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Neshev, D.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905, 1-4 (2004).
[CrossRef]

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. 66, 046602, 1-5 (2002).
[CrossRef]

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[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. 66, 046602, 1-5 (2002).
[CrossRef]

Siberberg, Y.

D. N. Christodoulides, F. Lederer and Y. Siberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

F. Lederer and Y. Silberberg, "Discrete solitons," Opt. Photon. News 13,48-53 (2002).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Staliunas, K.

K. Staliunas and R. Herrero, "Nondiffractive propagation of light in photonic crystals," Phys. Rev. E 73, 016601 1-6 (2006).
[CrossRef]

Sukhorukov, A. A.

I. L. Garanovich, A. A. Sukhorukov and Y. S. Kivshar, "Soliton control in modulated optically-induced photonic lattices," Opt. Express 13, 5704-5710 (2005).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905, 1-4 (2004).
[CrossRef]

Torner, L.

Vicencio, R. A.

Vysloukh, V. A.

Wu, Y.-D.

Zelenina, A. S.

Appl. Phys. B

T. J.  Alexander and Y. S.  Kivshar, "Soliton complexes and flat-top nonlinear modes in optical lattices," Appl. Phys. B 82, 203-206 (2006).
[CrossRef]

Nature

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer and Y. Siberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Opt. Photon. News

F. Lederer and Y. Silberberg, "Discrete solitons," Opt. Photon. News 13,48-53 (2002).
[CrossRef]

Phys. Rev. E

K. Staliunas and R. Herrero, "Nondiffractive propagation of light in photonic crystals," Phys. Rev. E 73, 016601 1-6 (2006).
[CrossRef]

Phys. Rev. E.

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. 66, 046602, 1-5 (2002).
[CrossRef]

Phys. Rev. Lett.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905, 1-4 (2004).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Phys. Today

D. Campbell, S. Flach and Y. S. Kivshar, "Localizing energy through nonlinearity and discreteness," Phys. Today,  57, 43-49 (2004).
[CrossRef]

Other

A. A. Sukhorukov and Y. S. Kivshar, "Soliton switching and Bloch-wave filtering in periodic photonic lattices," arXiv Physics/ 0412151 23, Dec 2004

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, 2003).

G. P. Agrawal, Nonlinear Fiber Optics (London, U.K, Academic, 1989), Ch. 2 and Ch. 4.

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. I. Stegeman, Y. Min, and W. Sohler, "Discrete Solitons in χ(2)-waveguide arrays," in Proc. Nonlinear Guided Waves and their Applications (Stresa, Italy, Sept. 2002), paper NLTuA1.

F. Lederer, S. Damanyan, A. Kobyakov, Discrete solitons, in: Spatial Solitons, S. Trillo and W. Torruellas, eds., (Springer, Berlin 2001) pp. 269-276.

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Figures (9)

Fig. 1.
Fig. 1.

(a). Photorefractive crystal with applied field. (b) Optical induced periodic waveguide lattice via plane waves interference.

Fig. 2.
Fig. 2.

Evolution of the beam at V 0 =1 (a) with optical lattice (d =2) and (b) without the lattices.

Fig. 3.
Fig. 3.

Propagation of the beam at three different sites along ξ direction at V 0 =30 (a) with optical lattice and (b) without the lattice in the photorefractive material; (c) corresponding to the case of (a) and (d) the case of (b).

Fig. 4.
Fig. 4.

Evolution of the amplitude of beams at three different sites along ξ direction at V 0 =80. (a) with optical lattice and (b) without the lattice in the photorefractive material.; (c) corresponding to the case of (a) and (d) the case of (b).

Fig. 5.
Fig. 5.

The amplitude |u| at the center site (η =0) versus biased field V0 for (a) with lattice spacing d =2 and (b) without the lattice.

Fig. 6.
Fig. 6.

Propagation of the beam in optical waveguide lattice with d =5 at η =0 for (a) V 0 =30, and (b) V 0 =80.

Fig. 7.
Fig. 7.

Propagation of the beam which is input at the first left lattice in optical waveguide lattice with d =2 for (a) V 0 =30,

Fig. 8.
Fig. 8.

Evolution of the beam at V 0 =80 for (a) Ω =0.4, I 0 =1; (b) Ω =0.2, I 0 =1. Other parameters are the same as in Fig. 3.

Fig. 9.
Fig. 9.

Evolution of the beam at V 0 =80 for (a) Ω =1, I 0 =10. (b) Ω =1, I 0 =20. Other parameters are the same as in Fig.3.

Equations (6)

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

I g ( x ) = I 0 sin 2 ( πx D )
i u z + 1 2 k 2 u x 2 k 0 n e 3 r 33 2 E sc u = 0
E sc = E 0 1 + I ( x ) K B T e I x 1 + I ( x )
i u ξ + 1 2 2 u η 2 V 0 u 1 + I g ( η ) + u 2 = 0
I g ( η ) = I 0 sin 2 ( πη d )
u 0 = sec h ( Ω ( η η 0 ) )

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