Abstract

We demonstrate, numerically, the existence and stability of multicomponent gap solitons in a Kerr nonlinear medium with a superposed grating based on a derived system of coupled-mode equations. Applications to all-optical logic and signal processing are discussed.

© 2005 Optical Society of America

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  1. H. G. Winful, J. H. Marburger, and E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
    [CrossRef]
  2. W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
    [CrossRef] [PubMed]
  3. D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
    [CrossRef] [PubMed]
  4. A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
    [CrossRef]
  5. C. M. de Sterke and J. E. Sipe, in Progress in Optics, E. Wolf, ed. (North-Holland, 1994), Vol. XXXIII, pp. 203–260.
    [CrossRef]
  6. C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997).
    [CrossRef]
  7. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
    [CrossRef] [PubMed]
  8. D. Taverner, N. G. R. Broderick, D. J. Richardson, M. Ibsen, and R. I. Laming, Opt. Lett. 23, 259 (1998).
    [CrossRef]
  9. A. Othonos, X. Lee, and R. M. Measures, Electron. Lett. 30, 1972 (1994).
    [CrossRef]
  10. D. Wei, T. Li, Y. Zhao, and S. Jian, Opt. Lett. 25, 1150 (2000).
    [CrossRef]
  11. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, Opt. Lett. 21, 1223 (1996).
    [CrossRef] [PubMed]
  12. O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
    [CrossRef]
  13. A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
    [CrossRef]
  14. C. Yeh and L. A. Bergman, Phys. Rev. E 60, 2306 (1999).
    [CrossRef]
  15. S. Lee and S.-T. Ho, Opt. Lett. 18, 962 (1993).
    [CrossRef] [PubMed]
  16. L. Tancevski and I. Andonovic, Electron. Lett. 30, 1388 (1994).
    [CrossRef]

2003 (2)

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

2000 (1)

1999 (1)

C. Yeh and L. A. Bergman, Phys. Rev. E 60, 2306 (1999).
[CrossRef]

1998 (1)

1997 (1)

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997).
[CrossRef]

1996 (2)

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, Opt. Lett. 21, 1223 (1996).
[CrossRef] [PubMed]

1994 (2)

A. Othonos, X. Lee, and R. M. Measures, Electron. Lett. 30, 1972 (1994).
[CrossRef]

L. Tancevski and I. Andonovic, Electron. Lett. 30, 1388 (1994).
[CrossRef]

1993 (1)

1989 (2)

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

1987 (1)

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

1979 (1)

H. G. Winful, J. H. Marburger, and E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

Aceves, A. B.

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

Andonovic, I.

L. Tancevski and I. Andonovic, Electron. Lett. 30, 1388 (1994).
[CrossRef]

Assanto, G.

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997).
[CrossRef]

Bergman, L. A.

C. Yeh and L. A. Bergman, Phys. Rev. E 60, 2306 (1999).
[CrossRef]

Broderick, N. G. R.

Chen, W.

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

Christodoulides, D. N.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

Cohen, O.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Conti, C.

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997).
[CrossRef]

de Sterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, Opt. Lett. 21, 1223 (1996).
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, in Progress in Optics, E. Wolf, ed. (North-Holland, 1994), Vol. XXXIII, pp. 203–260.
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, Opt. Lett. 21, 1223 (1996).
[CrossRef] [PubMed]

Fleischer, J. W.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Garmire, E.

H. G. Winful, J. H. Marburger, and E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

Ho, S.-T.

Ibsen, M.

Jian, S.

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Laming, R. I.

Lee, S.

Lee, X.

A. Othonos, X. Lee, and R. M. Measures, Electron. Lett. 30, 1972 (1994).
[CrossRef]

Li, T.

Marburger, J. H.

H. G. Winful, J. H. Marburger, and E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

Measures, R. M.

A. Othonos, X. Lee, and R. M. Measures, Electron. Lett. 30, 1972 (1994).
[CrossRef]

Mills, D. L.

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

Othonos, A.

A. Othonos, X. Lee, and R. M. Measures, Electron. Lett. 30, 1972 (1994).
[CrossRef]

Richardson, D. J.

Schwartz, T.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Segev, M.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, in Progress in Optics, E. Wolf, ed. (North-Holland, 1994), Vol. XXXIII, pp. 203–260.
[CrossRef]

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, Opt. Lett. 21, 1223 (1996).
[CrossRef] [PubMed]

Sukhorukov, A. A.

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

Tancevski, L.

L. Tancevski and I. Andonovic, Electron. Lett. 30, 1388 (1994).
[CrossRef]

Taverner, D.

Trillo, S.

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997).
[CrossRef]

Wabnitz, S.

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

Wei, D.

Winful, H. G.

H. G. Winful, J. H. Marburger, and E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

Yeh, C.

C. Yeh and L. A. Bergman, Phys. Rev. E 60, 2306 (1999).
[CrossRef]

Zhao, Y.

Appl. Phys. Lett. (1)

H. G. Winful, J. H. Marburger, and E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

Electron. Lett. (2)

A. Othonos, X. Lee, and R. M. Measures, Electron. Lett. 30, 1972 (1994).
[CrossRef]

L. Tancevski and I. Andonovic, Electron. Lett. 30, 1388 (1994).
[CrossRef]

Opt. Lett. (4)

Phys. Lett. A (1)

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

Phys. Rev. E (1)

C. Yeh and L. A. Bergman, Phys. Rev. E 60, 2306 (1999).
[CrossRef]

Phys. Rev. Lett. (6)

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

Other (1)

C. M. de Sterke and J. E. Sipe, in Progress in Optics, E. Wolf, ed. (North-Holland, 1994), Vol. XXXIII, pp. 203–260.
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Evolution of a multicomponent gap soliton (component u 1 ) with Q = 0.5 π , ϵ 2 = 0.99 , and ϵ 3 = 0.98 for (a)–(c) V = 0 , (d)–(f) V = 0.4 , (a) M = 1 , (b) M = 2 , (c) M = 3 , (d) M = 1 , (e) M = 2 , (f) M = 3 .

Equations (14)

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

E j ( Z , T ) = [ E j + ( Z , T ) exp ( i k j Z ) + E j ( Z , T ) exp ( i k j Z ) ] exp ( i ω j T ) + c.c.
n ( Z ) = n ¯ + Δ n m = 1 M cos ( 2 k m Z ) ,
i E j + Z + i n ¯ c E j + T + κ j E j + Γ j [ E j + 2 + 2 E j 2 + 2 m j ( E m + 2 + E m 2 ) ] E j + = 0 ,
i E j Z + i n ¯ c E j T + κ j E j + + Γ j [ E j 2 + 2 E j + 2 + 2 m j ( E m + 2 + E m 2 ) ] E j = 0 .
i u j z + i u j t + ϵ j v j + ϵ j [ 1 2 u j 2 + v j 2 + m j ( u m 2 + v m 2 ) ] u j = 0 ,
i v j z + i v j t + ϵ j u j + ϵ j [ 1 2 v j 2 + u j 2 + m j ( u m 2 + v m 2 ) ] v j = 0 ,
u 1 = α W ( ζ ) exp [ y 2 + i Φ ( ζ ) i τ cos Q + i ϕ 0 ] ,
v 1 = α W * ( ζ ) exp [ y 2 + i Φ ( ζ ) i τ cos Q + i ϕ 0 ] ,
α 2 ( 3 2 ) + V 2 , V tanh y ,
ζ t V z ( 1 V 2 ) 1 2 , τ z V t ( 1 V 2 ) 1 2 ,
W ( ζ ) = sin Q sech ( ζ sin Q i Q 2 ) ,
Φ ( ζ ) = α 2 sinh ( 2 y ) tan 1 [ tanh ( ζ sin Q ) tan ( Q 2 ) ] .
u j ( z = 0 , t ) = ( 2 M 1 ) 1 2 u 1 ( z = 0 , t ) ,
v j ( z = 0 , t ) = ( 2 M 1 ) 1 2 v 1 ( z = 0 , t ) .

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