Abstract

We analyze nonlinear collective effects near surfaces of semi-infinite periodic systems with multi-gap transmission spectra and introduce a novel concept of multi-gap surface solitons as mutually trapped surface states with the components associated with different spectral gaps. We find numerically discrete surface modes in semi-infinite binary waveguide arrays which can support simultaneously two types of discrete solitons, and analyze different multi-gap states including the soliton-induced waveguides with the guided modes from different gaps and composite vector solitons.

© 2006 Optical Society of America

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  1. S. G. Davidson and M. Steslicka, Basic theory of surface states (Oxford Science Publications, New York, 1996).
  2. I. E. Tamm, "A possible kind of electron binding on crystal surfaces," Z. Phys. 76,849-850 (1932).
    [CrossRef]
  3. P. Yeh, A. Yariv, and C. S. Hong, "Electromagnetic propagation in periodic stratified media. 1. General theory," J. Opt. Soc. Am. 67,423-438 (1977).
    [CrossRef]
  4. P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
    [CrossRef]
  5. W. J. Tomlinson, "Surface wave at a nonlinear interface," Opt. Lett. 5,323-325 (1980).
    [CrossRef] [PubMed]
  6. A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, "Third-order nonlinear electromagnetic TE and TM guided waves," in Nonlinear Surface Electromagnetic Phenomena, Vol. 29 of Modern Problems in Condensed Matter Sciences, H. E. Ponath and G.I. Stegeman, eds., (North-Holland, Amsterdam, 1991), pp. 73-287.
  7. D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," in Progress in Optics, E. Wolf, ed., (North-Holland, Amsterdam, 1989), 27, pp. 229-313.
  8. Yu. S. Kivshar, F. Zhang, and S. Takeno, "Multistable nonlinear surface modes," Physica D 119,125-133 (1998).
    [CrossRef]
  9. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30,2466-2468 (2005).
    [CrossRef] [PubMed]
  10. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-4 (2006).
    [CrossRef] [PubMed]
  11. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
  12. M. I. Molina, R. A. Vicencio, and Yu. S. Kivshar, "Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays," Opt. Lett. 31,1693-1695 (2006).
    [CrossRef] [PubMed]
  13. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-4 (2006).
    [CrossRef] [PubMed]
  14. C. R. Rosberg, D. N. Neshev, W. Krolikowski, Yu. S. Kivshar, A. Mitchell, R. A. Vicencio, and M. I. Molina, "Observation of surface gap solitons in semi-infinite waveguide arrays," arXiv physics/0603202 (2006).
  15. J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Vector discrete nonlinear surface waves," Opt. Express 13,7720-7725 (2005).
    [CrossRef] [PubMed]
  16. O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91,113901-4 (2003).
    [CrossRef] [PubMed]
  17. A. A. Sukhorukov and Yu. S. Kivshar, "Multigap discrete vector solitons," Phys. Rev. Lett. 91, 113902-4 (2003).
    [CrossRef] [PubMed]
  18. O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Observation of random-phase lattice solitons," Nature 433, 500-503 (2005).
    [CrossRef] [PubMed]
  19. C. R. Rosberg, B. Hanna, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Discrete interband mutual focusing in nonlinear photonic lattices," Opt. Express 13,5369-5376 (2005).
    [CrossRef] [PubMed]
  20. A. A. Sukhorukov and Yu. S. Kivshar, "Discrete gap solitons in modulated waveguide arrays," Opt. Lett. 27,2112-2114 (2002).
    [CrossRef]
  21. A. A. Sukhorukov and Yu. S. Kivshar, "Generation and stability of discrete gap solitons," Opt. Lett. 28,2345-2347 (2003).
    [CrossRef] [PubMed]
  22. R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, "Observation of discrete gap solitons in binary waveguide arrays," Opt. Lett. 29,2890-2892 (2004).
    [CrossRef]
  23. D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, "Bifurcations and stability of gap solitons in periodic potentials," Phys. Rev. E 70,036618(2004).
    [CrossRef]
  24. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Observation of mutually trapped multiband optical breathers in waveguide arrays," Phys. Rev. Lett. 90,253902-4 (2003).
    [CrossRef] [PubMed]

2006 (3)

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-4 (2006).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Yu. S. Kivshar, "Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays," Opt. Lett. 31,1693-1695 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-4 (2006).
[CrossRef] [PubMed]

2005 (4)

2004 (2)

2003 (4)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Observation of mutually trapped multiband optical breathers in waveguide arrays," Phys. Rev. Lett. 90,253902-4 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, "Generation and stability of discrete gap solitons," Opt. Lett. 28,2345-2347 (2003).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91,113901-4 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, "Multigap discrete vector solitons," Phys. Rev. Lett. 91, 113902-4 (2003).
[CrossRef] [PubMed]

2002 (1)

1998 (1)

Yu. S. Kivshar, F. Zhang, and S. Takeno, "Multistable nonlinear surface modes," Physica D 119,125-133 (1998).
[CrossRef]

1980 (1)

1978 (1)

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
[CrossRef]

1977 (1)

1932 (1)

I. E. Tamm, "A possible kind of electron binding on crystal surfaces," Z. Phys. 76,849-850 (1932).
[CrossRef]

Aitchison, J. S.

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, "Observation of discrete gap solitons in binary waveguide arrays," Opt. Lett. 29,2890-2892 (2004).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Observation of mutually trapped multiband optical breathers in waveguide arrays," Phys. Rev. Lett. 90,253902-4 (2003).
[CrossRef] [PubMed]

Bartal, G.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Observation of random-phase lattice solitons," Nature 433, 500-503 (2005).
[CrossRef] [PubMed]

Buljan, H.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Observation of random-phase lattice solitons," Nature 433, 500-503 (2005).
[CrossRef] [PubMed]

Carmon, T.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Observation of random-phase lattice solitons," Nature 433, 500-503 (2005).
[CrossRef] [PubMed]

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
[CrossRef]

Christodoulides, D. N.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-4 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30,2466-2468 (2005).
[CrossRef] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Observation of random-phase lattice solitons," Nature 433, 500-503 (2005).
[CrossRef] [PubMed]

J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Vector discrete nonlinear surface waves," Opt. Express 13,7720-7725 (2005).
[CrossRef] [PubMed]

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, "Observation of discrete gap solitons in binary waveguide arrays," Opt. Lett. 29,2890-2892 (2004).
[CrossRef]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91,113901-4 (2003).
[CrossRef] [PubMed]

Cohen, O.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Observation of random-phase lattice solitons," Nature 433, 500-503 (2005).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91,113901-4 (2003).
[CrossRef] [PubMed]

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Observation of mutually trapped multiband optical breathers in waveguide arrays," Phys. Rev. Lett. 90,253902-4 (2003).
[CrossRef] [PubMed]

Fleischer, J. W.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Observation of random-phase lattice solitons," Nature 433, 500-503 (2005).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91,113901-4 (2003).
[CrossRef] [PubMed]

Hache, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-4 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30,2466-2468 (2005).
[CrossRef] [PubMed]

Hanna, B.

Hong, C. S.

Hudock, J.

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-4 (2006).
[CrossRef] [PubMed]

Kivshar, Yu. S.

Krolikowski, W.

Makris, K. G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-4 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30,2466-2468 (2005).
[CrossRef] [PubMed]

Mandelik, D.

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, "Observation of discrete gap solitons in binary waveguide arrays," Opt. Lett. 29,2890-2892 (2004).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Observation of mutually trapped multiband optical breathers in waveguide arrays," Phys. Rev. Lett. 90,253902-4 (2003).
[CrossRef] [PubMed]

Molina, M. I.

Morandotti, R.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-4 (2006).
[CrossRef] [PubMed]

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, "Observation of discrete gap solitons in binary waveguide arrays," Opt. Lett. 29,2890-2892 (2004).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Observation of mutually trapped multiband optical breathers in waveguide arrays," Phys. Rev. Lett. 90,253902-4 (2003).
[CrossRef] [PubMed]

Neshev, D. N.

Pelinovsky, D. E.

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, "Bifurcations and stability of gap solitons in periodic potentials," Phys. Rev. E 70,036618(2004).
[CrossRef]

Rosberg, C. R.

Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-4 (2006).
[CrossRef] [PubMed]

Schwartz, T.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91,113901-4 (2003).
[CrossRef] [PubMed]

Segev, M.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Observation of random-phase lattice solitons," Nature 433, 500-503 (2005).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91,113901-4 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, "Observation of discrete gap solitons in binary waveguide arrays," Opt. Lett. 29,2890-2892 (2004).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Observation of mutually trapped multiband optical breathers in waveguide arrays," Phys. Rev. Lett. 90,253902-4 (2003).
[CrossRef] [PubMed]

Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-4 (2006).
[CrossRef] [PubMed]

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, "Observation of discrete gap solitons in binary waveguide arrays," Opt. Lett. 29,2890-2892 (2004).
[CrossRef]

Stegeman, G. I.

Sukhorukov, A. A.

Suntsov, S.

Takeno, S.

Yu. S. Kivshar, F. Zhang, and S. Takeno, "Multistable nonlinear surface modes," Physica D 119,125-133 (1998).
[CrossRef]

Tamm, I. E.

I. E. Tamm, "A possible kind of electron binding on crystal surfaces," Z. Phys. 76,849-850 (1932).
[CrossRef]

Tomlinson, W. J.

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-4 (2006).
[CrossRef] [PubMed]

Vicencio, R. A.

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-4 (2006).
[CrossRef] [PubMed]

Yang, H.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-4 (2006).
[CrossRef] [PubMed]

Yariv, A.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
[CrossRef]

P. Yeh, A. Yariv, and C. S. Hong, "Electromagnetic propagation in periodic stratified media. 1. General theory," J. Opt. Soc. Am. 67,423-438 (1977).
[CrossRef]

Yeh, P.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
[CrossRef]

P. Yeh, A. Yariv, and C. S. Hong, "Electromagnetic propagation in periodic stratified media. 1. General theory," J. Opt. Soc. Am. 67,423-438 (1977).
[CrossRef]

Zhang, F.

Yu. S. Kivshar, F. Zhang, and S. Takeno, "Multistable nonlinear surface modes," Physica D 119,125-133 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (1)

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Observation of random-phase lattice solitons," Nature 433, 500-503 (2005).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (6)

Phys. Rev. E (1)

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, "Bifurcations and stability of gap solitons in periodic potentials," Phys. Rev. E 70,036618(2004).
[CrossRef]

Phys. Rev. Lett. (5)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Observation of mutually trapped multiband optical breathers in waveguide arrays," Phys. Rev. Lett. 90,253902-4 (2003).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-4 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-4 (2006).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91,113901-4 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, "Multigap discrete vector solitons," Phys. Rev. Lett. 91, 113902-4 (2003).
[CrossRef] [PubMed]

Physica D (1)

Yu. S. Kivshar, F. Zhang, and S. Takeno, "Multistable nonlinear surface modes," Physica D 119,125-133 (1998).
[CrossRef]

Z. Phys. (1)

I. E. Tamm, "A possible kind of electron binding on crystal surfaces," Z. Phys. 76,849-850 (1932).
[CrossRef]

Other (5)

S. G. Davidson and M. Steslicka, Basic theory of surface states (Oxford Science Publications, New York, 1996).

A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, "Third-order nonlinear electromagnetic TE and TM guided waves," in Nonlinear Surface Electromagnetic Phenomena, Vol. 29 of Modern Problems in Condensed Matter Sciences, H. E. Ponath and G.I. Stegeman, eds., (North-Holland, Amsterdam, 1991), pp. 73-287.

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," in Progress in Optics, E. Wolf, ed., (North-Holland, Amsterdam, 1989), 27, pp. 229-313.

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

C. R. Rosberg, D. N. Neshev, W. Krolikowski, Yu. S. Kivshar, A. Mitchell, R. A. Vicencio, and M. I. Molina, "Observation of surface gap solitons in semi-infinite waveguide arrays," arXiv physics/0603202 (2006).

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Figures (5)

Fig. 1.
Fig. 1.

(a,b) Two types of a semi-infinite binary array truncated at wide or narrow waveguides. (c) Dispersion diagram of the binary array with the bands shaded and gaps marked. Detuning between the A and B-type waveguides is ρ=0.6.

Fig. 2.
Fig. 2.

(a) Families of the discrete surface solitons in the BR and TIR gaps, and (b,c) propagation constants of the localized linear modes from the other gaps guided by these solitons, in the binary array truncated at the narrow waveguide. Dashed curves in (a–c) mark unstable soliton branches. (d,e) Examples of two types of the discrete surface solitons (solid) and their guided linear modes localized in the other gaps (dashed), corresponding to the marked points “d” and “e” in (a–c). Detuning parameter of the binary array is ρ=0.6.

Fig. 3.
Fig. 3.

Same as in Fig. 2, but for the binary array truncated at the wide waveguide.

Fig. 4.
Fig. 4.

Examples of surface multi-gap vector solitons for different structure terminations; solid and dashed curves show the profiles of the soliton components from the TIR and BR gaps, respectively. For the termination on the narrow site (a), BR component propagation constant is β=-0.1 and its power is P=0.9. TIR component has β=2.6 and P=1.6. For the termination on the wide site (b), BR component propagation constant and power are β=0 and P=1.6, respectively, while TIR component has β=3.0 and P=4.6.

Fig. 5.
Fig. 5.

Density plots for the total intensity demonstrating (a,b) nonlinear dynamics of individual beams incident on the first or second waveguide with input powers P=1.3 and P=2.3, respectively; and (c) generation of a multi-gap state through the combined excitation of the first and second waveguides with the same two mutually incoherent beams. The array is truncated at a narrow waveguide.

Equations (1)

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i d a n d z + ρ a n + b n 1 + b n + ∣∣ a n ∣∣ 2 a n = 0 , i d b n d z ρ b n + a n + a n + 1 + ∣∣ b n ∣∣ 2 b n = 0 ,

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