Abstract

We analyze discrete surface modes in semi-infinite binary waveguide arrays, which can support simultaneously two types of discrete solitons. We demonstrate that the analysis of linear surface states in such arrays provides important information about the existence of nonlinear surface modes and their properties. We find numerically the families of both discrete surface solitons and nonlinear Tamm (gap) states and study their stability properties.

© 2006 Optical Society of America

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  1. Yu. S. Kivshar, F. Zhang, and S. Takeno, Physica D 119, 125 (1998).
    [CrossRef]
  2. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
    [CrossRef] [PubMed]
  3. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
    [CrossRef] [PubMed]
  4. M. I. Molina, R. A. Vicencio, and Yu. S. Kivshar, Opt. Lett. 31, 1693 (2006).
    [CrossRef] [PubMed]
  5. I. E. Tamm, Z. Phys. 76, 849 (1932).
    [CrossRef]
  6. P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
    [CrossRef]
  7. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  8. 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).
  9. A. A. Sukhorukov and Yu. S. Kivshar, Opt. Lett. 27, 2112 (2002).
    [CrossRef]
  10. A. A. Sukhorukov and Yu. S. Kivshar, Opt. Lett. 28, 2345 (2003).
    [CrossRef] [PubMed]
  11. R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Lett. 29, 2890 (2004).
    [CrossRef]
  12. D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
    [CrossRef]

2006 (3)

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Yu. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (2)

2003 (1)

2002 (1)

1998 (1)

Yu. S. Kivshar, F. Zhang, and S. Takeno, Physica D 119, 125 (1998).
[CrossRef]

1978 (1)

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

1932 (1)

I. E. Tamm, Z. Phys. 76, 849 (1932).
[CrossRef]

Aitchison, J. S.

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Christodoulides, D. N.

Hache, A.

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

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

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Kivshar, Yu. S.

M. I. Molina, R. A. Vicencio, and Yu. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Lett. 29, 2890 (2004).
[CrossRef]

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

A. A. Sukhorukov and Yu. S. Kivshar, Opt. Lett. 28, 2345 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, Opt. Lett. 27, 2112 (2002).
[CrossRef]

Yu. S. Kivshar, F. Zhang, and S. Takeno, Physica D 119, 125 (1998).
[CrossRef]

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).

Krolikowski, W.

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).

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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

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

Mandelik, D.

Mitchell, A.

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).

Molina, M. I.

M. I. Molina, R. A. Vicencio, and Yu. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

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).

Morandotti, R.

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

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Lett. 29, 2890 (2004).
[CrossRef]

Neshev, D. N.

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).

Pelinovsky, D. E.

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

Rosberg, C. R.

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).

Salamo, G.

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

Silberberg, Y.

Sorel, M.

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

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Lett. 29, 2890 (2004).
[CrossRef]

Stegeman, G. I.

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

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

Sukhorukov, A. A.

Suntsov, S.

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

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

Takeno, S.

Yu. S. Kivshar, F. Zhang, and S. Takeno, Physica D 119, 125 (1998).
[CrossRef]

Tamm, I. E.

I. E. Tamm, Z. Phys. 76, 849 (1932).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Vicencio, R. A.

M. I. Molina, R. A. Vicencio, and Yu. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

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).

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Yariv, A.

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Yeh, P.

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Zhang, F.

Yu. S. Kivshar, F. Zhang, and S. Takeno, Physica D 119, 125 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. E (1)

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Physica D (1)

Yu. S. Kivshar, F. Zhang, and S. Takeno, Physica D 119, 125 (1998).
[CrossRef]

Z. Phys. (1)

I. E. Tamm, Z. Phys. 76, 849 (1932).
[CrossRef]

Other (1)

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 (4)

Fig. 1
Fig. 1

(a), (b) Spectra of the linear surface modes in a binary array of alternating thick (A) and thin (B) optical waveguides with a surface defect (C) for two configurations of a semi-infinite structure shown schematically at the top. The shaded areas mark two bands of an infinite binary array ( ρ = 0.6 ) . The points labeled a–d correspond to the examples shown in Figs. 2a, 2b, 2c, 2d.

Fig. 2
Fig. 2

Examples of the linear surface modes in the binary waveguide array shown in Fig. 1a. The mode profiles in (a), (b), (c), and (d) are associated with different gaps of the linear spectrum and correspond to the points a, b, c, and d marked in Fig. 1a.

Fig. 3
Fig. 3

(a) Families of nonlinear Tamm (gap) states and discrete surface solitons in the binary array truncated at the narrow waveguide. The solid and dashed curves correspond to the stable and unstable branches, respectively. A schematic of the array is shown at the top. (b), (c) Characteristic examples of the soliton profiles corresponding to points b and c in (a). The detuning parameter of the array is ρ = 0.6 .

Fig. 4
Fig. 4

Same as in Fig. 3, but for the binary array truncated at the wide waveguide.

Equations (1)

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i d E n d z + ρ n E n + ( E n 1 + E n + 1 ) + γ n E n 2 E n = 0 ,

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