Abstract

We study light localization at a phase-slip defect created by two semi-infinite mismatched identical arrays of coupled optical waveguides. We demonstrate that the nonlinear defect modes possess the specific properties of both nonlinear surface modes and discrete solitons. We analyze the stability of the localized modes and their generation in both linear and nonlinear regimes.

© 2008 Optical Society of America

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References

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2007 (1)

2006 (4)

2005 (2)

2003 (4)

2001 (1)

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

1998 (1)

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

1996 (2)

W. Krolikowski and Y. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

1993 (1)

Yu. S. Kivshar, Phys. Rev. B 47, 11167 (1993).
[CrossRef]

Aceves, A. B.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003), p. 540.

Aimez, V.

Aitchison, J. S.

Apalkov, V. M.

V. M. Apalkov and M. E. Raikh, Phys. Rev. Lett. 90, 253901 (2003).
[CrossRef] [PubMed]

Arès, R.

Bräuer, A.

Chen, Z.

Christodoulides, D. N.

Darmanyan, S.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

De Angelis, C.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Eisenberg, H. S.

Fedele, F.

Haché, A.

Hudock, J.

Kip, D.

Kivshar, Y. S.

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

W. Krolikowski and Y. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
[CrossRef]

Kivshar, Yu. S.

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

Yu. S. Kivshar, Phys. Rev. B 47, 11167 (1993).
[CrossRef]

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003), p. 540.

Kobyakov, A.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Krolikowski, W.

Kunishi, W.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef] [PubMed]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, Opt. Express 11, 3404 (2003).
[CrossRef] [PubMed]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Makris, K. G.

Mandelik, D.

Manela, O.

Michaelis, D.

Miyai, E.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef] [PubMed]

Modotto, D.

Molina, M.

Morandotti, R.

Muschall, R.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Noda, S.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef] [PubMed]

Ohnishi, D.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef] [PubMed]

Okano, T.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef] [PubMed]

Pertsch, T.

Peschel, T.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Peschel, U.

Raikh, M. E.

V. M. Apalkov and M. E. Raikh, Phys. Rev. Lett. 90, 253901 (2003).
[CrossRef] [PubMed]

Rüter, C. E.

Sakai, K.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef] [PubMed]

Schmidt, E.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Segev, M.

Silberberg, Y.

Sorel, M.

Stanley, C. R.

Stegeman, G. I.

Streppel, U.

Sukhorukov, A. A.

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

Suntsov, S.

Trillo, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Trompeter, H.

Vicencio, R.

Volatier, M.

Wabnitz, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Wang, X.

Weinstein, D.

Yang, J.

Young, J.

J. Opt. Soc. Am. B (1)

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. B (1)

Yu. S. Kivshar, Phys. Rev. B 47, 11167 (1993).
[CrossRef]

Phys. Rev. E (2)

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

V. M. Apalkov and M. E. Raikh, Phys. Rev. Lett. 90, 253901 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

Other (1)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003), p. 540.

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Figures (6)

Fig. 1
Fig. 1

Transverse profile of the refractive index for an array of weakly coupled nonlinear optical waveguides with a phase-slip defect located between the waveguides at the sites m = 0 and m = 1 . Top, V > V ; bottom, V < V .

Fig. 2
Fig. 2

Linear (a) unstaggered and (b) staggered localized modes at the phase-slip defect for V V = 1.3 ( N = 100 , m = 50 ).

Fig. 3
Fig. 3

Power versus propagation constant for several families of nonlinear localized modes at the phase-slip defect for V V = 1.3 . Solid (dashed) curves denote stable (unstable) branches. Cases a–e are related to Fig. 4. Inset, minimum power to destabilize the fundamental mode versus coupling mismatch.

Fig. 4
Fig. 4

(a)–(e) Examples of the nonlinear localized modes marked by the letters a–e in Fig. 3.

Fig. 5
Fig. 5

Power versus propagation constant for several localized states at the phase-slip defect for V V = 0.7 . Solid (dashed) curves denote stable (unstable) branches.

Fig. 6
Fig. 6

One-waveguide excitation of the defect modes. Top, V V = 0.7 , i.e., for a weak bond defect for the input amplitude (a) E 0 = 1.0 and (b) E 0 = 2.0 . Bottom, same as top but for a stronger bond defect V V = 1.3 .

Equations (2)

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i d E n d z + V ( E n + 1 + E n 1 ) + m V n m E m + γ ǀ E n ǀ 2 E n = 0 ,
m V n m E m = ( V V ) [ δ n , m E m + 1 + δ n , m + 1 E m ] ,

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