Abstract

We report on the existence of nonlinear surface waves that, on the one hand, do not require the threshold energy flow for their excitation, and, on the other hand, extend into media at both sides of the interface at low powers, i.e., cannot be reduced to the conventional Tamm states. Such waves can be excited if the refractive index in at least one of the materials forming the interface is periodically modulated, with properly selected modulation depth and frequency. Thresholdless surface solitons can be stable in the entire existence domain.

© 2010 Optical Society of America

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    [CrossRef]
  2. P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
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  15. A. I. Anselm, Introduction to Semiconductor Theory(Prentice Hall, 1982).

2009 (3)

2008 (2)

2007 (1)

2006 (4)

E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, 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]

2005 (1)

1982 (1)

A. I. Anselm, Introduction to Semiconductor Theory(Prentice Hall, 1982).

1980 (1)

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]

Aimez, V.

Anselm, A. I.

A. I. Anselm, Introduction to Semiconductor Theory(Prentice Hall, 1982).

Arés, R.

Chen, Z.

Cho, A. Y.

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

Christodoulides, D. N.

Dong, L.

X. Yang, L. Dong, and G. Yin, Appl. Phys. B 95, 179 (2009).
[CrossRef]

Dreisow, F.

Garnett, B.

Hache, A.

Haché, A.

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

Heinrich, M.

Hromada, I.

Kartashov, Y. V.

Kip, D.

Kivshar, Y. S.

Y. S. Kivshar, Laser Phys. Lett. 5, 703 (2008).
[CrossRef]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Krolikowski, W.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Lederer, F.

Makris, K. G.

Malkova, N.

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Molina, M. I.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Morandotti, R.

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Nolte, S.

Pertsch, T.

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Rüter, C. E.

Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volatier, V. Aimez, R. Arés, E. H. Yang, and G. Salamo, Opt. Express 16, 10480 (2008).
[CrossRef] [PubMed]

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

Shandarov, V.

Smirnov, E.

Sorel, M.

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

Stegeman, G. I.

Stepic, M.

Suntsov, S.

Szameit, A.

Tamm, I. E.

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

Tomlinson, W. J.

Torner, L.

Tünnermann, A.

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Volatier, M.

Vysloukh, V. A.

Wang, X.

Yang, E. H.

Yang, H.

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

Yang, X.

X. Yang, L. Dong, and G. Yin, Appl. Phys. B 95, 179 (2009).
[CrossRef]

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]

Yin, G.

X. Yang, L. Dong, and G. Yin, Appl. Phys. B 95, 179 (2009).
[CrossRef]

Appl. Phys. B (1)

X. Yang, L. Dong, and G. Yin, Appl. Phys. B 95, 179 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

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

Laser Phys. Lett. (1)

Y. S. Kivshar, Laser Phys. Lett. 5, 703 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. Lett. (3)

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, 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]

Z. Phys. (1)

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

Other (1)

A. I. Anselm, Introduction to Semiconductor Theory(Prentice Hall, 1982).

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of interfaces (a) between homogeneous and periodic media and (b) between two different periodic media. Shadowed areas show a linear spectrum (allowed bands). The bold parts of axis b indicate the intervals of surface soliton existence. The bold horizontal line shows the edge of the linear spectrum, from which the thresholdless solitons bifurcate. The dashed lines show examples of the location of the propagation constants of such solitons. The values of b indicated in (a) and (b) correspond to the specific examples shown in Figs. 2, 4.

Fig. 2
Fig. 2

(a) Energy flow versus propagation constant for the interface between periodic R r = 3 and homogeneous R l , 0 = 0.9368 media for the focusing ( σ = 1 ) nonlinearity. Shaded area corresponds to the first allowed band of the lattice spectrum; (b) and (c) shapes of the surface solitons at corresponding points of panel (a) for b = 1.0 and b = 1.7132 , respectively. The zone structure for the situation is schematically depicted in Fig. 1a.

Fig. 3
Fig. 3

(a) Energy flow versus propagation constant for the interface between periodic R r = 3 and homogeneous R l , 0 = 2.166 media for the focusing nonlinearity. The left and right shaded areas correspond to the first and second allowed bands; (b) and (c) shapes of surface solitons at the corresponding points of panel (a) for b = 2.0 and b = 0 , respectively.

Fig. 4
Fig. 4

(a) Energy flow versus propagation constant for the interface between periodic media with parameters R r = 3 , R l , 0 = 0.815 , and R l , 1 = 1 for the focusing media. Shaded area corresponds to the first band of the spectrum; (b) and (c) shapes of surface solitons at corresponding points of panel (a) for b = 0.9734 and b = 1.7183 , respectively. The zone structure for this situation is schematically depicted in Fig. 1b.

Equations (1)

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i q ξ = q η η + R ( η ) q + σ | q | 2 q .

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