Abstract

We introduce a novel type of surface waves that form at the edge of guiding structures consisting of several concentric rings. Such surface waves rotate steadily upon propagation and, in contrast with nonrotating waves, for high rotation frequencies they do not exhibit power thresholds for their existence. There exists an upper limit for the surface wave rotation frequency, which depends on the radius of the outer guiding ring and on its depth.

© 2007 Optical Society of America

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  1. K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, Opt. Lett. 30, 2466 (2005).
    [Crossref] [PubMed]
  2. 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]
  3. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [Crossref] [PubMed]
  4. M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
    [Crossref] [PubMed]
  5. 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]
  6. E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
    [Crossref] [PubMed]
  7. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
    [Crossref] [PubMed]
  8. A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
    [Crossref]
  9. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
    [Crossref] [PubMed]
  10. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
    [Crossref] [PubMed]
  11. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 6, 444 (2004).
    [Crossref]
  12. Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
    [Crossref] [PubMed]
  13. E. Lidorikis, M. Soljacic, M. Ibanescu, Y. Fink, and J. D. Joannopoulos, Opt. Lett. 29, 851 (2004).
    [Crossref] [PubMed]
  14. Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
    [Crossref]
  15. B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
    [Crossref]
  16. X. S. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
    [Crossref] [PubMed]
  17. J. R. Salgueiro and Y. S. Kivshar, Opt. Express 15, 12916 (2007).
    [Crossref] [PubMed]

2007 (3)

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[Crossref] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[Crossref]

J. R. Salgueiro and Y. S. Kivshar, Opt. Express 15, 12916 (2007).
[Crossref] [PubMed]

2006 (7)

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
[Crossref]

X. S. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (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]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (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]

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

2005 (4)

2004 (3)

E. Lidorikis, M. Soljacic, M. Ibanescu, Y. Fink, and J. D. Joannopoulos, Opt. Lett. 29, 851 (2004).
[Crossref] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 6, 444 (2004).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[Crossref] [PubMed]

Baizakov, B. B.

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
[Crossref]

Bezryadina, A.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[Crossref] [PubMed]

Carretero-Gonzalez, R.

Chen, Z.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[Crossref] [PubMed]

X. S. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[Crossref] [PubMed]

Christodoulides, D. N.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[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]

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

Dreisow, F.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[Crossref]

Egorov, A. A.

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 6, 444 (2004).
[Crossref]

Fink, Y.

Frantzeskakis, D. J.

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
[Crossref]

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]

Hoq, Q. E.

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
[Crossref]

Ibanescu, M.

Joannopoulos, J. D.

Kartashov, Y. V.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[Crossref]

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 6, 444 (2004).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[Crossref] [PubMed]

Kevrekidis, P. G.

X. S. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[Crossref] [PubMed]

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
[Crossref]

Kip, D.

Kivshar, Y. S.

J. R. Salgueiro and Y. S. Kivshar, Opt. Express 15, 12916 (2007).
[Crossref] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (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]

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]

Lidorikis, E.

Makris, K. G.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[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]

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

Malomed, B. A.

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
[Crossref]

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
[Crossref]

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
[Crossref] [PubMed]

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]

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

Morandotti, R.

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]

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.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[Crossref]

Pertsch, T.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[Crossref]

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, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[Crossref] [PubMed]

Salerno, M.

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
[Crossref]

Salgueiro, J. R.

Shandarov, V.

Smirnov, E.

Soljacic, M.

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.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[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]

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

Stepic, M.

Suntsov, S.

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]

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

Szameit, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[Crossref]

Torner, L.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[Crossref]

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[Crossref] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 6, 444 (2004).
[Crossref]

Tünnermann, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[Crossref]

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]

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

Vysloukh, V. A.

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 6, 444 (2004).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[Crossref] [PubMed]

Wang, X.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[Crossref] [PubMed]

Wang, X. S.

X. S. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[Crossref] [PubMed]

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]

J. Opt. B: Quantum Semiclassical Opt. (1)

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 6, 444 (2004).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

Phys. Lett. A (1)

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
[Crossref]

Phys. Rev. E (1)

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
[Crossref]

Phys. Rev. Lett. (8)

X. S. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[Crossref] [PubMed]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[Crossref] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[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]

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Figures (4)

Fig. 1
Fig. 1

(a) Ring guiding structure corresponding to n = 5 . Field modulus distributions for surface solitons at (b) b = 6.45 , α = 0 , (c) b = 7 , α = 0.1 , (d) b = 6.45 , α = 0.1 , (e) b = 9.3 , α = 0.4 , and (f) b = 7 , α = 0.4 . (c) In all plots p = 10 and Ω = 2 . White circles indicate the center of the outer ring of guiding structure. In (b)–(e) n = 5 , while in (f) n = 3 .

Fig. 2
Fig. 2

(a) Energy flow versus propagation constant for α = 0 (curve 1), 0.1 (curve 2), and 0.15 (curve 3). Points marked by circles correspond to soliton profiles shown in Figs. 1b, 1c, 1d. (b) Energy flow versus rotation frequency for different propagation constants. In all cases p = 10 , Ω = 2 , and n = 5 .

Fig. 3
Fig. 3

(a) Propagation constant cutoff versus rotation frequency at n = 5 . (b) Maximal rotation frequency versus propagation constant at n = 5 . (c) Maximal rotation frequency versus number of rings in guiding structure at b = 9 . In all cases p = 10 and Ω = 2 .

Fig. 4
Fig. 4

Snapshot images showing stable rotation of surface solitons at (a) α = 0.1 , n = 5 (b) α = 0.29 , n = 5 , (c) α = 0.1 , n = 3 , and (d) α = 0.51 , n = 3 . In all cases input solitons correspond to b = 8 , p = 10 , and Ω = 2 . The right outermost image in each plot shows input field modulus distribution in the presence of white noise with variance σ noise 2 = 0.01 , while two other images superimposed onto input distribution are taken at proper distances exceeding ξ = 500 . White circles indicate the center of the outer ring of guiding structure.

Equations (1)

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i q ξ = 1 2 Δ q q 2 q p R ( η , ζ ) q ,

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