Abstract

We report on the existence of multicolor solitons supported by periodic lattices made from quadratic nonlinear media. Such lattice solitons bridge the gap between continuous solitons in uniform media and discrete solitons in strongly localized systems and exhibit a wealth of new features. We discovered that, in contrast to uniform media, multipeaked lattice solitons are stable. Thus they open new opportunities for all-optical switching based on soliton packets.

© 2004 Optical Society of America

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  1. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  2. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  3. A. A. Sukhorukov, Y. S. Kivshar, O. Bang, and C. M. Soukoulis, Phys. Rev. E 63, 016615 (2000).
    [CrossRef]
  4. O. Bang, P. L. Christiansen, and C. B. Clausen, Phys. Rev. E 56, 7257 (1997).
    [CrossRef]
  5. T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. E 57, 1127 (1998).
    [CrossRef]
  6. A. Kobyakov, S. Darmanyan, T. Pertsch, and F. Lederer, J. Opt. Soc. Am. B 16, 1737 (1999).
    [CrossRef]
  7. B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, Phys. Rev. E 65, 056606 (2002).
    [CrossRef]
  8. T. Pertsch, U. Peschel, and F. Lederer, Opt. Lett. 28, 102 (2003).
    [CrossRef] [PubMed]
  9. R. Muschall, C. Schmidt-Hattenberger, and F. Lederer, Opt. Lett. 19, 323 (1994).
    [CrossRef] [PubMed]
  10. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
    [CrossRef]
  11. W. Krolikowski and Y. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
    [CrossRef]
  12. O. Bang and P. D. Miller, Opt. Lett. 21, 1105 (1996).
    [CrossRef] [PubMed]
  13. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef]
  14. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  15. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  16. P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
    [CrossRef]
  17. N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
    [CrossRef]
  18. Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
    [CrossRef] [PubMed]
  19. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 1102 (2004).
    [CrossRef] [PubMed]
  20. D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, Opt. Eng. 35, 1616 (1996).
    [CrossRef]

2004 (2)

2003 (7)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

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

T. Pertsch, U. Peschel, and F. Lederer, Opt. Lett. 28, 102 (2003).
[CrossRef] [PubMed]

2002 (1)

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, Phys. Rev. E 65, 056606 (2002).
[CrossRef]

2000 (1)

A. A. Sukhorukov, Y. S. Kivshar, O. Bang, and C. M. Soukoulis, Phys. Rev. E 63, 016615 (2000).
[CrossRef]

1999 (1)

1998 (1)

T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. E 57, 1127 (1998).
[CrossRef]

1997 (1)

O. Bang, P. L. Christiansen, and C. B. Clausen, Phys. Rev. E 56, 7257 (1997).
[CrossRef]

1996 (4)

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, Opt. Eng. 35, 1616 (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]

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

O. Bang and P. D. Miller, Opt. Lett. 21, 1105 (1996).
[CrossRef] [PubMed]

1994 (1)

1988 (1)

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]

Bang, O.

A. A. Sukhorukov, Y. S. Kivshar, O. Bang, and C. M. Soukoulis, Phys. Rev. E 63, 016615 (2000).
[CrossRef]

O. Bang, P. L. Christiansen, and C. B. Clausen, Phys. Rev. E 56, 7257 (1997).
[CrossRef]

O. Bang and P. D. Miller, Opt. Lett. 21, 1105 (1996).
[CrossRef] [PubMed]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

Christiansen, P. L.

O. Bang, P. L. Christiansen, and C. B. Clausen, Phys. Rev. E 56, 7257 (1997).
[CrossRef]

Christodoulides, D. N.

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

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
[CrossRef] [PubMed]

Clausen, C. B.

O. Bang, P. L. Christiansen, and C. B. Clausen, Phys. Rev. E 56, 7257 (1997).
[CrossRef]

Crasovan, L. C.

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Darmanyan, S.

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]

Efremidis, N. K.

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Frantzeskakis, D. J.

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Joseph, R. I.

Kartashov, Y. V.

Kevrekidis, P. G.

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

A. A. Sukhorukov, Y. S. Kivshar, O. Bang, and C. M. Soukoulis, Phys. Rev. E 63, 016615 (2000).
[CrossRef]

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

Kobyakov, A.

Krolikowski, W.

Lederer, F.

T. Pertsch, U. Peschel, and F. Lederer, Opt. Lett. 28, 102 (2003).
[CrossRef] [PubMed]

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

A. Kobyakov, S. Darmanyan, T. Pertsch, and F. Lederer, J. Opt. Soc. Am. B 16, 1737 (1999).
[CrossRef]

T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. E 57, 1127 (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]

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

R. Muschall, C. Schmidt-Hattenberger, and F. Lederer, Opt. Lett. 19, 323 (1994).
[CrossRef] [PubMed]

Louis, P. J. Y.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Malomed, B. A.

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Mazilu, D.

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Mihalache, D.

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Miller, P. D.

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]

R. Muschall, C. Schmidt-Hattenberger, and F. Lederer, Opt. Lett. 19, 323 (1994).
[CrossRef] [PubMed]

Neshev, D.

Nistazakis, H. E.

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Ostrovskaya, E.

Ostrovskaya, E. A.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Pertsch, T.

Peschel, T.

T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. E 57, 1127 (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]

Peschel, U.

T. Pertsch, U. Peschel, and F. Lederer, Opt. Lett. 28, 102 (2003).
[CrossRef] [PubMed]

T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. E 57, 1127 (1998).
[CrossRef]

Savage, C. M.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Schmidt-Hattenberger, C.

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

Silberberg, Y.

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

Soukoulis, C. M.

A. A. Sukhorukov, Y. S. Kivshar, O. Bang, and C. M. Soukoulis, Phys. Rev. E 63, 016615 (2000).
[CrossRef]

Sukhorukov, A. A.

A. A. Sukhorukov, Y. S. Kivshar, O. Bang, and C. M. Soukoulis, Phys. Rev. E 63, 016615 (2000).
[CrossRef]

Torner, L.

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]

Vysloukh, V. A.

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]

Yannacopoulos, A. N.

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Zelenina, A. S.

J. Opt. Soc. Am. B (2)

Nature (2)

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

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Eng. (1)

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. A (2)

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

Phys. Rev. E (5)

A. A. Sukhorukov, Y. S. Kivshar, O. Bang, and C. M. Soukoulis, Phys. Rev. E 63, 016615 (2000).
[CrossRef]

O. Bang, P. L. Christiansen, and C. B. Clausen, Phys. Rev. E 56, 7257 (1997).
[CrossRef]

T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. E 57, 1127 (1998).
[CrossRef]

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, Phys. Rev. E 65, 056606 (2002).
[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]

Phys. Rev. Lett. (1)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Energy flow versus propagation constant for even and odd lattice solitons. The vertical dashed line in (a) stands for cutoff. (b) Cutoff of the propagation constant for odd and even solitons as a function of guiding parameter at β=0. Inset, cutoff versus phase mismatch at p=2. Profiles of odd (c) and even (d) solitons correspond to points marked by circles in (a). (a), (c), (d) p=2 and β=0. (c), (d) In white regions Rη0; in gray regions Rη<0.

Fig. 2
Fig. 2

Energy flow versus propagation constant for first and second twisted lattice solitons. The vertical dashed line in (a) stands for cutoff. (b) Cutoff of the propagation constant for the first twisted soliton as a function of guiding parameter at β=0. Inset, cutoff versus phase mismatch at p=2. Profiles of first (c) and second (d) twisted solitons correspond to points marked by circles in (a). (a), (c), (d) p=2 and β=0.

Fig. 3
Fig. 3

(a) Areas of stability and instability (shaded) for an odd soliton on the b1,p plane at β=0. Inset, the same areas on the b1,β plane at p=2. (b) Perturbation growth rate for an odd soliton versus propagation constant at β=0 and p=2. Inset, growth rate for an even soliton for the same parameters. (c) Perturbation-induced decay of an even soliton with b1=0.85 at β=0 and p=2. (d) Stable propagation of an odd soliton with b1=0.85 at β=0 and p=2 perturbed with white noise with variance σ1,22=0.02. (c), (d) Only the SH wave is shown.

Fig. 4
Fig. 4

Areas of stability and instability (shaded) for the first twisted soliton on the b1,p plane at β=0. Inset, same areas on the b1,β plane at p=2. (b) Real part of the perturbation growth rate for the first twisted soliton versus propagation constant at β=0 and p=0.3. Stable propagation of (c) the first and (d) the second twisted solitons with b1=1.2 at β=0 and p=2 in the presence of white input noise with variance σ1,22=0.02. (c), (d) Only the SH wave is shown.

Equations (1)

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iq1ξ=d122q1η2-q1*q2 exp-iβξ-pRηq1,iq2ξ=d222q2η2-q12 expiβξ-2pRηq2.

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