Abstract

We discuss potential applications of multicolor solitons supported by periodic lattices imprinted in quadratic nonlinear media. Such lattice solitons can be packed together with appropriate relative phases to form stable soliton trains that can be treated as bit sequences. We describe controllable splitting of the trains into their soliton constituents and the angle- and power-controlled steering and trapping of solitons moving across the lattice into the desired guiding channel.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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]
  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]
  9. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
    [CrossRef]
  10. W. Krolikowski and Y. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
    [CrossRef]
  11. O. Bang and P. D. Miller, Opt. Lett. 21, 1105 (1996).
    [CrossRef] [PubMed]
  12. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef]
  13. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  14. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  15. N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
    [CrossRef]
  16. Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
    [CrossRef]
  17. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 1102 (2004).
    [CrossRef]
  18. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 1117 (2004).
    [CrossRef] [PubMed]
  19. D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, Opt. Eng. 35, 1616 (1996).
    [CrossRef] [PubMed]

2004 (3)

2003 (6)

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

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

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

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]

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)

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] [PubMed]

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]

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]

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

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

Cohen, O.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

Crasovan, L. C.

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

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.

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

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

Fleischer, J. W.

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

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

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]

Hudock, J.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[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.

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.

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

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

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]

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

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

Mihalache, D.

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

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]

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.

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]

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

Segev, M.

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, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

Silberberg, Y.

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

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]

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] [PubMed]

Opt. Lett. (7)

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. (2)

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Energy flow versus propagation constant for an odd lattice soliton. (b) Profile of an odd soliton corresponding to the point marked by a circle in (a). (c) Energy flow versus propagation constant for twisted solitons of lowest orders. (d) Profile of the second twisted soliton, corresponding to the point marked by a circle in (c). (a), (c) Dashed curves, unstable branches; solid curves, stable branches. (b), (d) Shaded regions, Rη0; unshaded regions, Rη>0. p=2, β=0, T=π/2.

Fig. 2
Fig. 2

(a) Excitation of the second twisted lattice soliton and (b) real and imaginary parts of the FF wave field at ξ=512. At ξ=0, FF wave amplitude A1=8. (c) Change of propagation direction of the odd soliton with U=6 on entrance to a tilted lattice with αtilt=1. Dashed line, border between straight and tilted lattices. (d) Efficiency of energy transmission for odd solitons versus lattice tilt angle. In (a) and (c), only the SH wave is shown. β=0, p=2, T=π/2.

Fig. 3
Fig. 3

Decay of (a) the first and (b) the second twisted solitons at the boundary between a uniform medium and a medium with periodic modulation of the refractive index. Horizontal dashed lines, boundaries between two media. Energy flow, U=50; guiding parameter, p=2. Only the FF wave is shown. Escape angles for solitons that appear on decay of 1, the first and 2, the second twisted solitons (c) versus energy flow at p=2 and (d) versus the guiding parameter at U=100. β=0, T=π/2.

Fig. 4
Fig. 4

(a) Periodic oscillations of an odd soliton with U=10 within a central waveguide at p=2, α=1, T=4π. (b) Fast switching of an odd soliton with U=10 into a fourth lattice channel at p=0.25, α=0.62, T=π/2. In (a) and (b), only the SH wave is shown. (c) Dependence of the number of output channels on incident angle for different energy flows at p=0.5, T=π/2. (d) Dependence of the output channel number on energy flow for different guiding parameters at α=0.8, T=π/2. Phase mismatch, β=0.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

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

Metrics