Abstract

We report on the phenomenon of trapping and switching of one-dimensional spatial solitons in Kerr-type nonlinear media with transverse periodic modulation of the refractive index. The solitons slowly radiate upon propagation along the periodic structure and are finally trapped in one of its guiding channels. The position of the output channel can be varied by small changes in the launching angle.

© 2004 Optical Society of America

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

2003 (7)

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]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (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]

2002 (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

2001 (2)

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

D. N. Christodoulides and E. D. Eugenieva, Opt. Lett. 26, 1876 (2001).
[CrossRef]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1996 (2)

1994 (3)

1992 (1)

R. Scharf and A. R. Bishop, Phys. Rev. E 47, 1375 (1992).
[CrossRef]

1988 (1)

Aceves, A. B.

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Bang, O.

Bishop, A. R.

R. Scharf and A. R. Bishop, Phys. Rev. E 47, 1375 (1992).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Christodoulides, D. N.

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

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (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]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

D. N. Christodoulides and E. D. Eugenieva, Opt. Lett. 26, 1876 (2001).
[CrossRef]

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

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

Cohen, O.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Cronin-Golomb, M.

De Angelis, C.

Efremidis, N. K.

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]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Eugenieva, E. D.

D. N. Christodoulides and E. D. Eugenieva, Opt. Lett. 26, 1876 (2001).
[CrossRef]

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

Fleischer, J. W.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

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

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Joseph, R. I.

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]

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

Krolikowski, W.

Lederer, F.

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]

Miller, P. D.

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Muschall, R.

Neshev, D.

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, U.

Savage, C. M.

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

Scharf, R.

R. Scharf and A. R. Bishop, Phys. Rev. E 47, 1375 (1992).
[CrossRef]

Schmidt-Hattenberger, C.

Schmidt-Hattenberger, S.

Schwartz, T.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Segev, M.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

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

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Silberberg, Y.

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Trillo, S.

Trutschel, U.

Wabnitz, S.

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

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. Lett. (8)

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 (2)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

R. Scharf and A. R. Bishop, Phys. Rev. E 47, 1375 (1992).
[CrossRef]

Phys. Rev. Lett. (3)

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Different regimes of soliton propagation in the medium with harmonic modulation of the linear refractive index: (a) Undistorted propagation at T=π/4, p=1, α=0.05. (b) Oscillations within the central channel at T=4π, p=0.25, α=0.7. (c) Fast switching to the fifth channel at T=π/2, p=1, α=0.8. (d) Radiative decay at T=π, p=0.25, α=1.13.

Fig. 2
Fig. 2

(a) Critical angle and (b) amplitude of a stationary guided wave versus period of the refractive-index modulation at p=0.25 for various values of form factor χ. (c) Dependence of the number of the output channel on the incident angle at T=π/2 for different guiding parameters. (d) Dependence of the number of the output channel on the period of the refractive-index modulation at p=0.5 for different incident angles.

Fig. 3
Fig. 3

(a) Dependence of the number of the output channel on the guiding parameter at T=π/2 and α=0.5. (b) and (c) Modification of spatial soliton mobility for p=0.25 and p=0.7, respectively.

Equations (3)

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

iqξ=-122qη2-qq2-pRηq.
d2dξ2η=pU-q2dRdηdη,d2dξ2η-η2=2U-qη2+pq2dRdηη-η-12q4dη+2U2-qηq*dη2
d2dξ2η=-2πpTπ2/Tχsinhπ2/Tχsin2πηT,d2dξ2η-η2=23χ2-q02-2pπ2/Tχsinhπ2/Tχ×π2/Tχtanhπ2/Tχ-1cos2πηT.

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