Abstract

We demonstrate that spatiotemporal discrete solitons are possible in nonlinear photonic crystal structures. Analysis indicates that these states can propagate undistorted along a series of coupled resonators or defects by balancing of the effects of discrete lattice dispersion with material nonlinearity. In principle, these self-localized entities are capable of exhibiting very low velocities, depending on the coupling coefficient among successive microcavities. This class of solitons can follow any preassigned path in a three-dimensional environment.

© 2002 Optical Society of America

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  1. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  3. N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
    [CrossRef]
  4. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
    [CrossRef]
  5. M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. Lett. 84, 2140 (2000).
    [CrossRef] [PubMed]
  6. M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. B 61, R11855 (2000).
    [CrossRef]
  7. M. Bayindir and E. Ozbay, Phys. Rev. B 62, R2247 (2000).
    [CrossRef]
  8. S. Mookherjea and A. Yariv, Opt. Express 9, 91 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  9. Y. Xu, R. K. Lee, and A. Yariv, J. Opt. Soc. Am. B 17, 387 (2000).
    [CrossRef]
  10. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef]
  11. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
    [CrossRef]
  12. A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. Maagt, IEEE Trans. Microwave Theory Tech. 49, 1860 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef] [PubMed]
  16. Y. S. Kivshar, Opt. Lett. 14, 1147 (1993).
    [CrossRef]
  17. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef] [PubMed]
  18. D. N. Christodoulides and E. D. Eugenieva, Opt. Lett. 26, 1876 (2001).
    [CrossRef]
  19. D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
    [CrossRef]

2001 (6)

S. Mookherjea and A. Yariv, Opt. Express 9, 91 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. Maagt, IEEE Trans. Microwave Theory Tech. 49, 1860 (2001).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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]

2000 (5)

Y. Xu, R. K. Lee, and A. Yariv, J. Opt. Soc. Am. B 17, 387 (2000).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. Lett. 84, 2140 (2000).
[CrossRef] [PubMed]

M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. B 61, R11855 (2000).
[CrossRef]

M. Bayindir and E. Ozbay, Phys. Rev. B 62, R2247 (2000).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (2)

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

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

1996 (1)

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

1993 (1)

Y. S. Kivshar, Opt. Lett. 14, 1147 (1993).
[CrossRef]

1988 (1)

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

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

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. Lett. 84, 2140 (2000).
[CrossRef] [PubMed]

M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. B 61, R11855 (2000).
[CrossRef]

M. Bayindir and E. Ozbay, Phys. Rev. B 62, R2247 (2000).
[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.

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

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, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

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

Fan, S.

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

Joannopoulos, J. D.

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Joseph, R. I.

Kivshar, Y. S.

Y. S. Kivshar, Opt. Lett. 14, 1147 (1993).
[CrossRef]

Krauss, T. F.

A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. Maagt, IEEE Trans. Microwave Theory Tech. 49, 1860 (2001).
[CrossRef]

Lederer, F.

A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. Maagt, IEEE Trans. Microwave Theory Tech. 49, 1860 (2001).
[CrossRef]

Lee, R. K.

Maagt, P.

A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. Maagt, IEEE Trans. Microwave Theory Tech. 49, 1860 (2001).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Modinos, A.

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

Mookherjea, S.

Morandotti, R.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

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

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Ozbay, E.

M. Bayindir and E. Ozbay, Phys. Rev. B 62, R2247 (2000).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. Lett. 84, 2140 (2000).
[CrossRef] [PubMed]

M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. B 61, R11855 (2000).
[CrossRef]

Peschel, U.

A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. Maagt, IEEE Trans. Microwave Theory Tech. 49, 1860 (2001).
[CrossRef]

Reynolds, A. L.

A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. Maagt, IEEE Trans. Microwave Theory Tech. 49, 1860 (2001).
[CrossRef]

Roberts, P. J.

A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. Maagt, IEEE Trans. Microwave Theory Tech. 49, 1860 (2001).
[CrossRef]

Scherer, A.

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Silberberg, Y.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

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

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

Stefanou, N.

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. B 61, R11855 (2000).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. Lett. 84, 2140 (2000).
[CrossRef] [PubMed]

Villeneuve, P. R.

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Xu, Y.

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Yariv, A.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. Maagt, IEEE Trans. Microwave Theory Tech. 49, 1860 (2001).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. B (4)

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. B 61, R11855 (2000).
[CrossRef]

M. Bayindir and E. Ozbay, Phys. Rev. B 62, R2247 (2000).
[CrossRef]

Phys. Rev. Lett. (7)

M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. Lett. 84, 2140 (2000).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

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

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

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

Other (1)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

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Figures (3)

Fig. 1
Fig. 1

Array of microcavities or defects embedded in a photonic crystal structure. The distance between elements is D.

Fig. 2
Fig. 2

Temporal discrete soliton propagating along a nonlinear chain of coupled resonators at a group speed νe.

Fig. 3
Fig. 3

Three-dimensional pathway of coupled resonators.

Equations (8)

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

ds·E0*×H0+E0×H0*= dviω0-E0·E0*-E0*·E0t-μ0H0*·H0t.
idandt+cmnam+γan2an=0,
cmn=ω0dv-E0n*·E0mdvμ0H0n2+E0n2
γ=2n0n20ω0dvE0n4dvμ0H0n2+E0n2.
idandt+Δωan+can+1+an-1+γan2an=0.
iΦt+νeΦx+cD2 cosq2Φx2+γΦ2Φ=0,
Φ=Φ0 sechx-νetx0expiμt.
ΔΩc=-2κc1+κc cosq1-κ/c2.

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