Abstract

We suggest a novel approach to soliton control and routing based on Bloch-wave filtering in periodic photonic structures. Taking a binary waveguide array as an example, we demonstrate that spatial solitons that belong to different spectral gaps can be selectively reflected from or transmitted through an engineered defect, which acts as a low- or high-pass filter for Bloch waves.

© 2005 Optical Society of America

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References

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  2. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).
  3. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  4. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  5. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef]
  6. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  7. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
    [CrossRef]
  8. D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
    [CrossRef]
  9. R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
    [CrossRef] [PubMed]
  10. R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Lett. 29, 2890 (2004).
    [CrossRef]
  11. J. E. Sipe and H. G. Winful, Opt. Lett. 13, 132 (1988).
    [CrossRef]
  12. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

2004 (3)

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef]

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Lett. 29, 2890 (2004).
[CrossRef]

2003 (4)

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]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

1998 (1)

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

1988 (2)

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Aitchison, J. S.

Boyd, A. R.

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

Carmon, T.

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

Christodoulides, D.

Christodoulides, D. N.

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]

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

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

Efremidis, N. K.

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]

Eisenberg, H. S.

Fleischer, J. W.

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]

Hanna, B.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef]

Joseph, R. I.

Kivshar, Yu. S.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef]

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Lett. 29, 2890 (2004).
[CrossRef]

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Krolikowski, W.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef]

Lederer, F.

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

Mandelik, D.

Modotto, D.

Morandotti, R.

Neshev, D.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[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]

Silberberg, Y.

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. Christodoulides, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Lett. 29, 2890 (2004).
[CrossRef]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

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]

Sipe, J. E.

Sorel, M.

Stanley, C. R.

Sukhorukov, A. A.

Winful, H. G.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Nature (2)

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

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

Opt. Lett. (4)

Phys. Rev. Lett. (4)

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef]

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

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

Other (2)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

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Figures (3)

Fig. 1
Fig. 1

(a) Refractive-index profile in a binary waveguide array; (b) Bloch wave number versus the propagation constant (bands are shaded); (c), (d) profiles of gap and discrete solitons associated with bands 2 and 1, respectively. The parameters are d n = 2.5 μ m , d w = 4 μ m , d s = 5 μ m .

Fig. 2
Fig. 2

(a) Refractive-index profile of a waveguide array with a defect created by increasing the size of a single narrow waveguide; (b) Bloch-wave reflection coefficients for different defect widths: d m = 11 μ m (dashed), 11.5 μ m (solid), and 12 μ m (dotted).

Fig. 3
Fig. 3

Numerical simulations of (a) band-1 and (b) band-2 soliton interactions with an engineered defect corresponding to the solid curve in Fig. 2(b). Left, density plots of intensity evolution along the waveguide arrays; the dashed line marks the defect location. Right, intensity profiles of solitons before and after interaction with the defect; the shading marks regions of higher refractive index. The input profiles correspond to exact stationary solitons with an additional phase tilt 25% of the Bragg angle.

Equations (4)

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i E z + D 2 E x 2 + ν ( x ) E + F ( x , E 2 ) E = 0 ,
i A z + i V κ , n A x + D κ , n 2 A x 2 + γ κ , n A 2 A = 0 .
E = a i E κ , n ( x , z ) + a r E κ , n ( x , z ) , x < x d ,
E = a t E κ , n ( x , z ) , x > x d + ,

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