Abstract

We analyze stability and generation of discrete gap solitons in weakly coupled optical waveguides. We demonstrate how both stable and unstable solitons can be observed experimentally in the engineered binary waveguide arrays and also reveal a connection between the gap-soliton instabilities and limitations on the mutual beam focusing in periodic photonic structures.

© 2003 Optical Society of America

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References

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  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).
  2. A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
    [CrossRef]
  3. A. A. Sukhorukov and Yu. S. Kivshar, Opt. Lett. 27, 2112 (2002).
    [CrossRef]
  4. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
    [CrossRef]
  5. See, e.g., U. Peschel and F. Lederer, J. Opt. Soc. Am. B 19, 544 (2002).
    [CrossRef]
  6. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  7. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  8. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
    [CrossRef]
  9. I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
    [CrossRef]
  10. J. Feng, Opt. Lett. 18, 1302 (1993).
    [CrossRef]

2003 (1)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

2002 (2)

2001 (1)

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef]

1999 (1)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

1998 (2)

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
[CrossRef]

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

1993 (1)

1988 (1)

Agrawal, G. P.

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

Aitchison, J. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

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

Barashenkov, I. V.

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
[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.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

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

Feng, J.

Joseph, R. I.

Kivshar, Yu. S.

A. A. Sukhorukov and Yu. S. Kivshar, Opt. Lett. 27, 2112 (2002).
[CrossRef]

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef]

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

Lederer, F.

Mandelik, D.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

Morandotti, R.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

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

Pelinovsky, D. E.

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
[CrossRef]

Peschel, U.

See, e.g., U. Peschel and F. Lederer, J. Opt. Soc. Am. B 19, 544 (2002).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

Silberberg, Y.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

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

Sukhorukov, A. A.

A. A. Sukhorukov and Yu. S. Kivshar, Opt. Lett. 27, 2112 (2002).
[CrossRef]

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef]

Zemlyanaya, E. V.

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. Lett. (5)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef]

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).
[CrossRef]

Other (1)

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

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Figures (3)

Fig. 1
Fig. 1

Top, soliton power versus propagation constant for A-type (dashed gray curve) and B-type (black curve) discrete gap solitons. Solid curve, stable; dashed curve, unstable; dotted curve, oscillatory unstable. Bottom, examples of the soliton profiles of (a) A and (b) B symmetries at β=-1; filled circles and squares mark the field amplitudes at the narrow and wide waveguides, respectively.

Fig. 2
Fig. 2

Example of (a) external and (b) internal resonances between an eigenmode of the linear eigenvalue problem and the bandgap edges of the continuous spectrum that lead to an oscillatory instability of the B-type symmetry gap solitons.

Fig. 3
Fig. 3

Excitation of discrete gap solitons by two interfering Gaussian beams in the model [Eq. (1)]: (a) self-focusing and soliton formation, (b) self-defocusing when the interference maxima are located at narrow and wide waveguides, (c) soliton instability at high powers, and (d) soliton steering as a result of power imbalance. Parameters are d1=4 µm, d2=2.5 µm, ds=5 µm, refractive index n0=3.4, effective modulation Δn0=0.0014, vacuum wavelength 1.5 µm. The inset shows the geometry. The characteristic peak intensities are (a), (b), (d) 0.5 GW/cm2 and (c) 2 GW/cm2 in AlGaAs samples with the nonlinear coefficient n2=2×10-13 cm2/W.

Equations (4)

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iεz+2εx2+νxε+ε2ε=0,
idEndz+λnEn+En-1+En+1+γnEn2En=0.
Δ>4/maxβ,-ρ<β<0Reκβ=4/cosh-11+ρ2/8.
En=un+vn exp-iΓz+wn* expiΓ*zexpiβz

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