Abstract

We report families of discrete optical solitons in frequency space, or spectral-discrete solitons existing in a dispersive Raman medium, where individual sidebands are coupled by coherence. The associated time-domain patterns correspond either to trains of ultrashort pulses or to weakly modulated waves. We describe the physics behind the spectral localization and study soliton bifurcations, stability, and dynamics.

© 2006 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 (2004); and references therein.
    [CrossRef]
  2. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003); and references therein.
  3. A. V. Sokolov and S. E. Harris, J. Opt. B: Quantum Semiclassical Opt. 5, 1 (2003); and references therein.
    [CrossRef]
  4. S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
    [CrossRef]
  5. D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
    [CrossRef] [PubMed]
  6. S. Flach, M. V. Ivanchenko, and O. I. Kanakov, Phys. Rev. Lett. 95, 064102 (2005).
    [CrossRef] [PubMed]
  7. S. Longhi, Opt. Lett. 30, 786 (2005).
    [CrossRef] [PubMed]

2005 (2)

S. Flach, M. V. Ivanchenko, and O. I. Kanakov, Phys. Rev. Lett. 95, 064102 (2005).
[CrossRef] [PubMed]

S. Longhi, Opt. Lett. 30, 786 (2005).
[CrossRef] [PubMed]

2004 (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2004); and references therein.
[CrossRef]

2003 (1)

A. V. Sokolov and S. E. Harris, J. Opt. B: Quantum Semiclassical Opt. 5, 1 (2003); and references therein.
[CrossRef]

2000 (1)

D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
[CrossRef] [PubMed]

1997 (1)

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003); and references therein.

Christodoulides, D. N.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2004); and references therein.
[CrossRef]

Flach, S.

S. Flach, M. V. Ivanchenko, and O. I. Kanakov, Phys. Rev. Lett. 95, 064102 (2005).
[CrossRef] [PubMed]

Harris, S. E.

A. V. Sokolov and S. E. Harris, J. Opt. B: Quantum Semiclassical Opt. 5, 1 (2003); and references therein.
[CrossRef]

D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
[CrossRef] [PubMed]

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

Ivanchenko, M. V.

S. Flach, M. V. Ivanchenko, and O. I. Kanakov, Phys. Rev. Lett. 95, 064102 (2005).
[CrossRef] [PubMed]

Kanakov, O. I.

S. Flach, M. V. Ivanchenko, and O. I. Kanakov, Phys. Rev. Lett. 95, 064102 (2005).
[CrossRef] [PubMed]

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003); and references therein.

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2004); and references therein.
[CrossRef]

Longhi, S.

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2004); and references therein.
[CrossRef]

Sokolov, A. V.

A. V. Sokolov and S. E. Harris, J. Opt. B: Quantum Semiclassical Opt. 5, 1 (2003); and references therein.
[CrossRef]

D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
[CrossRef] [PubMed]

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

Yavuz, D. D.

D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
[CrossRef] [PubMed]

J. Opt. B: Quantum Semiclassical Opt. (1)

A. V. Sokolov and S. E. Harris, J. Opt. B: Quantum Semiclassical Opt. 5, 1 (2003); and references therein.
[CrossRef]

Nature (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2004); and references therein.
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
[CrossRef] [PubMed]

S. Flach, M. V. Ivanchenko, and O. I. Kanakov, Phys. Rev. Lett. 95, 064102 (2005).
[CrossRef] [PubMed]

Other (1)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003); and references therein.

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Figures (4)

Fig. 1
Fig. 1

Single-peak (ground state) and two-peak SDSs calculated for j = 1 . κ varies from 0.004 to 0.93 in (a) and from 0.009 to 0.79 in (b), which gives q from 0.005 to 0.5. p 2 = 0.01 , μ = 1 , α = 0 , p k > 2 = 0 .

Fig. 2
Fig. 2

Solid curves show (a) power of the first five SDSs versus q and (b) versus κ for j = 1 . Dashed curves in (b) show j = + 1 SDSs. The other parameters as in Fig. 1. Black or gray curves mark stable or unstable solutions.

Fig. 3
Fig. 3

Propagation of the unstable two-peak SDS (a) with noise added and (b) with its power increased by a regular correction. κ = 0.005 and q 0.013 . The other parameters are as in Fig. 1.

Fig. 4
Fig. 4

(a) Example of SDS for j = + 1 . κ = 0.01 , q 0.00035 (black curves and circles), κ = 0.02 , q 0.016 (gray curves and squares). (b) Examples of transformation of a single peak j = 1 SDS for nonzero p 3 = 0.005 (dashed curve, open circles) and nonzero α = 0.008 (solid gray curve, gray squares). The solid black curve and filled circles mark the p 3 = α = 0 case. κ = 0.004 for all solutions. The other parameters are as for Fig. 1.

Equations (7)

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i z E n = β n E n + q * E n 1 + q E n + 1 .
β n = k = 0 K p k n k ,
H ̂ = 1 2 ( j μ S S * j μ ) , S = n E n E n + 1 * .
q = j S 2 μ 2 + S 2 ,
i z E = β ( ω ) E + j q 2 E ω 2 + 2 j q E ,
q = P 2 μ 2 + P 2 , P = E ( z , ω ) 2 d ω .
E n ( z ) = B n exp ( i κ z + i α n z )

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