Abstract

We demonstrate that the dark soliton trains in optical fibers with a zero of the group-velocity dispersion can generate broad spectral distribution (continuum) associated with the resonant dispersive radiation emitted by solitons. This radiation is either enhanced or suppressed by the Raman scattering depending on the sign of the third-order dispersion.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
    [CrossRef]
  2. J. C. Knight and D. V. Skryabin, Opt. Express 15, 15365 (2007).
    [CrossRef] [PubMed]
  3. L. Mollenauer and J. Gordon, Solitons in Optical Fibers: Fundamentals and Applications (Academic, 2006).
  4. D. V. Skryabin, F. Luan, J. C. Knight, and P. S. Russell, Science 301, 1705 (2003).
    [CrossRef] [PubMed]
  5. P. Falk, M. H. Frosz, O. Bang, L. Thrane, P. E. Andersen, A. O. Bjarklev, K. P. Hansen, and J. Broeng, Opt. Lett. 33, 621 (2008).
    [CrossRef] [PubMed]
  6. B. W. Liu, M. L. Hu, X. H. Fang, Y. F. Li, L. Chai, C. Y. Wang, W. J. Tong, J. Luo, A. A. Voronin, and A. M. Zheltikov, Opt. Express 16, 14987 (2008).
    [CrossRef] [PubMed]
  7. Z. Chen, A. Efimov, and A. J. Taylor, Opt. Express 17, 5852 (2009).
    [CrossRef] [PubMed]
  8. J. K. Ranka, R. S. Windeler, and A. J. Stentz, Opt. Lett. 25, 25 (2000).
    [CrossRef]
  9. A. V. Gorbach and D. V. Skryabin, Nat. Photonics 1, 653 (2007).
    [CrossRef]
  10. B. A. Cumberland, J. C. Travers, S. V. Popov, and J. R. Taylor, Opt. Lett. 33, 2122 (2008).
    [CrossRef] [PubMed]
  11. P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
    [CrossRef] [PubMed]
  12. V. I. Karpman, Phys. Lett. A 181, 211 (1993).
    [CrossRef]
  13. V. V. Afanasjev, Y. S. Kivshar, and C. R. Menyuk, Opt. Lett. 21, 1975 (1996).
    [CrossRef] [PubMed]
  14. J. E. Rothenberg, Opt. Commun. 82, 107 (1991).
    [CrossRef]
  15. J. E. Rothenberg and H. K. Heinrich, Opt. Lett. 17, 261 (1992).
    [CrossRef] [PubMed]
  16. Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
    [CrossRef]
  17. A. M. Weiner, R. N. Thurston, W. J. Tomlinson, J. P. Heritage, D. E. Leaird, E. M. Kirschner, and R. J. Hawkins, Opt. Lett. 14, 868 (1989).
    [CrossRef] [PubMed]

2009

2008

2007

J. C. Knight and D. V. Skryabin, Opt. Express 15, 15365 (2007).
[CrossRef] [PubMed]

A. V. Gorbach and D. V. Skryabin, Nat. Photonics 1, 653 (2007).
[CrossRef]

2006

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

2003

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

2000

1998

Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

1996

1993

V. I. Karpman, Phys. Lett. A 181, 211 (1993).
[CrossRef]

1992

1991

J. E. Rothenberg, Opt. Commun. 82, 107 (1991).
[CrossRef]

1990

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

1989

Afanasjev, V. V.

Andersen, P. E.

Bang, O.

Bjarklev, A. O.

Broeng, J.

Chai, L.

Chen, H. H.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Chen, Z.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Cumberland, B. A.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Efimov, A.

Falk, P.

Fang, X. H.

Frosz, M. H.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, Nat. Photonics 1, 653 (2007).
[CrossRef]

Gordon, J.

L. Mollenauer and J. Gordon, Solitons in Optical Fibers: Fundamentals and Applications (Academic, 2006).

Hansen, K. P.

Hawkins, R. J.

Heinrich, H. K.

Heritage, J. P.

Hu, M. L.

Karpman, V. I.

V. I. Karpman, Phys. Lett. A 181, 211 (1993).
[CrossRef]

Kirschner, E. M.

Kivshar, Y. S.

Knight, J. C.

J. C. Knight and D. V. Skryabin, Opt. Express 15, 15365 (2007).
[CrossRef] [PubMed]

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Leaird, D. E.

Lee, Y. C.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Li, Y. F.

Liu, B. W.

Luan, F.

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Luo, J.

Luther-Davies, B.

Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

Menyuk, C. R.

Mollenauer, L.

L. Mollenauer and J. Gordon, Solitons in Optical Fibers: Fundamentals and Applications (Academic, 2006).

Popov, S. V.

Ranka, J. K.

Rothenberg, J. E.

Russell, P. S.

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Skryabin, D. V.

J. C. Knight and D. V. Skryabin, Opt. Express 15, 15365 (2007).
[CrossRef] [PubMed]

A. V. Gorbach and D. V. Skryabin, Nat. Photonics 1, 653 (2007).
[CrossRef]

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Stentz, A. J.

Taylor, A. J.

Taylor, J. R.

Thrane, L.

Thurston, R. N.

Tomlinson, W. J.

Tong, W. J.

Travers, J. C.

Voronin, A. A.

Wai, P. K. A.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Wang, C. Y.

Weiner, A. M.

Windeler, R. S.

Zheltikov, A. M.

Nat. Photonics

A. V. Gorbach and D. V. Skryabin, Nat. Photonics 1, 653 (2007).
[CrossRef]

Opt. Commun.

J. E. Rothenberg, Opt. Commun. 82, 107 (1991).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

V. I. Karpman, Phys. Lett. A 181, 211 (1993).
[CrossRef]

Phys. Rep.

Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

Phys. Rev. A

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Rev. Mod. Phys.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Science

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Other

L. Mollenauer and J. Gordon, Solitons in Optical Fibers: Fundamentals and Applications (Academic, 2006).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

XFROG spectrograms showing resonant radiation by a dark soliton without the Raman effect ( θ = 0 ) . Dashed vertical lines indicate ± δ r predicted by Eq. (4). Full vertical lines indicate the zero GVD frequency δ 0 . (a) ϵ = 0.0833 and (b) ϵ = 0.0833 . Other parameters are κ = 1 , ϕ = 0 , z = 30 .

Fig. 2
Fig. 2

The same as Fig. 1, but with the Raman effect ( θ = 0.18 ) . Strong emission of radiation by the black soliton [see (a)] is accompanied by creation of a shallow dark soliton with ϕ close to π / 2 (marked with an arrow).

Fig. 3
Fig. 3

(a) Time domain evolution of the dark soliton train in a fiber with positive TOD: ϵ = 0.0217 , θ = 0.18 . Initial condition is A = 10 [ sech ( t 3 ) + sech ( t + 3 ) ] . (b) is the same as (a), but for negative TOD: ϵ = 0.0217 .

Fig. 4
Fig. 4

Spectral development of continuum generation by a train of dark solitons corresponding to the time domain evolution in Fig. 3, but for larger z. Full vertical lines indicate the zero GVD frequency.

Fig. 5
Fig. 5

Solid curves in (a) and (b) show spectra corresponding to the z = 10 time domain signals in Fig. 3. Dashed curves show the corresponding spectra computed without the Raman effect ( θ = 0 ) .

Equations (6)

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

i z A = 1 2 t 2 A + i ϵ t 3 A ( 1 θ ) | A | 2 A θ A R ( t ) | A ( t t ) | 2 d t .
F = κ   tanh [ τ κ   cos   ϕ ] cos   ϕ i κ   sin   ϕ .
g = G 1 e i δ r τ i λ z i ϕ + G 2 e i δ r τ + i λ z + i ϕ .
δ r 2 = 1 2 ϵ 2 [ α + α 2 + 4 κ 2 ϵ 2 cos 2 ϕ ] ,     α 2 ϵ κ   sin   ϕ + 1 4 .
G 1 G 2 = 1 ϵ 2 κ 2 [ 1 + 4 κ ϵ   sin   ϕ + O ( ϵ 2 ) 1 + 7 sin 2 ϕ ] .
S ( δ 2 cos 2 ϕ + 2 δ   sin   ϕ   cos   ϕ + sin 2 ϕ ) sech 2 [ π δ / 2 ] .

Metrics