Abstract

A method for transforming fast solitons into slow ones in bandgap fibers is proposed. The approach is based on the deceleration of the solitons by intrapulse Raman scattering, which can be achieved for fiber modes having a cutoff frequency. We develop a comprehensive theory for the soliton slowdown and elucidate how the fiber losses introduce a fundamental minimum for the soliton velocity.

© 2006 Optical Society of America

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  1. M. D. Lukin and A. Imamoglu, Nature 413, 273 (2001).
    [CrossRef] [PubMed]
  2. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
    [CrossRef] [PubMed]
  3. J. Sharping, Y. Okawachi, and A. Gaeta, Opt. Express 13, 6092 (2005).
    [CrossRef] [PubMed]
  4. R.E.Slusher and B.J.Eggleton, eds.,Nonlinear Photonic Crystals (Springer, 2003).
  5. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
    [CrossRef] [PubMed]
  6. Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
    [CrossRef] [PubMed]
  7. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
    [CrossRef] [PubMed]
  8. M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Jaonnopoulos, Phys. Rev. Lett. 92, 063903 (2004).
    [CrossRef] [PubMed]
  9. M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. D. Joannopoulos, Opt. Lett. 30, 552 (2005).
    [CrossRef] [PubMed]
  10. E. Lidorikis, M. Soljacic, M. Ibanescu, Y. Fink, and J. D. Joannopoulos, Opt. Lett. 29, 851 (2004).
    [CrossRef] [PubMed]
  11. A. V. Rybin, I. P. Vadeiko, and A. R. Bishop, Phys. Rev. E 72, 026613 (2005).
    [CrossRef]
  12. H. G. Winful and V. Perlin, Phys. Rev. Lett. 84, 3586 (2000).
    [CrossRef] [PubMed]
  13. J. Sharping, Y. Okawachi, J. van Howe, C. Xu, Y. Wang, A. Willner, and A. Gaeta, Opt. Express 13, 7872 (2005).
    [CrossRef] [PubMed]
  14. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

2005

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

A. V. Rybin, I. P. Vadeiko, and A. R. Bishop, Phys. Rev. E 72, 026613 (2005).
[CrossRef]

M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. D. Joannopoulos, Opt. Lett. 30, 552 (2005).
[CrossRef] [PubMed]

J. Sharping, Y. Okawachi, and A. Gaeta, Opt. Express 13, 6092 (2005).
[CrossRef] [PubMed]

J. Sharping, Y. Okawachi, J. van Howe, C. Xu, Y. Wang, A. Willner, and A. Gaeta, Opt. Express 13, 7872 (2005).
[CrossRef] [PubMed]

2004

E. Lidorikis, M. Soljacic, M. Ibanescu, Y. Fink, and J. D. Joannopoulos, Opt. Lett. 29, 851 (2004).
[CrossRef] [PubMed]

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Jaonnopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef] [PubMed]

2001

M. D. Lukin and A. Imamoglu, Nature 413, 273 (2001).
[CrossRef] [PubMed]

2000

H. G. Winful and V. Perlin, Phys. Rev. Lett. 84, 3586 (2000).
[CrossRef] [PubMed]

1996

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Bishop, A. R.

A. V. Rybin, I. P. Vadeiko, and A. R. Bishop, Phys. Rev. E 72, 026613 (2005).
[CrossRef]

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Boyd, R. W.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

de Sterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Engelen, R. J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Fink, Y.

Gaeta, A.

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Gauthier, D. J.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Hamann, H. F.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Ibanescu, M.

Imamoglu, A.

M. D. Lukin and A. Imamoglu, Nature 413, 273 (2001).
[CrossRef] [PubMed]

Jaonnopoulos, J. D.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Jaonnopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef] [PubMed]

Joannopoulos, J. D.

Johnson, S. G.

M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. D. Joannopoulos, Opt. Lett. 30, 552 (2005).
[CrossRef] [PubMed]

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Jaonnopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef] [PubMed]

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Krauss, T. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Kuipers, L.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Lidorikis, E.

Lukin, M. D.

M. D. Lukin and A. Imamoglu, Nature 413, 273 (2001).
[CrossRef] [PubMed]

Luo, C.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Jaonnopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef] [PubMed]

McNab, S. J.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

O'Boyle, M.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Okawachi, Y.

Perlin, V.

H. G. Winful and V. Perlin, Phys. Rev. Lett. 84, 3586 (2000).
[CrossRef] [PubMed]

Roundy, D.

M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. D. Joannopoulos, Opt. Lett. 30, 552 (2005).
[CrossRef] [PubMed]

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Jaonnopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef] [PubMed]

Rybin, A. V.

A. V. Rybin, I. P. Vadeiko, and A. R. Bishop, Phys. Rev. E 72, 026613 (2005).
[CrossRef]

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Sharping, J.

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Soljacic, M.

Vadeiko, I. P.

A. V. Rybin, I. P. Vadeiko, and A. R. Bishop, Phys. Rev. E 72, 026613 (2005).
[CrossRef]

van Howe, J.

van Hulst, N. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Vlasov, Y. A.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Wang, Y.

Willner, A.

Winful, H. G.

H. G. Winful and V. Perlin, Phys. Rev. Lett. 84, 3586 (2000).
[CrossRef] [PubMed]

Xu, C.

Zhu, Z. M.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Nature

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

M. D. Lukin and A. Imamoglu, Nature 413, 273 (2001).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. E

A. V. Rybin, I. P. Vadeiko, and A. R. Bishop, Phys. Rev. E 72, 026613 (2005).
[CrossRef]

Phys. Rev. Lett.

H. G. Winful and V. Perlin, Phys. Rev. Lett. 84, 3586 (2000).
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Jaonnopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef] [PubMed]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Other

R.E.Slusher and B.J.Eggleton, eds.,Nonlinear Photonic Crystals (Springer, 2003).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

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Figures (2)

Fig. 1
Fig. 1

(a) Numerically computed spatial spectra of the soliton as a function of t. (b) Numerically (dashed curves) and analytically (circles) computed soliton velocity as a function of time for three different energies. The parameters of the system are Γ = 0 , γ = 0.77 , α 2 = 1 2 , and μ = 0.1 . Dimensionless energy W = 0.1 corresponds to 2 nJ and to input pulse duration 0.5 ps . v s = 1 corresponds to the velocity 0.15 c and t = 10 6 to time 1.2 × 10 8 s .

Fig. 2
Fig. 2

(a) Soliton velocity v s versus time for different values of loss parameter Γ for W 0 = 0.17 . The other parameters are the same as for Fig. 1. v s = 1 corresponds to physical velocity 0.15 c and t = 10 6 to time 1.2 × 10 8 s . (b) Soliton velocity v s versus the soliton coordinate x s . x s = 10 5 corresponds to the distance 6 cm . The solid and dashed curves in (a) and (b) are obtained from numerical modeling of Eqs. (3, 4), and the points are calculated from Eq. (11). The agreement between the two is perfect.

Equations (12)

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

i τ E = ( α ̃ 2 ξ 2 + α ̃ 4 ξ 4 + ) E κ [ ( 1 μ ) E 2 + Q ̃ ] E i γ a E .
2 Q ̃ τ 2 + γ R Q ̃ τ + ω R 2 Q ̃ = μ E 2 .
i t A = ( α 2 x 2 + α 4 x 4 + ) A ( 1 μ ) A 2 A Q A i Γ A ,
2 Q t 2 + γ Q t + Q = μ A 2 ,
Q = μ A 2 + γ μ t A 2 + .
A = F [ U ( v s t x ) d s ] e i k s x i ( δ s U 2 2 ) t , F ( η ) = U sech ( η ) .
W = A 2 d x , M = i 2 ( A x A * A * x A ) d x .
t W = 2 Γ W ,
t M = Q ( A x A * + A * x A ) d x .
t k s = μ γ 30 W 4 v s d s 3 .
v s = v s 0 exp [ ρ 8 Γ ( 1 e 8 Γ t ) ] , ρ = μ γ 30 W 0 4 .
x max = v s 0 ρ

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