Abstract

The Akhmediev breather formalism of modulation instability is extended to describe the spectral dynamics of induced multiple sideband generation from a modulated continuous wave field. Exact theoretical results describing the frequency domain evolution are compared with experiments performed using single mode fiber around 1550nm. The spectral theory is shown to reproduce the depletion dynamics of an injected modulated continuous wave pump and to describe the Fermi–Pasta–Ulam recurrence and recovery towards the initial state. Realistic simulations including higher-order dispersion, loss, and Raman scattering are used to identify that the primary physical factors that preclude perfect recurrence are related to imperfect initial conditions.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
    [Crossref]
  2. V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).
  3. G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 87, 033902 (2001).
    [Crossref] [PubMed]
  4. G. Cappellini and S. Trillo, J. Opt. Soc. Am. B 8, 824 (1991).
    [Crossref]
  5. S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
    [Crossref] [PubMed]
  6. N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
    [Crossref]
  7. B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. 6, 790 (2010).
    [Crossref]
  8. K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
    [Crossref] [PubMed]
  9. J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
    [Crossref] [PubMed]
  10. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
    [Crossref]
  11. D. L. Hart, A. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
    [Crossref]
  12. J. Beeckman, X. Hutsebaut, M. Haelterman, and K. Neyts, Opt. Express 15, 11185 (2007).
    [Crossref] [PubMed]
  13. M. P. Tulin and T. Waseda, J. Fluid Mech. 378, 197 (1999).
    [Crossref]
  14. N. Karjanto and E. van Groesen, J. Hydro-Environ. Res. 3, 186 (2010).
    [Crossref]
  15. M. M. Scott, B. A. Kalinikos, and C. E. Patton, J. Appl. Phys. 94, 5877 (2003).
    [Crossref]

2011 (2)

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[Crossref]

2010 (2)

N. Karjanto and E. van Groesen, J. Hydro-Environ. Res. 3, 186 (2010).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. 6, 790 (2010).
[Crossref]

2009 (1)

2007 (1)

2003 (1)

M. M. Scott, B. A. Kalinikos, and C. E. Patton, J. Appl. Phys. 94, 5877 (2003).
[Crossref]

2001 (1)

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 87, 033902 (2001).
[Crossref] [PubMed]

1999 (1)

M. P. Tulin and T. Waseda, J. Fluid Mech. 378, 197 (1999).
[Crossref]

1998 (1)

D. L. Hart, A. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[Crossref]

1994 (1)

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[Crossref] [PubMed]

1991 (1)

1986 (1)

N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[Crossref]

1967 (1)

T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[Crossref]

1966 (1)

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Akhmediev, N.

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. 6, 790 (2010).
[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[Crossref] [PubMed]

N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[Crossref]

Ankiewicz, A.

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[Crossref]

Beeckman, J.

Beletic, J. W.

D. L. Hart, A. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[Crossref]

Benjamin, T. B.

T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[Crossref]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Cappellini, G.

Dias, F.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. 6, 790 (2010).
[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[Crossref] [PubMed]

Dudley, J. M.

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. 6, 790 (2010).
[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[Crossref] [PubMed]

Emplit, P.

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 87, 033902 (2001).
[Crossref] [PubMed]

Fatome, J.

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. 6, 790 (2010).
[Crossref]

Feir, J. E.

T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[Crossref]

Finot, C.

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. 6, 790 (2010).
[Crossref]

Genty, G.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. 6, 790 (2010).
[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[Crossref] [PubMed]

Haelterman, M.

Hammani, K.

Hart, D. L.

D. L. Hart, A. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[Crossref]

Hutsebaut, X.

Judy, A.

D. L. Hart, A. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[Crossref]

Kalinikos, B. A.

M. M. Scott, B. A. Kalinikos, and C. E. Patton, J. Appl. Phys. 94, 5877 (2003).
[Crossref]

Karjanto, N.

N. Karjanto and E. van Groesen, J. Hydro-Environ. Res. 3, 186 (2010).
[Crossref]

Kennedy, T. A. B.

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[Crossref] [PubMed]

Kibler, B.

Korneev, V. I.

N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[Crossref]

Millot, G.

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. 6, 790 (2010).
[Crossref]

Morin, P.

Neyts, K.

Patton, C. E.

M. M. Scott, B. A. Kalinikos, and C. E. Patton, J. Appl. Phys. 94, 5877 (2003).
[Crossref]

Roy, R.

D. L. Hart, A. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[Crossref]

Scott, M. M.

M. M. Scott, B. A. Kalinikos, and C. E. Patton, J. Appl. Phys. 94, 5877 (2003).
[Crossref]

Soto-Crespo, J. M.

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[Crossref]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Trillo, S.

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[Crossref] [PubMed]

G. Cappellini and S. Trillo, J. Opt. Soc. Am. B 8, 824 (1991).
[Crossref]

Tulin, M. P.

M. P. Tulin and T. Waseda, J. Fluid Mech. 378, 197 (1999).
[Crossref]

van Groesen, E.

N. Karjanto and E. van Groesen, J. Hydro-Environ. Res. 3, 186 (2010).
[Crossref]

Van Simaeys, G.

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 87, 033902 (2001).
[Crossref] [PubMed]

Wabnitz, S.

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[Crossref] [PubMed]

Waseda, T.

M. P. Tulin and T. Waseda, J. Fluid Mech. 378, 197 (1999).
[Crossref]

J. Appl. Phys. (1)

M. M. Scott, B. A. Kalinikos, and C. E. Patton, J. Appl. Phys. 94, 5877 (2003).
[Crossref]

J. Fluid Mech. (2)

M. P. Tulin and T. Waseda, J. Fluid Mech. 378, 197 (1999).
[Crossref]

T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[Crossref]

J. Hydro-Environ. Res. (1)

N. Karjanto and E. van Groesen, J. Hydro-Environ. Res. 3, 186 (2010).
[Crossref]

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

JETP Lett. (1)

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Nature Phys. (1)

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. 6, 790 (2010).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Lett. A (1)

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[Crossref]

Phys. Rev. A (1)

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[Crossref] [PubMed]

Phys. Rev. E (1)

D. L. Hart, A. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[Crossref]

Phys. Rev. Lett. (1)

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 87, 033902 (2001).
[Crossref] [PubMed]

Theor. Math. Phys. (1)

N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[Crossref]

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 (3)

Fig. 1
Fig. 1

(a) Experimental setup. Diagnostics recorded power and spectra. (b) Solid curve, measured spectrum at maximum sideband generation; circles and crosses, simulation and analytic results.

Fig. 2
Fig. 2

Dynamics of multiple sideband generation. (a) Experimental results. (b) Results from numerical simulation using realistic NLSE model. The generation of multiple sidebands around 5 km and recovery back towards the initial state with further propagation is clearly seen.

Fig. 3
Fig. 3

Spectral dynamics for the pump and sideband orders as shown. Experiment (circles) is compared with simulation (blue dashed curve), the exact AB result Eq. (1) (black curve), and the truncated TW model (red dot-dashed curve).

Equations (2)

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

A 0 ( ξ ) = 1 i b sinh b ξ + p 2 cosh b ξ cosh 2 b ξ 2 a ,
A n ( ξ ) = i b sinh b ξ + p 2 cosh b ξ cosh 2 b ξ 2 a [ cosh b ξ cosh 2 b ξ 2 a 2 a ] | n | .

Metrics