Abstract

We propose an interpretation of the pronounced “M” spectral shape that is a recurrent feature in all-normal-dispersion mode-locked fiber laser dynamics. Our interpretation involves shock wave formation regularized by dissipation, modeled by a modified Burgers equation. The large fringes appearing at the edges of the spectrum result from discontinuities in the spectral phase.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Chong, J. Buckley, W. Renninger, and F. Wise, Opt. Express 14, 10095 (2006).
    [CrossRef]
  2. A. Chong, W. H. Renninger, and F. W. Wise, J. Opt. Soc. Am. B 25, 140 (2008).
    [CrossRef]
  3. K. Kieu, W. H. Renninger, A. Chong, and F. W. Wise, Opt. Lett. 34, 593 (2009).
    [CrossRef]
  4. B. Oktem, C. lgüdür, and F. Ö. Ilday, Nat. Photonics 4, 307 (2010).
    [CrossRef]
  5. Ph. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
    [CrossRef]
  6. C. Lecaplain, M. Baumgartl, T. Schreiber, and A. Hideur, Opt. Express 19, 26742 (2011).
    [CrossRef]
  7. C. Lecaplain, B. Ortac, G. Machinet, J. Boullet, M. Baumgartl, T. Schreiber, E. Cormier, and A. Hideur, Opt. Lett. 35, 3156 (2010).
    [CrossRef]
  8. M. Baumgartl, C. Lecaplain, A. Hideur, J. Limpert, and A. Tunnermann, Opt. Lett. 37, 1640 (2012).
    [CrossRef]
  9. N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
    [CrossRef]
  10. G. B. Whitman, Linear and Nonlinear Waves (Wiley, 1974).
  11. S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Phys. Rev. A 87, 053811 (2013).
    [CrossRef]
  12. R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
    [CrossRef]
  13. M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
    [CrossRef]
  14. W. Wan, S. Jia, and J. Fleischer, Nat. Phys. 3, 46 (2007).
    [CrossRef]
  15. J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
    [CrossRef]
  16. V. Folli and C. Conti, New J. Phys. 15, 085026 (2013).
    [CrossRef]
  17. Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
    [CrossRef]
  18. I. S. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002).
    [CrossRef]
  19. S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Opt. Express 20, 27369 (2012).
    [CrossRef]

2013

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Phys. Rev. A 87, 053811 (2013).
[CrossRef]

V. Folli and C. Conti, New J. Phys. 15, 085026 (2013).
[CrossRef]

2012

2011

2010

2009

2008

A. Chong, W. H. Renninger, and F. W. Wise, J. Opt. Soc. Am. B 25, 140 (2008).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
[CrossRef]

2007

W. Wan, S. Jia, and J. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

2006

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

A. Chong, J. Buckley, W. Renninger, and F. Wise, Opt. Express 14, 10095 (2006).
[CrossRef]

2002

I. S. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002).
[CrossRef]

1989

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

1976

Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
[CrossRef]

1970

R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
[CrossRef]

Ablowitz, M. J.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Akhmediev, N.

Ph. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
[CrossRef]

Aranson, I. S.

I. S. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002).
[CrossRef]

Baker, D. R.

R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
[CrossRef]

Baumgartl, M.

Boullet, J.

Buckley, J.

Chong, A.

Coddington, I.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Conti, C.

V. Folli and C. Conti, New J. Phys. 15, 085026 (2013).
[CrossRef]

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Phys. Rev. A 87, 053811 (2013).
[CrossRef]

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Opt. Express 20, 27369 (2012).
[CrossRef]

Cormier, E.

Cornell, E. A.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

DelRe, E.

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Phys. Rev. A 87, 053811 (2013).
[CrossRef]

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Opt. Express 20, 27369 (2012).
[CrossRef]

Engels, P.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Fleischer, J.

W. Wan, S. Jia, and J. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

Folli, V.

V. Folli and C. Conti, New J. Phys. 15, 085026 (2013).
[CrossRef]

Gentilini, S.

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Phys. Rev. A 87, 053811 (2013).
[CrossRef]

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Opt. Express 20, 27369 (2012).
[CrossRef]

Ghofraniha, N.

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Phys. Rev. A 87, 053811 (2013).
[CrossRef]

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Opt. Express 20, 27369 (2012).
[CrossRef]

Grelu, Ph.

Ph. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
[CrossRef]

Grischkowsky, D.

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

Hideur, A.

Hoefer, M. A.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Ikezi, H.

R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
[CrossRef]

Ilday, F. Ö.

B. Oktem, C. lgüdür, and F. Ö. Ilday, Nat. Photonics 4, 307 (2010).
[CrossRef]

Jia, S.

W. Wan, S. Jia, and J. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

Kieu, K.

Kramer, L.

I. S. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002).
[CrossRef]

Kuramoto, Y.

Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
[CrossRef]

Lecaplain, C.

lgüdür, C.

B. Oktem, C. lgüdür, and F. Ö. Ilday, Nat. Photonics 4, 307 (2010).
[CrossRef]

Limpert, J.

Machinet, G.

Oktem, B.

B. Oktem, C. lgüdür, and F. Ö. Ilday, Nat. Photonics 4, 307 (2010).
[CrossRef]

Ortac, B.

Renninger, W.

Renninger, W. H.

Rothenberg, J. E.

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

Schreiber, T.

Schweikhard, V.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Soto-Crespo, J. M.

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
[CrossRef]

Taylor, R. J.

R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
[CrossRef]

Tsuzuki, T.

Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
[CrossRef]

Tunnermann, A.

Wan, W.

W. Wan, S. Jia, and J. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

Whitman, G. B.

G. B. Whitman, Linear and Nonlinear Waves (Wiley, 1974).

Wise, F.

Wise, F. W.

J. Opt. Soc. Am. B

Nat. Photonics

B. Oktem, C. lgüdür, and F. Ö. Ilday, Nat. Photonics 4, 307 (2010).
[CrossRef]

Ph. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
[CrossRef]

Nat. Phys.

W. Wan, S. Jia, and J. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

New J. Phys.

V. Folli and C. Conti, New J. Phys. 15, 085026 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
[CrossRef]

Phys. Rev. A

S. Gentilini, N. Ghofraniha, E. DelRe, and C. Conti, Phys. Rev. A 87, 053811 (2013).
[CrossRef]

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Phys. Rev. Lett.

R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
[CrossRef]

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

Prog. Theor. Phys.

Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
[CrossRef]

Rev. Mod. Phys.

I. S. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002).
[CrossRef]

Other

G. B. Whitman, Linear and Nonlinear Waves (Wiley, 1974).

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 (4)

Fig. 1.
Fig. 1.

Evolution of the output optical spectrum (red) and the group delay time (blue) with the increase of saturation energy (from bottom to top).

Fig. 2.
Fig. 2.

(a) Intracavity spectral evolution at a high energy level. Optical spectra exhibit sharp peaks with deep fringes on their edges. The corresponding spectral phase is plotted in (b). A magnification of the region where discontinuities appear is shown in (c). Qsat=600nJ, Psat=900W, ΔT=0.9.

Fig. 3.
Fig. 3.

(a) Optical spectrum (red) and group delay time (blue) obtained at the end of the propagation displayed in Fig. 2(a) and (b) Corresponding temporal intensity (red) and frequency chirp (blue) profiles. Parameters are the same as for Fig. 2.

Fig. 4.
Fig. 4.

(a) Intensity (Q=2t0) and (b) chirp in the time domain for the dissipative shock solutions; (c) spectral intensity (units with t0=1) for increasing scaled energy 2ν/(β2t0)γQ/(8g0β): 5 (black), 15 (red), 40 (blue).

Equations (10)

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

iAz=β22Attγ|A|2A+igo1+Q/Qsat(A2+βAtt),
T=1ΔT1+|ψ(t)|2/Psat,
ϕz+β22ϕt2νϕtt=γρ(t)+νρtρϕt,
ν=g0β1+Q/Qsat.
ϕt=2νβ2t0tanh(tt0),
Q=(16g02β2)/[t0γβ2(1+Q/Qsat)2].
A˜(ω)=dtρ(t)eiϕ(t)+iωtρ(t˜)eiϕ(t˜)+iωt˜,
ω=ϕt(t˜).
I˜(ω)=|A˜(ω)|2=ρ(t˜)1ω2ωS2,
ωS=2νβ2t0=γQ4t0β2γQ8g0β,

Metrics