Abstract

By modeling giant chirped pulse formation in ultra-long, normally dispersive, mode-locked fiber lasers, we verify convergence to a steady-state consisting of highly chirped and coherent, nanosecond-scale pulses, which is in good agreement with recent experimental results. Numerical investigation of the transient dynamics reveals the existence of dark soliton-like structures within the envelope of the initial noisy pulse structure. Quasi-stationary dark solitons can persist throughout a large part of the evolution from noise to a stable dissipative soliton solution of the mode-locked laser cavity.

© 2014 Optical Society of America

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    [CrossRef]
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2013

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

I. A. Yarutkina, O. V. Shtyrina, M. P. Fedoruk, and S. K. Turitsyn, Opt. Express 21, 12942 (2013).
[CrossRef]

2012

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, Phys. Rev. A 85, 013828 (2012).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

2011

J. C. Travers, J. Morgenweg, E. D. Obraztsova, A. I. Chernov, E. J. R. Kelleher, and S. V. Popov, Laser Phys. Lett. 8, 144 (2011).
[CrossRef]

M. J. Ablowitz, T. P. Horikis, S. D. Nixon, and D. J. Frantzeskakis, Opt. Lett. 36, 793 (2011).
[CrossRef]

2010

H. Li, D. G. Ouzounov, and F. W. Wise, Opt. Lett. 35, 2403 (2010).
[CrossRef]

S. Coen and T. Sylvestre, Phys. Rev. A 82, 047801 (2010).
[CrossRef]

2009

E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 95, 111108 (2009).
[CrossRef]

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, Phys. Rev. A 80, 045803 (2009).
[CrossRef]

M. Erkintalo, J. M. Dudley, and G. Genty, Opt. Lett. 34, 2468 (2009).
[CrossRef]

E. J. R. Kelleher, J. C. Travers, E. P. Ippen, Z. Sun, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Opt. Lett. 34, 3526 (2009).
[CrossRef]

2008

2007

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

2002

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef]

J. M. Dudley and S. Coen, Opt. Lett. 27, 1180 (2002).
[CrossRef]

1998

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

1997

1991

1983

M. I. Dzhibladze, Z. G. Esiashvili, E. S. Teplitskii, S. K. Isaev, and V. R. Sagaradze, Sov. J. Quantum Electron. 13, 245 (1983).
[CrossRef]

Ablowitz, M. J.

Akhmediev, N.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

Babin, S. A.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

Barad, Y.

Chernov, A. I.

J. C. Travers, J. Morgenweg, E. D. Obraztsova, A. I. Chernov, E. J. R. Kelleher, and S. V. Popov, Laser Phys. Lett. 8, 144 (2011).
[CrossRef]

Chong, A.

W. H. Renninger, A. Chong, and F. W. Wise, Opt. Lett. 33, 3025 (2008).
[CrossRef]

W. H. Renninger, A. Chong, and F. W. Wise, Phys. Rev. A 77, 023814 (2008).
[CrossRef]

Churkin, D. V.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

Coen, S.

S. Coen and T. Sylvestre, Phys. Rev. A 82, 047801 (2010).
[CrossRef]

J. M. Dudley and S. Coen, Opt. Lett. 27, 1180 (2002).
[CrossRef]

Dudley, J. M.

Dzhibladze, M. I.

M. I. Dzhibladze, Z. G. Esiashvili, E. S. Teplitskii, S. K. Isaev, and V. R. Sagaradze, Sov. J. Quantum Electron. 13, 245 (1983).
[CrossRef]

Egorov, O.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, Phys. Rev. A 85, 013828 (2012).
[CrossRef]

Erkintalo, M.

Esiashvili, Z. G.

M. I. Dzhibladze, Z. G. Esiashvili, E. S. Teplitskii, S. K. Isaev, and V. R. Sagaradze, Sov. J. Quantum Electron. 13, 245 (1983).
[CrossRef]

Falkovich, G.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

Fedoruk, M. P.

Fedotov, Y.

Ferrari, A. C.

E. J. R. Kelleher, J. C. Travers, E. P. Ippen, Z. Sun, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Opt. Lett. 34, 3526 (2009).
[CrossRef]

E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 95, 111108 (2009).
[CrossRef]

Fischer, B.

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef]

Frantzeskakis, D. J.

Fujimoto, J. G.

Genty, G.

Gordon, A.

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef]

Grelu, Ph.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

Haus, H. A.

Herink, G.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

Horikis, T. P.

Horowitz, M.

Iliew, R.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, Phys. Rev. A 85, 013828 (2012).
[CrossRef]

Ippen, E. P.

Isaev, S. K.

M. I. Dzhibladze, Z. G. Esiashvili, E. S. Teplitskii, S. K. Isaev, and V. R. Sagaradze, Sov. J. Quantum Electron. 13, 245 (1983).
[CrossRef]

Jalali, B.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Kelleher, E. J. R.

J. C. Travers, J. Morgenweg, E. D. Obraztsova, A. I. Chernov, E. J. R. Kelleher, and S. V. Popov, Laser Phys. Lett. 8, 144 (2011).
[CrossRef]

E. J. R. Kelleher, J. C. Travers, E. P. Ippen, Z. Sun, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Opt. Lett. 34, 3526 (2009).
[CrossRef]

E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 95, 111108 (2009).
[CrossRef]

Kivshar, Y. S.

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

Kobtsev, S.

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Kukarin, S.

Lecaplain, C.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

Lederer, F.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, Phys. Rev. A 85, 013828 (2012).
[CrossRef]

Li, H.

Luther-Davies, B.

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

Morgenweg, J.

J. C. Travers, J. Morgenweg, E. D. Obraztsova, A. I. Chernov, E. J. R. Kelleher, and S. V. Popov, Laser Phys. Lett. 8, 144 (2011).
[CrossRef]

Nixon, S. D.

Obraztsova, E. D.

J. C. Travers, J. Morgenweg, E. D. Obraztsova, A. I. Chernov, E. J. R. Kelleher, and S. V. Popov, Laser Phys. Lett. 8, 144 (2011).
[CrossRef]

Ouzounov, D. G.

Podivilov, E. V.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

Popov, S. V.

J. C. Travers, J. Morgenweg, E. D. Obraztsova, A. I. Chernov, E. J. R. Kelleher, and S. V. Popov, Laser Phys. Lett. 8, 144 (2011).
[CrossRef]

E. J. R. Kelleher, J. C. Travers, E. P. Ippen, Z. Sun, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Opt. Lett. 34, 3526 (2009).
[CrossRef]

E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 95, 111108 (2009).
[CrossRef]

Renninger, W. H.

W. H. Renninger, A. Chong, and F. W. Wise, Opt. Lett. 33, 3025 (2008).
[CrossRef]

W. H. Renninger, A. Chong, and F. W. Wise, Phys. Rev. A 77, 023814 (2008).
[CrossRef]

Ropers, C.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Rozhin, A. G.

E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 95, 111108 (2009).
[CrossRef]

Sagaradze, V. R.

M. I. Dzhibladze, Z. G. Esiashvili, E. S. Teplitskii, S. K. Isaev, and V. R. Sagaradze, Sov. J. Quantum Electron. 13, 245 (1983).
[CrossRef]

Shtyrina, O. V.

Shu, X.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

Silberberg, Y.

Smirnov, S. V.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

Solli, D. R.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Soto-Crespo, J. M.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

Sugavanam, S.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

Sun, Z.

E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 95, 111108 (2009).
[CrossRef]

E. J. R. Kelleher, J. C. Travers, E. P. Ippen, Z. Sun, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Opt. Lett. 34, 3526 (2009).
[CrossRef]

Sylvestre, T.

S. Coen and T. Sylvestre, Phys. Rev. A 82, 047801 (2010).
[CrossRef]

Tang, D. Y.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, Phys. Rev. A 80, 045803 (2009).
[CrossRef]

Tarasov, N.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

Taylor, J. R.

E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 95, 111108 (2009).
[CrossRef]

E. J. R. Kelleher, J. C. Travers, E. P. Ippen, Z. Sun, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Opt. Lett. 34, 3526 (2009).
[CrossRef]

Teplitskii, E. S.

M. I. Dzhibladze, Z. G. Esiashvili, E. S. Teplitskii, S. K. Isaev, and V. R. Sagaradze, Sov. J. Quantum Electron. 13, 245 (1983).
[CrossRef]

Travers, J. C.

J. C. Travers, J. Morgenweg, E. D. Obraztsova, A. I. Chernov, E. J. R. Kelleher, and S. V. Popov, Laser Phys. Lett. 8, 144 (2011).
[CrossRef]

E. J. R. Kelleher, J. C. Travers, E. P. Ippen, Z. Sun, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Opt. Lett. 34, 3526 (2009).
[CrossRef]

E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 95, 111108 (2009).
[CrossRef]

Turitsyn, S. K.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

I. A. Yarutkina, O. V. Shtyrina, M. P. Fedoruk, and S. K. Turitsyn, Opt. Express 21, 12942 (2013).
[CrossRef]

Turitsyna, E. G.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

Wise, F. W.

Wu, X.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, Phys. Rev. A 80, 045803 (2009).
[CrossRef]

Yarutkina, I. A.

Zaviyalov, A.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, Phys. Rev. A 85, 013828 (2012).
[CrossRef]

Zhang, H.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, Phys. Rev. A 80, 045803 (2009).
[CrossRef]

Zhao, L. M.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, Phys. Rev. A 80, 045803 (2009).
[CrossRef]

Appl. Phys. Lett.

E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 95, 111108 (2009).
[CrossRef]

J. Opt. Soc. Am. B

Laser Phys. Lett.

J. C. Travers, J. Morgenweg, E. D. Obraztsova, A. I. Chernov, E. J. R. Kelleher, and S. V. Popov, Laser Phys. Lett. 8, 144 (2011).
[CrossRef]

Nat. Photonics

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

Nature

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rep.

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

Phys. Rev. A

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, Phys. Rev. A 80, 045803 (2009).
[CrossRef]

S. Coen and T. Sylvestre, Phys. Rev. A 82, 047801 (2010).
[CrossRef]

W. H. Renninger, A. Chong, and F. W. Wise, Phys. Rev. A 77, 023814 (2008).
[CrossRef]

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, Phys. Rev. A 85, 013828 (2012).
[CrossRef]

Phys. Rev. Lett.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef]

Sov. J. Quantum Electron.

M. I. Dzhibladze, Z. G. Esiashvili, E. S. Teplitskii, S. K. Isaev, and V. R. Sagaradze, Sov. J. Quantum Electron. 13, 245 (1983).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Spectrograms of the steady-state output pulse at a center wavelength of λc=1065nm. (a) numerical, (b) analytical and (c) experimental after [9].

Fig. 2.
Fig. 2.

Temporal [top, (a)–(c)], zoomed temporal [middle, (d), (e)], phase (f), and spectral [bottom, (h)–(j)] profiles for three different stages of the characteristic pulse evolution within the oscillator cavity. RT, round-trip number; min, internal pulse width; max, envelope duration. Center wavelength λc=1065nm.

Fig. 3.
Fig. 3.

(a) Spatiotemporal intensity evolution of a typical bright-pulse evolving from noise. Three distinct stages of pulse formation are identified (i, ii, iii); see text for a detailed description. (b) Spatiotemporal intensity evolution of an independent realization capturing a long-lived, quasi-stationary dark soliton. (c) Temporal intensity and phase slice, corresponding to the white dashed line in (b); the temporal phase shows an abrupt phase change approximately equal to π, across the black feature. The solid blue line is a fit to the functional form of a dark soliton [18], where τ0=6.68ps corresponding to a background power of 0.134 W for a fundamental dark soliton (indicated by the solid gray line).

Equations (1)

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zA˜(z,Ω)=iβ22Ω2A˜(z,Ω)α(Ω)2A˜(z,Ω)+iγF(A(z,τ)|A(z,τ)|2)

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