Abstract

We experimentally study the nonlinear dynamics of a femtosecond ytterbium doped mode-locked fiber laser. With the laser operating in the pulsed regime a route to chaos is presented, starting from stable mode-locking, period two, period four, chaos and period three regimes. Return maps and bifurcation diagrams were extracted from time series for each regime. The analysis of the time series with the laser operating in the quasi mode-locked regime presents deterministic chaos described by an unidimensional Rössler map. A positive Lyapunov exponent λ = 0.14 confirms the deterministic chaos of the system. We suggest an explanation about the observed map by relating gain saturation and intra-cavity loss.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2017 (1)

H. Wei, B. Li, W. Shi, X. Zhu, R. A. Norwood, N. Peyghambarian, and S. Jian, “General description and understanding of the nonlinear dynamics of mode-locked fiber lasers,” Sci. Rep. 7, 1292 (2017).
[Crossref] [PubMed]

2016 (1)

L Zhang, L. Yang, F. Wang, L. Cui, and J. Qin, “Investigation on chaotic dynamics of ytterbium-doped fiber laser with Mach-Zehnder interferometer,” Opt. Las. Technology 76, 113–120 (2016).
[Crossref]

2015 (4)

2014 (1)

2013 (3)

A. K. Zaytsev, C. H. Lin, Y. J. You, F. H. Tsai, C. L. Wang, and C. L. Pan, “A controllable noise-like operation regime in a Yb-doped dispersion-mapped fiber ring laser,” Las. Phys. Lett. 10(4), 045104 (2013).
[Crossref]

M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7, 868–874 (2013).
[Crossref]

C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7, 875–882 (2013).
[Crossref]

2012 (2)

2011 (2)

E. Ding and J. N. Kutz, “Operating regimes and performance optimizationin mode-locked fiber lasers,” Opt. Spectroscopy,  111(2), 166–177 (2011).
[Crossref]

L. Kong, X. Xiao, and C. Yang, “Polarization dynamics in dissipative soliton fiber lasers mode-locked by nonlinear polarization rotation,” Opt. Express 19(19), 18339–18344 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2008 (1)

A. Haboucha, A. Komarov, H. Leblond, F. Sanchez, and G. Martel, “Mechanism of multiple pulse formation in the normal dispersion regime of passively mode-locked fiber ring lasers,” Opt. Fib. Tech. 14, 262–267 (2008).
[Crossref]

2006 (1)

L. M. Zhao, D. Y. Tang, and A. Q. Liu, “Chaotic dynamics of a passively mode-locked soliton fiber ring laser,” Chaos 16(1), 013128 (2006).
[Crossref] [PubMed]

2005 (1)

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71, 053809 (2005).
[Crossref]

2004 (1)

M. G. Kovalsky and A. A. Hnilo, “Different routes to chaos in the Ti:sapphire laser,” Phys. Rev. A 70, 043813 (2004).
[Crossref]

2001 (2)

L. M. Sànchez and A. A. Hnilo, “Description of Kerr lens mode-locked lasers with Poincaré maps in the complex plane,” Opt. Commun. 199, 189–199 (2001).
[Crossref]

S. M. Kelly, K. Smith, K. J. Blow, and N. J. Doran, “Average soliton dynamics of a high gain erbium fiber laser,” Opt. Lett. 16(17), 1337–1339 (2001).
[Crossref]

2000 (2)

M. G. Kovalsky and A. A. Hnilo, “Stability and bifurcations in Kerr-lens mode-locked Ti:sapphire lasers,” Opt. Commun. 186, 155–166 (2000).
[Crossref]

E. J. Mozdy and C. R. Pollock, “Chaos in an additive-pulse mode-locked laser,” Appl. Phys. Lett. 77(12), 1771–1773 (2000).
[Crossref]

1998 (1)

1996 (1)

1995 (1)

1993 (1)

1991 (2)

D. J. Richardson, R. I. Fleming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[Crossref]

M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, and A. J. Schmidt, “Mode locking with cross-phase and self-phase modulation,” Opt. Lett.,  16(7), 502–504 (1991).
[Crossref] [PubMed]

1983 (1)

J. C. Roux, R. H. Simoyi, and H. L. Swinney, “Observation of a strange attractor,” Physica 8D, 257–266 (1983).

Aguergaray, C.

Akhmediev, N.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[Crossref]

Blow, K. J.

Bolton, S. R.

Broderick, N. G. R.

Chemla, D. S.

Chu, P. L.

Cui, L.

L Zhang, L. Yang, F. Wang, L. Cui, and J. Qin, “Investigation on chaotic dynamics of ytterbium-doped fiber laser with Mach-Zehnder interferometer,” Opt. Las. Technology 76, 113–120 (2016).
[Crossref]

Ding, E.

E. Ding and J. N. Kutz, “Operating regimes and performance optimizationin mode-locked fiber lasers,” Opt. Spectroscopy,  111(2), 166–177 (2011).
[Crossref]

Doran, N. J.

Erkintalo, M.

Fermann, M. E.

Fleming, R. I.

D. J. Richardson, R. I. Fleming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[Crossref]

Ganeev, R. A.

Grelu, P.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[Crossref]

Haberl, F.

Haboucha, A.

A. Haboucha, A. Komarov, H. Leblond, F. Sanchez, and G. Martel, “Mechanism of multiple pulse formation in the normal dispersion regime of passively mode-locked fiber ring lasers,” Opt. Fib. Tech. 14, 262–267 (2008).
[Crossref]

Hartl, I.

M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7, 868–874 (2013).
[Crossref]

Haus, H. A.

Hnilo, A. A.

M. G. Kovalsky and A. A. Hnilo, “Different routes to chaos in the Ti:sapphire laser,” Phys. Rev. A 70, 043813 (2004).
[Crossref]

L. M. Sànchez and A. A. Hnilo, “Description of Kerr lens mode-locked lasers with Poincaré maps in the complex plane,” Opt. Commun. 199, 189–199 (2001).
[Crossref]

M. G. Kovalsky and A. A. Hnilo, “Stability and bifurcations in Kerr-lens mode-locked Ti:sapphire lasers,” Opt. Commun. 186, 155–166 (2000).
[Crossref]

Hofer, M.

Ippen, E. P.

Ivanenko, A.

Jian, S.

H. Wei, B. Li, W. Shi, X. Zhu, R. A. Norwood, N. Peyghambarian, and S. Jian, “General description and understanding of the nonlinear dynamics of mode-locked fiber lasers,” Sci. Rep. 7, 1292 (2017).
[Crossref] [PubMed]

Kelly, S. M.

Kobtsev, S.

Komarov, A.

A. Haboucha, A. Komarov, H. Leblond, F. Sanchez, and G. Martel, “Mechanism of multiple pulse formation in the normal dispersion regime of passively mode-locked fiber ring lasers,” Opt. Fib. Tech. 14, 262–267 (2008).
[Crossref]

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71, 053809 (2005).
[Crossref]

Kong, L.

Kovalsky, M. G.

M. G. Kovalsky and A. A. Hnilo, “Different routes to chaos in the Ti:sapphire laser,” Phys. Rev. A 70, 043813 (2004).
[Crossref]

M. G. Kovalsky and A. A. Hnilo, “Stability and bifurcations in Kerr-lens mode-locked Ti:sapphire lasers,” Opt. Commun. 186, 155–166 (2000).
[Crossref]

Kukarin, S.

Kuroda, H.

Kutz, J. N.

E. Ding and J. N. Kutz, “Operating regimes and performance optimizationin mode-locked fiber lasers,” Opt. Spectroscopy,  111(2), 166–177 (2011).
[Crossref]

F. Li, P. K. A. Wai, and J. N. Kutz, “Geometrical description of the onset of multi-pulsing in mode-locked laser cavities,” J. Opt. Soc. Am. B,  27(10), 2068–2077 (2010).
[Crossref]

Latkin, A.

Leblond, H.

A. Haboucha, A. Komarov, H. Leblond, F. Sanchez, and G. Martel, “Mechanism of multiple pulse formation in the normal dispersion regime of passively mode-locked fiber ring lasers,” Opt. Fib. Tech. 14, 262–267 (2008).
[Crossref]

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71, 053809 (2005).
[Crossref]

Li, B.

H. Wei, B. Li, W. Shi, X. Zhu, R. A. Norwood, N. Peyghambarian, and S. Jian, “General description and understanding of the nonlinear dynamics of mode-locked fiber lasers,” Sci. Rep. 7, 1292 (2017).
[Crossref] [PubMed]

Li, F.

Lin, C. H.

A. K. Zaytsev, C. H. Lin, Y. J. You, F. H. Tsai, C. L. Wang, and C. L. Pan, “A controllable noise-like operation regime in a Yb-doped dispersion-mapped fiber ring laser,” Las. Phys. Lett. 10(4), 045104 (2013).
[Crossref]

Liu, A. Q.

L. M. Zhao, D. Y. Tang, and A. Q. Liu, “Chaotic dynamics of a passively mode-locked soliton fiber ring laser,” Chaos 16(1), 013128 (2006).
[Crossref] [PubMed]

Liu, Z.

Luo, L.

Martel, G.

A. Haboucha, A. Komarov, H. Leblond, F. Sanchez, and G. Martel, “Mechanism of multiple pulse formation in the normal dispersion regime of passively mode-locked fiber ring lasers,” Opt. Fib. Tech. 14, 262–267 (2008).
[Crossref]

Matsas, V. J.

D. J. Richardson, R. I. Fleming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[Crossref]

Mitschke, F.

Morgner, U.

Mozdy, E. J.

E. J. Mozdy and C. R. Pollock, “Chaos in an additive-pulse mode-locked laser,” Appl. Phys. Lett. 77(12), 1771–1773 (2000).
[Crossref]

Nelson, L. E.

Norwood, R. A.

H. Wei, B. Li, W. Shi, X. Zhu, R. A. Norwood, N. Peyghambarian, and S. Jian, “General description and understanding of the nonlinear dynamics of mode-locked fiber lasers,” Sci. Rep. 7, 1292 (2017).
[Crossref] [PubMed]

Ober, M. H.

Pan, C. L.

A. K. Zaytsev, C. H. Lin, Y. J. You, F. H. Tsai, C. L. Wang, and C. L. Pan, “A controllable noise-like operation regime in a Yb-doped dispersion-mapped fiber ring laser,” Las. Phys. Lett. 10(4), 045104 (2013).
[Crossref]

Payne, D. N.

D. J. Richardson, R. I. Fleming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[Crossref]

Peyghambarian, N.

H. Wei, B. Li, W. Shi, X. Zhu, R. A. Norwood, N. Peyghambarian, and S. Jian, “General description and understanding of the nonlinear dynamics of mode-locked fiber lasers,” Sci. Rep. 7, 1292 (2017).
[Crossref] [PubMed]

Phillips, M. W.

D. J. Richardson, R. I. Fleming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[Crossref]

Pollock, C. R.

E. J. Mozdy and C. R. Pollock, “Chaos in an additive-pulse mode-locked laser,” Appl. Phys. Lett. 77(12), 1771–1773 (2000).
[Crossref]

Qin, J.

L Zhang, L. Yang, F. Wang, L. Cui, and J. Qin, “Investigation on chaotic dynamics of ytterbium-doped fiber laser with Mach-Zehnder interferometer,” Opt. Las. Technology 76, 113–120 (2016).
[Crossref]

Richardson, D. J.

D. J. Richardson, R. I. Fleming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[Crossref]

Rolefs, L.

Roux, J. C.

J. C. Roux, R. H. Simoyi, and H. L. Swinney, “Observation of a strange attractor,” Physica 8D, 257–266 (1983).

Runge, A. F. J.

Sanchez, F.

A. Haboucha, A. Komarov, H. Leblond, F. Sanchez, and G. Martel, “Mechanism of multiple pulse formation in the normal dispersion regime of passively mode-locked fiber ring lasers,” Opt. Fib. Tech. 14, 262–267 (2008).
[Crossref]

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71, 053809 (2005).
[Crossref]

Sànchez, L. M.

L. M. Sànchez and A. A. Hnilo, “Description of Kerr lens mode-locked lasers with Poincaré maps in the complex plane,” Opt. Commun. 199, 189–199 (2001).
[Crossref]

Schmidt, A. J.

Shi, W.

H. Wei, B. Li, W. Shi, X. Zhu, R. A. Norwood, N. Peyghambarian, and S. Jian, “General description and understanding of the nonlinear dynamics of mode-locked fiber lasers,” Sci. Rep. 7, 1292 (2017).
[Crossref] [PubMed]

Shirakawa, A.

Simoyi, R. H.

J. C. Roux, R. H. Simoyi, and H. L. Swinney, “Observation of a strange attractor,” Physica 8D, 257–266 (1983).

Smirnov, S.

Smith, K.

Strogatz, S. H.

S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, 1994).

Sucha, G.

Suzuki, M.

Swinney, H. L.

J. C. Roux, R. H. Simoyi, and H. L. Swinney, “Observation of a strange attractor,” Physica 8D, 257–266 (1983).

Tamura, K.

Tang, D. Y.

L. M. Zhao, D. Y. Tang, and A. Q. Liu, “Chaotic dynamics of a passively mode-locked soliton fiber ring laser,” Chaos 16(1), 013128 (2006).
[Crossref] [PubMed]

Tee, T. J.

Tokurakawa, M.

Tsai, F. H.

A. K. Zaytsev, C. H. Lin, Y. J. You, F. H. Tsai, C. L. Wang, and C. L. Pan, “A controllable noise-like operation regime in a Yb-doped dispersion-mapped fiber ring laser,” Las. Phys. Lett. 10(4), 045104 (2013).
[Crossref]

Turitsyn, S.

Wai, P. K. A.

Wang, C. L.

A. K. Zaytsev, C. H. Lin, Y. J. You, F. H. Tsai, C. L. Wang, and C. L. Pan, “A controllable noise-like operation regime in a Yb-doped dispersion-mapped fiber ring laser,” Las. Phys. Lett. 10(4), 045104 (2013).
[Crossref]

Wang, F.

L Zhang, L. Yang, F. Wang, L. Cui, and J. Qin, “Investigation on chaotic dynamics of ytterbium-doped fiber laser with Mach-Zehnder interferometer,” Opt. Las. Technology 76, 113–120 (2016).
[Crossref]

Wei, H.

H. Wei, B. Li, W. Shi, X. Zhu, R. A. Norwood, N. Peyghambarian, and S. Jian, “General description and understanding of the nonlinear dynamics of mode-locked fiber lasers,” Sci. Rep. 7, 1292 (2017).
[Crossref] [PubMed]

Weiss, S.

Wise, F. W.

Z. Liu, S. Zhang, and F. W. Wise, “Rogue waves in a normal-dispersion fiber laser,” Opt. Lett. 40(7), 1366–1369 (2015).
[Crossref] [PubMed]

C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7, 875–882 (2013).
[Crossref]

Xiao, X.

Xu, C.

C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7, 875–882 (2013).
[Crossref]

Yang, C.

Yang, L.

L Zhang, L. Yang, F. Wang, L. Cui, and J. Qin, “Investigation on chaotic dynamics of ytterbium-doped fiber laser with Mach-Zehnder interferometer,” Opt. Las. Technology 76, 113–120 (2016).
[Crossref]

Yoneya, S.

You, Y. J.

A. K. Zaytsev, C. H. Lin, Y. J. You, F. H. Tsai, C. L. Wang, and C. L. Pan, “A controllable noise-like operation regime in a Yb-doped dispersion-mapped fiber ring laser,” Las. Phys. Lett. 10(4), 045104 (2013).
[Crossref]

Zaytsev, A. K.

A. K. Zaytsev, C. H. Lin, Y. J. You, F. H. Tsai, C. L. Wang, and C. L. Pan, “A controllable noise-like operation regime in a Yb-doped dispersion-mapped fiber ring laser,” Las. Phys. Lett. 10(4), 045104 (2013).
[Crossref]

Zhang, L

L Zhang, L. Yang, F. Wang, L. Cui, and J. Qin, “Investigation on chaotic dynamics of ytterbium-doped fiber laser with Mach-Zehnder interferometer,” Opt. Las. Technology 76, 113–120 (2016).
[Crossref]

Zhang, S.

Zhao, L. M.

L. M. Zhao, D. Y. Tang, and A. Q. Liu, “Chaotic dynamics of a passively mode-locked soliton fiber ring laser,” Chaos 16(1), 013128 (2006).
[Crossref] [PubMed]

Zhu, X.

H. Wei, B. Li, W. Shi, X. Zhu, R. A. Norwood, N. Peyghambarian, and S. Jian, “General description and understanding of the nonlinear dynamics of mode-locked fiber lasers,” Sci. Rep. 7, 1292 (2017).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

E. J. Mozdy and C. R. Pollock, “Chaos in an additive-pulse mode-locked laser,” Appl. Phys. Lett. 77(12), 1771–1773 (2000).
[Crossref]

Chaos (1)

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Supplementary Material (1)

NameDescription
» Visualization 1       Fig. 5 animation: going from 2D to a 3D bifurcation diagram.

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Figures (5)

Fig. 1
Fig. 1 (a) Schematics of the YFMLFL and data acquisition system: ytterbium doped fiber (YDF), Faraday isolator (FI), grating pair (GP), polarization beam splitter (PBS), wavelength division multiplexer (WDM) and detector (D). (b) Typical optical spectrum and (c) autocorrelation when the laser is in mode-locked operation. The optical spectrum and the autocorrelation were taken directly from the laser output, after the PBS.
Fig. 2
Fig. 2 (a) 3D Radio Frequency spectrum showing period two, four, chaos and period three. The repetition frequency is frep ≈ 130 MHz. RF spectra for individual currents for period two, four, chaos and three are presented in (b), (c), (d) and (e) respectively.
Fig. 3
Fig. 3 Time series (upper row) of the laser pulses and the corresponding peak value return maps (RM) (lower row): in (a) the laser is stable and the RM (f) has only one spot. In (b) the period two is seen and the RM (g) shows two distinct spots. In (c) period four dynamics is seen, after the second period doubling bifurcation and the RM (h) has four distinct spots. In (d), the pulse intensity is chaotic and the RM (i) is scattered over a relatively well defined region indicating deterministic chaos describable by a unidimensional map. In (e) there is a stable period three regime and the RM in (j) shows three dots.
Fig. 4
Fig. 4 Return map at the chaotic region from Fig. 3(i). This experimental map was fitted (continuous curve, red color) using a Rössler map. The inset figure is a set of points obtained by iterating the Rössler map function.
Fig. 5
Fig. 5 Bifurcation diagrams for Yb mode-locked laser: (a) is a conventional bifurcation diagram. The five red lines show five different dynamical regimes related to the time series of Fig. 3: (I) the laser is at standard mode-locked operation, (II) period two, (III) period four, (IV) chaos and (V) period three window. (b) is a tridimensional bifurcation diagram for a better visualization of all branches ( Visualization 1). In the supplementary material there is an animation of this figure going from 2D to 3D bifurcation diagram.

Equations (1)

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λ = lim N 1 N n = 1 N ln | d f ( x n ) d x n | .

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