Abstract

We present results of experimental investigation of the chaotic and quasi-periodic regime in the chirped-pulsed (dissipative soliton) Cr:ZnS and Cr:ZnSe mid-IR oscillators with significant third-order dispersion. The instability develops when the spectrum edge approaches resonance with a linear wave either due to power increase or by dispersion adjustment. In practice, this occurs when the spectrum edge reaches zero dispersion wavelength. The analysis suggests a three-oscillator chaos model, which is confirmed by numerical simulations. The regime is long-term stable and can be easily overlooked in similar systems. We show that chaotic regime is accompanied by a characteristic spectral shape and can be reliably recognized by using wavelength-skewed filters and by second-harmonic or two-photon absorption detectors.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  30. B. Per, B. Tomas, and J. Mogens Høgh, “Mode-locking and the transition to chaos in dissipative systems,” Phys. Scr.1985, 50–58 (1985).
  31. V. L. Kalashnikov and A. Chernykh, “Spectral anomalies and stability of chirped-pulse oscillators,” Phys. Rev. A75, 033820 (2007).
    [CrossRef]
  32. C. Baesens, J. Guckenheimer, S. Kim, and R. S. MacKay, “Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos,” Physica D Nonlinear Phenomena49, 387–475 (1991).
    [CrossRef]
  33. D. Pazó, E. Sánchez, and M. A. Matías, “Transition to high-dimensional chaos through quasiperiodic motion,” Int. J. Bifurc. Chaos11, 2683–2688 (2001).
    [CrossRef]
  34. H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys.65, 1331–1392 (1993).
    [CrossRef]
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    [CrossRef]
  36. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A45, 3403–3411 (1992).
    [CrossRef] [PubMed]

2013

Q. Wang, T. Chen, M. Li, B. Zhang, Y. Lu, and K. P. Chen, “All-fiber ultrafast thulium-doped fiber ring laser with dissipative soliton and noise-like output in normal dispersion by single-wall carbon nanotubes,” Appl. Phys. Lett.103, 011103 (2013).
[CrossRef]

N. Tolstik, E. Sorokin, and I. T. Sorokina, “Kerr-lens mode-locked Cr:ZnS laser,” Opt. Lett.38, 299–301 (2013).
[CrossRef] [PubMed]

E. Sorokin, N. Tolstik, and I. T. Sorokina, “1 Watt femtosecond mid-IR Cr:ZnS laser,” Proc. SPIE8599, 859916 (2013).
[CrossRef]

2012

2011

2010

2009

2008

E. Sorokin, V. L. Kalashnikov, J. Mandon, G. Guelachvili, N. Picque, and I. T. Sorokina, “Cr4+:YAG chirped-pulse oscillator,” New J. Phys.10, 083022 (2008).
[CrossRef]

V. L. Kalashnikov, A. Fernández, and A. Apolonski, “High-order dispersion in chirped-pulse oscillators,” Opt. Express16, 4206–4216 (2008).
[CrossRef] [PubMed]

2007

V. L. Kalashnikov and A. Chernykh, “Spectral anomalies and stability of chirped-pulse oscillators,” Phys. Rev. A75, 033820 (2007).
[CrossRef]

2006

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, “Chirped-pulse oscillators: theory and experiment,” Appl. Phys. B83, 503–510 (2006).
[CrossRef]

2005

E. Podivilov and V. L. Kalashnikov, “Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation,” JETP Lett.82, 467–471 (2005).
[CrossRef]

2004

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E70, 066612 (2004).
[CrossRef]

2003

J.-H. Lin and W.-F. Hsieh, “Three-frequency chaotic instability in soft-aperture Kerr-lens mode-locked laser around 1/3-degenerate cavity configuration,” Opt. Commun.225, 393–402 (2003).
[CrossRef]

2001

D. Pazó, E. Sánchez, and M. A. Matías, “Transition to high-dimensional chaos through quasiperiodic motion,” Int. J. Bifurc. Chaos11, 2683–2688 (2001).
[CrossRef]

1999

Q. Xing, L. Chai, W. Zhang, and C.-Y. Wang, “Regular, period-doubling, quasi-periodic, and chaotic behavior in a self-mode-locked Ti:sapphire laser,” Opt. Commun.162, 71–74 (1999).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B69, 327–332 (1999).
[CrossRef]

1997

1995

L. A. Aguirre, “A nonlinear correlation function for selecting the delay time in dynamical reconstructions,” Phys. Lett. A203, 88–94 (1995).
[CrossRef]

1994

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron.30, 1100–1114 (1994).
[CrossRef]

1993

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys.65, 1331–1392 (1993).
[CrossRef]

1992

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A45, 3403–3411 (1992).
[CrossRef] [PubMed]

1991

C. Baesens, J. Guckenheimer, S. Kim, and R. S. MacKay, “Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos,” Physica D Nonlinear Phenomena49, 387–475 (1991).
[CrossRef]

1989

H. I. Choi and W. J. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. Acoust. Speech Signal Process.37, 862–871 (1989).
[CrossRef]

1985

B. Per, B. Tomas, and J. Mogens Høgh, “Mode-locking and the transition to chaos in dissipative systems,” Phys. Scr.1985, 50–58 (1985).

Abarbanel, H. D. I.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys.65, 1331–1392 (1993).
[CrossRef]

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A45, 3403–3411 (1992).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2006).

Aguirre, L. A.

L. A. Aguirre, “A nonlinear correlation function for selecting the delay time in dynamical reconstructions,” Phys. Lett. A203, 88–94 (1995).
[CrossRef]

Akhmediev, N.

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E70, 066612 (2004).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman and Hall, 1997), Vol. 4.

Ankiewicz, A.

N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman and Hall, 1997), Vol. 4.

Apolonski, A.

V. L. Kalashnikov, A. Fernández, and A. Apolonski, “High-order dispersion in chirped-pulse oscillators,” Opt. Express16, 4206–4216 (2008).
[CrossRef] [PubMed]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, “Chirped-pulse oscillators: theory and experiment,” Appl. Phys. B83, 503–510 (2006).
[CrossRef]

Baesens, C.

C. Baesens, J. Guckenheimer, S. Kim, and R. S. MacKay, “Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos,” Physica D Nonlinear Phenomena49, 387–475 (1991).
[CrossRef]

Brabec, T.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron.30, 1100–1114 (1994).
[CrossRef]

Brown, R.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys.65, 1331–1392 (1993).
[CrossRef]

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A45, 3403–3411 (1992).
[CrossRef] [PubMed]

Chai, L.

Q. Xing, L. Chai, W. Zhang, and C.-Y. Wang, “Regular, period-doubling, quasi-periodic, and chaotic behavior in a self-mode-locked Ti:sapphire laser,” Opt. Commun.162, 71–74 (1999).
[CrossRef]

Chen, K. P.

Q. Wang, T. Chen, M. Li, B. Zhang, Y. Lu, and K. P. Chen, “All-fiber ultrafast thulium-doped fiber ring laser with dissipative soliton and noise-like output in normal dispersion by single-wall carbon nanotubes,” Appl. Phys. Lett.103, 011103 (2013).
[CrossRef]

Chen, T.

Q. Wang, T. Chen, M. Li, B. Zhang, Y. Lu, and K. P. Chen, “All-fiber ultrafast thulium-doped fiber ring laser with dissipative soliton and noise-like output in normal dispersion by single-wall carbon nanotubes,” Appl. Phys. Lett.103, 011103 (2013).
[CrossRef]

Chernykh, A.

V. L. Kalashnikov and A. Chernykh, “Spectral anomalies and stability of chirped-pulse oscillators,” Phys. Rev. A75, 033820 (2007).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, “Chirped-pulse oscillators: theory and experiment,” Appl. Phys. B83, 503–510 (2006).
[CrossRef]

Choi, H. I.

H. I. Choi and W. J. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. Acoust. Speech Signal Process.37, 862–871 (1989).
[CrossRef]

Chong, A.

Curley, P. F.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron.30, 1100–1114 (1994).
[CrossRef]

Duan, L.

Dunlop, A. E.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B69, 327–332 (1999).
[CrossRef]

Fernández, A.

Gadomski, W.

Gong, Y.

Grapinet, M.

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E70, 066612 (2004).
[CrossRef]

Grelu, P.

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E70, 066612 (2004).
[CrossRef]

Guckenheimer, J.

C. Baesens, J. Guckenheimer, S. Kim, and R. S. MacKay, “Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos,” Physica D Nonlinear Phenomena49, 387–475 (1991).
[CrossRef]

Guelachvili, G.

E. Sorokin, V. L. Kalashnikov, J. Mandon, G. Guelachvili, N. Picque, and I. T. Sorokina, “Cr4+:YAG chirped-pulse oscillator,” New J. Phys.10, 083022 (2008).
[CrossRef]

Hsieh, W.-F.

J.-H. Lin and W.-F. Hsieh, “Three-frequency chaotic instability in soft-aperture Kerr-lens mode-locked laser around 1/3-degenerate cavity configuration,” Opt. Commun.225, 393–402 (2003).
[CrossRef]

Ivanenko, A.

Jinmei, L.

Junsong, P.

Kalashnikov, V. L.

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, “Chirped dissipative soliton absorption spectroscopy,” Opt. Express19, 17480–17492 (2011).
[CrossRef] [PubMed]

V. L. Kalashnikov and E. Sorokin, “Soliton absorption spectroscopy,” Phys. Rev. A81, 033840 (2010).
[CrossRef]

V. L. Kalashnikov, A. Fernández, and A. Apolonski, “High-order dispersion in chirped-pulse oscillators,” Opt. Express16, 4206–4216 (2008).
[CrossRef] [PubMed]

E. Sorokin, V. L. Kalashnikov, J. Mandon, G. Guelachvili, N. Picque, and I. T. Sorokina, “Cr4+:YAG chirped-pulse oscillator,” New J. Phys.10, 083022 (2008).
[CrossRef]

V. L. Kalashnikov and A. Chernykh, “Spectral anomalies and stability of chirped-pulse oscillators,” Phys. Rev. A75, 033820 (2007).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, “Chirped-pulse oscillators: theory and experiment,” Appl. Phys. B83, 503–510 (2006).
[CrossRef]

E. Podivilov and V. L. Kalashnikov, “Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation,” JETP Lett.82, 467–471 (2005).
[CrossRef]

V. L. Kalashnikov, I. G. Poloyko, V. P. Mikhailov, and D. von der Linde, “Regular, quasi-periodic, and chaotic behavior in continuous-wave solid-state Kerr-lens mode-locked lasers,” J. Opt. Soc. Am. B14, 2691–2695 (1997).
[CrossRef]

V. L. Kalashnikov, “Dissipative solitons: perturbations and chaos formation,” in Chaos Theory. Modeling, Simulation and Applications, C. H. Skiadas, I. Dimotikalis, and C. Skiadas, eds. (World Scientific, 2011), pp. 199–206.

Kardas, T. M.

Keller, U.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B69, 327–332 (1999).
[CrossRef]

Kennel, M. B.

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A45, 3403–3411 (1992).
[CrossRef] [PubMed]

Kim, S.

C. Baesens, J. Guckenheimer, S. Kim, and R. S. MacKay, “Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos,” Physica D Nonlinear Phenomena49, 387–475 (1991).
[CrossRef]

Kobtsev, S.

Krausz, F.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron.30, 1100–1114 (1994).
[CrossRef]

Kukarin, S.

Kutz, J. N.

Latkin, A.

Li, F.

Li, M.

Q. Wang, T. Chen, M. Li, B. Zhang, Y. Lu, and K. P. Chen, “All-fiber ultrafast thulium-doped fiber ring laser with dissipative soliton and noise-like output in normal dispersion by single-wall carbon nanotubes,” Appl. Phys. Lett.103, 011103 (2013).
[CrossRef]

Li, Z.

Lin, J.-H.

J.-H. Lin and W.-F. Hsieh, “Three-frequency chaotic instability in soft-aperture Kerr-lens mode-locked laser around 1/3-degenerate cavity configuration,” Opt. Commun.225, 393–402 (2003).
[CrossRef]

Liu, X.

Lu, Y.

Q. Wang, T. Chen, M. Li, B. Zhang, Y. Lu, and K. P. Chen, “All-fiber ultrafast thulium-doped fiber ring laser with dissipative soliton and noise-like output in normal dispersion by single-wall carbon nanotubes,” Appl. Phys. Lett.103, 011103 (2013).
[CrossRef]

MacKay, R. S.

C. Baesens, J. Guckenheimer, S. Kim, and R. S. MacKay, “Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos,” Physica D Nonlinear Phenomena49, 387–475 (1991).
[CrossRef]

Mandon, J.

E. Sorokin, V. L. Kalashnikov, J. Mandon, G. Guelachvili, N. Picque, and I. T. Sorokina, “Cr4+:YAG chirped-pulse oscillator,” New J. Phys.10, 083022 (2008).
[CrossRef]

Mao, D.

Matías, M. A.

D. Pazó, E. Sánchez, and M. A. Matías, “Transition to high-dimensional chaos through quasiperiodic motion,” Int. J. Bifurc. Chaos11, 2683–2688 (2001).
[CrossRef]

Mikhailov, V. P.

Mogens Høgh, J.

B. Per, B. Tomas, and J. Mogens Høgh, “Mode-locking and the transition to chaos in dissipative systems,” Phys. Scr.1985, 50–58 (1985).

Pazó, D.

D. Pazó, E. Sánchez, and M. A. Matías, “Transition to high-dimensional chaos through quasiperiodic motion,” Int. J. Bifurc. Chaos11, 2683–2688 (2001).
[CrossRef]

Per, B.

B. Per, B. Tomas, and J. Mogens Høgh, “Mode-locking and the transition to chaos in dissipative systems,” Phys. Scr.1985, 50–58 (1985).

Picque, N.

E. Sorokin, V. L. Kalashnikov, J. Mandon, G. Guelachvili, N. Picque, and I. T. Sorokina, “Cr4+:YAG chirped-pulse oscillator,” New J. Phys.10, 083022 (2008).
[CrossRef]

Podivilov, E.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, “Chirped-pulse oscillators: theory and experiment,” Appl. Phys. B83, 503–510 (2006).
[CrossRef]

E. Podivilov and V. L. Kalashnikov, “Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation,” JETP Lett.82, 467–471 (2005).
[CrossRef]

Poloyko, I. G.

Pospischil, A.

N. Tolstik, I. T. Sorokina, A. Pospischil, and E. Sorokin, “Graphene mode-locked Cr:ZnS laser with 44 fs pulse duration,” in Advanced Solid-State Lasers Congress, M. Ebrahim-Zadeh and I. Sorokina, eds. (Optical Society of America, Paris, 2013), p. MW1C.1.

Qishun, S.

Ratajska-Gadomska, B.

Renninger, W. H.

Sánchez, E.

D. Pazó, E. Sánchez, and M. A. Matías, “Transition to high-dimensional chaos through quasiperiodic motion,” Int. J. Bifurc. Chaos11, 2683–2688 (2001).
[CrossRef]

Shouyu, L.

Sidorowich, J. J.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys.65, 1331–1392 (1993).
[CrossRef]

Smirnov, S.

Sorokin, E.

E. Sorokin, N. Tolstik, and I. T. Sorokina, “1 Watt femtosecond mid-IR Cr:ZnS laser,” Proc. SPIE8599, 859916 (2013).
[CrossRef]

N. Tolstik, E. Sorokin, and I. T. Sorokina, “Kerr-lens mode-locked Cr:ZnS laser,” Opt. Lett.38, 299–301 (2013).
[CrossRef] [PubMed]

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, “Chirped dissipative soliton absorption spectroscopy,” Opt. Express19, 17480–17492 (2011).
[CrossRef] [PubMed]

V. L. Kalashnikov and E. Sorokin, “Soliton absorption spectroscopy,” Phys. Rev. A81, 033840 (2010).
[CrossRef]

E. Sorokin, V. L. Kalashnikov, J. Mandon, G. Guelachvili, N. Picque, and I. T. Sorokina, “Cr4+:YAG chirped-pulse oscillator,” New J. Phys.10, 083022 (2008).
[CrossRef]

E. Sorokin and I. T. Sorokina, “Ultrashort-pulsed Kerr-lens modelocked Cr:ZnSe laser,” in European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference - CLEO Europe - EQEC, (IEEE, München, 2009), p. CF1_3.

N. Tolstik, I. T. Sorokina, A. Pospischil, and E. Sorokin, “Graphene mode-locked Cr:ZnS laser with 44 fs pulse duration,” in Advanced Solid-State Lasers Congress, M. Ebrahim-Zadeh and I. Sorokina, eds. (Optical Society of America, Paris, 2013), p. MW1C.1.

N. Tolstik, I. T. Sorokina, and E. Sorokin, “Watt-level Kerr-lens mode-locked Cr:ZnS laser at 2.4 μm,” in CLEO: Science and Innovations (Optical Society of America, San Jose, 2013), p. CTh1H.2.

Sorokina, I. T.

N. Tolstik, E. Sorokin, and I. T. Sorokina, “Kerr-lens mode-locked Cr:ZnS laser,” Opt. Lett.38, 299–301 (2013).
[CrossRef] [PubMed]

E. Sorokin, N. Tolstik, and I. T. Sorokina, “1 Watt femtosecond mid-IR Cr:ZnS laser,” Proc. SPIE8599, 859916 (2013).
[CrossRef]

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, “Chirped dissipative soliton absorption spectroscopy,” Opt. Express19, 17480–17492 (2011).
[CrossRef] [PubMed]

E. Sorokin, V. L. Kalashnikov, J. Mandon, G. Guelachvili, N. Picque, and I. T. Sorokina, “Cr4+:YAG chirped-pulse oscillator,” New J. Phys.10, 083022 (2008).
[CrossRef]

N. Tolstik, I. T. Sorokina, and E. Sorokin, “Watt-level Kerr-lens mode-locked Cr:ZnS laser at 2.4 μm,” in CLEO: Science and Innovations (Optical Society of America, San Jose, 2013), p. CTh1H.2.

E. Sorokin and I. T. Sorokina, “Ultrashort-pulsed Kerr-lens modelocked Cr:ZnSe laser,” in European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference - CLEO Europe - EQEC, (IEEE, München, 2009), p. CF1_3.

N. Tolstik, I. T. Sorokina, A. Pospischil, and E. Sorokin, “Graphene mode-locked Cr:ZnS laser with 44 fs pulse duration,” in Advanced Solid-State Lasers Congress, M. Ebrahim-Zadeh and I. Sorokina, eds. (Optical Society of America, Paris, 2013), p. MW1C.1.

Soto-Crespo, J. M.

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E70, 066612 (2004).
[CrossRef]

Spielmann, C.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron.30, 1100–1114 (1994).
[CrossRef]

Steinmeyer, G.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B69, 327–332 (1999).
[CrossRef]

Stenger, J.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B69, 327–332 (1999).
[CrossRef]

Sutter, D. H.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B69, 327–332 (1999).
[CrossRef]

Telle, H. R.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B69, 327–332 (1999).
[CrossRef]

Tolstik, N.

E. Sorokin, N. Tolstik, and I. T. Sorokina, “1 Watt femtosecond mid-IR Cr:ZnS laser,” Proc. SPIE8599, 859916 (2013).
[CrossRef]

N. Tolstik, E. Sorokin, and I. T. Sorokina, “Kerr-lens mode-locked Cr:ZnS laser,” Opt. Lett.38, 299–301 (2013).
[CrossRef] [PubMed]

N. Tolstik, I. T. Sorokina, and E. Sorokin, “Watt-level Kerr-lens mode-locked Cr:ZnS laser at 2.4 μm,” in CLEO: Science and Innovations (Optical Society of America, San Jose, 2013), p. CTh1H.2.

N. Tolstik, I. T. Sorokina, A. Pospischil, and E. Sorokin, “Graphene mode-locked Cr:ZnS laser with 44 fs pulse duration,” in Advanced Solid-State Lasers Congress, M. Ebrahim-Zadeh and I. Sorokina, eds. (Optical Society of America, Paris, 2013), p. MW1C.1.

Tomas, B.

B. Per, B. Tomas, and J. Mogens Høgh, “Mode-locking and the transition to chaos in dissipative systems,” Phys. Scr.1985, 50–58 (1985).

Tsimring, L. S.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys.65, 1331–1392 (1993).
[CrossRef]

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von der Linde, D.

Wai, P. K. A.

Wang, C.-Y.

Q. Xing, L. Chai, W. Zhang, and C.-Y. Wang, “Regular, period-doubling, quasi-periodic, and chaotic behavior in a self-mode-locked Ti:sapphire laser,” Opt. Commun.162, 71–74 (1999).
[CrossRef]

Wang, L.

Wang, Q.

Q. Wang, T. Chen, M. Li, B. Zhang, Y. Lu, and K. P. Chen, “All-fiber ultrafast thulium-doped fiber ring laser with dissipative soliton and noise-like output in normal dispersion by single-wall carbon nanotubes,” Appl. Phys. Lett.103, 011103 (2013).
[CrossRef]

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Williams, W. J.

H. I. Choi and W. J. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. Acoust. Speech Signal Process.37, 862–871 (1989).
[CrossRef]

Wise, F. W.

Xing, Q.

Q. Xing, L. Chai, W. Zhang, and C.-Y. Wang, “Regular, period-doubling, quasi-periodic, and chaotic behavior in a self-mode-locked Ti:sapphire laser,” Opt. Commun.162, 71–74 (1999).
[CrossRef]

Xuehao, S.

Zhang, B.

Q. Wang, T. Chen, M. Li, B. Zhang, Y. Lu, and K. P. Chen, “All-fiber ultrafast thulium-doped fiber ring laser with dissipative soliton and noise-like output in normal dispersion by single-wall carbon nanotubes,” Appl. Phys. Lett.103, 011103 (2013).
[CrossRef]

Zhang, W.

Q. Xing, L. Chai, W. Zhang, and C.-Y. Wang, “Regular, period-doubling, quasi-periodic, and chaotic behavior in a self-mode-locked Ti:sapphire laser,” Opt. Commun.162, 71–74 (1999).
[CrossRef]

Zhaochang, G.

Appl. Phys. B

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, “Chirped-pulse oscillators: theory and experiment,” Appl. Phys. B83, 503–510 (2006).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B69, 327–332 (1999).
[CrossRef]

Appl. Phys. Lett.

Q. Wang, T. Chen, M. Li, B. Zhang, Y. Lu, and K. P. Chen, “All-fiber ultrafast thulium-doped fiber ring laser with dissipative soliton and noise-like output in normal dispersion by single-wall carbon nanotubes,” Appl. Phys. Lett.103, 011103 (2013).
[CrossRef]

IEEE J. Quantum Electron.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron.30, 1100–1114 (1994).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process.

H. I. Choi and W. J. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. Acoust. Speech Signal Process.37, 862–871 (1989).
[CrossRef]

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[CrossRef]

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[CrossRef]

New J. Phys.

E. Sorokin, V. L. Kalashnikov, J. Mandon, G. Guelachvili, N. Picque, and I. T. Sorokina, “Cr4+:YAG chirped-pulse oscillator,” New J. Phys.10, 083022 (2008).
[CrossRef]

Opt. Commun.

Q. Xing, L. Chai, W. Zhang, and C.-Y. Wang, “Regular, period-doubling, quasi-periodic, and chaotic behavior in a self-mode-locked Ti:sapphire laser,” Opt. Commun.162, 71–74 (1999).
[CrossRef]

J.-H. Lin and W.-F. Hsieh, “Three-frequency chaotic instability in soft-aperture Kerr-lens mode-locked laser around 1/3-degenerate cavity configuration,” Opt. Commun.225, 393–402 (2003).
[CrossRef]

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[CrossRef] [PubMed]

V. L. Kalashnikov and E. Sorokin, “Soliton absorption spectroscopy,” Phys. Rev. A81, 033840 (2010).
[CrossRef]

V. L. Kalashnikov and A. Chernykh, “Spectral anomalies and stability of chirped-pulse oscillators,” Phys. Rev. A75, 033820 (2007).
[CrossRef]

Phys. Rev. E

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E70, 066612 (2004).
[CrossRef]

Phys. Scr.

B. Per, B. Tomas, and J. Mogens Høgh, “Mode-locking and the transition to chaos in dissipative systems,” Phys. Scr.1985, 50–58 (1985).

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[CrossRef]

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E. Sorokin, N. Tolstik, and I. T. Sorokina, “1 Watt femtosecond mid-IR Cr:ZnS laser,” Proc. SPIE8599, 859916 (2013).
[CrossRef]

Rev. Mod. Phys.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys.65, 1331–1392 (1993).
[CrossRef]

Other

N. Tolstik, I. T. Sorokina, A. Pospischil, and E. Sorokin, “Graphene mode-locked Cr:ZnS laser with 44 fs pulse duration,” in Advanced Solid-State Lasers Congress, M. Ebrahim-Zadeh and I. Sorokina, eds. (Optical Society of America, Paris, 2013), p. MW1C.1.

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N. Tolstik, I. T. Sorokina, and E. Sorokin, “Watt-level Kerr-lens mode-locked Cr:ZnS laser at 2.4 μm,” in CLEO: Science and Innovations (Optical Society of America, San Jose, 2013), p. CTh1H.2.

E. Sorokin and I. T. Sorokina, “Ultrashort-pulsed Kerr-lens modelocked Cr:ZnSe laser,” in European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference - CLEO Europe - EQEC, (IEEE, München, 2009), p. CF1_3.

Supplementary Material (1)

» Media 1: AVI (4063 KB)     

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of the femtosecond Kerr-lens mode-locked Cr:ZnS laser: FL – focusing lens, M1, M2, and M3 – high reflector mirrors (M1 could be substituted by a chirped mirror), Cr:ZnS – active element, YAG wedges – dispersion compensation, OC – output coupler, BS – beam splitter, SF – spectral filter, Out1 –laser output for controlling the wavelength, Out2 - main laser output; (b) typical laser spectrum (red) and spectral filter transmission (blue); (c) laser cavity round-trip GDD with bulk dispersion compensation (red), and with chirped mirror dispersion compensation (grey).

Fig. 2
Fig. 2

Chaotic regime in time domain. (a), (b) Signals from the Out1 channel (dark red, related to the central wavelength) and second-harmonic intensity (green, related to pulse peak power) of the Cr:ZnSe CPO laser in chaotic regime. (c) Interferometric autocorrelation traces recorded with the fast detector in chaotic (dark red) and regular chirped (grey) regimes. (d) Parametric diagram corresponding to the signals on graph (a) and (b) (grey and black lines, respectively), showing uncorrelated truly chaotic behaviour.

Fig. 3
Fig. 3

Output spectra (a) and corresponding dispersion values (b) of a CPO Cr:ZnS laser in various regimes: regular CPO (spectrum 1 and grey dot); stability border between regular and chaotic (spectrum 2 and dark red dots), and chaotic (spectrum 3 and red/violet dots). The red dots denote purely chaotic regime, violet dots denote quasiperiodic regime.

Fig. 4
Fig. 4

(a) Resonance condition (black crosses) for the CDS defines the spectrum width 2Δ. Changing the power and/or the dispersion (dashed lines) controls the spectrum width. Blue lines show the experimental spectra [20] corresponding to different energies. (b) For the conventional soliton laser (β2 < 0) a resonance is only possible with TOD, which generates a dispersive wave [21], illustrated by an experiment [22].The high-frequency modulation on the spectrum envelope in both graphs results from the intracavity water vapour [13, 23].

Fig. 5
Fig. 5

Time-frequency diagrams of the regular CDS regime with small TOD (a) and large TOD (b). Pseudocolor diagrams show the amplitude of the smoothed Wigner distribution [29] in logarithmic scale. The yellow curves at the bottom and to the right show the spectrum and time intensity, respectively. (c),(d): The corresponding round-trip phase delay (dark red) and group delay (blue) curves for the linear waves. Gray arrows denote the edge tails generated at the resonance positions R1 and R2.

Fig. 6
Fig. 6

Chaotic CDS regime. (a) Time-frequency diagram of a typical single round-trip and a corresponding round-trip phase and group delays (c). Spectra (b) of the 7000 round-trips and their accumulated spectrum (d), corresponding to the actual detector time constant. Media 1 provides the animated sequence of (a) and accumulation of (d) over the 7000 round-trips, as well as time dependencies of the pulse energy, SHG, wavelength, and r.m.s. spectral width.

Fig. 7
Fig. 7

(a) Phase portrait of the experimental CDS peak power set for 210 nJ of intracavity pulse energy. The 2 μs lag corresponds to 290 round-trips. The high-frequency detector noise is removed by the Fourier-filtering. (b) Calculated instantaneous phase portrait of a CDS. The wandering trajectory demonstrates the phase distortion and changes irregularly between the round-trips. The regular helicoidal trajectory corresponds to the pulse tail at the short-wavelength edge.

Equations (1)

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A ( z , t ) z = { σ + α 2 t 2 + [ κ ( 1 ζ | A ( z , t ) | 2 ) | A ( z , t ) | 2 ] } A ( z , t ) + i { β 2 2 2 t 2 γ | A ( z , t ) | 2 } A ( z , t ) + β 3 6 3 t 3 A ( z , t ) ,

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