Abstract

Multi-period pulsing instabilities in a Yb-doped ring fiber laser with a mode-locking mechanism provided by nonlinear polarization rotation are studied by means of numerical simulations. The impact of the third-order dispersion (TOD) of cavity elements on dynamic instabilities of the stretched-pulse mode-locked regime is elucidated. Different instability types with symmetry-preserving and symmetry-breaking features are found in a wide range of cavity group velocity dispersion (GVD). At a large anomalous cavity GVD, where a stretched-pulse mode-locked regime borders the soliton regime, multi-period pulsing instabilities result from the development of new resonant subsidebands associated with unstable dispersive waves. When a cavity GVD approaches zero and resonant sidebands are suppressed, multi-period pulsing is caused by parametric instability of the frequencies near the spectrum center. It is demonstrated that TOD suppresses both symmetry-preserving and symmetry-breaking multi-period instabilities in the stretched-pulse regime. From the analysis of the spectral sidebands, we conclude that instability suppression is related with a modification of the resonant coupling between the mode-locked pulse and the phase-velocity as well as group-velocity-matched dispersive waves.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]

2007

2006

L. M. Zhao, D. Y. Tang, and A. Q. Liu, “Chaotic dynamics of passively mode-locked soliton fiber ring laser,” Chaos 16, 013128-013137 (2006).
[CrossRef] [PubMed]

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, “High-power ultrafast fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 12, 233-244 (2006).
[CrossRef]

C. K. Nielsen, K. G. Jespersen, and S. R. Keiding, “A 158fs5.3nJ fiber-laser system at 1μm using photonic bandgap fibers for dispersion control and pulse compression,” Opt. Express 14, 6063-6068 (2006).
[CrossRef] [PubMed]

A. Isomäki and O. G. Okhotnikov, “Femtosecond soliton mode-locked laser based on ytterbium-doped photonic bandgap fiber,” Opt. Express 14, 9238-9243 (2006).
[CrossRef] [PubMed]

2004

2003

2002

2000

1999

H. D. I. Abarbanel, M. B. Kennel, M. Buhl, and C. T. Lewis, “Chaotic dynamics in erbium-doped fiber ring lasers,” Phys. Rev. A 60, 2360-2374 (1999).
[CrossRef]

1998

1997

1994

M. L. Dennis and I. N. Duling III, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469-1477 (1994).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200-208 (1994).
[CrossRef]

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photon. Technol. Lett. 6, 697-699 (1994).
[CrossRef]

M. L. Dennis and I. N. Duling III, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469-1477 (1994).
[CrossRef]

1993

1992

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806-807 (1992).
[CrossRef]

J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schroedinger equation,” J. Opt. Soc. Am. B 9, 91-97 (1992).
[CrossRef]

1990

R. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by solitons at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426-439 (1990).
[CrossRef] [PubMed]

1984

J. W. Swift and K. Wiesenfeld, “Suppression of period doubling in symmetric systems,” Phys. Rev. Lett. 52, 705-708 (1984).
[CrossRef]

1983

D. R. Moore, J. Toomre, E. Knobloch, and N. O. Weiss, “Period doubling and chaos in partial differential equations for thermosolutal convection,” Nature 303, 663-667 (1983).
[CrossRef]

Chaos

L. M. Zhao, D. Y. Tang, and A. Q. Liu, “Chaotic dynamics of passively mode-locked soliton fiber ring laser,” Chaos 16, 013128-013137 (2006).
[CrossRef] [PubMed]

Electron. Lett.

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806-807 (1992).
[CrossRef]

IEEE J. Quantum Electron.

M. L. Dennis and I. N. Duling III, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469-1477 (1994).
[CrossRef]

M. L. Dennis and I. N. Duling III, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469-1477 (1994).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200-208 (1994).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, “High-power ultrafast fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 12, 233-244 (2006).
[CrossRef]

IEEE Photon. Technol. Lett.

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photon. Technol. Lett. 6, 697-699 (1994).
[CrossRef]

J. Opt. Soc. Am. B

Nature

D. R. Moore, J. Toomre, E. Knobloch, and N. O. Weiss, “Period doubling and chaos in partial differential equations for thermosolutal convection,” Nature 303, 663-667 (1983).
[CrossRef]

Opt. Express

Opt. Lett.

A. Ruehl, O. Prochnow, M. Engelbrecht, D. Wandt, and D. Kracht, “Similariton fiber laser with a hollow-core photonic bandgap fiber for dispersion control,” Opt. Lett. 32, 1084-1086 (2007).
[CrossRef] [PubMed]

A. Ruehl, O. Prochnow, M. Schultz, D. Wandt, and D. Kracht, “Impact of third-order dispersion on the generation of wave-breaking free pulses in ultrafast fiber lasers,” Opt. Lett. 32, 2590-2592 (2007).
[CrossRef] [PubMed]

J. Herrmann, V. P. Kalosha, and M. Müller, “Higher-order phase dispersion in femtosecond Kerr-lens mode-locked solid-state lasers: sideband generation and pulse splitting,” Opt. Lett. 22, 236-238 (1997).
[CrossRef] [PubMed]

M. Horowitz, Y. Barad, and Y. Silberberg, “Noiselike pulses with broadband spectrum generated from an erbium-doped fiber laser,” Opt. Lett. 22, 799-801 (1997).
[CrossRef] [PubMed]

H. A. Haus, J. D. Moores, and L. E. Nelson, “Effect of third-order dispersion on passive mode locking,” Opt. Lett. 18, 51-53 (1993)
[CrossRef] [PubMed]

M. Fermann, M. J. Andrejco, Y. Silverberg, and M. L. Stock, “Passive mode locking by using nonlinear polarization evolution in a polarizing-maintaining erbium-doped fiber laser,” Opt. Lett. 18, 894-896 (1993).
[CrossRef] [PubMed]

K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18, 1080-1082 (1993).
[CrossRef] [PubMed]

F. Matera, A. Mecozzi, M. Romagnoli, and M. Settembre, “Sideband instability induced by periodic power variation in long-distance fiber links,” Opt. Lett. 18, 1499-1501 (1993).
[CrossRef] [PubMed]

T. Brabec and S. M. J. Kelly, “Third-order dispersion as a limiting factor to mode locking in femtosecond solitary lasers,” Opt. Lett. 18, 2002-2004 (1993).
[CrossRef] [PubMed]

Phys. Rev. A

R. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by solitons at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426-439 (1990).
[CrossRef] [PubMed]

H. D. I. Abarbanel, M. B. Kennel, M. Buhl, and C. T. Lewis, “Chaotic dynamics in erbium-doped fiber ring lasers,” Phys. Rev. A 60, 2360-2374 (1999).
[CrossRef]

V. L. Kalashnikov and A. Chernykh, “Spectral anomalies and stability of chirped-pulse oscillators,” Phys. Rev. A 75, 033820-033825 (2007).
[CrossRef]

Phys. Rev. E

N. Akhmediev and J. M. Soto-Crespo, “Strongly asymmetric soliton explosions,” Phys. Rev. E 70, 036613-036622 (2004).
[CrossRef]

Phys. Rev. Lett.

J. W. Swift and K. Wiesenfeld, “Suppression of period doubling in symmetric systems,” Phys. Rev. Lett. 52, 705-708 (1984).
[CrossRef]

Other

M. E. Fermann, A. Galvanauskas, and G. Sucha, Ultrafast Lasers (Marcel Dekker, 2002).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

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Figures (15)

Fig. 1
Fig. 1

Schematic of the Yb-doped fiber laser in the ring cavity configuration.

Fig. 2
Fig. 2

(a) Dependence of the mode-locked pulse energy on the pump gain. Stable mode-locked regime transforms into multi-period pulsing (MP) and then into chaos when the gain increases. Within the instability domain an AS-MP regime is found. (b) Dependence of pulse energy on the round-trip number for the symmetrical multi-period pulsing regime at a gain equal to 50 dB m .

Fig. 3
Fig. 3

(a) Intensity profiles and (b) corresponding phases of the mode-locked pulse at the end of the SMF section (solid curve, which shows intensity profile with five times magnification) and at the end of Yb-doped fiber (dashed curve). The phase demonstrates a flipping behavior that is an indication of the stretched-pulse regime.

Fig. 4
Fig. 4

(a) Pulse profiles and (b) corresponding spectra for pulses at the output from the Yb-doped fiber at two successive round trips for the symmetrical multi-period pulsing regime whose energy dependence versus round-trip number is shown in Fig. 2b. Asterisks mark the frequency positions for the basic sidebands, while the arrow corresponds to oscillating sidebands that emerged due to instability. Cavity GVD is 0.012 ps 2 .

Fig. 5
Fig. 5

Same as in Fig. 4 for the asymmetrical multi-period pulsing instability regime.

Fig. 6
Fig. 6

(a) Pulse profiles and (b) corresponding spectra for pulses at the output from the Yb-doped fiber at two successive round trips for the symmetrical multi-period pulsing regime. Cavity GVD is 0.001 ps 2 .

Fig. 7
Fig. 7

Same as in Fig. 6 for the symmetry-breaking multi-period pulsing instability regime.

Fig. 8
Fig. 8

Mode-locked pulse energy at the output from the Yb-doped fiber versus round-trip number at different TOD parameters: (a) β 3 = 0 , (b) β 3 = 130 fs 3 mm , (c) β 3 = 150 fs 3 mm , and (d) β 3 = 200 fs 3 mm .

Fig. 9
Fig. 9

Spectra at two successive round trips at β 3 = 150 fs 3 mm .

Fig. 10
Fig. 10

Sideband positions versus frequency offset for three values of the TOD parameter, β 3 = 0 fs 3 mm (solid curve), β 3 = 150 fs 3 mm (asterisks and dashed–dotted curve), β 3 = 320 fs 3 mm (open circles and dashed curve).

Fig. 11
Fig. 11

Duration of the chirp compensated pulses versus TOD parameter in the PBF for a gain of 50 dB m . In the multi-period pulsing regime at small β 3 , the lower and upper curves correspond to the shortest and longest mode-locked pulses, respectively. The period-two regime is found near β 3 = 300 fs 3 mm .

Fig. 12
Fig. 12

(a) Spectra of the mode-locked pulses in the unstable period-two regime (solid curve) at β 3 = 300 fs 3 mm and in the stable mode-locked regime at β 3 = 320 fs 3 mm (dashed curve). Spectrum in the unstable regime is shown as shifted down by 10 dB . Arrows show extra sidebands that arise in the unstable regime. (b) GVD of the laser cavity versus carrier frequency offset calculated for the parameters corresponding to the curves in (a).

Fig. 13
Fig. 13

Spectra at different TOD parameters β 3 for the stretched-pulse regime in the vicinity of zero cavity dispersion, GVD = 0.001 ps 2 . (a) Stable symmetrical mode-locked regime at zero β 3 slightly below the instability threshold, gain parameter g 0 = 48 dB m ; (b) symmetry-breaking unstable regime at zero β 3 , g 0 = 49 dB m ; (c) β 3 = 60 fs 3 mm , g 0 = 49 dB m ; and (d) stable regime at β 3 = 100 fs 3 mm , g 0 = 49 dB m .

Fig. 14
Fig. 14

Mode-locked pulse energy versus round-trip number for symmetry-breaking regimes whose spectra are presented in Fig. 13. (a) Regime with period of 16 round trips corresponding to parameters of Fig. 13b and (b) regime with period of 32 round trips corresponding to the spectrum snapshot in Fig. 13c.

Fig. 15
Fig. 15

Pulse profiles for the mode-locked regime at β 3 = 100 fs 3 mm , g 0 = 49 dB m corresponding to the spectrum in Fig. 13d. The solid curve is the pulse after the Yb-doped fiber, while the dashed curve is the pulse after SMF magnified by a factor of 10 for easy comparison.

Equations (3)

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A z = i β 2 2 2 A t 2 + i γ A 2 A + g 0 ( λ ) 1 + E pulse E sat A ,
A z = i β 2 2 2 A t 2 + β 3 6 3 A t 3 + i γ A 2 A ,
N = 1 4 π L β 2 ( Δ ω N 2 + Δ Ω 2 ) 1 12 π L β 3 Δ ω N 3 ,

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