Abstract

A comprehensive lumped model approach has been presented in this paper for the simulation of a dispersion-managed active mode-locked fiber laser. A key aspect of our model is that it operates simultaneously at two different spectral scales, corresponding to the gain bandwidth of the erbium-doped fiber and the frequency content of the mode-locked laser (MLL) pulse. The lumped model consists of a detailed amplifier model that is evolved using a predictor–corrector-based adaptive approach. Convergence analysis of this algorithm is also presented in this paper, highlighting the step size reduction achieved when the amplifier migrates from linear to saturation regime. A simple adaptive frequency domain approach is followed to control the fine grid spectral points and the coarse grid wavelengths. Such an approach has been used to simulate a harmonic MLL cavity in two widely different dispersion regimes facilitated by a pair of chirped fiber Bragg gratings. We validate our model by comparing such simulated results with carefully planned experiments.

© 2013 Optical Society of America

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References

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  1. U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003).
    [CrossRef]
  2. N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg–Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
    [CrossRef]
  3. K. Koizumi, M. Yoshida, T. Hirooka, and M. Nakazawa, “10 GHz 1.1 ps optical pulse generation from a regeneratively mode-locked Yb fiber laser in the 1.1 μm band,” Opt. Express 19, 25426 (2011).
    [CrossRef]
  4. D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene modelocked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
    [CrossRef]
  5. R. Wilbrandt and H. Weber, “Fluctuations in mode-locking threshold due to statistics of spontaneous emission,” IEEE J. Quantum Electron. 11, 186–190 (1975).
    [CrossRef]
  6. R. Paschotta, “Noise of mode-locked lasers (part I): numerical model,” Appl. Phys. B 79, 153–162 (2004).
    [CrossRef]
  7. Y. Yuhua, C. Lou, M. Han, and Y. Gao, “Detuning characteristics of the AM mode-locked fiber laser,” Opt. Quantum Electron. 33, 589–597 (2000).
  8. J. O’Neil, J. N. Kutz, and B. Sandstede, “Theory and simulation of the dynamics and stability of actively modelocked lasers,” IEEE J. Quantum Electron. 38, 1412–1419 (2002).
    [CrossRef]
  9. A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
    [CrossRef]
  10. L. N. Binh and N. Q. Ngo, Ultra-Fast Fiber Lasers (CRC Press, 2010).
  11. D. B. S. Soh, S. E. Bisson, B. D. Patterson, and S. W. Moore, “High-power all-fiber passively Q-switched laser using a doped fiber as a saturable absorber: numerical simulations,” Opt. Lett. 36, 2536–2538 (2011).
    [CrossRef]
  12. E. Desurvire, Erbium Doped Fiber Amplifier—Principles and Applications (Wiley, 2009).
  13. A. Bekal and B. Srinivasan, “Adaptive Adams–Bashforth method for modeling of highly doped fiber amplifiers and fiber lasers,” Opt. Eng. 51, 065005 (2012).
    [CrossRef]
  14. G. P. Agarwal, Nonlinear Fiber Optics. (Academic, 2001).
  15. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
    [CrossRef]
  16. Y. Wei, Y. Zhao, J. Yang, M. Wang, and X. Jiang, “Chirp characteristics of silicon Mach–Zehnder modulator under small-signal modulation,” J. Lightwave Technol. 29, 1011–1017 (2011).
    [CrossRef]
  17. L. R. Chen, J. E. Sipe, S. D. Benjamin, H. Jung, and P. W. E. Smith, “Dynamics of ultrashort pulse propagation through fiber gratings,” Opt. Express 1, 242–249 (1997).
    [CrossRef]
  18. http://www.photonics.umd.edu/software/ssprop/ (2011).
  19. N. Pandit, D. U. Noske, S. Kelly, and J. R. Taylor, “Characteristic instability of fibre loop soliton lasers,” Electron. Lett. 28, 455–457 (1992).
    [CrossRef]
  20. R. Paschotta, “Noise of mode-locked lasers (part II): timing jitter and other fluctuations,” Appl. Phys. B 79, 163–173 (2004).
    [CrossRef]

2012 (1)

A. Bekal and B. Srinivasan, “Adaptive Adams–Bashforth method for modeling of highly doped fiber amplifiers and fiber lasers,” Opt. Eng. 51, 065005 (2012).
[CrossRef]

2011 (3)

2010 (1)

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene modelocked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[CrossRef]

2005 (1)

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
[CrossRef]

2004 (2)

R. Paschotta, “Noise of mode-locked lasers (part I): numerical model,” Appl. Phys. B 79, 153–162 (2004).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (part II): timing jitter and other fluctuations,” Appl. Phys. B 79, 163–173 (2004).
[CrossRef]

2003 (1)

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003).
[CrossRef]

2002 (1)

J. O’Neil, J. N. Kutz, and B. Sandstede, “Theory and simulation of the dynamics and stability of actively modelocked lasers,” IEEE J. Quantum Electron. 38, 1412–1419 (2002).
[CrossRef]

2001 (1)

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg–Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
[CrossRef]

2000 (2)

Y. Yuhua, C. Lou, M. Han, and Y. Gao, “Detuning characteristics of the AM mode-locked fiber laser,” Opt. Quantum Electron. 33, 589–597 (2000).

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[CrossRef]

1997 (1)

1992 (1)

N. Pandit, D. U. Noske, S. Kelly, and J. R. Taylor, “Characteristic instability of fibre loop soliton lasers,” Electron. Lett. 28, 455–457 (1992).
[CrossRef]

1975 (1)

R. Wilbrandt and H. Weber, “Fluctuations in mode-locking threshold due to statistics of spontaneous emission,” IEEE J. Quantum Electron. 11, 186–190 (1975).
[CrossRef]

Agarwal, G. P.

G. P. Agarwal, Nonlinear Fiber Optics. (Academic, 2001).

Akhmediev, N.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg–Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
[CrossRef]

Bekal, A.

A. Bekal and B. Srinivasan, “Adaptive Adams–Bashforth method for modeling of highly doped fiber amplifiers and fiber lasers,” Opt. Eng. 51, 065005 (2012).
[CrossRef]

Benjamin, S. D.

Binh, L. N.

L. N. Binh and N. Q. Ngo, Ultra-Fast Fiber Lasers (CRC Press, 2010).

Bisson, S. E.

Chen, L. R.

Desurvire, E.

E. Desurvire, Erbium Doped Fiber Amplifier—Principles and Applications (Wiley, 2009).

Dudley, J. M.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[CrossRef]

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[CrossRef]

Ferrari, A. C.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene modelocked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[CrossRef]

Gao, Y.

Y. Yuhua, C. Lou, M. Han, and Y. Gao, “Detuning characteristics of the AM mode-locked fiber laser,” Opt. Quantum Electron. 33, 589–597 (2000).

Han, M.

Y. Yuhua, C. Lou, M. Han, and Y. Gao, “Detuning characteristics of the AM mode-locked fiber laser,” Opt. Quantum Electron. 33, 589–597 (2000).

Harvey, J. D.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[CrossRef]

Hasan, T.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene modelocked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[CrossRef]

Hirooka, T.

Jiang, X.

Jung, H.

Keller, U.

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003).
[CrossRef]

Kelly, S.

N. Pandit, D. U. Noske, S. Kelly, and J. R. Taylor, “Characteristic instability of fibre loop soliton lasers,” Electron. Lett. 28, 455–457 (1992).
[CrossRef]

Koizumi, K.

Komarov, A.

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
[CrossRef]

Kruglov, V. I.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[CrossRef]

Kutz, J. N.

J. O’Neil, J. N. Kutz, and B. Sandstede, “Theory and simulation of the dynamics and stability of actively modelocked lasers,” IEEE J. Quantum Electron. 38, 1412–1419 (2002).
[CrossRef]

Leblond, H.

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
[CrossRef]

Lou, C.

Y. Yuhua, C. Lou, M. Han, and Y. Gao, “Detuning characteristics of the AM mode-locked fiber laser,” Opt. Quantum Electron. 33, 589–597 (2000).

Moore, S. W.

Nakazawa, M.

Ngo, N. Q.

L. N. Binh and N. Q. Ngo, Ultra-Fast Fiber Lasers (CRC Press, 2010).

Noske, D. U.

N. Pandit, D. U. Noske, S. Kelly, and J. R. Taylor, “Characteristic instability of fibre loop soliton lasers,” Electron. Lett. 28, 455–457 (1992).
[CrossRef]

O’Neil, J.

J. O’Neil, J. N. Kutz, and B. Sandstede, “Theory and simulation of the dynamics and stability of actively modelocked lasers,” IEEE J. Quantum Electron. 38, 1412–1419 (2002).
[CrossRef]

Pandit, N.

N. Pandit, D. U. Noske, S. Kelly, and J. R. Taylor, “Characteristic instability of fibre loop soliton lasers,” Electron. Lett. 28, 455–457 (1992).
[CrossRef]

Paschotta, R.

R. Paschotta, “Noise of mode-locked lasers (part II): timing jitter and other fluctuations,” Appl. Phys. B 79, 163–173 (2004).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (part I): numerical model,” Appl. Phys. B 79, 153–162 (2004).
[CrossRef]

Patterson, B. D.

Popa, D.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene modelocked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[CrossRef]

Sanchez, F.

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
[CrossRef]

Sandstede, B.

J. O’Neil, J. N. Kutz, and B. Sandstede, “Theory and simulation of the dynamics and stability of actively modelocked lasers,” IEEE J. Quantum Electron. 38, 1412–1419 (2002).
[CrossRef]

Sipe, J. E.

Smith, P. W. E.

Soh, D. B. S.

Soto-Crespo, J. M.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg–Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
[CrossRef]

Srinivasan, B.

A. Bekal and B. Srinivasan, “Adaptive Adams–Bashforth method for modeling of highly doped fiber amplifiers and fiber lasers,” Opt. Eng. 51, 065005 (2012).
[CrossRef]

Sun, Z.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene modelocked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[CrossRef]

Taylor, J. R.

N. Pandit, D. U. Noske, S. Kelly, and J. R. Taylor, “Characteristic instability of fibre loop soliton lasers,” Electron. Lett. 28, 455–457 (1992).
[CrossRef]

Thomsen, B. C.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[CrossRef]

Torrisi, F.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene modelocked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[CrossRef]

Town, G.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg–Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
[CrossRef]

Wang, F.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene modelocked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[CrossRef]

Wang, M.

Weber, H.

R. Wilbrandt and H. Weber, “Fluctuations in mode-locking threshold due to statistics of spontaneous emission,” IEEE J. Quantum Electron. 11, 186–190 (1975).
[CrossRef]

Wei, Y.

Wilbrandt, R.

R. Wilbrandt and H. Weber, “Fluctuations in mode-locking threshold due to statistics of spontaneous emission,” IEEE J. Quantum Electron. 11, 186–190 (1975).
[CrossRef]

Yang, J.

Yoshida, M.

Yuhua, Y.

Y. Yuhua, C. Lou, M. Han, and Y. Gao, “Detuning characteristics of the AM mode-locked fiber laser,” Opt. Quantum Electron. 33, 589–597 (2000).

Zhao, Y.

Appl. Phys. B (2)

R. Paschotta, “Noise of mode-locked lasers (part I): numerical model,” Appl. Phys. B 79, 153–162 (2004).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (part II): timing jitter and other fluctuations,” Appl. Phys. B 79, 163–173 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene modelocked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[CrossRef]

Electron. Lett. (1)

N. Pandit, D. U. Noske, S. Kelly, and J. R. Taylor, “Characteristic instability of fibre loop soliton lasers,” Electron. Lett. 28, 455–457 (1992).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. Wilbrandt and H. Weber, “Fluctuations in mode-locking threshold due to statistics of spontaneous emission,” IEEE J. Quantum Electron. 11, 186–190 (1975).
[CrossRef]

J. O’Neil, J. N. Kutz, and B. Sandstede, “Theory and simulation of the dynamics and stability of actively modelocked lasers,” IEEE J. Quantum Electron. 38, 1412–1419 (2002).
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003).
[CrossRef]

Opt. Eng. (1)

A. Bekal and B. Srinivasan, “Adaptive Adams–Bashforth method for modeling of highly doped fiber amplifiers and fiber lasers,” Opt. Eng. 51, 065005 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

Y. Yuhua, C. Lou, M. Han, and Y. Gao, “Detuning characteristics of the AM mode-locked fiber laser,” Opt. Quantum Electron. 33, 589–597 (2000).

Phys. Rev. E (2)

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg–Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[CrossRef]

Other (4)

http://www.photonics.umd.edu/software/ssprop/ (2011).

E. Desurvire, Erbium Doped Fiber Amplifier—Principles and Applications (Wiley, 2009).

G. P. Agarwal, Nonlinear Fiber Optics. (Academic, 2001).

L. N. Binh and N. Q. Ngo, Ultra-Fast Fiber Lasers (CRC Press, 2010).

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Figures (12)

Fig. 1.
Fig. 1.

Schematic diagram of the MLL used in our simulations and experiments. The chirped gratings are used for dispersion management and an EOM is used to implement active mode locking.

Fig. 2.
Fig. 2.

Comparison between experimental and simulation generated CW power charactersistics curve using saturated gain model and the erbium-doped fiber amplifier model.

Fig. 3.
Fig. 3.

Salient features of adaptive algorithm to simulate EDF amplifier. (a) Coarse and fine grid structure for simulating the pulse propagation in the EDF amplifier. Coarse grid spans the entire gain bandwidth of EDF and the fine grid is used around the lasing wavelength. (b) Signal flow diagram for adaptive evaluation of pulse propagation using AB predictor–corrector method and SSFT.

Fig. 4.
Fig. 4.

Typical spectrum at the output of the simulated amplifier for an input pulse of 1 mW peak power and 1 ps of pulse width at a wavelength of 1550 nm. The signal wavelength is clearly evident from the coarse spectrum [(a)], and dispersion effects are evident in the phase profile in (b) frequency and (c) time domains from the fine spectrum.

Fig. 5.
Fig. 5.

Comparison of pulse parameter evolution between our adaptive scheme and the constant gain model. Input power of 1 mW peak power and 1 ps pulse width was used as input to both the models. Even though the peak power at the output is the same, the spectral width shows large change indicating a change in nonlinear evolution of the pulse.

Fig. 6.
Fig. 6.

Simulation with (b) constant gain across the fine grid allows nonlinear effects to act on the pulse more than that with (c) interpolated gain. The interpolated gain also emulates the gain bandwidth of the saturated EDF. This will be of importance while simulating pulses with large bandwidth, which is the case in passive MLLs.

Fig. 7.
Fig. 7.

Comparison between adaptive and constant step size evaluation of the pulse propagation through the amplifier.

Fig. 8.
Fig. 8.

Convergence analysis of adaptive scheme for constant step size scheme. (a) Convergence between constant step size and adaptive step size shows that their convergence characteristics are similar and both would take the same number of steps to converge. (b) Dependence of the number of steps on input peak power shows the advantage of using an adaptive scheme when the amplifier enters saturation, where the required number of steps reduces by a factor of 2.

Fig. 9.
Fig. 9.

Flow chart outlining our adaptive algorithm for modeling the MLL.

Fig. 10.
Fig. 10.

Simulated output of the mode-locked cavity with both CFBGs oriented to give positive dispersion. Average output power is 5.2 mW.

Fig. 11.
Fig. 11.

Comparison of simulated as well as experimentally measured spectral width and pulse width as a function of output power. (a) Spectral width of the output pulse train and (b) pulse width of the output pulse train.

Fig. 12.
Fig. 12.

Simulated output of the mode-locked cavity with CFBG1 providing positive dispersion and the CFBG2 providing negative dispersion (pump power of 200 mW).

Equations (12)

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

iTA=[((γiϵ)|A|2iδ)(D2iβ2)t2+iμ|A|4]A,
g=g01+PinPs,
Slope efficiency=PoutPp=(g0·Lgl·Lc1)·β·ILtotal·ILfrac·C0,
dPdz=2π(g(r,z)·I+σe(λ)N2·2·I0)rdr,
g(r,z)=σe(λ)N2/3(r,z)σa(λ)N1(r,z),
itA=α2Aβ22z2A+γ|A|2A,
dPdz=g·P+gse·PoP=(Pin+gse·Pog)·e(gz)gse·Pog,
Aout=g2·Ain+gse·Po2gexp(gz)1Pin·e(j·rand(π,π)).
T=cos(π4(m·sin(ωm·t)1)),
Φ=αchirp|T|2·d|T|2dt·dt=2αchirp·ln|T|.
β2=λ2πΔλ·(cvg),
Sw=(f·|A|)2·df(f·|A|2·df)2|A|2·df,

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