Abstract

We propose a combined model of the laser rate equation and the Ginzburg–Landau equation for simulation of the amplification of the ultrashort pulse in an ytterbium-doped fiber amplifier. An iterative procedure is designed for the repetition rate pulse sequence. The combined numerical model is compared with the pure dynamic rate equation for the amplification of a nanosecond single frequency pulse where both models are applicable. Good agreement is achieved. The combined model is then applied for the amplification of high repetition rate chirped pulse amplification in ytterbium-doped single-mode fiber. The slope efficiency, the wavelength shift, and the output spectrum width at different repetition rates are numerically investigated.

© 2012 Optical Society of America

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  1. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35, 94–96 (2010).
    [CrossRef]
  2. J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. G. P. Agrawal, Applications of Nonlinear Fiber Optics(Academic, 2001).
  7. K. Staliunas, “Laser Ginzburg-Landau equation and laser hydrodynamics,” Phys. Rev. A 48, 1573–1581 (1993).
    [CrossRef]
  8. N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and P. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
    [CrossRef]
  9. P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20, 863–870 (2003).
    [CrossRef]
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    [CrossRef]
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2010

2009

I. Martial, D. Papadopulos, M. Hanna, F. Druon, and P. Georges, “Nonlinear compression in a rod-type fiber for high energy ultrashort pulse generation,” Opt. Express 17, 11155–11160 (2009).
[CrossRef]

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

2008

2007

2006

2005

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and P. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

2003

2001

G. C. Valley, “Modeling cladding-pumped Er/Yb fiber amplifiers,” Opt. Fiber Technol. 7, 21–44 (2001).
[CrossRef]

1997

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997).
[CrossRef]

1993

K. Staliunas, “Laser Ginzburg-Landau equation and laser hydrodynamics,” Phys. Rev. A 48, 1573–1581 (1993).
[CrossRef]

1972

Acco, S.

Agrawal, G. P.

G. P. Agrawal, Applications of Nonlinear Fiber Optics(Academic, 2001).

G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2007).

Akhmediev, N.

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and P. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

Andersen, T. V.

Barty, C. P. J.

Beach, R. J.

Belhache, F.

Dangpeng, X.

Dawson, J. W.

Druon, F.

Eidam, T.

T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35, 94–96 (2010).
[CrossRef]

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

Englander, A.

Gabler, T.

Georges, P.

Glick, Y.

Gong, M.

Grapinet, M.

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and P. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

Grelu, P.

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and P. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20, 863–870 (2003).
[CrossRef]

Gutty, F.

Hadrich, S.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

Hanf, S.

Hanna, D. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997).
[CrossRef]

Hanna, M.

Heebner, J. E.

Honghuan, L.

Jianjun, W.

Jun, T.

Katz, O.

Lavi, R.

Lei, D.

Li, C.

Liao, S.

Limpert, J.

T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35, 94–96 (2010).
[CrossRef]

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

Martial, I.

Messerly, M. J.

Mingzhe, W.

Mingzhong, L.

Misas, C. J.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

Nafcha, Y.

Nilsson, J.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997).
[CrossRef]

Papadopulos, D.

Paschotta, R.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997).
[CrossRef]

Pax, P. H.

Qinghua, D.

Roser, F.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

Rothhardt, J.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

Rui, Z.

Schimpf, D. N.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

Schreiber, T.

Seise, E.

T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35, 94–96 (2010).
[CrossRef]

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

Shverdin, M. Y.

Siders, C. W.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Sintov, Y.

Smith, R. G.

Soto-Crespo, J. M.

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and P. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20, 863–870 (2003).
[CrossRef]

Sridharan, A. K.

Staliunas, K.

K. Staliunas, “Laser Ginzburg-Landau equation and laser hydrodynamics,” Phys. Rev. A 48, 1573–1581 (1993).
[CrossRef]

Stappaerts, E. A.

Tropper, A. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997).
[CrossRef]

Tunnermann, A.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

Tünnermann, A.

Valley, G. C.

G. C. Valley, “Modeling cladding-pumped Er/Yb fiber amplifiers,” Opt. Fiber Technol. 7, 21–44 (2001).
[CrossRef]

Wirth, C.

Xiaodong, H.

Yan, P.

Ying, D.

Yuan, Y.

Zhang, H.

Appl. Opt.

IEEE J. Quantum Electron.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15, 159–169 (2009).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Fiber Technol.

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and P. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

G. C. Valley, “Modeling cladding-pumped Er/Yb fiber amplifiers,” Opt. Fiber Technol. 7, 21–44 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. A

K. Staliunas, “Laser Ginzburg-Landau equation and laser hydrodynamics,” Phys. Rev. A 48, 1573–1581 (1993).
[CrossRef]

Other

A. E. Siegman, Lasers (University Science, 1986).

G. P. Agrawal, Applications of Nonlinear Fiber Optics(Academic, 2001).

G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2007).

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Figures (7)

Fig. 1.
Fig. 1.

Flow chart of the iterative procedure.

Fig. 2.
Fig. 2.

Calculation results of the combined model (dashed curves) and the pure DRE model (solid curves) for amplification of a single shot pulse. In (d), open circles denote the forward ASE, while no marker denotes the backward ASE.

Fig. 3.
Fig. 3.

Calculation results of the combined model (dashed curves) and the pure DRE model (solid curves) for amplification of a repetition rate pulse sequence. In (d), open circles denote the forward ASE, while no marker denotes the backward ASE.

Fig. 4.
Fig. 4.

(a) Pulse envelope and (b) spectral profile of the input (solid curves) and output (dashed curves) pulses.

Fig. 5.
Fig. 5.

Precise gain distribution (solid curves) and linear gain approximation (dashed curves) for pump power of (a) 10, (b) 100, and (c) 1000 mW. (d) Output average power for precise gain distribution (solid curve) and linear gain approximation (dashed curve).

Fig. 6.
Fig. 6.

Output average power (squares) and peak power (triangles) of the precise gain distribution (open) and linear gain approximation (solid) versus repetition rate.

Fig. 7.
Fig. 7.

Spectral width with (squares) and without (triangles) SPM versus repetition rate.

Tables (1)

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Table 1. Parameters Used in the Computation

Equations (14)

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t[n2(z,t)n]=l[Γp(σe,p,l+σa,p,l)hνp,lAdope(n2n)+Γpσa,p,lhνp,lAdope](Pp,l++Pp,l)+k[Γs(σe,s,k+σa,s,k)hνs,kAdope(n2n)+Γsσa,s,khνs,kAdope](Ps,k++Ps,k)1τ(n2n),
±Pp,l±(z,t)z+1υgp,lPp,l±(z,t)t=Γp(σa,p,l+σe,p,l)n(n2n)Pp,l±(Γpσa,p,ln+αp)Pp,l±,
±Ps,k±(z,t)z+1υgs,kPs,k±(z,t)t=Γs(σa,s,k+σe,s,k)n2Ps,k±(Γsσa,s,kn+αs)Ps,k±+2ΓsPs,kSEσe,s,kn2,
U(z,T)z=i2β2eff2UT2+12(gα)U+iγ|U|2U,
β2eff=β2+igT22[δ(δ23)+i(13δ2)31+δ2],
D=i2β22T2α2,
N=12g0(z,T)+iγ|U|2.
g0(z,T)=gss(z,ν0)exp(AeffEsatT|U(z,τ)|2dτ),
Esat=Aeffhv0Γs(σe,0+σa,0),
T(z,ν)=exp[(gss(z,ν)gss(z,ν0))dz],
gss(z,ν)=Γs(σe,νn2(z)σa,νn1(z)),
gsslin(z)=gss(0)+gss(L)gss(0)Lz,
n2new(z)n2old(z)Ep(z)Ep(zΔz)ηQhv0AdopeΔz,
Pth=17πAeff2gBLln(G),

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