Abstract

Understanding the gain dynamics of fiber amplifiers is essential for the implementation and active stabilization of low noise amplifiers or for coherent beam combining schemes. The gain dynamics of purely Er3+ or Yb3+ doped fiber amplifiers are well studied, whereas no analysis for co-doped systems, especially for Er3+:Yb3+ co-doped fiber amplifiers has been performed, so far. Here, we analyze for the first time the gain dynamics of Er3+:Yb3+ co-doped fiber amplifiers theoretically and experimentally. It is shown that due to the energy transfer between the Yb3+ and Er3+ ions a full analytical solution is not possible. Thus, we used numerical simulations to gain further insights. Comparison of experimental and numerical results shows good qualitative agreement. In addition, we were able to determine the Yb3+-Er3+ transfer function of the energy transfer experimentally.

© 2015 Optical Society of America

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References

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2014 (2)

2013 (1)

2012 (1)

2011 (1)

2010 (2)

M. Punturo and et al., “The third generation of gravitational wave observatories and their science reach,” Classical and Quantum Gravity 27, 084007 (2010).
[Crossref]

V. Kuhn, D. Kracht, J. Neumann, and P. Wessels, “Dependence of Er:Yb-codoped 1.5 μm amplifier on wavelength-tuned auxiliary seed signal at 1 μm wavelength,” Opt. Lett. 35, 4105–4107 (2010).
[Crossref] [PubMed]

2009 (1)

J. E. Guyer, D. Wheeler, and J. A. Warren, “FiPy: Partial Differential Equations with Python,” Computing in Science & Engineering 11(3), 6–15 (2009).
[Crossref]

2005 (1)

2004 (1)

2003 (1)

2002 (2)

S. Novak and A. Moesle, “Analytic model for gain modulation in EDFAs,” J. Lightwave Tech. 20, 975–985 (2002).
[Crossref]

S. Novak and R. Gieske, “SIMULINK model for EDFA dynamics applied to gain modulation,” J. Lightwave Tech. 6, 986–992 (2002).
[Crossref]

1998 (1)

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped Erbium-Ytterbium glass laser,” Appl. Phys. B 66, 19–26 (1998).
[Crossref]

1997 (2)

M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33, 1699–1705 (1997).
[Crossref]

M. A. Rebolledo, S. Jarabo, M. Hotoleanu, M. Karasek, E. Grolmus, and E. Jaunart, “Analysis of a technique to determine absolute values of the stimulated emission cross section in Erbium-doped silica fibres from gain measurements,” Pure Appl. Opt. 6, 425–433 (1997).
[Crossref]

1965 (1)

E. Snitzer and R. Woodcock, “Yb3+-Er3+ glass laser,” Applied Physics Letters 21, 45–46 (1965),
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Bouzinac, J. P.

Canat, G.

Cole, B.

Croteau, A.

De Geronimo, G.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped Erbium-Ytterbium glass laser,” Appl. Phys. B 66, 19–26 (1998).
[Crossref]

Gieske, R.

S. Novak and R. Gieske, “SIMULINK model for EDFA dynamics applied to gain modulation,” J. Lightwave Tech. 6, 986–992 (2002).
[Crossref]

Goldberg, L.

Grange, R.

Grolmus, E.

M. A. Rebolledo, S. Jarabo, M. Hotoleanu, M. Karasek, E. Grolmus, and E. Jaunart, “Analysis of a technique to determine absolute values of the stimulated emission cross section in Erbium-doped silica fibres from gain measurements,” Pure Appl. Opt. 6, 425–433 (1997).
[Crossref]

Guyer, J. E.

J. E. Guyer, D. Wheeler, and J. A. Warren, “FiPy: Partial Differential Equations with Python,” Computing in Science & Engineering 11(3), 6–15 (2009).
[Crossref]

Han, Q.

Hardy, Amos

He, Y.

Hotoleanu, M.

M. A. Rebolledo, S. Jarabo, M. Hotoleanu, M. Karasek, E. Grolmus, and E. Jaunart, “Analysis of a technique to determine absolute values of the stimulated emission cross section in Erbium-doped silica fibres from gain measurements,” Pure Appl. Opt. 6, 425–433 (1997).
[Crossref]

Jaouën, Y.

Jarabo, S.

M. A. Rebolledo, S. Jarabo, M. Hotoleanu, M. Karasek, E. Grolmus, and E. Jaunart, “Analysis of a technique to determine absolute values of the stimulated emission cross section in Erbium-doped silica fibres from gain measurements,” Pure Appl. Opt. 6, 425–433 (1997).
[Crossref]

Jaunart, E.

M. A. Rebolledo, S. Jarabo, M. Hotoleanu, M. Karasek, E. Grolmus, and E. Jaunart, “Analysis of a technique to determine absolute values of the stimulated emission cross section in Erbium-doped silica fibres from gain measurements,” Pure Appl. Opt. 6, 425–433 (1997).
[Crossref]

Jebali, M. A.

Karasek, M.

M. A. Rebolledo, S. Jarabo, M. Hotoleanu, M. Karasek, E. Grolmus, and E. Jaunart, “Analysis of a technique to determine absolute values of the stimulated emission cross section in Erbium-doped silica fibres from gain measurements,” Pure Appl. Opt. 6, 425–433 (1997).
[Crossref]

M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33, 1699–1705 (1997).
[Crossref]

Keller, U.

Kracht, D.

Kuhn, V.

Kulcsar, G.

Laperle, P.

Laporta, P.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped Erbium-Ytterbium glass laser,” Appl. Phys. B 66, 19–26 (1998).
[Crossref]

LaRochelle, S.

Maran, J. N.

Moesle, A.

S. Novak and A. Moesle, “Analytic model for gain modulation in EDFAs,” J. Lightwave Tech. 20, 975–985 (2002).
[Crossref]

Mollier, J. C.

Neumann, J.

Nicholson, J. W.

Ning, J.

Novak, S.

S. Novak and R. Gieske, “SIMULINK model for EDFA dynamics applied to gain modulation,” J. Lightwave Tech. 6, 986–992 (2002).
[Crossref]

S. Novak and A. Moesle, “Analytic model for gain modulation in EDFAs,” J. Lightwave Tech. 20, 975–985 (2002).
[Crossref]

Paré, C.

Paschotta, R.

Proulx, A.

Punturo, M.

M. Punturo and et al., “The third generation of gravitational wave observatories and their science reach,” Classical and Quantum Gravity 27, 084007 (2010).
[Crossref]

Rebolledo, M. A.

M. A. Rebolledo, S. Jarabo, M. Hotoleanu, M. Karasek, E. Grolmus, and E. Jaunart, “Analysis of a technique to determine absolute values of the stimulated emission cross section in Erbium-doped silica fibres from gain measurements,” Pure Appl. Opt. 6, 425–433 (1997).
[Crossref]

Schlatter, A.

Sheng, Z.

Snitzer, E.

E. Snitzer and R. Woodcock, “Yb3+-Er3+ glass laser,” Applied Physics Letters 21, 45–46 (1965),
[Crossref]

Steinke, M.

Supradeepa, V. R.

Svelto, O.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped Erbium-Ytterbium glass laser,” Appl. Phys. B 66, 19–26 (1998).
[Crossref]

Taccheo, S.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped Erbium-Ytterbium glass laser,” Appl. Phys. B 66, 19–26 (1998).
[Crossref]

Tuennermann, H.

Warren, J. A.

J. E. Guyer, D. Wheeler, and J. A. Warren, “FiPy: Partial Differential Equations with Python,” Computing in Science & Engineering 11(3), 6–15 (2009).
[Crossref]

Wessels, P.

Wheeler, D.

J. E. Guyer, D. Wheeler, and J. A. Warren, “FiPy: Partial Differential Equations with Python,” Computing in Science & Engineering 11(3), 6–15 (2009).
[Crossref]

Williams, G. M.

Woodcock, R.

E. Snitzer and R. Woodcock, “Yb3+-Er3+ glass laser,” Applied Physics Letters 21, 45–46 (1965),
[Crossref]

Xiao, H.

Yahel, E.

Zeller, S. C.

Zhang, W.

Zheng, H.

Appl. Phys. B (1)

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped Erbium-Ytterbium glass laser,” Appl. Phys. B 66, 19–26 (1998).
[Crossref]

Applied Physics Letters (1)

E. Snitzer and R. Woodcock, “Yb3+-Er3+ glass laser,” Applied Physics Letters 21, 45–46 (1965),
[Crossref]

Classical and Quantum Gravity (1)

M. Punturo and et al., “The third generation of gravitational wave observatories and their science reach,” Classical and Quantum Gravity 27, 084007 (2010).
[Crossref]

Computing in Science & Engineering (1)

J. E. Guyer, D. Wheeler, and J. A. Warren, “FiPy: Partial Differential Equations with Python,” Computing in Science & Engineering 11(3), 6–15 (2009).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33, 1699–1705 (1997).
[Crossref]

J. Lightwave Tech. (2)

S. Novak and A. Moesle, “Analytic model for gain modulation in EDFAs,” J. Lightwave Tech. 20, 975–985 (2002).
[Crossref]

S. Novak and R. Gieske, “SIMULINK model for EDFA dynamics applied to gain modulation,” J. Lightwave Tech. 6, 986–992 (2002).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Express (2)

Opt. Lett. (4)

Pure Appl. Opt. (1)

M. A. Rebolledo, S. Jarabo, M. Hotoleanu, M. Karasek, E. Grolmus, and E. Jaunart, “Analysis of a technique to determine absolute values of the stimulated emission cross section in Erbium-doped silica fibres from gain measurements,” Pure Appl. Opt. 6, 425–433 (1997).
[Crossref]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

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Figures (7)

Fig. 1
Fig. 1 Energy-level diagram of the co-doped Er3+:Yb3+ system. Not included are any upconversion processes, back-transfer of energy or absorption of pump light by the Er3+ ions.
Fig. 2
Fig. 2 Schematic overview of the used experimental setup to measure the transfer functions of the Er3+:Yb3+ co-doped fiber amplifier.
Fig. 3
Fig. 3 Computed transfer functions for the case of a seed power modulation: Magnitude (a) and phase (b). (c): Comparison of the numerically obtained magnitude and the magnitude of the first term in Eq. (24) for the lowest and highest pump power. (d): Comparison of the corner frequencies ω0 and ωeff of the first term in Eq. (24) and the corner frequencies of a damped high pass fit to the numerically obtained transfer functions.
Fig. 4
Fig. 4 Computed transfer functions of the energy transfer (dashed) and amplified seed (solid) for the case of a pump power modulation: Magnitude (a) and phase (b). Computed transfer function of the energy transfer and amplified seed for a 915 nm pumped amplifier (see text for further explanation): Magnitude (c) and phase (d).
Fig. 5
Fig. 5 Measured transfer functions (not normalized) for the case of a seed power modulation: Magnitude (a) and phase (b). Measured transfer functions (not normalized) for the case of a pump power modulation: Magnitude (c) and phase (d).
Fig. 6
Fig. 6 Comparison of the different corner frequencies obtained from the transfer functions for the case of a pump or seed power modulation.
Fig. 7
Fig. 7 Magnitude of the transfer function of the energy transfer for a pump power modulation.

Tables (1)

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Table 1 Parameters used in the numerical simulations

Equations (25)

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0 = p Er n 1 n 2 n 3 n 2 t = W 12 n 1 W 21 n 2 n 2 τ 21 + n 3 τ 32 n 3 t = n 3 τ 32 + R n 6 n 1 0 = p Yb n 5 n 6 n 6 t = W 56 n 5 W 65 n 6 n 6 τ 65 R n 6 n 1
W 56 = Γ p σ 56 P p ( z , t ) A c W 65 = Γ p σ 65 P p ( z , t ) A c
W 12 = Γ s σ 12 P s ( z , t ) A c W 21 = Γ s σ 21 P s ( z , t ) A c
Γ p , s = 1 e 2 r c 2 ω p , s 2
ω p , s = r c ( 0.65 + 1.619 V p , s 1.5 + 2.879 V p , s 6 )
V p , s = 2 π λ p , s r c N A c
0 = p E r n 1 n 2 n 2 t = W 12 n 1 W 21 n 2 n 2 τ 21 + R n 6 n 1 0 = p Y b n 5 n 6 n 6 t = W 56 n 5 W 65 n 6 n 6 τ 65 R n 6 n 1
d P p d z = Γ p ( n 6 σ 65 n 5 σ 56 ) P p = A c ( W 65 n 6 W 56 n 5 )
d P s d z = Γ s ( n 2 σ 21 n 1 σ 12 ) P s = A c ( W 21 n 2 W 12 n 1 ) .
P p ( z = 0 , t ) = P p , 0 ( t ) P s ( z = 0 , t ) = P s , 0 ( t ) .
N 2 t = P s ( z = 0 ) P s ( z = L ) N 2 τ 21 + X
X = R A c z = 0 z = L A c n 1 A c n 6
P s ( z = L , t ) = P s ( z = 0 , t ) e B s N 2 C s
B s = Γ s A c = ( σ 12 + σ 21 )
C s = Γ s σ 12 L p Er .
N 2 t = P s ( z = 0 ) ( 1 e B s N 2 C s ) N 2 τ 21 + X
P p , s ( z = 0 , t ) = P p , s , 0 ( 1 + m p , s e i ω t )
N 2 ( t ) = N 2 , 0 ( 1 + m 2 ( p , s ) e i ( ω t + ϕ 2 ( p , s ) ) )
X ( t ) = X 0 ( 1 + m X ( p , s ) e i ( ω t + ϕ X ( p , s ) ) )
N 2 , 0 m 2 ( p ) m p e i ϕ 2 ( p ) = X 0 m X ( p ) m p e i ϕ X ( p ) 1 ω eff + i ω
N 2 , 0 m 2 ( s ) m s e i ϕ 2 ( s ) = P s , 0 ( z = 0 ) P s , 0 ( z = L ) ω eff + i ω + X 0 m x ( s ) m s e i ϕ x ( s ) ω eff + i ω
ω eff = B s P s , 0 ( z = L ) + 1 τ 21 .
m s ( p ) m p e i ϕ s ( p ) = X 0 m X ( p ) m p e i ϕ X ( p ) B s ω eff + i ω
m s ( s ) m s e i ϕ s ( s ) = ω 0 + i ω ω eff + i ω + X 0 m X ( s ) m s e i ϕ X ( s ) ω eff + i ω
ω 0 = B s P s , 0 ( z = 0 ) + 1 τ 21 .

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