Abstract

Gain dynamics and refractive index changes in fiber amplifiers are important in many areas. For example, the knowledge of the frequency responses for seed and pump power modulation are required to actively stabilize low noise fiber amplifiers. Slow and fast light via coherent population oscillations rely on the change of group index to delay or advance pulses, and refractive index changes in fiber amplifiers are a possible explanation for mode fluctuations in high power fiber amplifiers. Here, we analyze the frequency dependent influence of seed and pump power modulation on the fiber amplifier output power and the refractive index. We explain the observed power and refractive index modulation with an analytic model originally developed for telecom amplifiers and discuss a further simplification of the model.

© 2012 OSA

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References

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  1. M. Digonnet, R. Sadowski, H. Shaw, and R. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low–power all–optical switching: a review,” Opt. Fiber Technol. 3, 44–64 (1997).
    [CrossRef]
  2. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19, 13218–13224 (2011).
    [CrossRef] [PubMed]
  3. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19, 10180–10192 (2011).
    [CrossRef] [PubMed]
  4. A. Fotiadi, O. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16, 12658–12663 (2008).
    [PubMed]
  5. H. Tünnermann, J. Neumann, D. Kracht, and P. Weßels, “All-fiber phase actuator based on an erbium-doped fiber amplifier for coherent beam combining at 1064 nm,” Opt. Lett. 36, 448–450 (2011).
    [CrossRef] [PubMed]
  6. S. Novak and A. Moesle, “Analytic model for gain modulation in EDFAs,” J. Lightwave Technol. 20, 975–985 (2002).
    [CrossRef]
  7. M. Tröbs, P. Weßels, and C. Fallnich, “Power- and frequency-noise characteristics of an Yb-doped fiber amplifier and actuators for stabilization,” Opt. Express 13, 2224–2235 (2005).
    [CrossRef] [PubMed]
  8. A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europys. Lett. 73, 218–224 (2006).
    [CrossRef]
  9. A. Fotiadi, N. Zakharov, O. Antipov, and P. Mégret, “All-fiber coherent combining of Er-doped amplifiers through refractive index control in Yb-doped fibers,” Opt. Lett. 34, 3574–3576 (2009).
    [CrossRef] [PubMed]
  10. J. J. Jou and C. Liu, “Equivalent circuit model for erbium-doped fibre amplifiers including amplified spontaneous emission,” IET Optoelectron. 2, 29–33 (2008).
    [CrossRef]
  11. W. A. Clarkson, “Thermal effects and their mitigation in end–pumped solid–state lasers,” J. Phys. D: Appl. Phys. 34, 2381–2395 (2001).
    [CrossRef]
  12. D. Brown, “Heat, fluorescence, and stimulated–emission power densities and fractions in Nd: YAG,” IEEE J. Quantum Electron. 34, 560–572 (2002).
    [CrossRef]

2011 (3)

2009 (1)

2008 (2)

J. J. Jou and C. Liu, “Equivalent circuit model for erbium-doped fibre amplifiers including amplified spontaneous emission,” IET Optoelectron. 2, 29–33 (2008).
[CrossRef]

A. Fotiadi, O. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16, 12658–12663 (2008).
[PubMed]

2006 (1)

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europys. Lett. 73, 218–224 (2006).
[CrossRef]

2005 (1)

2002 (2)

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

D. Brown, “Heat, fluorescence, and stimulated–emission power densities and fractions in Nd: YAG,” IEEE J. Quantum Electron. 34, 560–572 (2002).
[CrossRef]

2001 (1)

W. A. Clarkson, “Thermal effects and their mitigation in end–pumped solid–state lasers,” J. Phys. D: Appl. Phys. 34, 2381–2395 (2001).
[CrossRef]

1997 (1)

M. Digonnet, R. Sadowski, H. Shaw, and R. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low–power all–optical switching: a review,” Opt. Fiber Technol. 3, 44–64 (1997).
[CrossRef]

Antipov, O.

Bigelow, M. S.

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europys. Lett. 73, 218–224 (2006).
[CrossRef]

Boyd, R. W.

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europys. Lett. 73, 218–224 (2006).
[CrossRef]

Brown, D.

D. Brown, “Heat, fluorescence, and stimulated–emission power densities and fractions in Nd: YAG,” IEEE J. Quantum Electron. 34, 560–572 (2002).
[CrossRef]

Clarkson, W. A.

W. A. Clarkson, “Thermal effects and their mitigation in end–pumped solid–state lasers,” J. Phys. D: Appl. Phys. 34, 2381–2395 (2001).
[CrossRef]

Digonnet, M.

M. Digonnet, R. Sadowski, H. Shaw, and R. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low–power all–optical switching: a review,” Opt. Fiber Technol. 3, 44–64 (1997).
[CrossRef]

Eidam, T.

Fallnich, C.

Fotiadi, A.

Jansen, F.

Jarabo, S.

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europys. Lett. 73, 218–224 (2006).
[CrossRef]

Jauregui, C.

Jou, J. J.

J. J. Jou and C. Liu, “Equivalent circuit model for erbium-doped fibre amplifiers including amplified spontaneous emission,” IET Optoelectron. 2, 29–33 (2008).
[CrossRef]

Kracht, D.

Lepeshkin, N. N.

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europys. Lett. 73, 218–224 (2006).
[CrossRef]

Limpert, J.

Liu, C.

J. J. Jou and C. Liu, “Equivalent circuit model for erbium-doped fibre amplifiers including amplified spontaneous emission,” IET Optoelectron. 2, 29–33 (2008).
[CrossRef]

Mégret, P.

Moesle, A.

Neumann, J.

Novak, S.

Otto, H.-J.

Pantell, R.

M. Digonnet, R. Sadowski, H. Shaw, and R. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low–power all–optical switching: a review,” Opt. Fiber Technol. 3, 44–64 (1997).
[CrossRef]

Sadowski, R.

M. Digonnet, R. Sadowski, H. Shaw, and R. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low–power all–optical switching: a review,” Opt. Fiber Technol. 3, 44–64 (1997).
[CrossRef]

Schmidt, O.

Schreiber, T.

Schweinsberg, A.

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europys. Lett. 73, 218–224 (2006).
[CrossRef]

Shaw, H.

M. Digonnet, R. Sadowski, H. Shaw, and R. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low–power all–optical switching: a review,” Opt. Fiber Technol. 3, 44–64 (1997).
[CrossRef]

Smith, A. V.

Smith, J. J.

Stutzki, F.

Tröbs, M.

Tünnermann, A.

Tünnermann, H.

Weßels, P.

Wirth, C.

Zakharov, N.

Europys. Lett. (1)

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europys. Lett. 73, 218–224 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Brown, “Heat, fluorescence, and stimulated–emission power densities and fractions in Nd: YAG,” IEEE J. Quantum Electron. 34, 560–572 (2002).
[CrossRef]

IET Optoelectron. (1)

J. J. Jou and C. Liu, “Equivalent circuit model for erbium-doped fibre amplifiers including amplified spontaneous emission,” IET Optoelectron. 2, 29–33 (2008).
[CrossRef]

J. Lightwave Technol. (1)

J. Phys. D: Appl. Phys. (1)

W. A. Clarkson, “Thermal effects and their mitigation in end–pumped solid–state lasers,” J. Phys. D: Appl. Phys. 34, 2381–2395 (2001).
[CrossRef]

Opt. Express (4)

Opt. Fiber Technol. (1)

M. Digonnet, R. Sadowski, H. Shaw, and R. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low–power all–optical switching: a review,” Opt. Fiber Technol. 3, 44–64 (1997).
[CrossRef]

Opt. Lett. (2)

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Figures (9)

Fig. 1
Fig. 1

Example of a transfer function for pump and seed power modulation.

Fig. 2
Fig. 2

Amplifier setup.

Fig. 3
Fig. 3

Output power for the erbium doped fiber amplifier with seed modulation and 46 mW average seed power. Top: ΔPoutPin, not normalized, bottom: corresponding phase. Note that in all graphs we use the field dB scale for the magnitude as it common in signal processing.

Fig. 4
Fig. 4

Frequency response of the ytterbium doped fiber amplifier for seed modulation and 10 mW average seed power. Even low frequency modulations are amplified.

Fig. 5
Fig. 5

Gain of low frequency (10 Hz) and high frequency (100 kHz) modulation in dependence of output power in the ytterbium doped fiber amplifier.

Fig. 6
Fig. 6

Ytterbium doped fiber amplifiers’ frequency response of unabsorbed pump power.

Fig. 7
Fig. 7

Experimental setup for the phase measurement of an ytterbium doped fiber amplifier pumped at 976 nm and seeded by a 1064 nm diode. A 1550 nm single frequency probe beam is used in a Mach-Zehnder configuration to measure the refractive index change.

Fig. 8
Fig. 8

Frequency response of the 1550 nm phase / refractive index change.

Fig. 9
Fig. 9

The effect of seed modulation on the optical phase with and without pump light.

Tables (1)

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Table 1 Fiber Amplifier Parameters

Equations (16)

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ω eff = P s 0 ( L ) B s + P p 0 ( L ) B p + 1 / τ .
m s = m s ω 2 + ( ω eff + B s [ P s 0 ( 0 ) P s 0 ( L ) ] ) 2 ω 2 + ω eff 2
tan θ s = ω ω eff + ω 2 + ω eff 2 B s [ P s 0 ( 0 ) P s 0 ( L ) ] .
m s = m s ( P s 0 ( 0 ) B s + P p 0 ( L ) B p + 1 / τ P s 0 ( L ) B s + P p 0 ( L ) B p + 1 / τ ) .
m s = m s P s 0 ( L ) ( P s 0 ( 0 ) + 1 τ B s + P 0 0 ( L ) B p B s ) .
m p = m p B s [ P p 0 ( 0 ) P p 0 ( L ) ] ω 2 + ω eff 2 .
tan θ p = ω ω eff
m p = m p ( B s [ P p 0 ( 0 ) P p 0 ( L ) ] P s 0 ( L ) B s + P p 0 ( L ) B p + 1 / τ ) = m p ( B s [ P s 0 ( L ) P s 0 ( 0 ) + N 2 / τ ] P s 0 ( L ) B s + P p 0 ( L ) B p + 1 / τ ) .
m p m p ( 1 P s 0 ( 0 ) P s 0 ( L ) + N 2 / τ P s 0 ( L ) ) .
m s = m s B p ( P s 0 ( L ) P s 0 ( 0 ) ) ω 2 + ω eff 2
tan ( θ s ) = ω ω eff
m p = m p ω 2 + ( ω eff + B p [ P p 0 ( 0 ) P p 0 ( L ) ] ) 2 ω 2 + ω eff 2
tan ( θ p ) = ω ω eff + ω 2 + ω eff 2 B p ( P p 0 ( 0 ) P p 0 ( L ) ) .
N 2 0 δ = m p [ P p 0 ( 0 ) P p 0 ( L ) ] ω 2 + ω eff 2
N 2 0 δ = m s [ P s 0 ( 0 ) P s 0 ( L ) ] ω 2 + ω eff 2 ,
N 2 0 δ = P p mod [ 1 P p 0 ( L ) P p 0 ( 0 ) ] ω 2 + ω eff 2 .

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