Abstract

Optical gain and output power as a function of pump power has been calculated for short Er/Yb doped single mode fibers for various fiber parameters. The calculation shows that long fiber lengths provide both higher small signal gain and higher output power. Gain of 14 dB has been observed in a 30 mm long fiber at 400 mW of input pump power. The observed small signal gain is found to be linearly proportional to the length of the fiber with a slope of 0.44 dB/mm at 400 mW of pump power.

© 2004 Optical Society of America

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References

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  2. J. L. Wagener, P.F. Wysocki, M.J. Shaw, and D.J. DiGiovanni, ???Effects of concentration and clusters in erbium doped fiber lasers,??? Opt. Lett. 18, 2014-2016 (1993)
    [CrossRef] [PubMed]
  3. J.T. Kringlebotn, J.L. Archambault, L. Reekie, J.E. Townsend, G.G. Vienne, and D. N. Payne, ???Highly efficient, low-noise grating feedback Er:Yb codoped fiber lasers,??? Electron. Lett. 30, 972-973 (1994)
    [CrossRef]
  4. J.T. Kringlebotn, P.R. Morkel, L. Reekie, J.L. Archambault, and D. N. Payne, ???Efficient diode-pumped single frequency erbium:ytterbium fiber laser,??? IEEE Photon. Technol. Lett. 5, 1162-1164 (1993)
    [CrossRef]
  5. F. Di Pasquale and M. Federighi, ???Improved Gain Characteristics in High-Concentration Er3+/Yb3+ Codoped Glass Waveguide Amplifiers,??? IEEE J. Quantum Electron., 30, 2127-2131 (1994).
    [CrossRef]
  6. D. S. Knowles and H. P. Jenssen, ???Up-conversion in Erbium and its dependence on energy migration,??? in Conference on Lasers and Electro-optics Christopher Marshal, ed., Vol. 11 of OSA Technical Digest Series
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  8. O. Lumholt, T. Rasmussen and A. Bjarklev, ???Modeling of extremely high concentration erbium-doped silica waveguides,??? Electron. Lett. 29, 495-496 (1993)
    [CrossRef]
  9. M. Karasek, ???Optimum Design of Er3+/Yb3+ Co-doped Fibers for Large Signal High-Pump-Power Applications,??? IEEE J. Quantum Electron. 33, 1699-1705 (1997)
    [CrossRef]
  10. T. Y. Fan, ???Optimizing the Efficiency and Stored Energy in Quasi-Three-Level Lasers,??? IEEE J. Quantum Electron. 28, 2692-2697 (1992)
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    [CrossRef]
  12. D. Derickson, Fiber Optic Test and Measurement ( Prentice Hall PTR, Upper Saddle River, New Jersey 1998)

ECOC 93

C.C. Ye, P.R. Morkel, E.R. Taylor, and D. N. Payne, ???Direct observation of cooperative upconversion mechanisms in Erbium-doped fiber amplifiers,??? presented at ECOC 93, Montreux, Sept. 1993

Electron. Lett.

J.T. Kringlebotn, J.L. Archambault, L. Reekie, J.E. Townsend, G.G. Vienne, and D. N. Payne, ???Highly efficient, low-noise grating feedback Er:Yb codoped fiber lasers,??? Electron. Lett. 30, 972-973 (1994)
[CrossRef]

O. Lumholt, T. Rasmussen and A. Bjarklev, ???Modeling of extremely high concentration erbium-doped silica waveguides,??? Electron. Lett. 29, 495-496 (1993)
[CrossRef]

IEEE J. Quantum Electron.

M. Karasek, ???Optimum Design of Er3+/Yb3+ Co-doped Fibers for Large Signal High-Pump-Power Applications,??? IEEE J. Quantum Electron. 33, 1699-1705 (1997)
[CrossRef]

T. Y. Fan, ???Optimizing the Efficiency and Stored Energy in Quasi-Three-Level Lasers,??? IEEE J. Quantum Electron. 28, 2692-2697 (1992)
[CrossRef]

B. Majaron, H. Lukac, M. Conic, ???Population Dynamics in Yb:Er:Phosphate Glass Under Neodymium Laser Pumping,??? IEEE J. Quantum Electron. 31, 301-308 (1995)
[CrossRef]

F. Di Pasquale and M. Federighi, ???Improved Gain Characteristics in High-Concentration Er3+/Yb3+ Codoped Glass Waveguide Amplifiers,??? IEEE J. Quantum Electron., 30, 2127-2131 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

J.T. Kringlebotn, P.R. Morkel, L. Reekie, J.L. Archambault, and D. N. Payne, ???Efficient diode-pumped single frequency erbium:ytterbium fiber laser,??? IEEE Photon. Technol. Lett. 5, 1162-1164 (1993)
[CrossRef]

Opt. Lett.

Optical amplifiers technical digest

T. Georges, E. Delevaque, M. Monerie, P. Lamouler and J.F. Bayon, ???Pair induced quenching in Erbium doped silicate fibers,??? in Optical amplifiers and their applications technical digest, 17, 71-74 (1992)

OSA Technical Digest Series

D. S. Knowles and H. P. Jenssen, ???Up-conversion in Erbium and its dependence on energy migration,??? in Conference on Lasers and Electro-optics Christopher Marshal, ed., Vol. 11 of OSA Technical Digest Series

Other

D. Derickson, Fiber Optic Test and Measurement ( Prentice Hall PTR, Upper Saddle River, New Jersey 1998)

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Figures (5)

Fig. 1.
Fig. 1.

Energy level diagram of Er-Yb (erbium-ytterbium) system. The dashed lines, and, the solid lines represent non-radiative transitions, and radiative transitions respectively.

Fig. 2.
Fig. 2.

Calculated gain as a function of pump power for 1 cm, 2 cm and 3 cm long fibers. NEr=3×1026 m-3 and NYb=1.2×1027 m-3

Fig. 3.
Fig. 3.

Calculated gain as a function of pump power for 5cmlong fibers. NEr=3×1026m-3 and NYb=1.2×1027 m-3

Fig. 4.
Fig. 4.

Measured net gain as a function of pump power for fibers of three different lengths as indicated.

Fig. 5.
Fig. 5.

Measured net gain at 400 mW pump power as a function of fiber length.

Equations (17)

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d N 4 d t = C up N 2 2 γ 43 N 4
d N 3 d t = N 3 σ pe ϕ p + N 1 σ pa ϕ p + K N 6 N 1 K N 3 N 5 γ 32 N 3 + γ 43 N 4
d N 2 d t = A 21 N 2 2 C up N 2 2 + N 1 σ sa ϕ s N 2 σ se ϕ s + γ 32 N 3
N 1 + N 2 + N 3 + N 4 = N Er
d N 5 d t = K N 6 N 1 + K N 3 N 5 N 5 σ pa ϕ p + N 6 σ pe ϕ p + A 65 N 6
N 5 + N 6 = N Yb
N 4 = C up N 2 2 γ 43
γ 32 N 3 = N 1 ( σ pa ϕ p + K N 6 )
N 6 = ϕ p N Yb σ pa ϕ p σ pa + ϕ p σ pe + A 65 + K ( N Er N 2 )
N 2 = N Er ( σ sa ϕ s + σ pa ϕ p + K N 6 ) A 21 + σ se ϕ s + ( σ sa ϕ s + σ pa ϕ p + K N 6 )
N a = N 0 Z a exp ( E a / kT ) = f a N 0
Z a = i exp ( E i k T )
N 6 = ϕ p N Yb σ pa f a ϕ p σ pa f a + ϕ p σ pe f b + A 65 + K ( N Er N 2 )
α a = Γ p [ σ pa ( N Yb N 6 ) σ pe N 6 ] + Γ p [ σ pa ( N Er N 2 ) σ pe N 2 ]
g ( z ) = Γ s [ σ se N 2 σ sa ( N Er N 2 ) ]
d S d z = S A [ ( N Er N 2 ) σ sa N 2 σ se ] ψ s ( x , y ) dxdy + α S
G = exp ( 0 L g ( z ) dz )

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