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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  1. 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
  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-opticsChristopher Marshal, ed., Vol. 11 of OSA Technical Digest Series (Optical Society of America, Washington DC, 1993) pp. 310–311
  7. 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)
  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)
    [CrossRef]
  11. B. Majaron, H. Lukac, and M. Conic, “Population Dynamics in Yb:Er:Phosphate Glass Under Neodymium Laser Pumping,” IEEE J. Quantum Electron. 31, 301–308 (1995)
    [CrossRef]
  12. D. Derickson, Fiber Optic Test and Measurement (Prentice Hall PTR, Upper Saddle River, New Jersey1998)

1997 (1)

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]

1995 (1)

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

1994 (2)

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]

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]

1993 (3)

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]

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]

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

1992 (2)

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

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)

Archambault, J.L.

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]

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]

Bayon, J.F.

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)

Bjarklev, A.

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

Conic, M.

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

Delevaque, E.

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)

Derickson, D.

D. Derickson, Fiber Optic Test and Measurement (Prentice Hall PTR, Upper Saddle River, New Jersey1998)

Di Pasquale, F.

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]

DiGiovanni, D.J.

Fan, T. Y.

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

Federighi, M.

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]

Georges, T.

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)

Jenssen, H. P.

D. S. Knowles and H. P. Jenssen, “Up-conversion in Erbium and its dependence on energy migration,” in Conference on Lasers and Electro-opticsChristopher Marshal, ed., Vol. 11 of OSA Technical Digest Series (Optical Society of America, Washington DC, 1993) pp. 310–311

Karasek, M.

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]

Knowles, D. S.

D. S. Knowles and H. P. Jenssen, “Up-conversion in Erbium and its dependence on energy migration,” in Conference on Lasers and Electro-opticsChristopher Marshal, ed., Vol. 11 of OSA Technical Digest Series (Optical Society of America, Washington DC, 1993) pp. 310–311

Kringlebotn, J.T.

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]

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]

Lamouler, P.

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)

Lukac, H.

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

Lumholt, O.

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

Majaron, B.

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

Monerie, M.

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)

Morkel, P.R.

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]

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

Payne, D. N.

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]

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]

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

Rasmussen, T.

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

Reekie, L.

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]

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]

Shaw, M.J.

Taylor, E.R.

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

Townsend, J.E.

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]

Vienne, G.G.

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]

Wagener, J. L.

Wysocki, P.F.

Ye, C.C.

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. (2)

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. (4)

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, and 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. (1)

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]

in Optical amplifiers and their applications technical digest (1)

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)

Opt. Lett. (1)

Other (3)

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

D. Derickson, Fiber Optic Test and Measurement (Prentice Hall PTR, Upper Saddle River, New Jersey1998)

D. S. Knowles and H. P. Jenssen, “Up-conversion in Erbium and its dependence on energy migration,” in Conference on Lasers and Electro-opticsChristopher Marshal, ed., Vol. 11 of OSA Technical Digest Series (Optical Society of America, Washington DC, 1993) pp. 310–311

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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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