Abstract

We describe an analytic method that calculates accurately (within a 1.5-dB discrepancy with numerical models) the gain of an erbium-doped fiber amplifier. Amplified spontaneous emission (ASE) is taken into account so that the gain of ASE-saturated erbium-doped fiber amplifiers is calculated properly. It is effective for wavelength multiplexing (several signals) and for different pumping schemes (copropagating or counterpropagating or both).

© 1992 Optical Society of America

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References

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  1. C. R. Giles, E. Desurvire, IEEE J. Lightwave Technol. 9, 271 (1991).
    [Crossref]
  2. K. Dybdal, A. Bjarklev, C. Dam-Hansen, C. C. Larsen, B. Pedersen, J. Hedegaard Povlsen, H. Vendeltorp-Pommer, in European Conference on Optical Communications (Elsevier, Amsterdam, 1990), paper WeFl.3.
  3. D. Ronarc’h, M. Guibert, H. Ibrahim, M. Monerie, H. Poignant, A. Tromeur, Electron. Lett. 27, 908 (1991).
    [Crossref]
  4. J. R. Armitage, Appl. Opt. 27, 4831 (1988).
    [Crossref] [PubMed]
  5. M. Peroni, M. Tamburrini, Opt. Lett. 15, 842 (1990).
    [Crossref] [PubMed]
  6. M. Montecchi, A. Mecozzi, M. Settembre, M. Tamburrini, L. DiGaspare, J. Opt. Soc. Am. B 8, 134 (1991).
    [Crossref]
  7. A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, IEEE Photon. Technol. Lett. 2, 714 (1990).
    [Crossref]
  8. E. Desurvire, M. Zirngibl, H. M. Presby, D. DiGiovanni, IEEE Photon. Technol. Lett. 3, 127(1991).
    [Crossref]

1991 (4)

C. R. Giles, E. Desurvire, IEEE J. Lightwave Technol. 9, 271 (1991).
[Crossref]

D. Ronarc’h, M. Guibert, H. Ibrahim, M. Monerie, H. Poignant, A. Tromeur, Electron. Lett. 27, 908 (1991).
[Crossref]

M. Montecchi, A. Mecozzi, M. Settembre, M. Tamburrini, L. DiGaspare, J. Opt. Soc. Am. B 8, 134 (1991).
[Crossref]

E. Desurvire, M. Zirngibl, H. M. Presby, D. DiGiovanni, IEEE Photon. Technol. Lett. 3, 127(1991).
[Crossref]

1990 (2)

M. Peroni, M. Tamburrini, Opt. Lett. 15, 842 (1990).
[Crossref] [PubMed]

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, IEEE Photon. Technol. Lett. 2, 714 (1990).
[Crossref]

1988 (1)

Armitage, J. R.

Aspell, J.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, IEEE Photon. Technol. Lett. 2, 714 (1990).
[Crossref]

Bjarklev, A.

K. Dybdal, A. Bjarklev, C. Dam-Hansen, C. C. Larsen, B. Pedersen, J. Hedegaard Povlsen, H. Vendeltorp-Pommer, in European Conference on Optical Communications (Elsevier, Amsterdam, 1990), paper WeFl.3.

Dam-Hansen, C.

K. Dybdal, A. Bjarklev, C. Dam-Hansen, C. C. Larsen, B. Pedersen, J. Hedegaard Povlsen, H. Vendeltorp-Pommer, in European Conference on Optical Communications (Elsevier, Amsterdam, 1990), paper WeFl.3.

Desurvire, E.

C. R. Giles, E. Desurvire, IEEE J. Lightwave Technol. 9, 271 (1991).
[Crossref]

E. Desurvire, M. Zirngibl, H. M. Presby, D. DiGiovanni, IEEE Photon. Technol. Lett. 3, 127(1991).
[Crossref]

DiGaspare, L.

DiGiovanni, D.

E. Desurvire, M. Zirngibl, H. M. Presby, D. DiGiovanni, IEEE Photon. Technol. Lett. 3, 127(1991).
[Crossref]

Dybdal, K.

K. Dybdal, A. Bjarklev, C. Dam-Hansen, C. C. Larsen, B. Pedersen, J. Hedegaard Povlsen, H. Vendeltorp-Pommer, in European Conference on Optical Communications (Elsevier, Amsterdam, 1990), paper WeFl.3.

Evankow, J. D.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, IEEE Photon. Technol. Lett. 2, 714 (1990).
[Crossref]

Giles, C. R.

C. R. Giles, E. Desurvire, IEEE J. Lightwave Technol. 9, 271 (1991).
[Crossref]

Guibert, M.

D. Ronarc’h, M. Guibert, H. Ibrahim, M. Monerie, H. Poignant, A. Tromeur, Electron. Lett. 27, 908 (1991).
[Crossref]

Hedegaard Povlsen, J.

K. Dybdal, A. Bjarklev, C. Dam-Hansen, C. C. Larsen, B. Pedersen, J. Hedegaard Povlsen, H. Vendeltorp-Pommer, in European Conference on Optical Communications (Elsevier, Amsterdam, 1990), paper WeFl.3.

Ibrahim, H.

D. Ronarc’h, M. Guibert, H. Ibrahim, M. Monerie, H. Poignant, A. Tromeur, Electron. Lett. 27, 908 (1991).
[Crossref]

Jopson, R. M.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, IEEE Photon. Technol. Lett. 2, 714 (1990).
[Crossref]

Larsen, C. C.

K. Dybdal, A. Bjarklev, C. Dam-Hansen, C. C. Larsen, B. Pedersen, J. Hedegaard Povlsen, H. Vendeltorp-Pommer, in European Conference on Optical Communications (Elsevier, Amsterdam, 1990), paper WeFl.3.

Mecozzi, A.

Monerie, M.

D. Ronarc’h, M. Guibert, H. Ibrahim, M. Monerie, H. Poignant, A. Tromeur, Electron. Lett. 27, 908 (1991).
[Crossref]

Montecchi, M.

Pedersen, B.

K. Dybdal, A. Bjarklev, C. Dam-Hansen, C. C. Larsen, B. Pedersen, J. Hedegaard Povlsen, H. Vendeltorp-Pommer, in European Conference on Optical Communications (Elsevier, Amsterdam, 1990), paper WeFl.3.

Peroni, M.

Poignant, H.

D. Ronarc’h, M. Guibert, H. Ibrahim, M. Monerie, H. Poignant, A. Tromeur, Electron. Lett. 27, 908 (1991).
[Crossref]

Presby, H. M.

E. Desurvire, M. Zirngibl, H. M. Presby, D. DiGiovanni, IEEE Photon. Technol. Lett. 3, 127(1991).
[Crossref]

Ronarc’h, D.

D. Ronarc’h, M. Guibert, H. Ibrahim, M. Monerie, H. Poignant, A. Tromeur, Electron. Lett. 27, 908 (1991).
[Crossref]

Saleh, A. A. M.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, IEEE Photon. Technol. Lett. 2, 714 (1990).
[Crossref]

Settembre, M.

Tamburrini, M.

Tromeur, A.

D. Ronarc’h, M. Guibert, H. Ibrahim, M. Monerie, H. Poignant, A. Tromeur, Electron. Lett. 27, 908 (1991).
[Crossref]

Vendeltorp-Pommer, H.

K. Dybdal, A. Bjarklev, C. Dam-Hansen, C. C. Larsen, B. Pedersen, J. Hedegaard Povlsen, H. Vendeltorp-Pommer, in European Conference on Optical Communications (Elsevier, Amsterdam, 1990), paper WeFl.3.

Zirngibl, M.

E. Desurvire, M. Zirngibl, H. M. Presby, D. DiGiovanni, IEEE Photon. Technol. Lett. 3, 127(1991).
[Crossref]

Appl. Opt. (1)

Electron. Lett. (1)

D. Ronarc’h, M. Guibert, H. Ibrahim, M. Monerie, H. Poignant, A. Tromeur, Electron. Lett. 27, 908 (1991).
[Crossref]

IEEE J. Lightwave Technol. (1)

C. R. Giles, E. Desurvire, IEEE J. Lightwave Technol. 9, 271 (1991).
[Crossref]

IEEE Photon. Technol. Lett. (2)

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, IEEE Photon. Technol. Lett. 2, 714 (1990).
[Crossref]

E. Desurvire, M. Zirngibl, H. M. Presby, D. DiGiovanni, IEEE Photon. Technol. Lett. 3, 127(1991).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Other (1)

K. Dybdal, A. Bjarklev, C. Dam-Hansen, C. C. Larsen, B. Pedersen, J. Hedegaard Povlsen, H. Vendeltorp-Pommer, in European Conference on Optical Communications (Elsevier, Amsterdam, 1990), paper WeFl.3.

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Figures (3)

Fig. 1
Fig. 1

Total ASE power (right scale), the relative error on ASE power, and δ = |δPΓ|/(|δPΓ| + δPASE) (left scale) versus pump power for a length optimized amplifier (at λs = 1544 nm) and for two input signal powers: −70 dBm (solid curves) and −20 dBm (dashed curves). The gains are large (ASE-saturated regime) in the gray area.

Fig. 2
Fig. 2

Gain versus pump power for a length-optimized amplifier given by three models and for two input signal power. Crosses (−70 dBm) and squares (−20 dBm), numerical model; dashed curves, analytical model without ASE solid curves, our model.

Fig. 3
Fig. 3

Wavelength gain dependence for various input signal power (−50, −20, −7, and 3 dBm): a comparison of our model (solid curves) with the numerical model (circles).

Equations (13)

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i P i in = i P i out + P ASE + P spont ,
P spont = N A L τ x = K spont x , A = Ψ 0 ,             x = 1 A L 0 L Ψ 2 d z ,
g i = log ( P i out P i in ) = ( σ i T Γ i x - σ i a Γ i ) N L ,
Γ i = Φ i Ψ 0 Φ i ,             Γ i = 1 x L 0 L Φ i Ψ 2 Φ i d z ,
g i ( x ) = g i ( x ) + δ g i ,
g i ( x ) = ( σ i T x - σ i a ) Γ i N L , δ g i = ( θ i - θ s ) σ i T x Γ i N L .
P ASE ana ( x ) = 4 { exp [ g ν ( x ) ] - 1 } β ( ν , x ) d ν , β ( ν , x ) = σ ν e x Γ ν N g ν ( x ) .
H ( x ) + δ P = 0 ,
H ( x ) = i P i in { exp [ g i ( x ) ] - 1 } + P ASE ana ( x ) + K spont x , δ P = δ P ASE + δ P Γ , δ P Γ = K spont ( 1 - θ s ) x + i P i out [ exp ( δ g i ) - 1 ] .
Δ g s = δ P P s sat ( 1 + i P i out P i sat ) + 1 σ s T Γ s N L d P ana d x ,
G A 20 β Δ ν τ σ s T Γ s ω s 2 ,
P s in 20 Δ ν ( corresponds to - 18 dBm ) .
P loss = α EL 0 L P ( z ) d z .

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