Abstract

An analytically expression for the temperature dependence of the signal gain of an erbium-doped fiber amplifier (EDFA) pumped at 1480 nm are theoretically obtained by solving the propagation equations with the amplified spontaneous emission (ASE). It is seen that the temperature dependence of the gain strongly depends on the distribution of population of Er3+-ions in the second level. In addition, the output pump power and the intrinsic saturation power of the signal beam are obtained as a function of the temperature. Numerical calculations are carried out for the temperature range from -20 to +60 °C and the various fiber lengths. But the other gain parameters, such as the pump and signal wavelengths and their powers, are taken as constants. It is shown that the gain decreases with increasing temperature within the range of L≤27 m.

© 2005 Optical Society of America

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References

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  1. J. Kemtchou, M. Duhamel, and P. Lecoy, “Gain Temperature Dependence of Erbium-Doped silica and Fluoride Fiber Amplifiers in Multichannel Wavelength-Multiplexed Transmission Systems,” IEEE J. Lightwave Tech. 15 (11), 2083–2090 (1997).
    [Crossref]
  2. M. Peroni and M. Tamburrini, “Gain in erbium-doped fiber amplifiers: a simple analytical solution for the rate equations,” Opt. Lett. 15, 842–844 (1990).
    [Crossref] [PubMed]
  3. N. Kagi, A. Oyobe, and K. Nakamura, “Temperature Dependence of the Gain in Erbium-Doped Fibers,” IEEE J. Lightwave Tech. 9 (2), 261–265 (1991).
    [Crossref]
  4. H. Wei, Z. Tong, and S. Jian, “Use of a genetic algorithm to optimize multistage erbium-doped amplifier systems with complex structures,” Opt. Express 12 (4), 531–544 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-531.
    [Crossref]
  5. K. Furusawa, T. M. Monro, and D. J. Richardson, “High gain efficiency amplifier based on an erbium doped aluminosilicate holey fiber,” Opt. Express 12 (15), 3452–3458 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3452.
    [Crossref]
  6. M. Yamada, M. Shimizu, M. Horiguchi, and M. Okayasu, “Temperature Dependence of Signal Gain in Er3+-Doped Optical Fiber Amplifiers,” IEEE J. Quantum Electron. 28 (3), 640–649 (1992).
    [Crossref]
  7. Q. Mao, J. Wang, X. Sun, and M. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifier with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).
    [Crossref]
  8. F. Prudenzano, “Erbium-Doped Hole-Assisted optical Fiber Amplifier: Design and Optimization,” IEEE J. Light-wave Tech. 23 (1), 330–340 (2005).
    [Crossref]
  9. C. Berkdemir and S. Özsoy, “An investigation on the temperature dependence of the relative population inversion and the gain in EDFAs by the modified rate equations,” accepted for publication in Opt. Commun. (2005).
  10. E. Desurvire, Erbium-Doped fiber Amplifiers; Principle and Applications (John Wiley and Sons. Inc, New York, 1994).
  11. H. Zech, “Measurment Technique for the Quotient of Cross Section σe(λS)/σa(λS) of Erbium-Doped Fibers,” IEEE Photonics Tech. Lett. 7 (9), 986–988 (1995).
    [Crossref]
  12. M. C. Lin and S. Chi, “The Gain and Optimal Length in the Erbium-Doped Fiber Amplifiers with 1480 nm Pumping,” IEEE Photonics Tech. Lett. 4 (4), 354–356 (1992).
    [Crossref]
  13. OptiAmplifier Version 4.0; Optical Fiber Amplifier and Laser Design Software (Copyright © 2002 Optiwave Corporation, 2002).

2005 (1)

F. Prudenzano, “Erbium-Doped Hole-Assisted optical Fiber Amplifier: Design and Optimization,” IEEE J. Light-wave Tech. 23 (1), 330–340 (2005).
[Crossref]

2004 (2)

H. Wei, Z. Tong, and S. Jian, “Use of a genetic algorithm to optimize multistage erbium-doped amplifier systems with complex structures,” Opt. Express 12 (4), 531–544 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-531.
[Crossref]

K. Furusawa, T. M. Monro, and D. J. Richardson, “High gain efficiency amplifier based on an erbium doped aluminosilicate holey fiber,” Opt. Express 12 (15), 3452–3458 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3452.
[Crossref]

1999 (1)

Q. Mao, J. Wang, X. Sun, and M. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifier with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).
[Crossref]

1997 (1)

J. Kemtchou, M. Duhamel, and P. Lecoy, “Gain Temperature Dependence of Erbium-Doped silica and Fluoride Fiber Amplifiers in Multichannel Wavelength-Multiplexed Transmission Systems,” IEEE J. Lightwave Tech. 15 (11), 2083–2090 (1997).
[Crossref]

1995 (1)

H. Zech, “Measurment Technique for the Quotient of Cross Section σe(λS)/σa(λS) of Erbium-Doped Fibers,” IEEE Photonics Tech. Lett. 7 (9), 986–988 (1995).
[Crossref]

1992 (2)

M. C. Lin and S. Chi, “The Gain and Optimal Length in the Erbium-Doped Fiber Amplifiers with 1480 nm Pumping,” IEEE Photonics Tech. Lett. 4 (4), 354–356 (1992).
[Crossref]

M. Yamada, M. Shimizu, M. Horiguchi, and M. Okayasu, “Temperature Dependence of Signal Gain in Er3+-Doped Optical Fiber Amplifiers,” IEEE J. Quantum Electron. 28 (3), 640–649 (1992).
[Crossref]

1991 (1)

N. Kagi, A. Oyobe, and K. Nakamura, “Temperature Dependence of the Gain in Erbium-Doped Fibers,” IEEE J. Lightwave Tech. 9 (2), 261–265 (1991).
[Crossref]

1990 (1)

Berkdemir, C.

C. Berkdemir and S. Özsoy, “An investigation on the temperature dependence of the relative population inversion and the gain in EDFAs by the modified rate equations,” accepted for publication in Opt. Commun. (2005).

Chi, S.

M. C. Lin and S. Chi, “The Gain and Optimal Length in the Erbium-Doped Fiber Amplifiers with 1480 nm Pumping,” IEEE Photonics Tech. Lett. 4 (4), 354–356 (1992).
[Crossref]

Desurvire, E.

E. Desurvire, Erbium-Doped fiber Amplifiers; Principle and Applications (John Wiley and Sons. Inc, New York, 1994).

Duhamel, M.

J. Kemtchou, M. Duhamel, and P. Lecoy, “Gain Temperature Dependence of Erbium-Doped silica and Fluoride Fiber Amplifiers in Multichannel Wavelength-Multiplexed Transmission Systems,” IEEE J. Lightwave Tech. 15 (11), 2083–2090 (1997).
[Crossref]

Furusawa, K.

K. Furusawa, T. M. Monro, and D. J. Richardson, “High gain efficiency amplifier based on an erbium doped aluminosilicate holey fiber,” Opt. Express 12 (15), 3452–3458 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3452.
[Crossref]

Horiguchi, M.

M. Yamada, M. Shimizu, M. Horiguchi, and M. Okayasu, “Temperature Dependence of Signal Gain in Er3+-Doped Optical Fiber Amplifiers,” IEEE J. Quantum Electron. 28 (3), 640–649 (1992).
[Crossref]

Jian, S.

H. Wei, Z. Tong, and S. Jian, “Use of a genetic algorithm to optimize multistage erbium-doped amplifier systems with complex structures,” Opt. Express 12 (4), 531–544 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-531.
[Crossref]

Kagi, N.

N. Kagi, A. Oyobe, and K. Nakamura, “Temperature Dependence of the Gain in Erbium-Doped Fibers,” IEEE J. Lightwave Tech. 9 (2), 261–265 (1991).
[Crossref]

Kemtchou, J.

J. Kemtchou, M. Duhamel, and P. Lecoy, “Gain Temperature Dependence of Erbium-Doped silica and Fluoride Fiber Amplifiers in Multichannel Wavelength-Multiplexed Transmission Systems,” IEEE J. Lightwave Tech. 15 (11), 2083–2090 (1997).
[Crossref]

Lecoy, P.

J. Kemtchou, M. Duhamel, and P. Lecoy, “Gain Temperature Dependence of Erbium-Doped silica and Fluoride Fiber Amplifiers in Multichannel Wavelength-Multiplexed Transmission Systems,” IEEE J. Lightwave Tech. 15 (11), 2083–2090 (1997).
[Crossref]

Lin, M. C.

M. C. Lin and S. Chi, “The Gain and Optimal Length in the Erbium-Doped Fiber Amplifiers with 1480 nm Pumping,” IEEE Photonics Tech. Lett. 4 (4), 354–356 (1992).
[Crossref]

Mao, Q.

Q. Mao, J. Wang, X. Sun, and M. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifier with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).
[Crossref]

Monro, T. M.

K. Furusawa, T. M. Monro, and D. J. Richardson, “High gain efficiency amplifier based on an erbium doped aluminosilicate holey fiber,” Opt. Express 12 (15), 3452–3458 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3452.
[Crossref]

Nakamura, K.

N. Kagi, A. Oyobe, and K. Nakamura, “Temperature Dependence of the Gain in Erbium-Doped Fibers,” IEEE J. Lightwave Tech. 9 (2), 261–265 (1991).
[Crossref]

Okayasu, M.

M. Yamada, M. Shimizu, M. Horiguchi, and M. Okayasu, “Temperature Dependence of Signal Gain in Er3+-Doped Optical Fiber Amplifiers,” IEEE J. Quantum Electron. 28 (3), 640–649 (1992).
[Crossref]

Oyobe, A.

N. Kagi, A. Oyobe, and K. Nakamura, “Temperature Dependence of the Gain in Erbium-Doped Fibers,” IEEE J. Lightwave Tech. 9 (2), 261–265 (1991).
[Crossref]

Özsoy, S.

C. Berkdemir and S. Özsoy, “An investigation on the temperature dependence of the relative population inversion and the gain in EDFAs by the modified rate equations,” accepted for publication in Opt. Commun. (2005).

Peroni, M.

Prudenzano, F.

F. Prudenzano, “Erbium-Doped Hole-Assisted optical Fiber Amplifier: Design and Optimization,” IEEE J. Light-wave Tech. 23 (1), 330–340 (2005).
[Crossref]

Richardson, D. J.

K. Furusawa, T. M. Monro, and D. J. Richardson, “High gain efficiency amplifier based on an erbium doped aluminosilicate holey fiber,” Opt. Express 12 (15), 3452–3458 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3452.
[Crossref]

Shimizu, M.

M. Yamada, M. Shimizu, M. Horiguchi, and M. Okayasu, “Temperature Dependence of Signal Gain in Er3+-Doped Optical Fiber Amplifiers,” IEEE J. Quantum Electron. 28 (3), 640–649 (1992).
[Crossref]

Sun, X.

Q. Mao, J. Wang, X. Sun, and M. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifier with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).
[Crossref]

Tamburrini, M.

Tong, Z.

H. Wei, Z. Tong, and S. Jian, “Use of a genetic algorithm to optimize multistage erbium-doped amplifier systems with complex structures,” Opt. Express 12 (4), 531–544 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-531.
[Crossref]

Wang, J.

Q. Mao, J. Wang, X. Sun, and M. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifier with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).
[Crossref]

Wei, H.

H. Wei, Z. Tong, and S. Jian, “Use of a genetic algorithm to optimize multistage erbium-doped amplifier systems with complex structures,” Opt. Express 12 (4), 531–544 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-531.
[Crossref]

Yamada, M.

M. Yamada, M. Shimizu, M. Horiguchi, and M. Okayasu, “Temperature Dependence of Signal Gain in Er3+-Doped Optical Fiber Amplifiers,” IEEE J. Quantum Electron. 28 (3), 640–649 (1992).
[Crossref]

Zech, H.

H. Zech, “Measurment Technique for the Quotient of Cross Section σe(λS)/σa(λS) of Erbium-Doped Fibers,” IEEE Photonics Tech. Lett. 7 (9), 986–988 (1995).
[Crossref]

Zhang, M.

Q. Mao, J. Wang, X. Sun, and M. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifier with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).
[Crossref]

IEEE J. Light-wave Tech. (1)

F. Prudenzano, “Erbium-Doped Hole-Assisted optical Fiber Amplifier: Design and Optimization,” IEEE J. Light-wave Tech. 23 (1), 330–340 (2005).
[Crossref]

IEEE J. Lightwave Tech. (2)

J. Kemtchou, M. Duhamel, and P. Lecoy, “Gain Temperature Dependence of Erbium-Doped silica and Fluoride Fiber Amplifiers in Multichannel Wavelength-Multiplexed Transmission Systems,” IEEE J. Lightwave Tech. 15 (11), 2083–2090 (1997).
[Crossref]

N. Kagi, A. Oyobe, and K. Nakamura, “Temperature Dependence of the Gain in Erbium-Doped Fibers,” IEEE J. Lightwave Tech. 9 (2), 261–265 (1991).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Yamada, M. Shimizu, M. Horiguchi, and M. Okayasu, “Temperature Dependence of Signal Gain in Er3+-Doped Optical Fiber Amplifiers,” IEEE J. Quantum Electron. 28 (3), 640–649 (1992).
[Crossref]

IEEE Photonics Tech. Lett. (2)

H. Zech, “Measurment Technique for the Quotient of Cross Section σe(λS)/σa(λS) of Erbium-Doped Fibers,” IEEE Photonics Tech. Lett. 7 (9), 986–988 (1995).
[Crossref]

M. C. Lin and S. Chi, “The Gain and Optimal Length in the Erbium-Doped Fiber Amplifiers with 1480 nm Pumping,” IEEE Photonics Tech. Lett. 4 (4), 354–356 (1992).
[Crossref]

Opt. Commun. (1)

Q. Mao, J. Wang, X. Sun, and M. Zhang, “A theoretical analysis of amplification characteristics of bi-directional erbium-doped fiber amplifier with single erbium-doped fiber,” Opt. Commun. 159, 149–157 (1999).
[Crossref]

Opt. Express (2)

H. Wei, Z. Tong, and S. Jian, “Use of a genetic algorithm to optimize multistage erbium-doped amplifier systems with complex structures,” Opt. Express 12 (4), 531–544 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-531.
[Crossref]

K. Furusawa, T. M. Monro, and D. J. Richardson, “High gain efficiency amplifier based on an erbium doped aluminosilicate holey fiber,” Opt. Express 12 (15), 3452–3458 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3452.
[Crossref]

Opt. Lett. (1)

Other (3)

C. Berkdemir and S. Özsoy, “An investigation on the temperature dependence of the relative population inversion and the gain in EDFAs by the modified rate equations,” accepted for publication in Opt. Commun. (2005).

E. Desurvire, Erbium-Doped fiber Amplifiers; Principle and Applications (John Wiley and Sons. Inc, New York, 1994).

OptiAmplifier Version 4.0; Optical Fiber Amplifier and Laser Design Software (Copyright © 2002 Optiwave Corporation, 2002).

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Figures (3)

Fig. 1.
Fig. 1.

Two level amplification system and main transitions of erbium ion.

Fig. 2.
Fig. 2.

Simulation setup for measurement of the co-propagating ASE power in an Er3+-doped optical fiber amplifier (from OptiAmplifier 4.0).

Fig. 3.
Fig. 3.

Gain as a function of fiber length. Pp (0)=30 mW and Ps (0)=10 µW.

Tables (2)

Tables Icon

Table 1. Typical fiber parameters for an Al/P-silica erbium-doped fiber (from Ref.[12]).

Tables Icon

Table 2. The relevant fiber parameters as a function of temperature.

Equations (20)

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β = N 2 + N 2 = C nr + C nr = exp ( Δ E 2 k B T )
d N 2 + dt = R p a N 1 R p e N 2 + + C nr N 2 C nr + N 2 + ,
d N 2 dt = S 12 N 1 S 21 N 2 N 2 γ C nr N 2 + C nr + N 2 + ,
d N 1 dt = R p e N 2 + R p a N 1 + S 21 N 2 S 12 N 1 + N 2 γ .
N 2 = τ [ ( σ p a N 1 β σ p e N 2− ) I p h v p + ( σ s a N 1 σ s e N 2 ) ( I s + I ASE ± ) h v s ] ,
N 2 N = I p b p a + ( I s + I ASE ± ) b s a ( 1 + β ) I p b p a + β I p b p e + ( 1 + β + η ) ( I s + I ASE ± ) b s a + 1
d P s d z = 2 π 0 I s [ σ s e N 2 ( r ) σ s a N 1 ( r ) ] rdr ,
d P p dz = ± 2 π 0 I p [ β σ p e N 2 ( r ) σ p a N 1 ( r ) ] rdr ,
d P ASE ± dz = ± 2 h v s 0 2 π σ s e N 2 f ASE ± ( r ) rdr ± 2 π 0 [ σ s e N 2− ( r ) σ s a N 1 ( r ) ] P ASE ± f ASE ± rdr ,
P ASE ± = P ASE + + P ASE .
d P s dz = 2 π σ s a P s ( 1 + β + η ) 0 N 2 f 2 ( r ) rdr P s α s ,
0 N 2 rdr = 0 τ I p h v p ( σ p a N 1 β σ p e N 2 ) rdr + 0 τ I s h v s ( σ s a N 1 σ s e N 2 ) rdr
+ 0 τ I ASE + h v s ( σ s a N 1 σ s e N 2 ) rdr ,
0 N 2 rdr = τ 2 π h v p d P p dz τ 2 π h v s d P s dz τ 2 π h v s d P ASE + dz + 2 τ σ s e 0 N 2 f ( r ) rdr ,
0 N 2 f ( r ) rdr = τ 2 π ( A Γ 2 τ σ s e ) [ 1 h v p d P p dz + 1 h v s ( d P s dz + d P ASE + dz ) ] ,
d P s dz = P s ( α s + h v s P s int [ 1 h v p d P p dz + 1 h v s ( d P s dz + d P ASE + dz ) ] ) ,
P s int = h v s ( A 2 τ σ s e Γ ) τ σ s a Γ ( 1 + β + η ) .
P s ( L ) P s ( 0 ) = exp ( α s L ) exp ( h v s P s int [ P p ( 0 ) P p ( L ) h v p + ( P s ( 0 ) + P ASE + ( 0 ) ) ( P s ( L ) + P ASE + ( L ) ) h v s ] ) .
G = exp ( α s L ) exp ( h v s P s int [ P p ( 0 ) P p ( L ) h v p P s ( 0 ) h v s ( 1 G ) P ASE + ( L ) h v s ] ) ,
P p ( L ) = 1 R ( η b p a β b p e ) ,

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