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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 7 — Apr. 3, 2006
  • pp: 2589–2595
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An automatic step adjustment method for average power analysis technique used in fiber amplifiers

Xue-Ming Liu  »View Author Affiliations


Optics Express, Vol. 14, Issue 7, pp. 2589-2595 (2006)
http://dx.doi.org/10.1364/OE.14.002589


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Abstract

An automatic step adjustment (ASA) method for average power analysis (APA) technique used in fiber amplifiers is proposed in this paper for the first time. In comparison with the traditional APA technique, the proposed method has suggested two unique merits such as a higher order accuracy and an ASA mechanism, so that it can significantly shorten the computing time and improve the solution accuracy. A test example demonstrates that, by comparing to the APA technique, the proposed method increases the computing speed by more than a hundredfold under the same errors. By computing the model equations of erbium-doped fiber amplifiers, the numerical results show that our method can improve the solution accuracy by over two orders of magnitude at the same amplifying section number. The proposed method has the capacity to rapidly and effectively compute the model equations of fiber Raman amplifiers and semiconductor lasers.

© 2006 Optical Society of America

1. Introduction

Erbium-doped fiber amplifiers (EDFAs) are key components for wavelength-division-multiplexed (WDM) transmission systems [1

1. C. Berkdemir and S. Ozsoy “The temperature dependent performance analysis of EDFAs pumped at 1480 nm: A more accurate propagation equation,” Opt. Express 13, 5179–5185 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-5179 [CrossRef] [PubMed]

]-[4

4. J. B. Rosolem, A. Juriollo, R. Arradi, A. D. Coral, J. C. R. Oliveira, and M. A. Romero, “All silica S-band double-pass erbium-doped fiber amplifier,” IEEE Photonics Technol. Lett. 17, 1399–1401 (2005). [CrossRef]

]. To reduce costs and optimize system performance, the effective methods for designing EDFAs are necessary [4

4. J. B. Rosolem, A. Juriollo, R. Arradi, A. D. Coral, J. C. R. Oliveira, and M. A. Romero, “All silica S-band double-pass erbium-doped fiber amplifier,” IEEE Photonics Technol. Lett. 17, 1399–1401 (2005). [CrossRef]

]-[6

6. E. Desurvire, Erbium-doped fiber amplifiers: Principles and Applications, (John Wiley, New York, 1994).

]. If the traditional numerical tools such as Runge-Kutta methods and Adams methods are used to solve the propagation equations of EDFAs, the required computation time makes this task be a serious problem. To overcome this difficulty, Hodgkinson had proposed an average power analysis (APA) technique [7

7. T. G. Hodgkinson, “Average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 3, 1082–1084 (1991). [CrossRef]

] and its improved modification [8

8. T. G. Hodgkinson, “Improved average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 4, 1273–1275 (1992). [CrossRef]

] on the basis of the semiconductor laser analysis technique [9

9. M. J. Adams, J. V. Collins, and I. D. Henning, “Analysis of semiconductor laser optical amplifiers”, IEE. Proc. J Optoelectron. 132, 58–63 (1985). [CrossRef]

]. Hereafter, the simulation tools for the system model of fiber amplifiers are originated from the APA technique [6

6. E. Desurvire, Erbium-doped fiber amplifiers: Principles and Applications, (John Wiley, New York, 1994).

], [10

10. C. Glingener, J. -P. Elbers, and E. Voges, “Simulation tool for WDM networks,” in WDM Technology and Applications (Digest No. 1997/036), IEE Colloquium on 6 Feb. 1997 Page(s): 17/1–17/4

]-[14

14. S. K. Kim, S. Chang, and J. Han, et al., “Design of hybrid optical amplifiers for high capacity optical transmission,” ETRI J. 24, 81–96 (2002). [CrossRef]

]. However, this technique employed a fixed constant step-size, i.e., the total amplifier length was divided into a number of fixed elemental lengths. To overcome this limitation, an automatic step adjustment (ASA) method for the APA technique has been proposed in this paper for the first time to author’s best knowledge.

2. Theoretical modeling and APA technique

The spectral gain and the spectral noise figure of EDFAs can be completely described by the propagation and rate equations modeling the interaction of the optical field with erbium ions [15

15. A. Bononi and L. Rusch, “Doped-fiber amplifier dynamics: a system perspective,” J. Lightwave Technol. 16, 945–956 (1998). [CrossRef]

]-[21

21. R. J. Mears and S. R. Baker, “Erbium fiber amplifiers and lasers,” Opt. Quantum Electron. 24, 517–538 (1992). [CrossRef]

]. Usually, EDFAs are modeled by a two-level system [22

22. A. A. Rieznik and H. Fragnito, “Analytical solution for the dynamic behavior of erbium-doped fiber amplifiers with constant population inversion along the fiber,” J. Opt. Soc. Am. B 21, 1732–1739 (2004). [CrossRef]

]-[24

24. C. Cheng and M. Xiao, “Optimization of an erbium-doped fiber amplifier with radial effects,” Opt. Commun. 254, 215–222 (2005). [CrossRef]

]. When there are M input wavelengths, the equations, which describe the power evolution and govern the amplifier behavior, can be expressed as [8

8. T. G. Hodgkinson, “Improved average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 4, 1273–1275 (1992). [CrossRef]

]

dPk±dz=±{[(σ21k+σ12k)N2(z)σ12kNt]Γkαk}Pk±(z),
(1a)
dPi±dz=±({[(σ21i+σ12i)N2(z)σ12iNt]Γiαi}+2σ12iN2(z)ΓihviΔvPi±(z))Pi±(z).
(1b)

Here, + means forward propagating (+) and backward propagating (-), k is the wavelength identifier, i is the ASE wavelength identifier, P is optical power, α is the fiber background loss coefficient, Γ is the overlap integral factor between the dopant and the optical mode, Nt is the local erbium ion density, N 2 is the metastable level population density, h is Planck’s constant, σ 21 and σ 12 are, respectively, stimulated emission and absorption cross-sections, and Pi represents ASE power in the frequency interval Δv at the center of vi.

Since the power evolution of light along the erbium-doped fiber resembles exponential pattern, it is intuitive that the exponential change of a variable may lead to faster convergence and higher speed than some linear or polygonal approximation. Taking advantage of this property, the APA technique is constructed to increase the computing speed [7

7. T. G. Hodgkinson, “Average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 3, 1082–1084 (1991). [CrossRef]

], [8

8. T. G. Hodgkinson, “Improved average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 4, 1273–1275 (1992). [CrossRef]

].

Pk±out=Pk±inGk(z),Pi±out=2hvinspΔv(Gi(z)1),
(2)

where the power gain Gk,i (z) and the population inversion factor nsp are defined as

Gk,i(z)=exp({[(σ21k,i+σ12k,i)N2σ12k,iNt]Γk,iαk,i}z),
(3)
nsp=N2[(1+σ12k,iσ21k,i)N2Ntσ12k,iσ21k,iαk,iΓk,iσ21k,i].
(4)

After averaging Eq. (2), the length-averaged power in each elemental amplifier section can be written as the following expression

Pk=Pk±in(Gk1In(Gk)),Pi=2hvinspΔv(Gi1In(Gi)1).
(5)

Therefore, the relatively simple algebraic calculations replace the time-consuming numerical integrations so that the computation time is decreased.

3. Adaptive step-size control algorithm

When the APA technique is implemented to solve the propagation equations of EDFAs, its two disadvantages, i.e., the fixed step-size and the two-order accuracy, obstruct the enhancement of the computing speed. Here, the n-order accuracy is defined as εhn, i.e., the local truncation error ε is proportional to n power of the step size h. In order to overcome this limitation, an adaptive step-size control algorithm has been proposed to increase the computing speed and improve the accuracy.

By introducing vectors P and f, Eq. (1) can be recast in a concise notation, i.e.,

dPdz=fzPP.
(6)

By substituting y to ln(P) [i.e., y =ln(P)], Eq. (6) is changed to

dydz=f(z).
(7)

yn+1,1=yn+hfznyn,
(8a)
yn+1,2=yn+0.5hfznyn+0.5hf(zn+0.5h,yn+0.5hfznyn),
(8b)
yn+1,3=2yn+1,2yn+1,1.
(8c)

After Taylor expansion, the corresponding local truncation errors ε of Eqs. (8a)-(8c) can be expressed as, respectively,

ε1=y(zn+h)yn+1,1=Kh2+O1(h3),
(9a)
ε2=y(zn+h)yn+1,2=0.5Kh2+O2(h3),
(9b)
ε3=y(zn+h)yn+1,3=2O2(h3)O1(h3),
(9c)

where K=12d2y(x)dz2z=z0,O1(h3)=16h3d3y(z)dz3z=ξ1andO2(h3)=16h3d3y(z)dz3z=ξ2..The corresponding error difference rate between Eq. (9a) and Eq. (9b) is about

εr=yn+1,2yn+1,1h0.5Kh.
(10)

If εr is less than a required error ε 0 (i.e., εr > ε 0), we can accept y n+1,3 as an approximate value of y(zn+h). In contrast, if εr > ε 0, we reject y n+1,3 and repeat the current step with a new trial step-size h´. The old and new step sizes have the following relationship

h'=ε0hεr.
(11)

By substituting P to exp(y) [i.e., P =exp(y)], Eqs. (8a)-(8c) can be rewritten as

Pn+1,1=Pn.exp(hfznPn),
(12a)
Pn+1,2=Pnexp[0.5hfznPn]exp{0.5hf(zn+0.5h,Pnexp[0.5hfznPn])},
(12b)
Pn+1,3=Pn+1,22Pn+1,1.
(12c)

The corresponding εr is changed as

εr=In(Pn+1,2)In(Pn+1,1)h0.5Kh.
(13)

Therefore, on the basis of Eqs. (11)-(13), an adaptive step-size control algorithm can be constructed. The ASA method is shown as follow:

oe-14-7-2589-i001

4. Test, results and discussion

In comparison with the APA technique, the proposed method has suggested two key merits:

  1. The traditional APA technique is originated from Eq. (12a) with the error shown in Eq. (9a), but the proposed method is based on Eq. (12c) with the error given by Eq. (9c). The error is the three-order accuracy in the latter rather than the two-order accuracy in the former, so that the proposed method improves the accuracy of the numerical solutions.
  2. Based on Eqs. (11) and (13), the adaptive step-size control algorithm can be implemented in this paper. Unfortunately, the APA technique used so far was lacking an ASA mechanism. Therefore, the combination of the ASA method and the APA technique can increase the computing speed and improve the solution accuracy.

In order to compare the proposed method to the traditional APA technique, an ordinary differential equation is tested, i.e.,

dxdt=xt+1=(1tx+1x)x, andx(2)=exp(2)+2.
(14)

Figure 1 illustrates the relative error between the numerical value xn and exact value x(tn), i.e., |(x(tn)-xn)/x(tn)|. From Fig. 1, we can see that, in order to reach the relative error of <2.5×10-4 at t=20, (1) only 38 steps are enough when the proposed method is used to solve Eq. (14); (2) there are 4287 steps with the step-size of 0.0042 for the fixed step method used in the APA technique; and (3) the proposed method shortens the CPU time by more than a hundredfold in comparison with the APA technique. Moreover, the step-size h used in the ASA method is larger and larger when t increases. The reasons why the computing speed of the proposed method is two orders of magnitude faster than that of the APA technique originate from two factors: an ASA mechanism and a higher order accuracy.

Fig. 1. Relationship of relative error with t. The circular symbols in figure represent the points that are calculated in the computing procedure.

On the basis of the parameters used in Ref. [7

7. T. G. Hodgkinson, “Average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 3, 1082–1084 (1991). [CrossRef]

], the model equations of EDFAs are computed by the traditional APA technique and the proposed method, respectively. The corresponding numerical results are shown in Fig. 2. This figure demonstrates the relationship between the relative error Er and the elemental amplifying section number n, where the whole amplifier length L is partitioned into n sections and each section length h is L/n in the APA technique. Note that the relative error Er is defined by |(P(ZL)-PL)/P(ZL)|, where P(ZL) and PL are the exact value and the numerical value at the total amplifier length L, respectively. From Fig. 2, we can see that (1) when n>20, the relative error Er of the proposed method is two orders of magnitude less than that of the APA technique; (2) at the same Er of 2×10-2, the elemental amplifying section number n used in the proposed method is ~7 instead of ~100 in the APA technique; (3) with the increase of n, the solution accuracy in the proposed method is better and better than that in the APA technique, i.e., the difference of their Er is greater and greater.

Numerical results also show that, if the solution accuracy is higher, the speed of convergence is faster and the CPU time efficiency is more. For instance, the computational time of the proposed method is about 15 times less than that of the APA technique at the same relative error Er of 10-2, while the computational speed of the proposed method can be increased by more than two orders of magnitude in comparison with that of the APA technique at the same Er of 10-4. However, the improvement of the computational efficiency is at the cost of the stability. For example, when L>120 m, our method is unstable to solve Eq. (1) whereas the APA technique is still stable.

Fig. 2. Relationship of the relative error Er with the elemental amplifying section number n. Each section length h is L/n in the APA technique, but the length h is adaptive in the proposed method.

In additional, since the power of lightwave in the fiber Raman amplifiers exponentially evolves, the APA technique has been used for the Raman amplifier modeling [26

26. B. K. Min, W. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000). [CrossRef]

]-[28

28. M. Menif, M. Karasek, and L. Rusch, “Cross-gain modulation in Raman fiber amplifier: Experimentation and Modeling,” IEEE Photonics Technol. Lett. 14, 1261–1263 (2002). [CrossRef]

]. Therefore, the proposed method has the capacity to rapidly and accurately solve the propagation equations of fiber Raman amplifiers and semiconductor lasers.

5. Conclusion

In this paper, we have proposed an adaptive step-size control algorithm for the traditional APA technique used in fiber amplifiers for the first time. Compared to the conventional APA technique, the proposed method has two unique merits, i.e., a higher order accuracy and an ASA mechanism. So the computing time is significantly reduced and the solution accuracy is effectively improved. A test example shows that, in comparison with the APA technique, the proposed method increases the computing speed by two orders of magnitude under the same relative error. The model equations of EDFAs are solved and compared by the proposed method and the APA technique, respectively, and the numerical results show that the solution accuracy in the former is about two orders of magnitude higher than that in the latter at the same elemental amplifying section number n. Moreover, our method can effectively be used to fast solve the propagation equations of fiber Raman amplifiers and semiconductor lasers.

References and links

1.

C. Berkdemir and S. Ozsoy “The temperature dependent performance analysis of EDFAs pumped at 1480 nm: A more accurate propagation equation,” Opt. Express 13, 5179–5185 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-5179 [CrossRef] [PubMed]

2.

M. A. Quintela, J. Lopez-Higuera, and C. Jauregui, “Polarization characteristics of a reflective erbium doped fiber amplifier with temperature changes at the Faraday rotator mirror,” Opt. Express 13, 1368–1376 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1368 [CrossRef] [PubMed]

3.

M. Bolshtyansky, I. Mandelbaum, and F. Pan, “Signal excited-state absorption in the L-band EDFA: Simulation and measurements,” J. Lightwave Technol. 23, 2796–2799 (2005). [CrossRef]

4.

J. B. Rosolem, A. Juriollo, R. Arradi, A. D. Coral, J. C. R. Oliveira, and M. A. Romero, “All silica S-band double-pass erbium-doped fiber amplifier,” IEEE Photonics Technol. Lett. 17, 1399–1401 (2005). [CrossRef]

5.

P. S. Chan and H. K. Tsang, “Minimizing gain transient dynamics by optimizing the erbium concentration and cavity length of a gain clamped EDFA,” Opt. Express 13, 7520–7526 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7520 [CrossRef] [PubMed]

6.

E. Desurvire, Erbium-doped fiber amplifiers: Principles and Applications, (John Wiley, New York, 1994).

7.

T. G. Hodgkinson, “Average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 3, 1082–1084 (1991). [CrossRef]

8.

T. G. Hodgkinson, “Improved average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 4, 1273–1275 (1992). [CrossRef]

9.

M. J. Adams, J. V. Collins, and I. D. Henning, “Analysis of semiconductor laser optical amplifiers”, IEE. Proc. J Optoelectron. 132, 58–63 (1985). [CrossRef]

10.

C. Glingener, J. -P. Elbers, and E. Voges, “Simulation tool for WDM networks,” in WDM Technology and Applications (Digest No. 1997/036), IEE Colloquium on 6 Feb. 1997 Page(s): 17/1–17/4

11.

M. Karasek, M. Menif, and A. Bellemare, “Design of wideband hybrid amplifiers for local area networks,” IEE Proc. J. Optoelectron. 148, 150–155 (2001). [CrossRef]

12.

L. Zhu, Y. Ma, and G. Wang, et al., “General computer model for both erbium-doped fiber amplifier and fiber Raman amplifier,” Opt. Eng. 41, 1805–1808 (2002). [CrossRef]

13.

M. M. Tiesler, J. Witkowski, and K. Abramski, “Quality criterion for numerical methods in EDFA modeling,” Optica Applicata 32, 187–196 (2002).

14.

S. K. Kim, S. Chang, and J. Han, et al., “Design of hybrid optical amplifiers for high capacity optical transmission,” ETRI J. 24, 81–96 (2002). [CrossRef]

15.

A. Bononi and L. Rusch, “Doped-fiber amplifier dynamics: a system perspective,” J. Lightwave Technol. 16, 945–956 (1998). [CrossRef]

16.

J. Bryce, Y. Zhao, and R. Minasian, “Modeling and optimization of add-drop dynamics in gain-clamped fiber amplifiers,” Appl. Opt. 39, 4270–4277 (2000). [CrossRef]

17.

I. Roudas, D. Richards, and N. Antoniades, et al., “An efficient simulation model of the erbium-doped fiber for the study of multiwavelength optical networks,” Opt. Fiber Technol. 5, 363–389 (1999). [CrossRef]

18.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991). [CrossRef]

19.

B. Pedersen, K. Dybdal, and C. D. Hansen, et al., “Detailed theoretical and experimental investigation of high-gain erbium-doped fiber amplifier,” IEEE Photonics Technol. Lett. 2, 863–865 (1990). [CrossRef]

20.

B. Pedersen, S. A. Zemon, and W. J. Miniscalco, “Analysis of erbium-doped fiber amplifiers pumped at 800nm,” Fiber and Integr. Opt. , 10, 127–136 (1991). [CrossRef]

21.

R. J. Mears and S. R. Baker, “Erbium fiber amplifiers and lasers,” Opt. Quantum Electron. 24, 517–538 (1992). [CrossRef]

22.

A. A. Rieznik and H. Fragnito, “Analytical solution for the dynamic behavior of erbium-doped fiber amplifiers with constant population inversion along the fiber,” J. Opt. Soc. Am. B 21, 1732–1739 (2004). [CrossRef]

23.

Z. G. Lu, J. Liu, and F. Sun, et al., “A hybrid fiber amplifier with 36.9-dBm output power and 70-dB gain,” Opt. Commun. 256, 352–357 (2005). [CrossRef]

24.

C. Cheng and M. Xiao, “Optimization of an erbium-doped fiber amplifier with radial effects,” Opt. Commun. 254, 215–222 (2005). [CrossRef]

25.

U. M. Ascher and L. R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (SIAM, Philadelphia, 1998). [CrossRef]

26.

B. K. Min, W. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000). [CrossRef]

27.

Z. Tong, H. Wei, and S. Jian, “A novel algorithm to simulate DWDM transmission systems amplified by backward multipumped fiber Raman amplifiers,” Microwave Opt. Technol. Lett. 35, 333–337 (2002). [CrossRef]

28.

M. Menif, M. Karasek, and L. Rusch, “Cross-gain modulation in Raman fiber amplifier: Experimentation and Modeling,” IEEE Photonics Technol. Lett. 14, 1261–1263 (2002). [CrossRef]

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.2410) Fiber optics and optical communications : Fibers, erbium

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: December 19, 2005
Revised Manuscript: March 13, 2006
Manuscript Accepted: March 23, 2006
Published: April 3, 2006

Citation
Xue-Ming Liu, "An automatic step adjustment method for average power analysis technique used in fiber amplifiers," Opt. Express 14, 2589-2595 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-7-2589


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References

  1. C. Berkdemir, and S. Ozsoy "The temperature dependent performance analysis of EDFAs pumped at 1480 nm: A more accurate propagation equation," Opt. Express 13, 5179-5185 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-5179 [CrossRef] [PubMed]
  2. M. A. Quintela, J. Lopez-Higuera, and C. Jauregui, "Polarization characteristics of a reflective erbium doped fiber amplifier with temperature changes at the Faraday rotator mirror," Opt. Express 13, 1368-1376 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1368 [CrossRef] [PubMed]
  3. M. Bolshtyansky, I. Mandelbaum, and F. Pan, "Signal excited-state absorption in the L-band EDFA: Simulation and measurements," J. Lightwave Technol. 23, 2796-2799 (2005). [CrossRef]
  4. J. B. Rosolem, A. Juriollo, R. Arradi, A. D. Coral, J. C. R. Oliveira and M. A. Romero, "All silica S-band double-pass erbium-doped fiber amplifier," IEEE Photonics Technol. Lett. 17, 1399-1401 (2005). [CrossRef]
  5. P. S. Chan and H. K. Tsang, "Minimizing gain transient dynamics by optimizing the erbium concentration and cavity length of a gain clamped EDFA," Opt. Express 13, 7520-7526 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7520 [CrossRef] [PubMed]
  6. E. Desurvire, Erbium-doped fiber amplifiers: Principles and Applications, (John Wiley, New York, 1994).
  7. T. G. Hodgkinson, "Average power analysis technique for erbium-doped fiber amplifiers," IEEE Photonics Technol. Lett. 3, 1082-1084 (1991). [CrossRef]
  8. T. G. Hodgkinson, "Improved average power analysis technique for erbium-doped fiber amplifiers," IEEE Photonics Technol. Lett. 4, 1273-1275 (1992). [CrossRef]
  9. M. J. Adams, J. V. Collins, and I. D. Henning, "Analysis of semiconductor laser optical amplifiers", IEE. Proc.J Optoelectron. 132, 58-63 (1985). [CrossRef]
  10. C. Glingener, J. -P. Elbers, and E. Voges, "Simulation tool for WDM networks," in WDM Technology and Applications (Digest No. 1997/036), IEE Colloquium on 6 Feb. 1997 Page(s): 17/1-17/4
  11. M. Karasek, M. Menif, A. Bellemare, "Design of wideband hybrid amplifiers for local area networks," IEE Proc. J. Optoelectron. 148, 150-155 (2001). [CrossRef]
  12. L. Zhu, Y. Ma, G. Wang,  et al., "General computer model for both erbium-doped fiber amplifier and fiber Raman amplifier," Opt. Eng. 41, 1805-1808 (2002). [CrossRef]
  13. M. M. Tiesler, J. Witkowski, and K. Abramski, "Quality criterion for numerical methods in EDFA modeling," Optica Applicata 32, 187-196 (2002).
  14. S. K. Kim, S. Chang, J. Han,  et al., "Design of hybrid optical amplifiers for high capacity optical transmission," ETRI J. 24, 81-96 (2002). [CrossRef]
  15. A. Bononi, and L. Rusch, "Doped-fiber amplifier dynamics: a system perspective," J. Lightwave Technol. 16, 945-956 (1998). [CrossRef]
  16. J. Bryce, Y. Zhao, and R. Minasian, "Modeling and optimization of add-drop dynamics in gain-clamped fiber amplifiers," Appl. Opt. 39, 4270-4277 (2000). [CrossRef]
  17. I. Roudas, D. Richards, N. Antoniades,  et al., "An efficient simulation model of the erbium-doped fiber for the study of multiwavelength optical networks," Opt. Fiber Technol. 5, 363-389 (1999). [CrossRef]
  18. C. R. Giles and E. Desurvire, ‘‘Modeling erbium-doped fiber amplifiers,’’J. Lightwave Technol. 9, 271-283 (1991). [CrossRef]
  19. B. Pedersen, K. Dybdal, C. D. Hansen,  et al., "Detailed theoretical and experimental investigation of high-gain erbium-doped fiber amplifier," IEEE Photonics Technol. Lett. 2, 863-865 (1990). [CrossRef]
  20. B. Pedersen, S. A. Zemon, and W. J. Miniscalco, "Analysis of erbium-doped fiber amplifiers pumped at 800nm," Fiber and Integr. Opt.,  10, 127-136 (1991). [CrossRef]
  21. R. J. Mears, and S. R. Baker, "Erbium fiber amplifiers and lasers," Opt. Quantum Electron. 24, 517-538 (1992). [CrossRef]
  22. A. A. Rieznik, and H. Fragnito, "Analytical solution for the dynamic behavior of erbium-doped fiber amplifiers with constant population inversion along the fiber," J. Opt. Soc. Am. B 21, 1732-1739 (2004). [CrossRef]
  23. Z. G. Lu, J. Liu, F. Sun,  et al., "A hybrid fiber amplifier with 36.9-dBm output power and 70-dB gain," Opt. Commun. 256, 352-357 (2005). [CrossRef]
  24. C. Cheng, and M. Xiao, "Optimization of an erbium-doped fiber amplifier with radial effects," Opt. Commun. 254, 215-222 (2005). [CrossRef]
  25. U. M. Ascher and L. R. Petzold, Computer Methods for Ordinary Differential Equations and Differential- Algebraic Equations (SIAM, Philadelphia, 1998). [CrossRef]
  26. B. K. Min, W. Lee, and N. Park, "Efficient formulation of Raman amplifier propagation equations with average power analysis," IEEE Photon. Technol. Lett. 12, 1486-1488 (2000). [CrossRef]
  27. Z. Tong, H. Wei, and S. Jian, "A novel algorithm to simulate DWDM transmission systems amplified by backward multipumped fiber Raman amplifiers," Microwave Opt. Technol. Lett. 35, 333-337 (2002). [CrossRef]
  28. M. Menif, M. Karasek, and L. Rusch, "Cross-gain modulation in Raman fiber amplifier: Experimentation and Modeling," IEEE Photonics Technol. Lett. 14, 1261-1263 (2002). [CrossRef]

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