Abstract

In wavelength-division-multiplexing systems with optical amplifiers, channel drop or add can cause power changes in the existing channels. We present an analytical formula for the transient power of the existing channels as a function of time when one or more input channel is dropped or added on an erbium-doped fiber amplifier (EDFA). Although this formula was originally derived from perturbation theory of single-stage EDFA’s, it is a good approximation of large-power excursion cases as well as two-stage EDFA’s.

© 1999 Optical Society of America

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  1. J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, A. J. Lucero, C. Wolf, R. W. Tkach, “Fast power transients in optically amplified multiwavelength optical networks,” in Optical Fiber Communication Conference, Postdeadline Papers, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), PD31.
  2. M. Maeda, “Operations and management of WDM optical networks,” in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 318.
  3. J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.
  4. E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, New York, 1994).
  5. Y. Sun, G. Luo, J. L. Zyskind, A. A. M. Saleh, A. K. Srivastava, J. W. Sulhoff, “Model for gain dynamics in erbium-doped fiber amplifiers,” Electron. Lett. 32, 1490–1491 (1996).
    [CrossRef]
  6. A. K. Srivastava, Y. Sun, J. L. Zyskind, J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission systems,” IEEE Photon. Technol. Lett. 9, 386–388 (1997).
    [CrossRef]
  7. A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
    [CrossRef]
  8. A. A. M. Saleh, “Overview of the MONET, multiwavelength optical networking,” in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 240.
  9. R. E. Wagner, R. C. Alferness, A. A. M. Saleh, M. S. Goodman, “MONET: multiwavelength optical networking,” J. Lightwave Technol. 14, 1349–1355 (1996).
    [CrossRef]
  10. R. G. Smart, J. L. Zyskind, D. J. DiGiovanni, “Two-stage erbium-doped fiber amplifiers suitable for use in long-haul soliton systems,” Electron. Lett. 30, 50–52 (1994).
    [CrossRef]
  11. E. Desurvire, “Analysis of transient gain saturation and recovery in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 1, 196–199 (1990).
    [CrossRef]
  12. M. Sumida, S. Furukawa, K. Tanaka, M. Aiki, “High-accuracy fault location technology using FSK–ASK probe backscattering reflectometry in optical amplifier submarine transmission systems,” J. Lightwave Technol. 14, 2108–2116 (1996).
    [CrossRef]

1997

A. K. Srivastava, Y. Sun, J. L. Zyskind, J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission systems,” IEEE Photon. Technol. Lett. 9, 386–388 (1997).
[CrossRef]

1996

R. E. Wagner, R. C. Alferness, A. A. M. Saleh, M. S. Goodman, “MONET: multiwavelength optical networking,” J. Lightwave Technol. 14, 1349–1355 (1996).
[CrossRef]

Y. Sun, G. Luo, J. L. Zyskind, A. A. M. Saleh, A. K. Srivastava, J. W. Sulhoff, “Model for gain dynamics in erbium-doped fiber amplifiers,” Electron. Lett. 32, 1490–1491 (1996).
[CrossRef]

M. Sumida, S. Furukawa, K. Tanaka, M. Aiki, “High-accuracy fault location technology using FSK–ASK probe backscattering reflectometry in optical amplifier submarine transmission systems,” J. Lightwave Technol. 14, 2108–2116 (1996).
[CrossRef]

1994

R. G. Smart, J. L. Zyskind, D. J. DiGiovanni, “Two-stage erbium-doped fiber amplifiers suitable for use in long-haul soliton systems,” Electron. Lett. 30, 50–52 (1994).
[CrossRef]

1990

E. Desurvire, “Analysis of transient gain saturation and recovery in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 1, 196–199 (1990).
[CrossRef]

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[CrossRef]

Aiki, M.

M. Sumida, S. Furukawa, K. Tanaka, M. Aiki, “High-accuracy fault location technology using FSK–ASK probe backscattering reflectometry in optical amplifier submarine transmission systems,” J. Lightwave Technol. 14, 2108–2116 (1996).
[CrossRef]

Alferness, R. C.

R. E. Wagner, R. C. Alferness, A. A. M. Saleh, M. S. Goodman, “MONET: multiwavelength optical networking,” J. Lightwave Technol. 14, 1349–1355 (1996).
[CrossRef]

Aspell, J.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[CrossRef]

Chraplyvy, A. R.

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

Desurvire, E.

E. Desurvire, “Analysis of transient gain saturation and recovery in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 1, 196–199 (1990).
[CrossRef]

E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, New York, 1994).

DiGiovanni, D. J.

R. G. Smart, J. L. Zyskind, D. J. DiGiovanni, “Two-stage erbium-doped fiber amplifiers suitable for use in long-haul soliton systems,” Electron. Lett. 30, 50–52 (1994).
[CrossRef]

Ellson, J. C.

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

Evankow, J. D.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[CrossRef]

Furukawa, S.

M. Sumida, S. Furukawa, K. Tanaka, M. Aiki, “High-accuracy fault location technology using FSK–ASK probe backscattering reflectometry in optical amplifier submarine transmission systems,” J. Lightwave Technol. 14, 2108–2116 (1996).
[CrossRef]

Goodman, M. S.

R. E. Wagner, R. C. Alferness, A. A. M. Saleh, M. S. Goodman, “MONET: multiwavelength optical networking,” J. Lightwave Technol. 14, 1349–1355 (1996).
[CrossRef]

Jopson, R. M.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[CrossRef]

Lucero, A. J.

J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, A. J. Lucero, C. Wolf, R. W. Tkach, “Fast power transients in optically amplified multiwavelength optical networks,” in Optical Fiber Communication Conference, Postdeadline Papers, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), PD31.

Luo, G.

Y. Sun, G. Luo, J. L. Zyskind, A. A. M. Saleh, A. K. Srivastava, J. W. Sulhoff, “Model for gain dynamics in erbium-doped fiber amplifiers,” Electron. Lett. 32, 1490–1491 (1996).
[CrossRef]

Maeda, M.

M. Maeda, “Operations and management of WDM optical networks,” in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 318.

Newsome, G. W.

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

Pedrazzani, J. R.

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

Saleh, A. A. M.

Y. Sun, G. Luo, J. L. Zyskind, A. A. M. Saleh, A. K. Srivastava, J. W. Sulhoff, “Model for gain dynamics in erbium-doped fiber amplifiers,” Electron. Lett. 32, 1490–1491 (1996).
[CrossRef]

R. E. Wagner, R. C. Alferness, A. A. M. Saleh, M. S. Goodman, “MONET: multiwavelength optical networking,” J. Lightwave Technol. 14, 1349–1355 (1996).
[CrossRef]

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[CrossRef]

A. A. M. Saleh, “Overview of the MONET, multiwavelength optical networking,” in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 240.

Smart, R. G.

R. G. Smart, J. L. Zyskind, D. J. DiGiovanni, “Two-stage erbium-doped fiber amplifiers suitable for use in long-haul soliton systems,” Electron. Lett. 30, 50–52 (1994).
[CrossRef]

Srivastava, A. K.

A. K. Srivastava, Y. Sun, J. L. Zyskind, J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission systems,” IEEE Photon. Technol. Lett. 9, 386–388 (1997).
[CrossRef]

Y. Sun, G. Luo, J. L. Zyskind, A. A. M. Saleh, A. K. Srivastava, J. W. Sulhoff, “Model for gain dynamics in erbium-doped fiber amplifiers,” Electron. Lett. 32, 1490–1491 (1996).
[CrossRef]

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, A. J. Lucero, C. Wolf, R. W. Tkach, “Fast power transients in optically amplified multiwavelength optical networks,” in Optical Fiber Communication Conference, Postdeadline Papers, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), PD31.

Strasser, T. A.

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

Sulhoff, J. W.

A. K. Srivastava, Y. Sun, J. L. Zyskind, J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission systems,” IEEE Photon. Technol. Lett. 9, 386–388 (1997).
[CrossRef]

Y. Sun, G. Luo, J. L. Zyskind, A. A. M. Saleh, A. K. Srivastava, J. W. Sulhoff, “Model for gain dynamics in erbium-doped fiber amplifiers,” Electron. Lett. 32, 1490–1491 (1996).
[CrossRef]

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, A. J. Lucero, C. Wolf, R. W. Tkach, “Fast power transients in optically amplified multiwavelength optical networks,” in Optical Fiber Communication Conference, Postdeadline Papers, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), PD31.

Sumida, M.

M. Sumida, S. Furukawa, K. Tanaka, M. Aiki, “High-accuracy fault location technology using FSK–ASK probe backscattering reflectometry in optical amplifier submarine transmission systems,” J. Lightwave Technol. 14, 2108–2116 (1996).
[CrossRef]

Sun, Y.

A. K. Srivastava, Y. Sun, J. L. Zyskind, J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission systems,” IEEE Photon. Technol. Lett. 9, 386–388 (1997).
[CrossRef]

Y. Sun, G. Luo, J. L. Zyskind, A. A. M. Saleh, A. K. Srivastava, J. W. Sulhoff, “Model for gain dynamics in erbium-doped fiber amplifiers,” Electron. Lett. 32, 1490–1491 (1996).
[CrossRef]

J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, A. J. Lucero, C. Wolf, R. W. Tkach, “Fast power transients in optically amplified multiwavelength optical networks,” in Optical Fiber Communication Conference, Postdeadline Papers, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), PD31.

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

Tanaka, K.

M. Sumida, S. Furukawa, K. Tanaka, M. Aiki, “High-accuracy fault location technology using FSK–ASK probe backscattering reflectometry in optical amplifier submarine transmission systems,” J. Lightwave Technol. 14, 2108–2116 (1996).
[CrossRef]

Tkach, R. W.

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, A. J. Lucero, C. Wolf, R. W. Tkach, “Fast power transients in optically amplified multiwavelength optical networks,” in Optical Fiber Communication Conference, Postdeadline Papers, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), PD31.

Wagner, R. E.

R. E. Wagner, R. C. Alferness, A. A. M. Saleh, M. S. Goodman, “MONET: multiwavelength optical networking,” J. Lightwave Technol. 14, 1349–1355 (1996).
[CrossRef]

Wolf, C.

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, A. J. Lucero, C. Wolf, R. W. Tkach, “Fast power transients in optically amplified multiwavelength optical networks,” in Optical Fiber Communication Conference, Postdeadline Papers, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), PD31.

Zyskind, J. L.

A. K. Srivastava, Y. Sun, J. L. Zyskind, J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission systems,” IEEE Photon. Technol. Lett. 9, 386–388 (1997).
[CrossRef]

Y. Sun, G. Luo, J. L. Zyskind, A. A. M. Saleh, A. K. Srivastava, J. W. Sulhoff, “Model for gain dynamics in erbium-doped fiber amplifiers,” Electron. Lett. 32, 1490–1491 (1996).
[CrossRef]

R. G. Smart, J. L. Zyskind, D. J. DiGiovanni, “Two-stage erbium-doped fiber amplifiers suitable for use in long-haul soliton systems,” Electron. Lett. 30, 50–52 (1994).
[CrossRef]

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, A. J. Lucero, C. Wolf, R. W. Tkach, “Fast power transients in optically amplified multiwavelength optical networks,” in Optical Fiber Communication Conference, Postdeadline Papers, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), PD31.

Electron. Lett.

Y. Sun, G. Luo, J. L. Zyskind, A. A. M. Saleh, A. K. Srivastava, J. W. Sulhoff, “Model for gain dynamics in erbium-doped fiber amplifiers,” Electron. Lett. 32, 1490–1491 (1996).
[CrossRef]

R. G. Smart, J. L. Zyskind, D. J. DiGiovanni, “Two-stage erbium-doped fiber amplifiers suitable for use in long-haul soliton systems,” Electron. Lett. 30, 50–52 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

E. Desurvire, “Analysis of transient gain saturation and recovery in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 1, 196–199 (1990).
[CrossRef]

A. K. Srivastava, Y. Sun, J. L. Zyskind, J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission systems,” IEEE Photon. Technol. Lett. 9, 386–388 (1997).
[CrossRef]

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[CrossRef]

J. Lightwave Technol.

M. Sumida, S. Furukawa, K. Tanaka, M. Aiki, “High-accuracy fault location technology using FSK–ASK probe backscattering reflectometry in optical amplifier submarine transmission systems,” J. Lightwave Technol. 14, 2108–2116 (1996).
[CrossRef]

R. E. Wagner, R. C. Alferness, A. A. M. Saleh, M. S. Goodman, “MONET: multiwavelength optical networking,” J. Lightwave Technol. 14, 1349–1355 (1996).
[CrossRef]

Other

A. A. M. Saleh, “Overview of the MONET, multiwavelength optical networking,” in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 240.

J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, A. J. Lucero, C. Wolf, R. W. Tkach, “Fast power transients in optically amplified multiwavelength optical networks,” in Optical Fiber Communication Conference, Postdeadline Papers, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), PD31.

M. Maeda, “Operations and management of WDM optical networks,” in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 318.

J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani, C. Wolf, “Fast link control protection for surviving channels in multiwavelength optical networks,” in Proceedings of European Conference on Fiber Communications, Postdeadline Papers, Vol. 5, (Telenor R&D, Kjeller, Norway, 1996), pp. 49–52.

E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, New York, 1994).

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Figures (4)

Fig. 1
Fig. 1

Comparison between analytical calculation (solid curves) and numerical simulation (solid circles) for a single-stage EDFA.

Fig. 2
Fig. 2

Fitted saturation factors and relative error predicted by perturbation theory, Eq. (10), for the cases in Fig. 1.

Fig. 3
Fig. 3

Comparison between analytical calculation (solid curves) and numerical simulation (solid circles) for a two-stage EDFA.

Fig. 4
Fig. 4

Fitted saturation factors for Fig. 3.

Tables (2)

Tables Icon

Table 1 Simulation Parameters

Tables Icon

Table 2 EDFA Parameters

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

τ ddt PkISg¯ktL+PkISg¯ktL+PkISαktL=-j=1N Pjin×expPkISg¯kt-g¯kj0+αkjexp-t/τ+αkjPjIS L-1,
g¯kj0=PkISg¯k0-PjISg¯j0,
αkj=PkISαk-PjISαj.
g¯kj0+αkj=0.
τ ddt PkISg¯ktL+PkISg¯ktL+PkISαktL=-j=1N Pjin×expPkISg¯kt+αkjPjIS L-1.
g¯kt=g¯k01+g¯ktt,
|g¯ktt|  1.
PkISg¯k0L+PkISαkL=-j=1N Pjinexpg¯j0L-1
τ ddt g¯ktt+g¯ktt=-g¯kttj=1NPjinPjIS expg¯j0L,
γ=-j=1NPjinPjIS expg¯j0L=j=1NPjoutPjIS,
τ ddt g¯ktt+1+γg¯ktt=0.
g¯ktt=g¯kt0 exp-tτe,
τe=τ1+γ.
g¯kt=g¯k01+g¯kt0 exp-tτe.
g¯kt=g¯k+g¯k0-g¯kexp-tτe,
Pkoutt=Pkin expg¯ktL=PkoutPkout0Pkoutexp-t/τe,
γ=γ0+γ2,

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