Abstract

We report an improved transient response of an Er3+-doped fiber-optic amplifier with combined electronic feedforward (EFF) and optical feedback (OFB) control systems. We find, theoretically and experimentally, that the time delay of an EFF response leads to control instabilities in the form of erbium-doped fiber amplifier gain auto-oscillations, which can be suppressed by an appropriate choice of OFB wavelength and control system design.

© 2002 Optical Society of America

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References

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  1. K. Motoshima, K. Shimizu, K. Takano, T. Mizuochi, and T. Kitayama, in Conference on Optical Fiber Communications, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 191–192.
  2. E. Goobar, J. Sandell, S. Wingstrand, K. Käyhkö, K. Nilssson, L. Persson, and A. Lundberg, presented at the 25th European Conference on Optical Communication, Nice, France, September 26–30, 1999.
  3. G. Luo, J. L. Zyskind, J. A. Nagel, and M. A. Ali, J. Lightwave Technol. 16, 527 (1998).
    [Crossref]
  4. A. Bononi and L. Barbieri, J. Lightwave Technol. 17, 1229 (1999).
    [Crossref]
  5. C.-C. Wang and G. J. Cowle, IEEE Photon. Technol. Lett. 12, 483 (2000).
    [Crossref]
  6. Y. Liu and M. F. Krol, IEEE Photon. Technol. Lett. 11, 1381 (1999).
    [Crossref]
  7. M. Fukutoku and M. Jinno, in Optical Amplifiers and Their Applications, D. Baney, K. Emura, and J. Wiesenfeld, eds., Vol. 25 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 32–35.
  8. S. Sergeyev, E. Vanin, J. Sandell, G. Jacobsen, and M. Resare, in Conference on Lasers and Electro-Optics (CLEO/Europe–EQEC) Focus Meetings (Optical Society of America, Washington, D.C., 2001), p. 221.
  9. S. Sergeyev, E. Vanin, and G. Jacobsen, in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2002), paper ThR6.
  10. H. S. Carslaw and J. C. Jaeger, Operational Methods in Applied Mathematics (Oxford University, New York, 1953) p. 279.
  11. B. D. Hasssard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation (Cambridge University, Cambridge, England, 1981), p. 181.

2000 (1)

C.-C. Wang and G. J. Cowle, IEEE Photon. Technol. Lett. 12, 483 (2000).
[Crossref]

1999 (2)

Y. Liu and M. F. Krol, IEEE Photon. Technol. Lett. 11, 1381 (1999).
[Crossref]

A. Bononi and L. Barbieri, J. Lightwave Technol. 17, 1229 (1999).
[Crossref]

1998 (1)

Ali, M. A.

Barbieri, L.

Bononi, A.

Carslaw, H. S.

H. S. Carslaw and J. C. Jaeger, Operational Methods in Applied Mathematics (Oxford University, New York, 1953) p. 279.

Cowle, G. J.

C.-C. Wang and G. J. Cowle, IEEE Photon. Technol. Lett. 12, 483 (2000).
[Crossref]

Fukutoku, M.

M. Fukutoku and M. Jinno, in Optical Amplifiers and Their Applications, D. Baney, K. Emura, and J. Wiesenfeld, eds., Vol. 25 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 32–35.

Goobar, E.

E. Goobar, J. Sandell, S. Wingstrand, K. Käyhkö, K. Nilssson, L. Persson, and A. Lundberg, presented at the 25th European Conference on Optical Communication, Nice, France, September 26–30, 1999.

Hasssard, B. D.

B. D. Hasssard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation (Cambridge University, Cambridge, England, 1981), p. 181.

Jacobsen, G.

S. Sergeyev, E. Vanin, and G. Jacobsen, in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2002), paper ThR6.

S. Sergeyev, E. Vanin, J. Sandell, G. Jacobsen, and M. Resare, in Conference on Lasers and Electro-Optics (CLEO/Europe–EQEC) Focus Meetings (Optical Society of America, Washington, D.C., 2001), p. 221.

Jaeger, J. C.

H. S. Carslaw and J. C. Jaeger, Operational Methods in Applied Mathematics (Oxford University, New York, 1953) p. 279.

Jinno, M.

M. Fukutoku and M. Jinno, in Optical Amplifiers and Their Applications, D. Baney, K. Emura, and J. Wiesenfeld, eds., Vol. 25 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 32–35.

Käyhkö, K.

E. Goobar, J. Sandell, S. Wingstrand, K. Käyhkö, K. Nilssson, L. Persson, and A. Lundberg, presented at the 25th European Conference on Optical Communication, Nice, France, September 26–30, 1999.

Kazarinoff, N. D.

B. D. Hasssard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation (Cambridge University, Cambridge, England, 1981), p. 181.

Kitayama, T.

K. Motoshima, K. Shimizu, K. Takano, T. Mizuochi, and T. Kitayama, in Conference on Optical Fiber Communications, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 191–192.

Krol, M. F.

Y. Liu and M. F. Krol, IEEE Photon. Technol. Lett. 11, 1381 (1999).
[Crossref]

Liu, Y.

Y. Liu and M. F. Krol, IEEE Photon. Technol. Lett. 11, 1381 (1999).
[Crossref]

Lundberg, A.

E. Goobar, J. Sandell, S. Wingstrand, K. Käyhkö, K. Nilssson, L. Persson, and A. Lundberg, presented at the 25th European Conference on Optical Communication, Nice, France, September 26–30, 1999.

Luo, G.

Mizuochi, T.

K. Motoshima, K. Shimizu, K. Takano, T. Mizuochi, and T. Kitayama, in Conference on Optical Fiber Communications, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 191–192.

Motoshima, K.

K. Motoshima, K. Shimizu, K. Takano, T. Mizuochi, and T. Kitayama, in Conference on Optical Fiber Communications, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 191–192.

Nagel, J. A.

Nilssson, K.

E. Goobar, J. Sandell, S. Wingstrand, K. Käyhkö, K. Nilssson, L. Persson, and A. Lundberg, presented at the 25th European Conference on Optical Communication, Nice, France, September 26–30, 1999.

Persson, L.

E. Goobar, J. Sandell, S. Wingstrand, K. Käyhkö, K. Nilssson, L. Persson, and A. Lundberg, presented at the 25th European Conference on Optical Communication, Nice, France, September 26–30, 1999.

Resare, M.

S. Sergeyev, E. Vanin, J. Sandell, G. Jacobsen, and M. Resare, in Conference on Lasers and Electro-Optics (CLEO/Europe–EQEC) Focus Meetings (Optical Society of America, Washington, D.C., 2001), p. 221.

Sandell, J.

S. Sergeyev, E. Vanin, J. Sandell, G. Jacobsen, and M. Resare, in Conference on Lasers and Electro-Optics (CLEO/Europe–EQEC) Focus Meetings (Optical Society of America, Washington, D.C., 2001), p. 221.

E. Goobar, J. Sandell, S. Wingstrand, K. Käyhkö, K. Nilssson, L. Persson, and A. Lundberg, presented at the 25th European Conference on Optical Communication, Nice, France, September 26–30, 1999.

Sergeyev, S.

S. Sergeyev, E. Vanin, and G. Jacobsen, in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2002), paper ThR6.

S. Sergeyev, E. Vanin, J. Sandell, G. Jacobsen, and M. Resare, in Conference on Lasers and Electro-Optics (CLEO/Europe–EQEC) Focus Meetings (Optical Society of America, Washington, D.C., 2001), p. 221.

Shimizu, K.

K. Motoshima, K. Shimizu, K. Takano, T. Mizuochi, and T. Kitayama, in Conference on Optical Fiber Communications, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 191–192.

Takano, K.

K. Motoshima, K. Shimizu, K. Takano, T. Mizuochi, and T. Kitayama, in Conference on Optical Fiber Communications, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 191–192.

Vanin, E.

S. Sergeyev, E. Vanin, J. Sandell, G. Jacobsen, and M. Resare, in Conference on Lasers and Electro-Optics (CLEO/Europe–EQEC) Focus Meetings (Optical Society of America, Washington, D.C., 2001), p. 221.

S. Sergeyev, E. Vanin, and G. Jacobsen, in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2002), paper ThR6.

Wan, Y. H.

B. D. Hasssard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation (Cambridge University, Cambridge, England, 1981), p. 181.

Wang, C.-C.

C.-C. Wang and G. J. Cowle, IEEE Photon. Technol. Lett. 12, 483 (2000).
[Crossref]

Wingstrand, S.

E. Goobar, J. Sandell, S. Wingstrand, K. Käyhkö, K. Nilssson, L. Persson, and A. Lundberg, presented at the 25th European Conference on Optical Communication, Nice, France, September 26–30, 1999.

Zyskind, J. L.

IEEE Photon. Technol. Lett. (2)

C.-C. Wang and G. J. Cowle, IEEE Photon. Technol. Lett. 12, 483 (2000).
[Crossref]

Y. Liu and M. F. Krol, IEEE Photon. Technol. Lett. 11, 1381 (1999).
[Crossref]

J. Lightwave Technol. (2)

Other (7)

K. Motoshima, K. Shimizu, K. Takano, T. Mizuochi, and T. Kitayama, in Conference on Optical Fiber Communications, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 191–192.

E. Goobar, J. Sandell, S. Wingstrand, K. Käyhkö, K. Nilssson, L. Persson, and A. Lundberg, presented at the 25th European Conference on Optical Communication, Nice, France, September 26–30, 1999.

M. Fukutoku and M. Jinno, in Optical Amplifiers and Their Applications, D. Baney, K. Emura, and J. Wiesenfeld, eds., Vol. 25 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 32–35.

S. Sergeyev, E. Vanin, J. Sandell, G. Jacobsen, and M. Resare, in Conference on Lasers and Electro-Optics (CLEO/Europe–EQEC) Focus Meetings (Optical Society of America, Washington, D.C., 2001), p. 221.

S. Sergeyev, E. Vanin, and G. Jacobsen, in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2002), paper ThR6.

H. S. Carslaw and J. C. Jaeger, Operational Methods in Applied Mathematics (Oxford University, New York, 1953) p. 279.

B. D. Hasssard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation (Cambridge University, Cambridge, England, 1981), p. 181.

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Figures (2)

Fig. 1
Fig. 1

EFF combined with an OFB, control scheme: VOA, variable optical attenuator; TF, tunable filter; C/L C, C/L band combiner; C, coupler; EDFA, erbium-doped fiber amplifier; PD, photodetector. The input signal was modulated at 1-kHz frequency between -21 and -6 dBm, λOFB1=1565 nm, λOFB2=1570 nm.

Fig. 2
Fig. 2

EDFA transient gain error for (a) curve 1, an EFF and curve 2, OFB and (b) curve 3, optimal operation and curve 4, auto-oscillation in a combined EFF and OFB scheme. The input signal was modulated at 1-kHz frequency between -21 and -6 dBm, λOFB1=1565 nm, λOFB2=1570 nm.

Equations (8)

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drdt=-rτ+Qst+QASEint1-GSt+j=p,lQjt1-Gjt,Qlt=αQlt-τlGlt-τl+Ql,ASEt-τl,
Gjt=expBjr-Aj,  Aj=ρΓjσjaL, Bj=Γjσja+σje/Aeff,  r=N2LAeff.
r0=Al+ln1αBl, Ql,0=j=s,pQj,01-Gj,0-r0τ1α-1.
j=s,lΔQjt-τp1-Gj0+ΔQpt1-Gp0=0.
du1dζ=-χ0+ϵu1+u2ζ-u2ζ-1×1-1α, u2t=αϵu1ζ-ξ+u2ζ-ξ,
ζ=t/τp,  ϵ=Ql,0Blτpα,  ξ=τl/τp, χ0=1τ+j=x,pQjBjGj,0+ΔQsGs,0Bs2-1-Gs,01-Gp,0Gp,0Bp2τp.
χ0+ϵ+λ1-exp-λξ-ϵα-11-exp-λexp-λξ=0.
ω=2n+1π,  ϵ=2n+1π221-αξ, n=0,1,2.

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