Abstract

An analytical expression for the carrier recovery time in semiconductor optical amplifiers (SOAs) that employ holding beams is presented. The amplifier model from which the expression is derived assumes a uniform carrier density along the SOA’s length and that the signal and the holding beams both receive amplification. Simulations and experiments show that the expression predicts the recovery time well over a wide range of amplifier gains, holding beam powers, and configurations.

© 2002 Optical Society of America

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  1. D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
    [CrossRef] [PubMed]
  2. T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
    [CrossRef]
  3. R. J. Manning and D. A. O. Davies, Opt. Lett. 19, 889 (1994).
    [CrossRef] [PubMed]
  4. R. J. Manning, D. A. O. Davies, and J. K. Lucek, Electron. Lett. 30, 1233 (1994).
    [CrossRef]
  5. M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, and J. Y. Emery, IEEE Photon. Technol. Lett. 12, 1453 (2000).
    [CrossRef]
  6. M. P. van Exter, W. A. Hamel, J. P. Woerdman, and B. R. P. Zeijlmans, IEEE J. Quantum Electron. 28, 1470 (1992).
    [CrossRef]
  7. A. Mecozzi, IEEE Photon. Technol. Lett. 8, 1471 (1996).
    [CrossRef]
  8. D. D. Marcenac, A. E. Kelly, D. Nesset, and D. A. O. Davies, Electron. Lett. 31, 1442 (1995).
    [CrossRef]
  9. M. J. Adams, J. V. Collins, and I. D. Henning, Proc. Inst. Electr. Eng. Part J 132, 58 (1985).

2000 (1)

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, and J. Y. Emery, IEEE Photon. Technol. Lett. 12, 1453 (2000).
[CrossRef]

1999 (1)

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

1996 (2)

T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

A. Mecozzi, IEEE Photon. Technol. Lett. 8, 1471 (1996).
[CrossRef]

1995 (1)

D. D. Marcenac, A. E. Kelly, D. Nesset, and D. A. O. Davies, Electron. Lett. 31, 1442 (1995).
[CrossRef]

1994 (2)

R. J. Manning and D. A. O. Davies, Opt. Lett. 19, 889 (1994).
[CrossRef] [PubMed]

R. J. Manning, D. A. O. Davies, and J. K. Lucek, Electron. Lett. 30, 1233 (1994).
[CrossRef]

1992 (1)

M. P. van Exter, W. A. Hamel, J. P. Woerdman, and B. R. P. Zeijlmans, IEEE J. Quantum Electron. 28, 1470 (1992).
[CrossRef]

1985 (1)

M. J. Adams, J. V. Collins, and I. D. Henning, Proc. Inst. Electr. Eng. Part J 132, 58 (1985).

Adams, M. J.

M. J. Adams, J. V. Collins, and I. D. Henning, Proc. Inst. Electr. Eng. Part J 132, 58 (1985).

Blow, K. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Collins, J. V.

M. J. Adams, J. V. Collins, and I. D. Henning, Proc. Inst. Electr. Eng. Part J 132, 58 (1985).

Cotter, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Dagens, B.

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, and J. Y. Emery, IEEE Photon. Technol. Lett. 12, 1453 (2000).
[CrossRef]

Danielsen, S. L.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Davies, D. A. O.

D. D. Marcenac, A. E. Kelly, D. Nesset, and D. A. O. Davies, Electron. Lett. 31, 1442 (1995).
[CrossRef]

R. J. Manning, D. A. O. Davies, and J. K. Lucek, Electron. Lett. 30, 1233 (1994).
[CrossRef]

R. J. Manning and D. A. O. Davies, Opt. Lett. 19, 889 (1994).
[CrossRef] [PubMed]

Deveaud, B.

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, and J. Y. Emery, IEEE Photon. Technol. Lett. 12, 1453 (2000).
[CrossRef]

Dupertuis, M. A.

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, and J. Y. Emery, IEEE Photon. Technol. Lett. 12, 1453 (2000).
[CrossRef]

Durhuus, T.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Ellis, A. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Emery, J. Y.

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, and J. Y. Emery, IEEE Photon. Technol. Lett. 12, 1453 (2000).
[CrossRef]

Hamel, W. A.

M. P. van Exter, W. A. Hamel, J. P. Woerdman, and B. R. P. Zeijlmans, IEEE J. Quantum Electron. 28, 1470 (1992).
[CrossRef]

Henning, I. D.

M. J. Adams, J. V. Collins, and I. D. Henning, Proc. Inst. Electr. Eng. Part J 132, 58 (1985).

Hessler, T. P.

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, and J. Y. Emery, IEEE Photon. Technol. Lett. 12, 1453 (2000).
[CrossRef]

Joergensen, C.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Kelly, A. E.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

D. D. Marcenac, A. E. Kelly, D. Nesset, and D. A. O. Davies, Electron. Lett. 31, 1442 (1995).
[CrossRef]

Lucek, J. K.

R. J. Manning, D. A. O. Davies, and J. K. Lucek, Electron. Lett. 30, 1233 (1994).
[CrossRef]

Manning, R. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

R. J. Manning and D. A. O. Davies, Opt. Lett. 19, 889 (1994).
[CrossRef] [PubMed]

R. J. Manning, D. A. O. Davies, and J. K. Lucek, Electron. Lett. 30, 1233 (1994).
[CrossRef]

Marcenac, D. D.

D. D. Marcenac, A. E. Kelly, D. Nesset, and D. A. O. Davies, Electron. Lett. 31, 1442 (1995).
[CrossRef]

Mecozzi, A.

A. Mecozzi, IEEE Photon. Technol. Lett. 8, 1471 (1996).
[CrossRef]

Mikkelsen, B.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Nesset, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

D. D. Marcenac, A. E. Kelly, D. Nesset, and D. A. O. Davies, Electron. Lett. 31, 1442 (1995).
[CrossRef]

Phillips, I. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Pleumeekers, J. L.

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, and J. Y. Emery, IEEE Photon. Technol. Lett. 12, 1453 (2000).
[CrossRef]

Poustie, A. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Rogers, D. C.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Selbmann, P. E.

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, and J. Y. Emery, IEEE Photon. Technol. Lett. 12, 1453 (2000).
[CrossRef]

Stubkjaer, K. E.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

van Exter, M. P.

M. P. van Exter, W. A. Hamel, J. P. Woerdman, and B. R. P. Zeijlmans, IEEE J. Quantum Electron. 28, 1470 (1992).
[CrossRef]

Woerdman, J. P.

M. P. van Exter, W. A. Hamel, J. P. Woerdman, and B. R. P. Zeijlmans, IEEE J. Quantum Electron. 28, 1470 (1992).
[CrossRef]

Zeijlmans, B. R. P.

M. P. van Exter, W. A. Hamel, J. P. Woerdman, and B. R. P. Zeijlmans, IEEE J. Quantum Electron. 28, 1470 (1992).
[CrossRef]

Electron. Lett. (2)

R. J. Manning, D. A. O. Davies, and J. K. Lucek, Electron. Lett. 30, 1233 (1994).
[CrossRef]

D. D. Marcenac, A. E. Kelly, D. Nesset, and D. A. O. Davies, Electron. Lett. 31, 1442 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. P. van Exter, W. A. Hamel, J. P. Woerdman, and B. R. P. Zeijlmans, IEEE J. Quantum Electron. 28, 1470 (1992).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

A. Mecozzi, IEEE Photon. Technol. Lett. 8, 1471 (1996).
[CrossRef]

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, and J. Y. Emery, IEEE Photon. Technol. Lett. 12, 1453 (2000).
[CrossRef]

J. Lightwave Technol. (1)

T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Opt. Lett. (1)

Proc. Inst. Electr. Eng. Part J (1)

M. J. Adams, J. V. Collins, and I. D. Henning, Proc. Inst. Electr. Eng. Part J 132, 58 (1985).

Science (1)

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Setup for measurement of recovery times of carriers in a SOA. cw holding beams of total power P1 were injected into the SOA. Experiments were performed with holding beams of equal power injected from both sides of the SOA and for a single holding beam only, of power P1, injected into the left-hand side of the SOA. A 1.4-ps-wide optical pulse was injected at regular intervals into the SOA. PD, photodiode; C, Circulator.

Fig. 2
Fig. 2

Simulation and analytical results showing 1/τeff for various holding beam powers and for SOA gains of (a) 10 and (b) 200. Also shown is the line described by Eq. (7), which gives the predicted 1/τeff.

Fig. 3
Fig. 3

Experimental results showing 1/τeff for various SOA gains, holding beam powers, and configurations: (a) bidirectional holding beam configuration, (b) unidirectional configuration.

Tables (1)

Tables Icon

Table 1 List of Linear Fit Parameters for Various SOA Gains and Holding Beam Configurations

Equations (7)

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

dNdt=Iq-Nτe-FNP1hν1-FNP2hν2,
FN=ΓaALN-N0×expΓa/ALN-N0-αintL-1Γa/ALN-N0-αint,
GN=expΓaALN-N0-αintL.
dNdt=Iq-Nτe-FNsP1hν1-FNsN-NsP1hν1,
FNs=γΓaLαint/A,
γ=1αintL+1ln Gs-1ln Gs2Gs+1ln Gs2.
1τeff=1τe+γΓaLαintAP1hν1.

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