Abstract

We investigate the dependence of the speed of recovery of optically excited semiconductor optical amplifiers (SOAs) on the active region dimensions. We use a picosecond pump-probe arrangement to experimentally measure and compare the gain and phase dynamics of four SOAs with varying active region dimensions. A sophisticated time domain SOA model incorporating amplified spontaneous emission (ASE) agrees well with the measurements and shows that, in the absence of a continuous wave (CW) beam, the ASE plays a similar role to such a holding beam. The experimental results are shown to be consistent with a recovery rate which is inversely proportional to the optical area. A significant speed increase is predicted for an appropriate choice of active region dimensions.

© 2007 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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
    [CrossRef] [PubMed]
  2. J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).
  3. R. J. Manning, X. Yang, R. P. Webb, and R. Giller, "The ‘turbo-switch’ - a novel technique to increase the high-speed response of SOAs for wavelength conversion," in Proceedings of OFC (Anaheim, Calif. 2006), OWS8.
  4. Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave. Technol. 24, 230-236 (2006).
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  17. K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, "Subpicosecond gain and index nonlinearities in InGaAsP Diode Lasers," Opt. Commun. 111, 589-612 (1994).
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    [CrossRef]
  24. F. Ginovart and J. C. Simon, "Semiconductor optical amplifier length effects on gain dynamics," J. Phys. D: Appl. Phys. 36, 1473-1476 (2003).
    [CrossRef]
  25. L. Schares, C. Schubert, C. Schmidt, H. G. Weber, L. Occhi, and G. Guekos, "Phase dynamics of semiconductor optical amplifiers at 10-40 GHz," IEEE J. Quantum. Electron. 39, 1394-1408 (2003).
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    [CrossRef]

2006

Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave. Technol. 24, 230-236 (2006).
[CrossRef]

R. Giller, R. J. Manning, and D. Cotter, "Gain and phase recovery of optically excited semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 18, 1061-1063 (2006).
[CrossRef]

L. Zhang, I. Kang, A. Bhardwaj, N. Sauer, S. Cabot, J. Jaques, and D. T. Nielson, "Reduced recovery time semiconductor optical amplifier using p-type-doped multiple quantum wells,"IEEE Photon. Technol. Lett. 18, 2323-2325 (2006).
[CrossRef]

2005

X. Li, D. Alexandropoulos, M. J. Adams, and I. F. Lealman, "Wavelength dependence of gain recovery time in semiconductor optical amplifiers," Proc. SPIE 5722, 343-350 (2005).
[CrossRef]

R. P. Webb, R. J. Manning, X. Yang, and R. Giller, "All-optical 40Gb/s XOR gate with dual ultrafast nonlinear interferometers," Electron. Lett. 41, 1396-1397 (2005).
[CrossRef]

2003

G. Talli and M. J. Adams, "Gain dynamics of semiconductor optical amplifiers and three-wavelength devices,"IEEE J. Quantum. Electron. 39, 1305-1313 (2003).
[CrossRef]

F. Ginovart and J. C. Simon, "Semiconductor optical amplifier length effects on gain dynamics," J. Phys. D: Appl. Phys. 36, 1473-1476 (2003).
[CrossRef]

L. Schares, C. Schubert, C. Schmidt, H. G. Weber, L. Occhi, and G. Guekos, "Phase dynamics of semiconductor optical amplifiers at 10-40 GHz," IEEE J. Quantum. Electron. 39, 1394-1408 (2003).
[CrossRef]

2001

F. Ginovart, J. C. Simon, and I. Valiente, "Gain recovery dynamics in semiconductor optical amplifier," Opt. Commun. 199, 111-115 (2001).
[CrossRef]

2000

J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).

1999

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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
[CrossRef] [PubMed]

B. Dagens, C. Janz, D. Leclerc, V. Verdrager, F. Poingt, I. Guillemot, F. Gaborit, and D. Ottenwalder, "Design optimization of all-active Mach-Zehnder wavelength converters," IEEE Photon. Technol. Lett. 11, 424-426 (1999).
[CrossRef]

1998

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

K. L. Hall and K. A. Rauschenbach, "100 Gbit/s bitwise logic," Opt. Lett. 23, 1271-1273 (1998).
[CrossRef]

1997

T. Ito, N. Yoshimoto, K. Magari, K. Kishi, and Y. Kondo, "Extremely low power consumption semiconductor optical amplifier gate for WDM applications," Electron. Lett. 33, 1791-1792 (1997).
[CrossRef]

1996

1995

M. Eiselt, W. Pieper, and H. G. Weber, "SLALOM: semiconductor laser amplifier in a loop mirror," J. Lightwave. Technol. 13, 2099-2112 (1995).
[CrossRef]

1994

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, "Subpicosecond gain and index nonlinearities in InGaAsP Diode Lasers," Opt. Commun. 111, 589-612 (1994).
[CrossRef]

R. J. Manning and D. A. O. Davies, "Three-wavelength device for all-optical signal processing," Opt. Lett 19, 889-891 (1994).
[CrossRef] [PubMed]

1993

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, "A terahertz optical asymmetric demultiplexer (TOAD)," IEEE Photon. Technol. Lett. 5,787-790 (1993).
[CrossRef]

1989

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[CrossRef]

1985

J. A. Kash, J. C. Tsang, and J. M. Hvam, "Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs," Phys. Rev. Lett. 54, 2151-2154 (1985).
[CrossRef] [PubMed]

Adams, M. J.

X. Li, D. Alexandropoulos, M. J. Adams, and I. F. Lealman, "Wavelength dependence of gain recovery time in semiconductor optical amplifiers," Proc. SPIE 5722, 343-350 (2005).
[CrossRef]

G. Talli and M. J. Adams, "Gain dynamics of semiconductor optical amplifiers and three-wavelength devices,"IEEE J. Quantum. Electron. 39, 1305-1313 (2003).
[CrossRef]

Alexandropoulos, D.

X. Li, D. Alexandropoulos, M. J. Adams, and I. F. Lealman, "Wavelength dependence of gain recovery time in semiconductor optical amplifiers," Proc. SPIE 5722, 343-350 (2005).
[CrossRef]

Besse, P. A.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Bhardwaj, A.

L. Zhang, I. Kang, A. Bhardwaj, N. Sauer, S. Cabot, J. Jaques, and D. T. Nielson, "Reduced recovery time semiconductor optical amplifier using p-type-doped multiple quantum wells,"IEEE Photon. Technol. Lett. 18, 2323-2325 (2006).
[CrossRef]

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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
[CrossRef] [PubMed]

Bouchoule, S.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Bridges, T. J.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[CrossRef]

Burrus, C. A.

J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[CrossRef]

Cabot, S.

L. Zhang, I. Kang, A. Bhardwaj, N. Sauer, S. Cabot, J. Jaques, and D. T. Nielson, "Reduced recovery time semiconductor optical amplifier using p-type-doped multiple quantum wells,"IEEE Photon. Technol. Lett. 18, 2323-2325 (2006).
[CrossRef]

Caraccia-Gross, M.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Cotter, D.

R. Giller, R. J. Manning, and D. Cotter, "Gain and phase recovery of optically excited semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 18, 1061-1063 (2006).
[CrossRef]

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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
[CrossRef] [PubMed]

Dagens, B.

B. Dagens, C. Janz, D. Leclerc, V. Verdrager, F. Poingt, I. Guillemot, F. Gaborit, and D. Ottenwalder, "Design optimization of all-active Mach-Zehnder wavelength converters," IEEE Photon. Technol. Lett. 11, 424-426 (1999).
[CrossRef]

Darwish, A. M.

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, "Subpicosecond gain and index nonlinearities in InGaAsP Diode Lasers," Opt. Commun. 111, 589-612 (1994).
[CrossRef]

Davies, D. A. O.

R. J. Manning and D. A. O. Davies, "Three-wavelength device for all-optical signal processing," Opt. Lett 19, 889-891 (1994).
[CrossRef] [PubMed]

de Waardt, H.

Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave. Technol. 24, 230-236 (2006).
[CrossRef]

Dorren, H. J. S.

Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave. Technol. 24, 230-236 (2006).
[CrossRef]

Dreyer, K.

J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).

Duelk, M.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Eiselt, M.

M. Eiselt, W. Pieper, and H. G. Weber, "SLALOM: semiconductor laser amplifier in a loop mirror," J. Lightwave. Technol. 13, 2099-2112 (1995).
[CrossRef]

Eisenstein, G.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
[CrossRef] [PubMed]

Gaborit, F.

B. Dagens, C. Janz, D. Leclerc, V. Verdrager, F. Poingt, I. Guillemot, F. Gaborit, and D. Ottenwalder, "Design optimization of all-active Mach-Zehnder wavelength converters," IEEE Photon. Technol. Lett. 11, 424-426 (1999).
[CrossRef]

Gamper, E.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Giller, R.

R. Giller, R. J. Manning, and D. Cotter, "Gain and phase recovery of optically excited semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 18, 1061-1063 (2006).
[CrossRef]

R. P. Webb, R. J. Manning, X. Yang, and R. Giller, "All-optical 40Gb/s XOR gate with dual ultrafast nonlinear interferometers," Electron. Lett. 41, 1396-1397 (2005).
[CrossRef]

Gini, E.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Ginovart, F.

F. Ginovart and J. C. Simon, "Semiconductor optical amplifier length effects on gain dynamics," J. Phys. D: Appl. Phys. 36, 1473-1476 (2003).
[CrossRef]

F. Ginovart, J. C. Simon, and I. Valiente, "Gain recovery dynamics in semiconductor optical amplifier," Opt. Commun. 199, 111-115 (2001).
[CrossRef]

Glesk, I.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, "A terahertz optical asymmetric demultiplexer (TOAD)," IEEE Photon. Technol. Lett. 5,787-790 (1993).
[CrossRef]

Guekos, G.

L. Schares, C. Schubert, C. Schmidt, H. G. Weber, L. Occhi, and G. Guekos, "Phase dynamics of semiconductor optical amplifiers at 10-40 GHz," IEEE J. Quantum. Electron. 39, 1394-1408 (2003).
[CrossRef]

Guillemot, I.

B. Dagens, C. Janz, D. Leclerc, V. Verdrager, F. Poingt, I. Guillemot, F. Gaborit, and D. Ottenwalder, "Design optimization of all-active Mach-Zehnder wavelength converters," IEEE Photon. Technol. Lett. 11, 424-426 (1999).
[CrossRef]

Hall, K. L.

K. L. Hall and K. A. Rauschenbach, "100 Gbit/s bitwise logic," Opt. Lett. 23, 1271-1273 (1998).
[CrossRef]

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, "Subpicosecond gain and index nonlinearities in InGaAsP Diode Lasers," Opt. Commun. 111, 589-612 (1994).
[CrossRef]

Hansen, P. B.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[CrossRef]

Hess, R.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Hvam, J. M.

J. A. Kash, J. C. Tsang, and J. M. Hvam, "Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs," Phys. Rev. Lett. 54, 2151-2154 (1985).
[CrossRef] [PubMed]

Ippen, E. P.

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, "Subpicosecond gain and index nonlinearities in InGaAsP Diode Lasers," Opt. Commun. 111, 589-612 (1994).
[CrossRef]

Ito, T.

T. Ito, N. Yoshimoto, K. Magari, K. Kishi, and Y. Kondo, "Extremely low power consumption semiconductor optical amplifier gate for WDM applications," Electron. Lett. 33, 1791-1792 (1997).
[CrossRef]

Janz, C.

B. Dagens, C. Janz, D. Leclerc, V. Verdrager, F. Poingt, I. Guillemot, F. Gaborit, and D. Ottenwalder, "Design optimization of all-active Mach-Zehnder wavelength converters," IEEE Photon. Technol. Lett. 11, 424-426 (1999).
[CrossRef]

Jaques, J.

L. Zhang, I. Kang, A. Bhardwaj, N. Sauer, S. Cabot, J. Jaques, and D. T. Nielson, "Reduced recovery time semiconductor optical amplifier using p-type-doped multiple quantum wells,"IEEE Photon. Technol. Lett. 18, 2323-2325 (2006).
[CrossRef]

Jepsen, K. S.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Johnson, B. C.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[CrossRef]

Joyner, C. H.

J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).

Kane, M.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, "A terahertz optical asymmetric demultiplexer (TOAD)," IEEE Photon. Technol. Lett. 5,787-790 (1993).
[CrossRef]

Kang, I.

L. Zhang, I. Kang, A. Bhardwaj, N. Sauer, S. Cabot, J. Jaques, and D. T. Nielson, "Reduced recovery time semiconductor optical amplifier using p-type-doped multiple quantum wells,"IEEE Photon. Technol. Lett. 18, 2323-2325 (2006).
[CrossRef]

Kash, J. A.

J. A. Kash, J. C. Tsang, and J. M. Hvam, "Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs," Phys. Rev. Lett. 54, 2151-2154 (1985).
[CrossRef] [PubMed]

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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
[CrossRef] [PubMed]

Khoe, G. D.

Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave. Technol. 24, 230-236 (2006).
[CrossRef]

Kishi, K.

T. Ito, N. Yoshimoto, K. Magari, K. Kishi, and Y. Kondo, "Extremely low power consumption semiconductor optical amplifier gate for WDM applications," Electron. Lett. 33, 1791-1792 (1997).
[CrossRef]

Kondo, Y.

T. Ito, N. Yoshimoto, K. Magari, K. Kishi, and Y. Kondo, "Extremely low power consumption semiconductor optical amplifier gate for WDM applications," Electron. Lett. 33, 1791-1792 (1997).
[CrossRef]

Lealman, I. F.

X. Li, D. Alexandropoulos, M. J. Adams, and I. F. Lealman, "Wavelength dependence of gain recovery time in semiconductor optical amplifiers," Proc. SPIE 5722, 343-350 (2005).
[CrossRef]

Leclerc, D.

B. Dagens, C. Janz, D. Leclerc, V. Verdrager, F. Poingt, I. Guillemot, F. Gaborit, and D. Ottenwalder, "Design optimization of all-active Mach-Zehnder wavelength converters," IEEE Photon. Technol. Lett. 11, 424-426 (1999).
[CrossRef]

Lenz, G.

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, "Subpicosecond gain and index nonlinearities in InGaAsP Diode Lasers," Opt. Commun. 111, 589-612 (1994).
[CrossRef]

Leuthold, J.

J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).

Li, X.

X. Li, D. Alexandropoulos, M. J. Adams, and I. F. Lealman, "Wavelength dependence of gain recovery time in semiconductor optical amplifiers," Proc. SPIE 5722, 343-350 (2005).
[CrossRef]

Li, Z.

Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave. Technol. 24, 230-236 (2006).
[CrossRef]

Liu, Y.

Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave. Technol. 24, 230-236 (2006).
[CrossRef]

Magari, K.

T. Ito, N. Yoshimoto, K. Magari, K. Kishi, and Y. Kondo, "Extremely low power consumption semiconductor optical amplifier gate for WDM applications," Electron. Lett. 33, 1791-1792 (1997).
[CrossRef]

Manning, R. J.

R. Giller, R. J. Manning, and D. Cotter, "Gain and phase recovery of optically excited semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 18, 1061-1063 (2006).
[CrossRef]

R. P. Webb, R. J. Manning, X. Yang, and R. Giller, "All-optical 40Gb/s XOR gate with dual ultrafast nonlinear interferometers," Electron. Lett. 41, 1396-1397 (2005).
[CrossRef]

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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
[CrossRef] [PubMed]

R. J. Manning and D. A. O. Davies, "Three-wavelength device for all-optical signal processing," Opt. Lett 19, 889-891 (1994).
[CrossRef] [PubMed]

Mecozzi, A.

Melchior, H.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Mikkelsen, B.

J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Miller, B. I.

J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).

Mork, J.

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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
[CrossRef] [PubMed]

Nielson, D. T.

L. Zhang, I. Kang, A. Bhardwaj, N. Sauer, S. Cabot, J. Jaques, and D. T. Nielson, "Reduced recovery time semiconductor optical amplifier using p-type-doped multiple quantum wells,"IEEE Photon. Technol. Lett. 18, 2323-2325 (2006).
[CrossRef]

Occhi, L.

L. Schares, C. Schubert, C. Schmidt, H. G. Weber, L. Occhi, and G. Guekos, "Phase dynamics of semiconductor optical amplifiers at 10-40 GHz," IEEE J. Quantum. Electron. 39, 1394-1408 (2003).
[CrossRef]

Ottenwalder, D.

B. Dagens, C. Janz, D. Leclerc, V. Verdrager, F. Poingt, I. Guillemot, F. Gaborit, and D. Ottenwalder, "Design optimization of all-active Mach-Zehnder wavelength converters," IEEE Photon. Technol. Lett. 11, 424-426 (1999).
[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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
[CrossRef] [PubMed]

Pieper, W.

M. Eiselt, W. Pieper, and H. G. Weber, "SLALOM: semiconductor laser amplifier in a loop mirror," J. Lightwave. Technol. 13, 2099-2112 (1995).
[CrossRef]

Pleumeekers, J. L.

J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).

Poingt, F.

B. Dagens, C. Janz, D. Leclerc, V. Verdrager, F. Poingt, I. Guillemot, F. Gaborit, and D. Ottenwalder, "Design optimization of all-active Mach-Zehnder wavelength converters," IEEE Photon. Technol. Lett. 11, 424-426 (1999).
[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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
[CrossRef] [PubMed]

Prucnal, P. R.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, "A terahertz optical asymmetric demultiplexer (TOAD)," IEEE Photon. Technol. Lett. 5,787-790 (1993).
[CrossRef]

Rauschenbach, K. A.

Raybon, G.

J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[CrossRef]

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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
[CrossRef] [PubMed]

Sauer, N.

L. Zhang, I. Kang, A. Bhardwaj, N. Sauer, S. Cabot, J. Jaques, and D. T. Nielson, "Reduced recovery time semiconductor optical amplifier using p-type-doped multiple quantum wells,"IEEE Photon. Technol. Lett. 18, 2323-2325 (2006).
[CrossRef]

Schares, L.

L. Schares, C. Schubert, C. Schmidt, H. G. Weber, L. Occhi, and G. Guekos, "Phase dynamics of semiconductor optical amplifiers at 10-40 GHz," IEEE J. Quantum. Electron. 39, 1394-1408 (2003).
[CrossRef]

Schmidt, C.

L. Schares, C. Schubert, C. Schmidt, H. G. Weber, L. Occhi, and G. Guekos, "Phase dynamics of semiconductor optical amplifiers at 10-40 GHz," IEEE J. Quantum. Electron. 39, 1394-1408 (2003).
[CrossRef]

Schubert, C.

L. Schares, C. Schubert, C. Schmidt, H. G. Weber, L. Occhi, and G. Guekos, "Phase dynamics of semiconductor optical amplifiers at 10-40 GHz," IEEE J. Quantum. Electron. 39, 1394-1408 (2003).
[CrossRef]

Simon, J. C.

F. Ginovart and J. C. Simon, "Semiconductor optical amplifier length effects on gain dynamics," J. Phys. D: Appl. Phys. 36, 1473-1476 (2003).
[CrossRef]

F. Ginovart, J. C. Simon, and I. Valiente, "Gain recovery dynamics in semiconductor optical amplifier," Opt. Commun. 199, 111-115 (2001).
[CrossRef]

Sokoloff, J. P.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, "A terahertz optical asymmetric demultiplexer (TOAD)," IEEE Photon. Technol. Lett. 5,787-790 (1993).
[CrossRef]

Storz, F. G.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[CrossRef]

Stubkjaer, K. E.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Talli, G.

G. Talli and M. J. Adams, "Gain dynamics of semiconductor optical amplifiers and three-wavelength devices,"IEEE J. Quantum. Electron. 39, 1305-1313 (2003).
[CrossRef]

Tangdiongga, E.

Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave. Technol. 24, 230-236 (2006).
[CrossRef]

Tsang, J. C.

J. A. Kash, J. C. Tsang, and J. M. Hvam, "Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs," Phys. Rev. Lett. 54, 2151-2154 (1985).
[CrossRef] [PubMed]

Tucker, R. S.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[CrossRef]

Vaa, M.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Valiente, I.

F. Ginovart, J. C. Simon, and I. Valiente, "Gain recovery dynamics in semiconductor optical amplifier," Opt. Commun. 199, 111-115 (2001).
[CrossRef]

Verdrager, V.

B. Dagens, C. Janz, D. Leclerc, V. Verdrager, F. Poingt, I. Guillemot, F. Gaborit, and D. Ottenwalder, "Design optimization of all-active Mach-Zehnder wavelength converters," IEEE Photon. Technol. Lett. 11, 424-426 (1999).
[CrossRef]

Vogt, W.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

Webb, R. P.

R. P. Webb, R. J. Manning, X. Yang, and R. Giller, "All-optical 40Gb/s XOR gate with dual ultrafast nonlinear interferometers," Electron. Lett. 41, 1396-1397 (2005).
[CrossRef]

Weber, H. G.

L. Schares, C. Schubert, C. Schmidt, H. G. Weber, L. Occhi, and G. Guekos, "Phase dynamics of semiconductor optical amplifiers at 10-40 GHz," IEEE J. Quantum. Electron. 39, 1394-1408 (2003).
[CrossRef]

M. Eiselt, W. Pieper, and H. G. Weber, "SLALOM: semiconductor laser amplifier in a loop mirror," J. Lightwave. Technol. 13, 2099-2112 (1995).
[CrossRef]

Wiesenfeld, J. M.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[CrossRef]

Yang, X.

R. P. Webb, R. J. Manning, X. Yang, and R. Giller, "All-optical 40Gb/s XOR gate with dual ultrafast nonlinear interferometers," Electron. Lett. 41, 1396-1397 (2005).
[CrossRef]

Yoshimoto, N.

T. Ito, N. Yoshimoto, K. Magari, K. Kishi, and Y. Kondo, "Extremely low power consumption semiconductor optical amplifier gate for WDM applications," Electron. Lett. 33, 1791-1792 (1997).
[CrossRef]

Zhang, L.

L. Zhang, I. Kang, A. Bhardwaj, N. Sauer, S. Cabot, J. Jaques, and D. T. Nielson, "Reduced recovery time semiconductor optical amplifier using p-type-doped multiple quantum wells,"IEEE Photon. Technol. Lett. 18, 2323-2325 (2006).
[CrossRef]

Zhang, S.

Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave. Technol. 24, 230-236 (2006).
[CrossRef]

AppL. Phys. Lett

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, "Gain recovery time of traveling-wave semiconductor optical amplifiers," AppL. Phys. Lett 54, 454-456 (1989).
[CrossRef]

Electron. Lett.

T. Ito, N. Yoshimoto, K. Magari, K. Kishi, and Y. Kondo, "Extremely low power consumption semiconductor optical amplifier gate for WDM applications," Electron. Lett. 33, 1791-1792 (1997).
[CrossRef]

J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, "100 Gbit/s all-optical wavelength conversion with integrated SOA delayed-interference configuration," IEEE Electron. Lett. 36, 1129-1130 (2000).

R. P. Webb, R. J. Manning, X. Yang, and R. Giller, "All-optical 40Gb/s XOR gate with dual ultrafast nonlinear interferometers," Electron. Lett. 41, 1396-1397 (2005).
[CrossRef]

J. Lightwave. Technol.

Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave. Technol. 24, 230-236 (2006).
[CrossRef]

M. Eiselt, W. Pieper, and H. G. Weber, "SLALOM: semiconductor laser amplifier in a loop mirror," J. Lightwave. Technol. 13, 2099-2112 (1995).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. D: Appl. Phys.

F. Ginovart and J. C. Simon, "Semiconductor optical amplifier length effects on gain dynamics," J. Phys. D: Appl. Phys. 36, 1473-1476 (2003).
[CrossRef]

J. Quantum. Electron.

L. Schares, C. Schubert, C. Schmidt, H. G. Weber, L. Occhi, and G. Guekos, "Phase dynamics of semiconductor optical amplifiers at 10-40 GHz," IEEE J. Quantum. Electron. 39, 1394-1408 (2003).
[CrossRef]

G. Talli and M. J. Adams, "Gain dynamics of semiconductor optical amplifiers and three-wavelength devices,"IEEE J. Quantum. Electron. 39, 1305-1313 (2003).
[CrossRef]

Opt. Commun.

F. Ginovart, J. C. Simon, and I. Valiente, "Gain recovery dynamics in semiconductor optical amplifier," Opt. Commun. 199, 111-115 (2001).
[CrossRef]

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, "Subpicosecond gain and index nonlinearities in InGaAsP Diode Lasers," Opt. Commun. 111, 589-612 (1994).
[CrossRef]

Opt. Lett

R. J. Manning and D. A. O. Davies, "Three-wavelength device for all-optical signal processing," Opt. Lett 19, 889-891 (1994).
[CrossRef] [PubMed]

Opt. Lett.

Photon. Technol. Lett.

R. Hess, M. Caraccia-Gross, W. Vogt, E. Gamper, P. A. Besse, M. Duelk, E. Gini, H. Melchior, B. Mikkelsen, M. Vaa, K. S. Jepsen, K. E. Stubkjaer, and S. Bouchoule, "All-optical demultiplexing of 80 to 10 Gb/s signals with monolithic integrated high-performance Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 10, 165-167 (1998).
[CrossRef]

B. Dagens, C. Janz, D. Leclerc, V. Verdrager, F. Poingt, I. Guillemot, F. Gaborit, and D. Ottenwalder, "Design optimization of all-active Mach-Zehnder wavelength converters," IEEE Photon. Technol. Lett. 11, 424-426 (1999).
[CrossRef]

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, "A terahertz optical asymmetric demultiplexer (TOAD)," IEEE Photon. Technol. Lett. 5,787-790 (1993).
[CrossRef]

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[CrossRef]

R. Giller, R. J. Manning, and D. Cotter, "Gain and phase recovery of optically excited semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 18, 1061-1063 (2006).
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Phys. Rev. Lett.

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[CrossRef]

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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, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
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Figures (9)

Fig. 1.
Fig. 1.

Experimental pump-probe arrangement. TMLL: tunable mode-locked laser; EDFA: erbium doped fibre amplifier; BPF: band pass filter; VOA: variable optical attenuator; PC: polarization controller; R: reflected signal from the TOAD; T: transmitted signal.

Fig. 2.
Fig. 2.

(a) Typical normalized R (heavy line) and T (light line) co-efficients from pump-probe measurements; (b) typical normalized gain measured from amplitude modulation monitor.

Fig. 3.
Fig. 3.

(a) Normalised gain dynamics calculation (open squares) and fit (line); (b) phase dynamics calculation (open squares) and fit (line).

Fig. 4.
Fig. 4.

Band filling recovery time constant as a function of injection current for each SOA.

Fig. 5.
Fig. 5.

(a) Phase shift obtained from 1mm long, 0.1μm deep SOA as a function of pump pulse energy for different values of bias current (indicated in legend); (b) phase shift obtained from 1.8mm and 1mm long SOAs, both of cross-sectional area 0.2μm2 as a function of bias current.

Fig. 6.
Fig. 6.

Logarithmic plot of recovery time constant versus SOA current data (points) and numerical model fit (solid line) for each SOA. Length and depth parameters of the SOA are indicated in the upper and lower portions of each legend respectively.

Fig. 7.
Fig. 7.

Variation of the Γ/A ratio with active region width for a device of fixed depth.

Fig. 8.
Fig. 8.

Modelled recovery time constant as a function of active region width (points) and modelled area to confinement factor ratio (solid line) overlaid for comparison.

Fig. 9.
Fig. 9.

Γ/A ratio as a function of active region width for SOAs of differing depths.

Tables (1)

Tables Icon

Table 1. Set of parameters used in model calculations

Equations (6)

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G ( t ) = R ( t ) + T ( t ) d 2 k 2
ϕ ( t ) = cos 1 [ R ( t ) T ( t ) + ( d 2 k 2 ) ( d 2 k 2 G ( t ) ) 4 d 2 k 2 G ( t ) ]
G ( t ) = exp ( ae t τ bf + b ( 1 e t τ delay ) e t τ ch )
ϕ ( t ) = bf e t τ bf + ch ( 1 e t τ delay ) e t τ ch
1 τ bf = 1 τ Auger + 1 τ ASE
1 τ ASE = P ASE E SAT = Γ A gP ASE hv

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