Abstract

The consequences of tailoring the longitudinal carrier density along the active layer of a multi-contact bulk semiconductor optical amplifier (SOA) are investigated using a rate equation model. It is shown that both the noise figure and output power saturation can be optimized for a fixed total injected bias current. The simulation results are validated by comparison with experiment using a multi-contact SOA. The inter-contact resistance is increased using a focused ion beam in order to optimize the carrier density control. A chip noise figure of 3.8 dB and a saturation output power of 9 dBm are measured experimentally for a total bias current of 150 mA.

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2012

2011

2010

K. Carney, R. Lennox, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Noise controlled semiconductor optical amplifier based on lateral cavity laser,” Electron. Lett. 46(18), 1288–1289 (2010).
[CrossRef]

2007

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Y. Liu, E. Tangdiongga, Z. Li, H. de Waardt, A. M. J. Koonen, G. D. Khoe, X. Shu, I. Bennion, and H. J. S. Dorren, “Error free 320Gb/s all-optical wavelength conversion using a single semiconductor optical amplifier,” J. Lightwave Technol. 25(1), 103–108 (2007).
[CrossRef]

2006

2005

F. Crottini, P. Salleras, M. A. Moreno, B. Dupertuis, B. Deveaud, and R. Brenot, “Noise figure improvement in semiconductor optical amplifiers by holding beam at transparency scheme,” IEEE Photon. Technol. Lett. 17(5), 977–979 (2005).
[CrossRef]

K. Morito, S. Tanaka, S. Tomabechi, and A. Kuramata, “A broadband MQW semiconductor optical amplifier with high saturation output power and low noise figure,” IEEE Photon. Technol. Lett. 17(5), 974–976 (2005).
[CrossRef]

2003

J. Mørk, M. L. Nielsen, and T. W. Berg, “The dynamics of semiconductor optical amplifiers: modeling and applications,” Opt. Photonics News 14(7), 42–48 (2003).
[CrossRef]

Y. Yamamoto and K. Inoue, “Noise in amplifiers,” J. Lightwave Technol. 21(11), 2895–2915 (2003).
[CrossRef]

2002

E. Staffan Bjorlin and J. E. Bowers, “Noise figure of vertial-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. 38(1), 61–66 (2002).
[CrossRef]

2001

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37(3), 439–447 (2001).
[CrossRef]

2000

G. Giuliani and D. D’Alessandro, “Noise analysis of conventional and gain-clamped semiconductor optical amplifiers,” J. Lightwave Technol. 18(9), 1256–1263 (2000).
[CrossRef]

D. M. Baney, P. Gallion, and R. S. Tucker, “Theory and measurement techniques for the noise figure of optical amplifiers,” Opt. Fiber Technol. 6(2), 122–154 (2000).
[CrossRef]

1999

E. Desurvire, “On the physical origin of the 3dB noise figure limit in laser and parametric optical amplifiers,” Opt. Fiber Technol. 5(1), 40–61 (1999).
[CrossRef]

1998

M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
[CrossRef]

H. A. Haus, “The noise figure of optical smplifiers,” IEEE Photon. Technol. Lett. 10(11), 1602–1604 (1998).
[CrossRef]

1996

M. Yoshino and K. Inoue, “Improvement of saturation output power in a semiconductor laser amplifier through pumping light injection,” IEEE Photon. Technol. Lett. 8(1), 58–59 (1996).
[CrossRef]

1992

T. Durhuus, B. Mikkelsen, and K. E. Stubkjaer, “Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and intermodulation distortion,” J. Lightwave Technol. 10(8), 1056–1069 (1992).
[CrossRef]

1991

G. Bendelli, K. Komori, S. Arai, and Y. Suematsu, “A new structure for high-power TW-SLA,” IEEE Photon. Technol. Lett. 3(1), 42–44 (1991).
[CrossRef]

1982

T. Mukai and Y. Yamamoto, “Noise in an AlGaAs semiconductor laser amplifier,” IEEE J. Quantum Electron. 18(4), 564–575 (1982).
[CrossRef]

Arai, S.

G. Bendelli, K. Komori, S. Arai, and Y. Suematsu, “A new structure for high-power TW-SLA,” IEEE Photon. Technol. Lett. 3(1), 42–44 (1991).
[CrossRef]

Back, J.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Baney, D. M.

D. M. Baney, P. Gallion, and R. S. Tucker, “Theory and measurement techniques for the noise figure of optical amplifiers,” Opt. Fiber Technol. 6(2), 122–154 (2000).
[CrossRef]

Bellemain, A.

Bendelli, G.

G. Bendelli, K. Komori, S. Arai, and Y. Suematsu, “A new structure for high-power TW-SLA,” IEEE Photon. Technol. Lett. 3(1), 42–44 (1991).
[CrossRef]

Bennion, I.

Berg, T. W.

J. Mørk, M. L. Nielsen, and T. W. Berg, “The dynamics of semiconductor optical amplifiers: modeling and applications,” Opt. Photonics News 14(7), 42–48 (2003).
[CrossRef]

Bonk, R.

Bowers, J. E.

E. Staffan Bjorlin and J. E. Bowers, “Noise figure of vertial-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. 38(1), 61–66 (2002).
[CrossRef]

Bradley, A. L.

R. Lennox, K. Carney, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Impact of bias current distribution on the noise figure and power saturation of a multicontact semiconductor optical amplifier,” Opt. Lett. 36(13), 2521–2523 (2011).
[CrossRef] [PubMed]

K. Carney, R. Lennox, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Noise controlled semiconductor optical amplifier based on lateral cavity laser,” Electron. Lett. 46(18), 1288–1289 (2010).
[CrossRef]

Brenot, R.

Briant, T.

Carney, K.

R. Lennox, K. Carney, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Impact of bias current distribution on the noise figure and power saturation of a multicontact semiconductor optical amplifier,” Opt. Lett. 36(13), 2521–2523 (2011).
[CrossRef] [PubMed]

K. Carney, R. Lennox, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Noise controlled semiconductor optical amplifier based on lateral cavity laser,” Electron. Lett. 46(18), 1288–1289 (2010).
[CrossRef]

Conforti, E.

Connelly, M. J.

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37(3), 439–447 (2001).
[CrossRef]

Crottini, F.

F. Crottini, P. Salleras, M. A. Moreno, B. Dupertuis, B. Deveaud, and R. Brenot, “Noise figure improvement in semiconductor optical amplifiers by holding beam at transparency scheme,” IEEE Photon. Technol. Lett. 17(5), 977–979 (2005).
[CrossRef]

D’Alessandro, D.

de Waardt, H.

Dentai, A. G.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Desurvire, E.

E. Desurvire, “On the physical origin of the 3dB noise figure limit in laser and parametric optical amplifiers,” Opt. Fiber Technol. 5(1), 40–61 (1999).
[CrossRef]

Deveaud, B.

F. Crottini, P. Salleras, M. A. Moreno, B. Dupertuis, B. Deveaud, and R. Brenot, “Noise figure improvement in semiconductor optical amplifiers by holding beam at transparency scheme,” IEEE Photon. Technol. Lett. 17(5), 977–979 (2005).
[CrossRef]

Dominic, V. G.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Dorren, H. J. S.

Duan, G. H.

Dupertuis, B.

F. Crottini, P. Salleras, M. A. Moreno, B. Dupertuis, B. Deveaud, and R. Brenot, “Noise figure improvement in semiconductor optical amplifiers by holding beam at transparency scheme,” IEEE Photon. Technol. Lett. 17(5), 977–979 (2005).
[CrossRef]

Durhuus, T.

T. Durhuus, B. Mikkelsen, and K. E. Stubkjaer, “Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and intermodulation distortion,” J. Lightwave Technol. 10(8), 1056–1069 (1992).
[CrossRef]

Eisenstein, G.

M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
[CrossRef]

Evans, P. W.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Fragnito, H.

Frateschi, N.

Freude, W.

Friis, H. T.

H. T. Friis, “Noise figures of radio receivers,” Proc. IRE 32, 419–422 (1944).
[CrossRef]

Gallep, C.

Gallion, P.

D. M. Baney, P. Gallion, and R. S. Tucker, “Theory and measurement techniques for the noise figure of optical amplifiers,” Opt. Fiber Technol. 6(2), 122–154 (2000).
[CrossRef]

Giuliani, G.

Grangier, P.

Grubb, S. G.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Haus, H. A.

H. A. Haus, “The noise figure of optical smplifiers,” IEEE Photon. Technol. Lett. 10(11), 1602–1604 (1998).
[CrossRef]

Hillerkuss, D.

Huber, G.

Hurtt, S. K.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Inoue, K.

Y. Yamamoto and K. Inoue, “Noise in amplifiers,” J. Lightwave Technol. 21(11), 2895–2915 (2003).
[CrossRef]

M. Yoshino and K. Inoue, “Improvement of saturation output power in a semiconductor laser amplifier through pumping light injection,” IEEE Photon. Technol. Lett. 8(1), 58–59 (1996).
[CrossRef]

Joyner, C. H.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Kato, M.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Kauffman, M.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Kawakami, Y.

Khoe, G. D.

Kim, H. J.

Kish, F. A.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Koenig, S.

Komori, K.

G. Bendelli, K. Komori, S. Arai, and Y. Suematsu, “A new structure for high-power TW-SLA,” IEEE Photon. Technol. Lett. 3(1), 42–44 (1991).
[CrossRef]

Koonen, A. M. J.

Koos, C.

Kuramata, A.

K. Morito, S. Tanaka, S. Tomabechi, and A. Kuramata, “A broadband MQW semiconductor optical amplifier with high saturation output power and low noise figure,” IEEE Photon. Technol. Lett. 17(5), 974–976 (2005).
[CrossRef]

Lambert, D. J. H.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Landais, P.

R. Lennox, K. Carney, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Impact of bias current distribution on the noise figure and power saturation of a multicontact semiconductor optical amplifier,” Opt. Lett. 36(13), 2521–2523 (2011).
[CrossRef] [PubMed]

K. Carney, R. Lennox, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Noise controlled semiconductor optical amplifier based on lateral cavity laser,” Electron. Lett. 46(18), 1288–1289 (2010).
[CrossRef]

Lelarge, F.

Lennox, R.

R. Lennox, K. Carney, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Impact of bias current distribution on the noise figure and power saturation of a multicontact semiconductor optical amplifier,” Opt. Lett. 36(13), 2521–2523 (2011).
[CrossRef] [PubMed]

K. Carney, R. Lennox, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Noise controlled semiconductor optical amplifier based on lateral cavity laser,” Electron. Lett. 46(18), 1288–1289 (2010).
[CrossRef]

Leuthold, J.

Li, Z.

Liu, Y.

Maldonado-Basilio, R.

R. Lennox, K. Carney, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Impact of bias current distribution on the noise figure and power saturation of a multicontact semiconductor optical amplifier,” Opt. Lett. 36(13), 2521–2523 (2011).
[CrossRef] [PubMed]

K. Carney, R. Lennox, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Noise controlled semiconductor optical amplifier based on lateral cavity laser,” Electron. Lett. 46(18), 1288–1289 (2010).
[CrossRef]

Mathur, A.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Mehuys, D. G.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Melle, S.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Mikkelsen, B.

T. Durhuus, B. Mikkelsen, and K. E. Stubkjaer, “Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and intermodulation distortion,” J. Lightwave Technol. 10(8), 1056–1069 (1992).
[CrossRef]

Missey, M.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Mitchell, M. L.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Moreno, M. A.

F. Crottini, P. Salleras, M. A. Moreno, B. Dupertuis, B. Deveaud, and R. Brenot, “Noise figure improvement in semiconductor optical amplifiers by holding beam at transparency scheme,” IEEE Photon. Technol. Lett. 17(5), 977–979 (2005).
[CrossRef]

Morito, K.

K. Morito, S. Tanaka, S. Tomabechi, and A. Kuramata, “A broadband MQW semiconductor optical amplifier with high saturation output power and low noise figure,” IEEE Photon. Technol. Lett. 17(5), 974–976 (2005).
[CrossRef]

Mørk, J.

J. Mørk, M. L. Nielsen, and T. W. Berg, “The dynamics of semiconductor optical amplifiers: modeling and applications,” Opt. Photonics News 14(7), 42–48 (2003).
[CrossRef]

Mukai, T.

T. Mukai and Y. Yamamoto, “Noise in an AlGaAs semiconductor laser amplifier,” IEEE J. Quantum Electron. 18(4), 564–575 (1982).
[CrossRef]

Murthy, S.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Nagarajan, R.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Nielsen, M. L.

J. Mørk, M. L. Nielsen, and T. W. Berg, “The dynamics of semiconductor optical amplifiers: modeling and applications,” Opt. Photonics News 14(7), 42–48 (2003).
[CrossRef]

Nilsson, A. C.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Park, J.

Perkins, D.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Philippe, S.

R. Lennox, K. Carney, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Impact of bias current distribution on the noise figure and power saturation of a multicontact semiconductor optical amplifier,” Opt. Lett. 36(13), 2521–2523 (2011).
[CrossRef] [PubMed]

K. Carney, R. Lennox, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Noise controlled semiconductor optical amplifier based on lateral cavity laser,” Electron. Lett. 46(18), 1288–1289 (2010).
[CrossRef]

Pleumeekers, J. L.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Reffle, M.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Rieznik, A.

Salleras, P.

F. Crottini, P. Salleras, M. A. Moreno, B. Dupertuis, B. Deveaud, and R. Brenot, “Noise figure improvement in semiconductor optical amplifiers by holding beam at transparency scheme,” IEEE Photon. Technol. Lett. 17(5), 977–979 (2005).
[CrossRef]

Salvatore, R. A.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Schmogrow, R.

Schneider, R. P.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Shtaif, M.

M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
[CrossRef]

Shu, X.

Song, J. I.

Staffan Bjorlin, E.

E. Staffan Bjorlin and J. E. Bowers, “Noise figure of vertial-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. 38(1), 61–66 (2002).
[CrossRef]

Stubkjaer, K. E.

T. Durhuus, B. Mikkelsen, and K. E. Stubkjaer, “Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and intermodulation distortion,” J. Lightwave Technol. 10(8), 1056–1069 (1992).
[CrossRef]

Suematsu, Y.

G. Bendelli, K. Komori, S. Arai, and Y. Suematsu, “A new structure for high-power TW-SLA,” IEEE Photon. Technol. Lett. 3(1), 42–44 (1991).
[CrossRef]

Sygletos, S.

Tanaka, S.

K. Morito, S. Tanaka, S. Tomabechi, and A. Kuramata, “A broadband MQW semiconductor optical amplifier with high saturation output power and low noise figure,” IEEE Photon. Technol. Lett. 17(5), 974–976 (2005).
[CrossRef]

Tangdiongga, E.

Thedrez, B.

Tomabechi, S.

K. Morito, S. Tanaka, S. Tomabechi, and A. Kuramata, “A broadband MQW semiconductor optical amplifier with high saturation output power and low noise figure,” IEEE Photon. Technol. Lett. 17(5), 974–976 (2005).
[CrossRef]

Tromborg, B.

M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
[CrossRef]

Tualle-Brouri, R.

Tucker, R. S.

D. M. Baney, P. Gallion, and R. S. Tucker, “Theory and measurement techniques for the noise figure of optical amplifiers,” Opt. Fiber Technol. 6(2), 122–154 (2000).
[CrossRef]

Vallaitis, T.

Van Leeuwen, M. F.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Webjorn, J.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Welch, D. F.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Yamamoto, Y.

Y. Yamamoto and K. Inoue, “Noise in amplifiers,” J. Lightwave Technol. 21(11), 2895–2915 (2003).
[CrossRef]

T. Mukai and Y. Yamamoto, “Noise in an AlGaAs semiconductor laser amplifier,” IEEE J. Quantum Electron. 18(4), 564–575 (1982).
[CrossRef]

Yoshino, M.

M. Yoshino and K. Inoue, “Improvement of saturation output power in a semiconductor laser amplifier through pumping light injection,” IEEE Photon. Technol. Lett. 8(1), 58–59 (1996).
[CrossRef]

Ziari, M.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

Electron. Lett.

K. Carney, R. Lennox, R. Maldonado-Basilio, S. Philippe, A. L. Bradley, and P. Landais, “Noise controlled semiconductor optical amplifier based on lateral cavity laser,” Electron. Lett. 46(18), 1288–1289 (2010).
[CrossRef]

IEEE J. Quantum Electron.

E. Staffan Bjorlin and J. E. Bowers, “Noise figure of vertial-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. 38(1), 61–66 (2002).
[CrossRef]

T. Mukai and Y. Yamamoto, “Noise in an AlGaAs semiconductor laser amplifier,” IEEE J. Quantum Electron. 18(4), 564–575 (1982).
[CrossRef]

M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
[CrossRef]

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37(3), 439–447 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

D. F. Welch, F. A. Kish, S. Melle, R. Nagarajan, M. Kato, C. H. Joyner, J. L. Pleumeekers, R. P. Schneider, J. Back, A. G. Dentai, V. G. Dominic, P. W. Evans, M. Kauffman, D. J. H. Lambert, S. K. Hurtt, A. Mathur, M. L. Mitchell, M. Missey, S. Murthy, A. C. Nilsson, R. A. Salvatore, M. F. Van Leeuwen, J. Webjorn, M. Ziari, S. G. Grubb, D. Perkins, M. Reffle, and D. G. Mehuys, “Large-scale InP photonic integrated circuits: enabling efficient scaling of optical transport networks,” IEEE J. Sel. Top. Quantum Electron. 13(1), 22–31 (2007).
[CrossRef]

IEEE Photon. Technol. Lett.

F. Crottini, P. Salleras, M. A. Moreno, B. Dupertuis, B. Deveaud, and R. Brenot, “Noise figure improvement in semiconductor optical amplifiers by holding beam at transparency scheme,” IEEE Photon. Technol. Lett. 17(5), 977–979 (2005).
[CrossRef]

K. Morito, S. Tanaka, S. Tomabechi, and A. Kuramata, “A broadband MQW semiconductor optical amplifier with high saturation output power and low noise figure,” IEEE Photon. Technol. Lett. 17(5), 974–976 (2005).
[CrossRef]

G. Bendelli, K. Komori, S. Arai, and Y. Suematsu, “A new structure for high-power TW-SLA,” IEEE Photon. Technol. Lett. 3(1), 42–44 (1991).
[CrossRef]

H. A. Haus, “The noise figure of optical smplifiers,” IEEE Photon. Technol. Lett. 10(11), 1602–1604 (1998).
[CrossRef]

M. Yoshino and K. Inoue, “Improvement of saturation output power in a semiconductor laser amplifier through pumping light injection,” IEEE Photon. Technol. Lett. 8(1), 58–59 (1996).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Opt. Fiber Technol.

E. Desurvire, “On the physical origin of the 3dB noise figure limit in laser and parametric optical amplifiers,” Opt. Fiber Technol. 5(1), 40–61 (1999).
[CrossRef]

D. M. Baney, P. Gallion, and R. S. Tucker, “Theory and measurement techniques for the noise figure of optical amplifiers,” Opt. Fiber Technol. 6(2), 122–154 (2000).
[CrossRef]

Opt. Lett.

Opt. Photonics News

J. Mørk, M. L. Nielsen, and T. W. Berg, “The dynamics of semiconductor optical amplifiers: modeling and applications,” Opt. Photonics News 14(7), 42–48 (2003).
[CrossRef]

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R. Brenot, F. Pommereau, O. Le Gouez, J. Landreau, F. Poingt, L. Le Gouezigou, B. Rousseau, F. Lelarge, F. Martin, and G. H. Duan, “Experimental study of the impact of optical confinement on saturation effects in SOA,” in Optical Fiber Communications Conference (OFC 2005) paper OME50.
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A. Borghesani, “Semiconductor optical amplifiers for advanced optical applications,” in International Conference on Transparent Optical Networks, ICTON 2006, 119–122.
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L. H. Spiekman, “Ubiquitous amplification: applications of the semiconductor optical amplifier,” in the Joint International Conference on Optical Internet and Next Generation Network (COIN-NGNCON 2006), 292–294.
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M. J. Connolly, Semiconductor Optical Amplifiers (Kluwer Academic Publishers, 2002), Chap. 3.

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

S. S. Saini, J. Bowser, R. Enke, V. Luciani, P. J. S. Heim, and M. Dagenais, “A semiconductor optical amplifier with high saturation power, low noise figure and low polarization dependent gain over the C-band,” in Lasers and Electro-Optics Society (LEOS 2004), 102–103.

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Figures (15)

Fig. 1
Fig. 1

Schematic of simulated SOA, indicating carrier density (green) and forward (blue) and backward (red) travelling spontaneous emission.

Fig. 2
Fig. 2

Simulated carrier density and inversion factor dependence along the length of the device, for two opposite longitudinal carrier density profiles.

Fig. 3
Fig. 3

Graphical illustration of the Friis equation for three separate bias configurations depicting the increase in NF for each successive subsection. Also indicated are the initial subsection NF and final NF values, illustrating the extent of NF increase at each bias configuration

Fig. 4
Fig. 4

NF as a function of bias current applied to the middle and end contact of a simulated 3 contact SOA. The first contact is biased at 80 mA, for 1570 nm with signal power –20 dBm.

Fig. 5
Fig. 5

Photon density for an input signal of 5 dBm as it propagates through waveguide, for three bias configurations.

Fig. 6
Fig. 6

Saturation output power, in dBm, as a function of input and middle section bias current. Output section bias is set to 90 mA. Highlighted is the region of values corresponding to 150 mA.

Fig. 7
Fig. 7

Simulated gain, noise figure and saturation power for various bias configurations. The overall bias current is 150mA.

Fig. 8
Fig. 8

Simulated evolution of ASE photon density along waveguide for the standard, low noise and high Psat cases

Fig. 9
Fig. 9

Simulated gain (dash) and NF (solid) spectra, for input signal power of −15 dBm. The overall bias current of the SOA is 150 mA.

Fig. 10
Fig. 10

Gain (dash) as a function of the output power for the simulated device with an injected signal at 1570 nm. The overall bias current of these three SOAs is 150 mA.

Fig. 11
Fig. 11

Schematic of multi-contact SOA, with three sections, driven by three separate current sources.

Fig. 12
Fig. 12

Measured gain (square) and noise figure (triangles) spectra for SOA under investigation, for an input signal of −15 dBm.

Fig. 13
Fig. 13

Gain vs output power at 1570 nm injected wavelength.

Fig. 14
Fig. 14

Gain as a function of wavelength for low noise and standard profiles, at various stages of FIB etching. Standard profile represented by closed symbols, low noise profile by open symbols.

Fig. 15
Fig. 15

Noise figure as a function of wavelength for low noise and standard profiles, both before and after the FIB etching.

Tables (1)

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Table 1 Parameters used in SOA Model

Equations (14)

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nf= SN R in SN R out ,
NF=10 log 10 ( 2 ρ ASE Ghν + 1 G ).
P sat,out = A I sat,out Γ ,
I sat,out = ln( 2 ) G 0 I sat G 0 2 ,
I m,sp + (ω, z m )= I m1,sp + (ω, z m1 + ),m1 I m,sp (ω, z m + )= I m+1,sp (ω, z m+1 ),mn I 1,sp + (ω, z 1 )= r 1 2 I 1,sp (ω, z 1 ),m=1 I n,sp (ω, z n + )= r 2 2 I n,sp + (ω, z n + ),m=n
F m + (t, z m )= F m1 + (t, z m1 + ),m1 F m (t, z m + )= F m+1 (t, z m+1 ),mn F 1 + (t, z 1 )= r 1 F 1 (t, z 1 )+ F in (t) e i( ω po ω o )t ,m=1 F n (t, z n + )= r 2 F n + (t, z n + ),m=n
S m,spon = 4π n g,o ω p0 c ×[ ( I m,sp + ( z m )+ I m,sp ( z m + )+ βR r ( N m ). ω p0 2π(Γg( ω p0 , N m ) α i ) ) G m 1 ln( G m ) ] 2βR r ( N m ). n g,o (Γg( ω p0 , N m )α i ).c ,
S m,sig = G m 1 ln( G m ) π n g,0 c.ξ ×( | 1 hω F m + (t, z m ) | 2 + | 1 h ω F m (t, z m + ) | 2 ).
d N m dt = i m qV R( N m ) v g [ g( ω sig , N m ) S m,sig +g( ω spon , N m ) S m,spon ],
n sp = γ γα ,
P ASE = n sp ( G1 )hν B 0 ,
ρ ASE = n sp ( G1 )hν.
nf= 2 n sp ( G1 ) G + 1 G .
n f total =n f 1 + n f 2 1 g 1 +...+ n f m 1 g 1 ... g m1 ,

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