Abstract

We model the non-linear gain characteristics of a Fabry-Perot semiconductor optical amplifier using a modified photon density rate equation. Good agreement is found with experimental results, with the simulation accurately reproducing all the major characteristics of the amplifier. To our knowledge, this is the first calculation using only the rate equations that accurately predicts the gain and nonlinear behavior of FPSOAs.

© 2003 Optical Society of America

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References

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  1. D. Wiedenmann, B. Moeller, R. Michalzik, and K.J. Ebeling, “Performance characteristics of vertical-cavity semiconductor laser amplifiers,” Electron. Lett. 32, 342–343 (1996)
    [Crossref]
  2. C. Tombing, T. Saitoh, and T. Mukai, “Performance prediction for vertical-cavity semiconductor laser amplifiers,” IEEE J. Quantum Electron. 30, 2491–2499 (1994)
    [Crossref]
  3. J. Piprek, S. Bjorlin, and E. Bowers, “Design and analysis of vertical-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. 37, 127–134 (2001)
    [Crossref]
  4. Daniel T. Cassidy, “Comparison of rate equation and Fabry-Perot approaches to modeling a diode laser” Appl. Opt. 22, 3321–3326 (1983)
    [Crossref] [PubMed]
  5. M.J. Adams, J.V. Collins, and I.D. Henning, “Analysis of semiconductor laser optical amplifiers”, IEE Proc. J Optoelectron. 132, 58–63, (1985).
    [Crossref]
  6. G. P. Agrawal and N. K. Dutta, Semiconductor lasers, (Kluwer Academic, 1993)
  7. M.J. Adams, “Time Dependent Analysis of Active and Passive Optical Bistability in Semiconductors”, IEE Proceedings J Optoelectron. 132, 343–348, (1985).
    [Crossref]
  8. P. Wen, M. Sánchez, M. Gross, O. Kibar, and S. Esener, “New photon density rate equation for Fabry-Perot semiconductor optical amplifiers (FP SOAs),” in Physics and Simulation of Optoelectronic Devices X, Proc. SPIE 4646, 243–250, (2002).
    [Crossref]
  9. P Royo, R Koda, and L.A. Coldren, “Vertical cavity semiconductor optical amplifiers: comparison of Fabry-Perot and rate equation approaches.”, IEEE J. Quantum Electron. 38, 279–284, (2002).
    [Crossref]
  10. M. Sánchez, P. Wen, M. Gross, and S. Esener, “Nonlinear gain in vertical-cavity semiconductor optical amplifiers.” IEEE Phot. Tech. Lett. 15, 507–509, (2003).
    [Crossref]
  11. P. Wen, M. Sánchez, M. Gross, and S. Esener, “Vertical-cavity optical AND gate”, Opt. Commun. 219, 383–387, (2003)
    [Crossref]
  12. T.E. Sale, Vertical Cavity Surface Emitting Lasers, (Research Studies Press, Somerset, England, 1995)
  13. L Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits, (Wiley-Interscience, New York, NY, 1995)
  14. J.H. Shin, J.K Hwang, H Ha, and Y.H. Lee, “Anamalous above-threshold spontaneous emission in gainguided vertical-cavity surface-emitting lasers”, Appl. Phys. Lett. 68, 2180–2182, (1996)
    [Crossref]
  15. KH Ha and YH Lee, “Determiniation of Cavity Loss in Proton Implanted Vertical-Cavity Surface Emitting Lasers,” Jpn. J. Appl. Phys. 37, L372–L374, (1998)
    [Crossref]

2003 (2)

M. Sánchez, P. Wen, M. Gross, and S. Esener, “Nonlinear gain in vertical-cavity semiconductor optical amplifiers.” IEEE Phot. Tech. Lett. 15, 507–509, (2003).
[Crossref]

P. Wen, M. Sánchez, M. Gross, and S. Esener, “Vertical-cavity optical AND gate”, Opt. Commun. 219, 383–387, (2003)
[Crossref]

2002 (2)

P. Wen, M. Sánchez, M. Gross, O. Kibar, and S. Esener, “New photon density rate equation for Fabry-Perot semiconductor optical amplifiers (FP SOAs),” in Physics and Simulation of Optoelectronic Devices X, Proc. SPIE 4646, 243–250, (2002).
[Crossref]

P Royo, R Koda, and L.A. Coldren, “Vertical cavity semiconductor optical amplifiers: comparison of Fabry-Perot and rate equation approaches.”, IEEE J. Quantum Electron. 38, 279–284, (2002).
[Crossref]

2001 (1)

J. Piprek, S. Bjorlin, and E. Bowers, “Design and analysis of vertical-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. 37, 127–134 (2001)
[Crossref]

1998 (1)

KH Ha and YH Lee, “Determiniation of Cavity Loss in Proton Implanted Vertical-Cavity Surface Emitting Lasers,” Jpn. J. Appl. Phys. 37, L372–L374, (1998)
[Crossref]

1996 (2)

J.H. Shin, J.K Hwang, H Ha, and Y.H. Lee, “Anamalous above-threshold spontaneous emission in gainguided vertical-cavity surface-emitting lasers”, Appl. Phys. Lett. 68, 2180–2182, (1996)
[Crossref]

D. Wiedenmann, B. Moeller, R. Michalzik, and K.J. Ebeling, “Performance characteristics of vertical-cavity semiconductor laser amplifiers,” Electron. Lett. 32, 342–343 (1996)
[Crossref]

1994 (1)

C. Tombing, T. Saitoh, and T. Mukai, “Performance prediction for vertical-cavity semiconductor laser amplifiers,” IEEE J. Quantum Electron. 30, 2491–2499 (1994)
[Crossref]

1985 (2)

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

M.J. Adams, “Time Dependent Analysis of Active and Passive Optical Bistability in Semiconductors”, IEE Proceedings J Optoelectron. 132, 343–348, (1985).
[Crossref]

1983 (1)

Adams, M.J.

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

M.J. Adams, “Time Dependent Analysis of Active and Passive Optical Bistability in Semiconductors”, IEE Proceedings J Optoelectron. 132, 343–348, (1985).
[Crossref]

Agrawal, G. P.

G. P. Agrawal and N. K. Dutta, Semiconductor lasers, (Kluwer Academic, 1993)

Bjorlin, S.

J. Piprek, S. Bjorlin, and E. Bowers, “Design and analysis of vertical-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. 37, 127–134 (2001)
[Crossref]

Bowers, E.

J. Piprek, S. Bjorlin, and E. Bowers, “Design and analysis of vertical-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. 37, 127–134 (2001)
[Crossref]

Cassidy, Daniel T.

Coldren, L

L Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits, (Wiley-Interscience, New York, NY, 1995)

Coldren, L.A.

P Royo, R Koda, and L.A. Coldren, “Vertical cavity semiconductor optical amplifiers: comparison of Fabry-Perot and rate equation approaches.”, IEEE J. Quantum Electron. 38, 279–284, (2002).
[Crossref]

Collins, J.V.

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

Corzine, S.

L Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits, (Wiley-Interscience, New York, NY, 1995)

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, Semiconductor lasers, (Kluwer Academic, 1993)

Ebeling, K.J.

D. Wiedenmann, B. Moeller, R. Michalzik, and K.J. Ebeling, “Performance characteristics of vertical-cavity semiconductor laser amplifiers,” Electron. Lett. 32, 342–343 (1996)
[Crossref]

Esener, S.

P. Wen, M. Sánchez, M. Gross, and S. Esener, “Vertical-cavity optical AND gate”, Opt. Commun. 219, 383–387, (2003)
[Crossref]

M. Sánchez, P. Wen, M. Gross, and S. Esener, “Nonlinear gain in vertical-cavity semiconductor optical amplifiers.” IEEE Phot. Tech. Lett. 15, 507–509, (2003).
[Crossref]

P. Wen, M. Sánchez, M. Gross, O. Kibar, and S. Esener, “New photon density rate equation for Fabry-Perot semiconductor optical amplifiers (FP SOAs),” in Physics and Simulation of Optoelectronic Devices X, Proc. SPIE 4646, 243–250, (2002).
[Crossref]

Gross, M.

M. Sánchez, P. Wen, M. Gross, and S. Esener, “Nonlinear gain in vertical-cavity semiconductor optical amplifiers.” IEEE Phot. Tech. Lett. 15, 507–509, (2003).
[Crossref]

P. Wen, M. Sánchez, M. Gross, and S. Esener, “Vertical-cavity optical AND gate”, Opt. Commun. 219, 383–387, (2003)
[Crossref]

P. Wen, M. Sánchez, M. Gross, O. Kibar, and S. Esener, “New photon density rate equation for Fabry-Perot semiconductor optical amplifiers (FP SOAs),” in Physics and Simulation of Optoelectronic Devices X, Proc. SPIE 4646, 243–250, (2002).
[Crossref]

Ha, H

J.H. Shin, J.K Hwang, H Ha, and Y.H. Lee, “Anamalous above-threshold spontaneous emission in gainguided vertical-cavity surface-emitting lasers”, Appl. Phys. Lett. 68, 2180–2182, (1996)
[Crossref]

Ha, KH

KH Ha and YH Lee, “Determiniation of Cavity Loss in Proton Implanted Vertical-Cavity Surface Emitting Lasers,” Jpn. J. Appl. Phys. 37, L372–L374, (1998)
[Crossref]

Henning, I.D.

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

Hwang, J.K

J.H. Shin, J.K Hwang, H Ha, and Y.H. Lee, “Anamalous above-threshold spontaneous emission in gainguided vertical-cavity surface-emitting lasers”, Appl. Phys. Lett. 68, 2180–2182, (1996)
[Crossref]

Kibar, O.

P. Wen, M. Sánchez, M. Gross, O. Kibar, and S. Esener, “New photon density rate equation for Fabry-Perot semiconductor optical amplifiers (FP SOAs),” in Physics and Simulation of Optoelectronic Devices X, Proc. SPIE 4646, 243–250, (2002).
[Crossref]

Koda, R

P Royo, R Koda, and L.A. Coldren, “Vertical cavity semiconductor optical amplifiers: comparison of Fabry-Perot and rate equation approaches.”, IEEE J. Quantum Electron. 38, 279–284, (2002).
[Crossref]

Lee, Y.H.

J.H. Shin, J.K Hwang, H Ha, and Y.H. Lee, “Anamalous above-threshold spontaneous emission in gainguided vertical-cavity surface-emitting lasers”, Appl. Phys. Lett. 68, 2180–2182, (1996)
[Crossref]

Lee, YH

KH Ha and YH Lee, “Determiniation of Cavity Loss in Proton Implanted Vertical-Cavity Surface Emitting Lasers,” Jpn. J. Appl. Phys. 37, L372–L374, (1998)
[Crossref]

Michalzik, R.

D. Wiedenmann, B. Moeller, R. Michalzik, and K.J. Ebeling, “Performance characteristics of vertical-cavity semiconductor laser amplifiers,” Electron. Lett. 32, 342–343 (1996)
[Crossref]

Moeller, B.

D. Wiedenmann, B. Moeller, R. Michalzik, and K.J. Ebeling, “Performance characteristics of vertical-cavity semiconductor laser amplifiers,” Electron. Lett. 32, 342–343 (1996)
[Crossref]

Mukai, T.

C. Tombing, T. Saitoh, and T. Mukai, “Performance prediction for vertical-cavity semiconductor laser amplifiers,” IEEE J. Quantum Electron. 30, 2491–2499 (1994)
[Crossref]

Piprek, J.

J. Piprek, S. Bjorlin, and E. Bowers, “Design and analysis of vertical-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. 37, 127–134 (2001)
[Crossref]

Royo, P

P Royo, R Koda, and L.A. Coldren, “Vertical cavity semiconductor optical amplifiers: comparison of Fabry-Perot and rate equation approaches.”, IEEE J. Quantum Electron. 38, 279–284, (2002).
[Crossref]

Saitoh, T.

C. Tombing, T. Saitoh, and T. Mukai, “Performance prediction for vertical-cavity semiconductor laser amplifiers,” IEEE J. Quantum Electron. 30, 2491–2499 (1994)
[Crossref]

Sale, T.E.

T.E. Sale, Vertical Cavity Surface Emitting Lasers, (Research Studies Press, Somerset, England, 1995)

Sánchez, M.

P. Wen, M. Sánchez, M. Gross, and S. Esener, “Vertical-cavity optical AND gate”, Opt. Commun. 219, 383–387, (2003)
[Crossref]

M. Sánchez, P. Wen, M. Gross, and S. Esener, “Nonlinear gain in vertical-cavity semiconductor optical amplifiers.” IEEE Phot. Tech. Lett. 15, 507–509, (2003).
[Crossref]

P. Wen, M. Sánchez, M. Gross, O. Kibar, and S. Esener, “New photon density rate equation for Fabry-Perot semiconductor optical amplifiers (FP SOAs),” in Physics and Simulation of Optoelectronic Devices X, Proc. SPIE 4646, 243–250, (2002).
[Crossref]

Shin, J.H.

J.H. Shin, J.K Hwang, H Ha, and Y.H. Lee, “Anamalous above-threshold spontaneous emission in gainguided vertical-cavity surface-emitting lasers”, Appl. Phys. Lett. 68, 2180–2182, (1996)
[Crossref]

Tombing, C.

C. Tombing, T. Saitoh, and T. Mukai, “Performance prediction for vertical-cavity semiconductor laser amplifiers,” IEEE J. Quantum Electron. 30, 2491–2499 (1994)
[Crossref]

Wen, P.

P. Wen, M. Sánchez, M. Gross, and S. Esener, “Vertical-cavity optical AND gate”, Opt. Commun. 219, 383–387, (2003)
[Crossref]

M. Sánchez, P. Wen, M. Gross, and S. Esener, “Nonlinear gain in vertical-cavity semiconductor optical amplifiers.” IEEE Phot. Tech. Lett. 15, 507–509, (2003).
[Crossref]

P. Wen, M. Sánchez, M. Gross, O. Kibar, and S. Esener, “New photon density rate equation for Fabry-Perot semiconductor optical amplifiers (FP SOAs),” in Physics and Simulation of Optoelectronic Devices X, Proc. SPIE 4646, 243–250, (2002).
[Crossref]

Wiedenmann, D.

D. Wiedenmann, B. Moeller, R. Michalzik, and K.J. Ebeling, “Performance characteristics of vertical-cavity semiconductor laser amplifiers,” Electron. Lett. 32, 342–343 (1996)
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J.H. Shin, J.K Hwang, H Ha, and Y.H. Lee, “Anamalous above-threshold spontaneous emission in gainguided vertical-cavity surface-emitting lasers”, Appl. Phys. Lett. 68, 2180–2182, (1996)
[Crossref]

Electron. Lett. (1)

D. Wiedenmann, B. Moeller, R. Michalzik, and K.J. Ebeling, “Performance characteristics of vertical-cavity semiconductor laser amplifiers,” Electron. Lett. 32, 342–343 (1996)
[Crossref]

IEE Proc. J Optoelectron. (1)

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

IEE Proceedings J Optoelectron. (1)

M.J. Adams, “Time Dependent Analysis of Active and Passive Optical Bistability in Semiconductors”, IEE Proceedings J Optoelectron. 132, 343–348, (1985).
[Crossref]

IEEE J. Quantum Electron. (3)

C. Tombing, T. Saitoh, and T. Mukai, “Performance prediction for vertical-cavity semiconductor laser amplifiers,” IEEE J. Quantum Electron. 30, 2491–2499 (1994)
[Crossref]

J. Piprek, S. Bjorlin, and E. Bowers, “Design and analysis of vertical-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. 37, 127–134 (2001)
[Crossref]

P Royo, R Koda, and L.A. Coldren, “Vertical cavity semiconductor optical amplifiers: comparison of Fabry-Perot and rate equation approaches.”, IEEE J. Quantum Electron. 38, 279–284, (2002).
[Crossref]

IEEE Phot. Tech. Lett. (1)

M. Sánchez, P. Wen, M. Gross, and S. Esener, “Nonlinear gain in vertical-cavity semiconductor optical amplifiers.” IEEE Phot. Tech. Lett. 15, 507–509, (2003).
[Crossref]

Jpn. J. Appl. Phys. (1)

KH Ha and YH Lee, “Determiniation of Cavity Loss in Proton Implanted Vertical-Cavity Surface Emitting Lasers,” Jpn. J. Appl. Phys. 37, L372–L374, (1998)
[Crossref]

Opt. Commun. (1)

P. Wen, M. Sánchez, M. Gross, and S. Esener, “Vertical-cavity optical AND gate”, Opt. Commun. 219, 383–387, (2003)
[Crossref]

Proc. SPIE (1)

P. Wen, M. Sánchez, M. Gross, O. Kibar, and S. Esener, “New photon density rate equation for Fabry-Perot semiconductor optical amplifiers (FP SOAs),” in Physics and Simulation of Optoelectronic Devices X, Proc. SPIE 4646, 243–250, (2002).
[Crossref]

Other (3)

T.E. Sale, Vertical Cavity Surface Emitting Lasers, (Research Studies Press, Somerset, England, 1995)

L Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits, (Wiley-Interscience, New York, NY, 1995)

G. P. Agrawal and N. K. Dutta, Semiconductor lasers, (Kluwer Academic, 1993)

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Figures (5)

Fig. 1.
Fig. 1.

General schematic of VCSOA, showing the transverse (left) and longitudinal (right) optical intensity profile.

Fig. 2.
Fig. 2.

L-I curve. Dots are measured data, solid line is calculation

Fig. 3.
Fig. 3.

Gain vs. detuning for several input powers. Calculated result on the left, measured data on the right.

Fig. 4.
Fig. 4.

Output vs. input power for several detunings at 5.8mA bias. Symbols are measured data, solid lines are calculated. Detunings are (mrad): a) 0.5, b) 0.05, c) -0.4, d) -0.78

Fig. 5.
Fig. 5.

Output vs. input power for several detunings at 5.6mA bias. Symbols are measured data, solid lines are calculated. Detunings are (mrad): a) 0.6, b) 0.1, c) -0.35, d) -0.65

Tables (1)

Tables Icon

Table 1: Rate equation parameters for VCSOA

Equations (8)

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d N e dt = η e I q γ e N e G N p , d N p dt = ( G γ p ) N P + R sp + C p N inj
γ e = 1 τ e = A + Bn + C n 2
G = Γ v g g , g = a ( n n 0 ) , v g = c μ g
γ p = 1 τ p = v g ( α m + α i ) , α m = ( 1 2 L ) ln [ 1 R 1 R 2 ]
R sp = β sp Bn N e = β sp B n 2 V , V = Γ l V
C p N inj = η in ( 1 + G s ) ( 1 R g Cos 2 ϕ ) + ( R 2 G 2 kL ) ( 1 R g ) Sin ( 2 ϕ ) ( 1 R g ) 2 + 4 R g Sin 2 ϕ × ( 1 R 1 ) τ RT N inj ,
R g = R 1 R 2 G s
G s = e ( Γ Γ l gL α i L ) , ϕ = ϕ 0 ( β c 2 ) Γ Γ l La ( n n 1 )

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