Abstract

Passive electrical circuits whose voltage and current equations are exactly equivalent to the small-signal rate equations of a semiconductor laser are derived to model an electrically modulated laser (verified to be the same as that given in the literature), an optically modulated laser (i.e., a laser used as an optical amplifier), and a multimode laser. These circuits offer a fast and efficient simulation tool with little computational complexity in which the small-signal assumption (i.e., small modulation range) is neither violated nor insufficient for the simulation.

© 1998 Optical Society of America

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  1. R. S. Tucker, “Large-signal circuit model for simulation of injection-laser modulation dynamics,” IEE Proc. 128, 180–184 (1981).
  2. M. F. Lu, J. S. Deng, C. Juang, M. J. Jou, B. J. Lee, “Equivalent circuit model of quantum-well lasers,” IEEE J. Quantum Electron. 31, 1418–1421 (1995).
    [CrossRef]
  3. D. Marcuse, “Computer model of an injection laser amplifier,” IEEE J. Quantum Electron. QE-19, 63–73 (1983).
    [CrossRef]
  4. M. J. Adams, J. V. Collins, I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEEE Proc. Part J 132, 58–63 (1985).
  5. D. E. Dodds, M. J. Sieben, “Electric circuit model of a Fabry–Perot semiconductor laser,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering, C. R. Baird, M. E. El-Hawarg, eds. (Institute of Electrical and Electronics Engineers, New York, 1994), Vol. 1, pp. 371–374.
    [CrossRef]
  6. M. Morishita, T. Ohmi, J. Nishizawa, “Impedance characteristics of double-heterostructure laser diodes,” Solid-State Electron. 22, 951–962 (1979).
    [CrossRef]
  7. J. Katz, S. Margalit, C. Harder, D. Wilt, A. Yariv, “The intrinsic electrical equivalent circuit of a laser diode,” IEEE J. Quantum Electron. QE-17, 4–7 (1981).
    [CrossRef]
  8. R. S. Tucker, D. J. Pope, “Circuit modeling of the effect of diffusion on damping in a narrow-stripe semiconductor laser,” IEEE J. Quantum Electron. QE-19, 1179–1183 (1983).
    [CrossRef]
  9. R. S. Tucker, D. J. Pope, “Microwave circuit models of semiconductor injection lasers,” IEEE Trans. Microwave Theory Technol. MTT-31, 289–294 (1983).
    [CrossRef]
  10. G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand-Reinhold, New York, 1993), Chap. 6.
  11. J. A. Arnaud, “Enhancement of optical receiver sensitivities by amplification of the carrier,” IEEE J. Quantum Electron. QE-4, 893–899 (1968).
    [CrossRef]
  12. S. D. Personick, “Applications for quantum amplifiers in simple digital optical communication system,” Bell Syst. Tech. J. 52, 117–133 (1973).
  13. F. Koyama, S. Kubota, K. Iga, “GaAlAs/GaAs active filter based on vertical cavity surface emitting laser,” Electron. Lett. 27, 1093–1095 (1991).
    [CrossRef]
  14. R. Raj, J. L. Oudar, M. Bensoussan, “Vertical cavity amplifying photonic switch,” Appl. Phys. Lett. 65, 2359–2361 (1994).
    [CrossRef]
  15. E. Hecht, Optics (Addison Wesley, Reading, Mass., 1990), pp. 363–370.

1995 (1)

M. F. Lu, J. S. Deng, C. Juang, M. J. Jou, B. J. Lee, “Equivalent circuit model of quantum-well lasers,” IEEE J. Quantum Electron. 31, 1418–1421 (1995).
[CrossRef]

1994 (1)

R. Raj, J. L. Oudar, M. Bensoussan, “Vertical cavity amplifying photonic switch,” Appl. Phys. Lett. 65, 2359–2361 (1994).
[CrossRef]

1991 (1)

F. Koyama, S. Kubota, K. Iga, “GaAlAs/GaAs active filter based on vertical cavity surface emitting laser,” Electron. Lett. 27, 1093–1095 (1991).
[CrossRef]

1985 (1)

M. J. Adams, J. V. Collins, I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEEE Proc. Part J 132, 58–63 (1985).

1983 (3)

D. Marcuse, “Computer model of an injection laser amplifier,” IEEE J. Quantum Electron. QE-19, 63–73 (1983).
[CrossRef]

R. S. Tucker, D. J. Pope, “Circuit modeling of the effect of diffusion on damping in a narrow-stripe semiconductor laser,” IEEE J. Quantum Electron. QE-19, 1179–1183 (1983).
[CrossRef]

R. S. Tucker, D. J. Pope, “Microwave circuit models of semiconductor injection lasers,” IEEE Trans. Microwave Theory Technol. MTT-31, 289–294 (1983).
[CrossRef]

1981 (2)

R. S. Tucker, “Large-signal circuit model for simulation of injection-laser modulation dynamics,” IEE Proc. 128, 180–184 (1981).

J. Katz, S. Margalit, C. Harder, D. Wilt, A. Yariv, “The intrinsic electrical equivalent circuit of a laser diode,” IEEE J. Quantum Electron. QE-17, 4–7 (1981).
[CrossRef]

1979 (1)

M. Morishita, T. Ohmi, J. Nishizawa, “Impedance characteristics of double-heterostructure laser diodes,” Solid-State Electron. 22, 951–962 (1979).
[CrossRef]

1973 (1)

S. D. Personick, “Applications for quantum amplifiers in simple digital optical communication system,” Bell Syst. Tech. J. 52, 117–133 (1973).

1968 (1)

J. A. Arnaud, “Enhancement of optical receiver sensitivities by amplification of the carrier,” IEEE J. Quantum Electron. QE-4, 893–899 (1968).
[CrossRef]

Adams, M. J.

M. J. Adams, J. V. Collins, I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEEE Proc. Part J 132, 58–63 (1985).

Agrawal, G. P.

G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand-Reinhold, New York, 1993), Chap. 6.

Arnaud, J. A.

J. A. Arnaud, “Enhancement of optical receiver sensitivities by amplification of the carrier,” IEEE J. Quantum Electron. QE-4, 893–899 (1968).
[CrossRef]

Bensoussan, M.

R. Raj, J. L. Oudar, M. Bensoussan, “Vertical cavity amplifying photonic switch,” Appl. Phys. Lett. 65, 2359–2361 (1994).
[CrossRef]

Collins, J. V.

M. J. Adams, J. V. Collins, I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEEE Proc. Part J 132, 58–63 (1985).

Deng, J. S.

M. F. Lu, J. S. Deng, C. Juang, M. J. Jou, B. J. Lee, “Equivalent circuit model of quantum-well lasers,” IEEE J. Quantum Electron. 31, 1418–1421 (1995).
[CrossRef]

Dodds, D. E.

D. E. Dodds, M. J. Sieben, “Electric circuit model of a Fabry–Perot semiconductor laser,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering, C. R. Baird, M. E. El-Hawarg, eds. (Institute of Electrical and Electronics Engineers, New York, 1994), Vol. 1, pp. 371–374.
[CrossRef]

Dutta, N. K.

G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand-Reinhold, New York, 1993), Chap. 6.

Harder, C.

J. Katz, S. Margalit, C. Harder, D. Wilt, A. Yariv, “The intrinsic electrical equivalent circuit of a laser diode,” IEEE J. Quantum Electron. QE-17, 4–7 (1981).
[CrossRef]

Hecht, E.

E. Hecht, Optics (Addison Wesley, Reading, Mass., 1990), pp. 363–370.

Henning, I. D.

M. J. Adams, J. V. Collins, I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEEE Proc. Part J 132, 58–63 (1985).

Iga, K.

F. Koyama, S. Kubota, K. Iga, “GaAlAs/GaAs active filter based on vertical cavity surface emitting laser,” Electron. Lett. 27, 1093–1095 (1991).
[CrossRef]

Jou, M. J.

M. F. Lu, J. S. Deng, C. Juang, M. J. Jou, B. J. Lee, “Equivalent circuit model of quantum-well lasers,” IEEE J. Quantum Electron. 31, 1418–1421 (1995).
[CrossRef]

Juang, C.

M. F. Lu, J. S. Deng, C. Juang, M. J. Jou, B. J. Lee, “Equivalent circuit model of quantum-well lasers,” IEEE J. Quantum Electron. 31, 1418–1421 (1995).
[CrossRef]

Katz, J.

J. Katz, S. Margalit, C. Harder, D. Wilt, A. Yariv, “The intrinsic electrical equivalent circuit of a laser diode,” IEEE J. Quantum Electron. QE-17, 4–7 (1981).
[CrossRef]

Koyama, F.

F. Koyama, S. Kubota, K. Iga, “GaAlAs/GaAs active filter based on vertical cavity surface emitting laser,” Electron. Lett. 27, 1093–1095 (1991).
[CrossRef]

Kubota, S.

F. Koyama, S. Kubota, K. Iga, “GaAlAs/GaAs active filter based on vertical cavity surface emitting laser,” Electron. Lett. 27, 1093–1095 (1991).
[CrossRef]

Lee, B. J.

M. F. Lu, J. S. Deng, C. Juang, M. J. Jou, B. J. Lee, “Equivalent circuit model of quantum-well lasers,” IEEE J. Quantum Electron. 31, 1418–1421 (1995).
[CrossRef]

Lu, M. F.

M. F. Lu, J. S. Deng, C. Juang, M. J. Jou, B. J. Lee, “Equivalent circuit model of quantum-well lasers,” IEEE J. Quantum Electron. 31, 1418–1421 (1995).
[CrossRef]

Marcuse, D.

D. Marcuse, “Computer model of an injection laser amplifier,” IEEE J. Quantum Electron. QE-19, 63–73 (1983).
[CrossRef]

Margalit, S.

J. Katz, S. Margalit, C. Harder, D. Wilt, A. Yariv, “The intrinsic electrical equivalent circuit of a laser diode,” IEEE J. Quantum Electron. QE-17, 4–7 (1981).
[CrossRef]

Morishita, M.

M. Morishita, T. Ohmi, J. Nishizawa, “Impedance characteristics of double-heterostructure laser diodes,” Solid-State Electron. 22, 951–962 (1979).
[CrossRef]

Nishizawa, J.

M. Morishita, T. Ohmi, J. Nishizawa, “Impedance characteristics of double-heterostructure laser diodes,” Solid-State Electron. 22, 951–962 (1979).
[CrossRef]

Ohmi, T.

M. Morishita, T. Ohmi, J. Nishizawa, “Impedance characteristics of double-heterostructure laser diodes,” Solid-State Electron. 22, 951–962 (1979).
[CrossRef]

Oudar, J. L.

R. Raj, J. L. Oudar, M. Bensoussan, “Vertical cavity amplifying photonic switch,” Appl. Phys. Lett. 65, 2359–2361 (1994).
[CrossRef]

Personick, S. D.

S. D. Personick, “Applications for quantum amplifiers in simple digital optical communication system,” Bell Syst. Tech. J. 52, 117–133 (1973).

Pope, D. J.

R. S. Tucker, D. J. Pope, “Microwave circuit models of semiconductor injection lasers,” IEEE Trans. Microwave Theory Technol. MTT-31, 289–294 (1983).
[CrossRef]

R. S. Tucker, D. J. Pope, “Circuit modeling of the effect of diffusion on damping in a narrow-stripe semiconductor laser,” IEEE J. Quantum Electron. QE-19, 1179–1183 (1983).
[CrossRef]

Raj, R.

R. Raj, J. L. Oudar, M. Bensoussan, “Vertical cavity amplifying photonic switch,” Appl. Phys. Lett. 65, 2359–2361 (1994).
[CrossRef]

Sieben, M. J.

D. E. Dodds, M. J. Sieben, “Electric circuit model of a Fabry–Perot semiconductor laser,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering, C. R. Baird, M. E. El-Hawarg, eds. (Institute of Electrical and Electronics Engineers, New York, 1994), Vol. 1, pp. 371–374.
[CrossRef]

Tucker, R. S.

R. S. Tucker, D. J. Pope, “Circuit modeling of the effect of diffusion on damping in a narrow-stripe semiconductor laser,” IEEE J. Quantum Electron. QE-19, 1179–1183 (1983).
[CrossRef]

R. S. Tucker, D. J. Pope, “Microwave circuit models of semiconductor injection lasers,” IEEE Trans. Microwave Theory Technol. MTT-31, 289–294 (1983).
[CrossRef]

R. S. Tucker, “Large-signal circuit model for simulation of injection-laser modulation dynamics,” IEE Proc. 128, 180–184 (1981).

Wilt, D.

J. Katz, S. Margalit, C. Harder, D. Wilt, A. Yariv, “The intrinsic electrical equivalent circuit of a laser diode,” IEEE J. Quantum Electron. QE-17, 4–7 (1981).
[CrossRef]

Yariv, A.

J. Katz, S. Margalit, C. Harder, D. Wilt, A. Yariv, “The intrinsic electrical equivalent circuit of a laser diode,” IEEE J. Quantum Electron. QE-17, 4–7 (1981).
[CrossRef]

Appl. Phys. Lett. (1)

R. Raj, J. L. Oudar, M. Bensoussan, “Vertical cavity amplifying photonic switch,” Appl. Phys. Lett. 65, 2359–2361 (1994).
[CrossRef]

Bell Syst. Tech. J. (1)

S. D. Personick, “Applications for quantum amplifiers in simple digital optical communication system,” Bell Syst. Tech. J. 52, 117–133 (1973).

Electron. Lett. (1)

F. Koyama, S. Kubota, K. Iga, “GaAlAs/GaAs active filter based on vertical cavity surface emitting laser,” Electron. Lett. 27, 1093–1095 (1991).
[CrossRef]

IEE Proc. (1)

R. S. Tucker, “Large-signal circuit model for simulation of injection-laser modulation dynamics,” IEE Proc. 128, 180–184 (1981).

IEEE J. Quantum Electron. (5)

M. F. Lu, J. S. Deng, C. Juang, M. J. Jou, B. J. Lee, “Equivalent circuit model of quantum-well lasers,” IEEE J. Quantum Electron. 31, 1418–1421 (1995).
[CrossRef]

D. Marcuse, “Computer model of an injection laser amplifier,” IEEE J. Quantum Electron. QE-19, 63–73 (1983).
[CrossRef]

J. Katz, S. Margalit, C. Harder, D. Wilt, A. Yariv, “The intrinsic electrical equivalent circuit of a laser diode,” IEEE J. Quantum Electron. QE-17, 4–7 (1981).
[CrossRef]

R. S. Tucker, D. J. Pope, “Circuit modeling of the effect of diffusion on damping in a narrow-stripe semiconductor laser,” IEEE J. Quantum Electron. QE-19, 1179–1183 (1983).
[CrossRef]

J. A. Arnaud, “Enhancement of optical receiver sensitivities by amplification of the carrier,” IEEE J. Quantum Electron. QE-4, 893–899 (1968).
[CrossRef]

IEEE Proc. Part J (1)

M. J. Adams, J. V. Collins, I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEEE Proc. Part J 132, 58–63 (1985).

IEEE Trans. Microwave Theory Technol. (1)

R. S. Tucker, D. J. Pope, “Microwave circuit models of semiconductor injection lasers,” IEEE Trans. Microwave Theory Technol. MTT-31, 289–294 (1983).
[CrossRef]

Solid-State Electron. (1)

M. Morishita, T. Ohmi, J. Nishizawa, “Impedance characteristics of double-heterostructure laser diodes,” Solid-State Electron. 22, 951–962 (1979).
[CrossRef]

Other (3)

E. Hecht, Optics (Addison Wesley, Reading, Mass., 1990), pp. 363–370.

G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand-Reinhold, New York, 1993), Chap. 6.

D. E. Dodds, M. J. Sieben, “Electric circuit model of a Fabry–Perot semiconductor laser,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering, C. R. Baird, M. E. El-Hawarg, eds. (Institute of Electrical and Electronics Engineers, New York, 1994), Vol. 1, pp. 371–374.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Small-signal circuit model of a single-mode laser in the presence of small perturbation: δ P t = Li L t q   H / s ,   δ N t = Cv C t q ,   L = H / s σ P N , C = 1 H / s   σ N P ,   R n = H / s   σ N P Γ N ,   R p = H / s   Γ P σ P N .

Fig. 2
Fig. 2

Small-signal circuit model of a single-mode laser with electrical modulation.

Fig. 3
Fig. 3

Small-signal circuit model of a single-mode laser with optical modulation: V in t = q   H / s   η c P in t h ν .

Fig. 4
Fig. 4

Small-signal circuit model of a multimode laser: R n = H / s   σ N P 1 Γ N ,   C = 1 H / s   σ N P 1 ,   L j = H / s σ P j N j = 1 , ,   k , L xj = L j σ N P 1 σ N P j - 1 ,     j = 1 , ,   k , R P j = H / s   Γ P j σ P j N σ N P 1 σ N P j ,     j = 1 , ,   k , V in j t = q   H / s   η c P in j t h ν σ N P 1 σ N P j ,     j = 1 , ,   k .

Equations (26)

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P ˙ t = GP t - γ P t + R sp ,
N ˙ t = I bias q - γ e N t - GP t ,
δ P ˙ t = - Γ P δ P t + σ N P δ N t ,
δ N ˙ t = - Γ N δ N t - σ P N δ P t ,
Γ P = R sp P - G P P ,
Γ N = γ e + γ e N N + G N P ,
σ N P = G N P + R sp N ,
σ P N = G + G P P ,
δ P t = Ψ t q H / s ,     δ N t = Q t q ,
v L t = - Γ P Li L t + σ N P Cv C t H / s ,
i C t = - Γ N Cv C t - σ P N Li L t H / s .
δ P out t = α m Li L t q H / s   h ν .
δ N ˙ t = - Γ N δ N t - σ P N δ P t + i m t q ,
i C t = - Γ N Cv C t - σ P N Li L t H / s + i m t .
P ˙ t = GP t - γ P t + R sp + η c P in t h ν ,
δ P ˙ t = - Γ P δ P t + σ N P δ N t + η c P in t h ν ,
v L t = - Γ P Li L t + σ N P Cv C t H / s + q H / s η c P in t h ν ,
η c = T 1 1 - R 2 1 + R 1 R 2 - 2 R 1 R 2 1 / 2 cos   δ .
P ˙ k t = G k P k t - γ k P k t + R sp k ,
N ˙ t = I bias q - γ e N t - k   G k P k t ,
δ P ˙ 1 ( t ) = - Γ P 1 δ P 1 ( t ) + σ N P 1 δ N ( t ) , δ P ˙ k ( t ) = - Γ P k δ P k ( t ) + σ N P k δ N ( t ) ,
δ N ˙ t = - Γ N δ N t - k   σ P k N δ P k t ,
v L 1 ( t ) = - Γ P 1 L 1 i L 1 ( t ) + σ N P 1 Cv C ( t ) ( H / s ) , v L k ( t ) = - Γ P k L k i L k ( t ) + σ N P k Cv C ( t ) ( H / s ) ,
i C t = - Γ N Cv C t - k σ P k N L k i L k t H / s ,
δ P t = Li L t q   H / s ,   δ N t = Cv C t q ,   L = H / s σ P N , C = 1 H / s   σ N P ,   R n = H / s   σ N P Γ N ,   R p = H / s   Γ P σ P N .
R n = H / s   σ N P 1 Γ N ,   C = 1 H / s   σ N P 1 ,   L j = H / s σ P j N j = 1 , ,   k , L xj = L j σ N P 1 σ N P j - 1 ,     j = 1 , ,   k , R P j = H / s   Γ P j σ P j N σ N P 1 σ N P j ,     j = 1 , ,   k , V in j t = q   H / s   η c P in j t h ν σ N P 1 σ N P j ,     j = 1 , ,   k .

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