Abstract

To derive a simple form of the multimode laser diode rate equations incorporating the band filling effect, the laser diode gain in the direct bandgap model is introduced into the conventional multimode laser diode rate equations. By numerically examining each modal gain under the gain-switching condition, it is found that both the differential gain coefficient and the carrier density at transparency show an approximately linear dependency on the oscillation frequency. As a result, it is possible to derive a simple form of the multimode laser diode rate equations with linearized gain, which can be used to simulate the behaviors of a gain-switched laser diode characterized by the band filling effect, in both the multimode and single-mode oscillation cases.

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References

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    [Crossref]
  3. D. J. Channin, “Effect of gain saturation on injection laser switching,” J. Appl. Phys. 50, 3858–3860 (1979).
    [Crossref]
  4. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron.16, 347–355 (1980).
    [Crossref]
  5. S. Tarucha and K. Otsuka, “Response of semiconductor laser to deep sinusoidal injection current modulation,” IEEE J. Quantum Electron. 17, 810–816 (1981).
    [Crossref]
  6. C. B. Su, V. Lanzisera, and R. Olshansky, “Measurement of nonlinear gain from FM modulation index of In-GaAsP lasers,” Electron. Lett. 21, 893–895 (1985).
    [Crossref]
  7. P. M. Downey, J. E. Bowers, R. S. Tucker, and E. Agyekum, “Picosecond dynamics of a gain-switched InGaAsP laser,” IEEE J. Quantum Electron. 23, 1039–1047 (1987).
    [Crossref]
  8. R. Olshansky, P. Hill, V. Lanzisera, and W. Powazinik, “Frequency response of 1.3 μm InGaAsP high speed semiconductor lasers,” IEEE J. Quantum Electron. 23, 1410–1418 (1987).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  21. M. Osinski and M. J. Adams, “Picosecond pulse analysis of gain-switched 1.55 μm InGaAsP lasers,” IEEE J. Quantum Electron. 21, 1929–1936 (1985).
    [Crossref]
  22. M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21, 981–982 (1985).
    [Crossref]
  23. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
    [Crossref]
  24. B. Sermage, J. P. Heritage, and N. K. Dutta, “Temperature dependence of carrier lifetime and Auger recombination in 1.3 μm InGaAsP,” J. Appl. Phys. 57, 5443–5449 (1985).
    [Crossref]
  25. B. W. Hakki, “Optical and microwave instabilities in injection lasers,” J. Appl. Phys. 51, 68–73 (1980).
    [Crossref]
  26. P. -L Liu, C. Lin, I. P. Kaminow, and J. J. Hsieh, “Picosecond pulse generation from InGaAsP lasers at 1.25 and 1.3 μm by electrical pulse pumping,” IEEE J. Quantum Electron. 17, 671–674 (1981).
    [Crossref]
  27. G. Lasher and F. Stern, “Spontaneous and stimulated recombination radiation in semiconductors,” Phys. Rev. 133, A553–A563 (1964).
    [Crossref]
  28. T. Suhara, Semiconductor laser fundamentals (Kyoritsu, 1998), Chap. 3. in Japanese.
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    [Crossref]
  30. A. E. Siegman, Lasers (University science books, 1986), Chap. 26.
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    [Crossref]
  32. K. Wada, J. Fujita, J. Yamada, T. Matsuyama, and H. Horinaka, “Simple method for estimating shape functions of optical spectra,” Opt. Commun. 281, 368–373 (2008).
    [Crossref]
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    [Crossref]

2008 (1)

K. Wada, J. Fujita, J. Yamada, T. Matsuyama, and H. Horinaka, “Simple method for estimating shape functions of optical spectra,” Opt. Commun. 281, 368–373 (2008).
[Crossref]

2005 (1)

K. Wada, H. Sato, H. Yoshioka, T. Matsuyama, and H. Horinaka, “Suppression of side fringes in low-coherence interferometric measurements using gain- or loss modulated multimode laser diodes,” Jpn. J. Appl. Phys. 44, 8484–8490 (2005).
[Crossref]

2004 (1)

I. V. Koryukin and P. Mandel, “Dynamics of semiconductor lasers with optical feedback: Comparison of multimode models in the low-frequency fluctuation regime,” Phys. Rev. A 70, 053819 (2004).
[Crossref]

2000 (1)

K. A. Corbett and M. W. Hamilton, “Comparison of the bifurcation scenarios predicted by the single-mode and multimode semiconductor laser rate equations,” Phys. Rev. E 62, 6487–6495 (2000).
[Crossref]

1998 (1)

T. Suhara, Semiconductor laser fundamentals (Kyoritsu, 1998), Chap. 3. in Japanese.

1988 (1)

K. Y. Lau, “Gain switching of semiconductor injection lasers,” Appl. Phys. Lett. 52, 257–259 (1988).
[Crossref]

1987 (2)

P. M. Downey, J. E. Bowers, R. S. Tucker, and E. Agyekum, “Picosecond dynamics of a gain-switched InGaAsP laser,” IEEE J. Quantum Electron. 23, 1039–1047 (1987).
[Crossref]

R. Olshansky, P. Hill, V. Lanzisera, and W. Powazinik, “Frequency response of 1.3 μm InGaAsP high speed semiconductor lasers,” IEEE J. Quantum Electron. 23, 1410–1418 (1987).
[Crossref]

1985 (5)

C. B. Su, V. Lanzisera, and R. Olshansky, “Measurement of nonlinear gain from FM modulation index of In-GaAsP lasers,” Electron. Lett. 21, 893–895 (1985).
[Crossref]

M. Osinski and M. J. Adams, “Picosecond pulse analysis of gain-switched 1.55 μm InGaAsP lasers,” IEEE J. Quantum Electron. 21, 1929–1936 (1985).
[Crossref]

M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21, 981–982 (1985).
[Crossref]

B. Sermage, J. P. Heritage, and N. K. Dutta, “Temperature dependence of carrier lifetime and Auger recombination in 1.3 μm InGaAsP,” J. Appl. Phys. 57, 5443–5449 (1985).
[Crossref]

R. A. Linke, “Modulation induced transient chirping in single frequency lasers,” IEEE J. Quantum Electron. 21, 593–597 (1985).
[Crossref]

1984 (1)

M. Osinski and M. J. Adams, “Intrinsic manifestation of regular pulsations in time-averaged spectra of semiconductor lasers,” Electron. Lett. 20, 525–526 (1984).
[Crossref]

1982 (1)

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[Crossref]

1981 (2)

S. Tarucha and K. Otsuka, “Response of semiconductor laser to deep sinusoidal injection current modulation,” IEEE J. Quantum Electron. 17, 810–816 (1981).
[Crossref]

P. -L Liu, C. Lin, I. P. Kaminow, and J. J. Hsieh, “Picosecond pulse generation from InGaAsP lasers at 1.25 and 1.3 μm by electrical pulse pumping,” IEEE J. Quantum Electron. 17, 671–674 (1981).
[Crossref]

1980 (1)

B. W. Hakki, “Optical and microwave instabilities in injection lasers,” J. Appl. Phys. 51, 68–73 (1980).
[Crossref]

1979 (1)

D. J. Channin, “Effect of gain saturation on injection laser switching,” J. Appl. Phys. 50, 3858–3860 (1979).
[Crossref]

1977 (1)

W. B. Joyce and R. W. Dixon, “Analytic approximations for the Fermi energy of an ideal Fermi gas,” Appl. Phys. Lett. 31, 354–356 (1977).
[Crossref]

1975 (1)

P. M. Boers and M. Danielsen, “Dynamic behaviour of semiconductor lasers,” Electron. Lett. 15, 206–208 (1975).
[Crossref]

1971 (1)

F. Stern, “Band-tail model for optical absorption and for the mobility edge in amorphous silicon,” Phys. Rev. B 3, 2636–2645 (1971).
[Crossref]

1970 (1)

T. Ikegami, K. Kobayashi, and Y. Suematsu, “Transient behaviour of semiconductor injection lasers,” Electron. Commun. Jpn. 53B, 82–89 (1970).

1964 (1)

G. Lasher and F. Stern, “Spontaneous and stimulated recombination radiation in semiconductors,” Phys. Rev. 133, A553–A563 (1964).
[Crossref]

Adams, M. J.

M. Osinski and M. J. Adams, “Picosecond pulse analysis of gain-switched 1.55 μm InGaAsP lasers,” IEEE J. Quantum Electron. 21, 1929–1936 (1985).
[Crossref]

M. Osinski and M. J. Adams, “Intrinsic manifestation of regular pulsations in time-averaged spectra of semiconductor lasers,” Electron. Lett. 20, 525–526 (1984).
[Crossref]

Agyekum, E.

P. M. Downey, J. E. Bowers, R. S. Tucker, and E. Agyekum, “Picosecond dynamics of a gain-switched InGaAsP laser,” IEEE J. Quantum Electron. 23, 1039–1047 (1987).
[Crossref]

Boers, P. M.

P. M. Boers and M. Danielsen, “Dynamic behaviour of semiconductor lasers,” Electron. Lett. 15, 206–208 (1975).
[Crossref]

Bowers, J. E.

P. M. Downey, J. E. Bowers, R. S. Tucker, and E. Agyekum, “Picosecond dynamics of a gain-switched InGaAsP laser,” IEEE J. Quantum Electron. 23, 1039–1047 (1987).
[Crossref]

Channin, D. J.

D. J. Channin, “Effect of gain saturation on injection laser switching,” J. Appl. Phys. 50, 3858–3860 (1979).
[Crossref]

Chow, W. W.

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor-Laser Physics, (Springer-Verlag, 1994).
[Crossref]

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals, (Springer-Verlag, 1999).

Corbett, K. A.

K. A. Corbett and M. W. Hamilton, “Comparison of the bifurcation scenarios predicted by the single-mode and multimode semiconductor laser rate equations,” Phys. Rev. E 62, 6487–6495 (2000).
[Crossref]

Danielsen, M.

P. M. Boers and M. Danielsen, “Dynamic behaviour of semiconductor lasers,” Electron. Lett. 15, 206–208 (1975).
[Crossref]

Dixon, R. W.

W. B. Joyce and R. W. Dixon, “Analytic approximations for the Fermi energy of an ideal Fermi gas,” Appl. Phys. Lett. 31, 354–356 (1977).
[Crossref]

Downey, P. M.

P. M. Downey, J. E. Bowers, R. S. Tucker, and E. Agyekum, “Picosecond dynamics of a gain-switched InGaAsP laser,” IEEE J. Quantum Electron. 23, 1039–1047 (1987).
[Crossref]

Dutta, N. K.

B. Sermage, J. P. Heritage, and N. K. Dutta, “Temperature dependence of carrier lifetime and Auger recombination in 1.3 μm InGaAsP,” J. Appl. Phys. 57, 5443–5449 (1985).
[Crossref]

Fujita, J.

K. Wada, J. Fujita, J. Yamada, T. Matsuyama, and H. Horinaka, “Simple method for estimating shape functions of optical spectra,” Opt. Commun. 281, 368–373 (2008).
[Crossref]

Gallagher, D. F. G.

M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21, 981–982 (1985).
[Crossref]

Hakki, B. W.

B. W. Hakki, “Optical and microwave instabilities in injection lasers,” J. Appl. Phys. 51, 68–73 (1980).
[Crossref]

Hamilton, M. W.

K. A. Corbett and M. W. Hamilton, “Comparison of the bifurcation scenarios predicted by the single-mode and multimode semiconductor laser rate equations,” Phys. Rev. E 62, 6487–6495 (2000).
[Crossref]

Henry, C. H.

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[Crossref]

Heritage, J. P.

B. Sermage, J. P. Heritage, and N. K. Dutta, “Temperature dependence of carrier lifetime and Auger recombination in 1.3 μm InGaAsP,” J. Appl. Phys. 57, 5443–5449 (1985).
[Crossref]

Hill, P.

R. Olshansky, P. Hill, V. Lanzisera, and W. Powazinik, “Frequency response of 1.3 μm InGaAsP high speed semiconductor lasers,” IEEE J. Quantum Electron. 23, 1410–1418 (1987).
[Crossref]

Horinaka, H.

K. Wada, J. Fujita, J. Yamada, T. Matsuyama, and H. Horinaka, “Simple method for estimating shape functions of optical spectra,” Opt. Commun. 281, 368–373 (2008).
[Crossref]

K. Wada, H. Sato, H. Yoshioka, T. Matsuyama, and H. Horinaka, “Suppression of side fringes in low-coherence interferometric measurements using gain- or loss modulated multimode laser diodes,” Jpn. J. Appl. Phys. 44, 8484–8490 (2005).
[Crossref]

Hsieh, J. J.

P. -L Liu, C. Lin, I. P. Kaminow, and J. J. Hsieh, “Picosecond pulse generation from InGaAsP lasers at 1.25 and 1.3 μm by electrical pulse pumping,” IEEE J. Quantum Electron. 17, 671–674 (1981).
[Crossref]

Ikegami, T.

T. Ikegami, K. Kobayashi, and Y. Suematsu, “Transient behaviour of semiconductor injection lasers,” Electron. Commun. Jpn. 53B, 82–89 (1970).

Joyce, W. B.

W. B. Joyce and R. W. Dixon, “Analytic approximations for the Fermi energy of an ideal Fermi gas,” Appl. Phys. Lett. 31, 354–356 (1977).
[Crossref]

Kaminow, I. P.

P. -L Liu, C. Lin, I. P. Kaminow, and J. J. Hsieh, “Picosecond pulse generation from InGaAsP lasers at 1.25 and 1.3 μm by electrical pulse pumping,” IEEE J. Quantum Electron. 17, 671–674 (1981).
[Crossref]

Kobayashi, K.

T. Ikegami, K. Kobayashi, and Y. Suematsu, “Transient behaviour of semiconductor injection lasers,” Electron. Commun. Jpn. 53B, 82–89 (1970).

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron.16, 347–355 (1980).
[Crossref]

Koch, S. W.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals, (Springer-Verlag, 1999).

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor-Laser Physics, (Springer-Verlag, 1994).
[Crossref]

Koryukin, I. V.

I. V. Koryukin and P. Mandel, “Dynamics of semiconductor lasers with optical feedback: Comparison of multimode models in the low-frequency fluctuation regime,” Phys. Rev. A 70, 053819 (2004).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron.16, 347–355 (1980).
[Crossref]

Lanzisera, V.

R. Olshansky, P. Hill, V. Lanzisera, and W. Powazinik, “Frequency response of 1.3 μm InGaAsP high speed semiconductor lasers,” IEEE J. Quantum Electron. 23, 1410–1418 (1987).
[Crossref]

C. B. Su, V. Lanzisera, and R. Olshansky, “Measurement of nonlinear gain from FM modulation index of In-GaAsP lasers,” Electron. Lett. 21, 893–895 (1985).
[Crossref]

Lasher, G.

G. Lasher and F. Stern, “Spontaneous and stimulated recombination radiation in semiconductors,” Phys. Rev. 133, A553–A563 (1964).
[Crossref]

Lau, K. Y.

K. Y. Lau, “Gain switching of semiconductor injection lasers,” Appl. Phys. Lett. 52, 257–259 (1988).
[Crossref]

Lin, C.

P. -L Liu, C. Lin, I. P. Kaminow, and J. J. Hsieh, “Picosecond pulse generation from InGaAsP lasers at 1.25 and 1.3 μm by electrical pulse pumping,” IEEE J. Quantum Electron. 17, 671–674 (1981).
[Crossref]

Linke, R. A.

R. A. Linke, “Modulation induced transient chirping in single frequency lasers,” IEEE J. Quantum Electron. 21, 593–597 (1985).
[Crossref]

Liu, P. -L

P. -L Liu, C. Lin, I. P. Kaminow, and J. J. Hsieh, “Picosecond pulse generation from InGaAsP lasers at 1.25 and 1.3 μm by electrical pulse pumping,” IEEE J. Quantum Electron. 17, 671–674 (1981).
[Crossref]

Mandel, P.

I. V. Koryukin and P. Mandel, “Dynamics of semiconductor lasers with optical feedback: Comparison of multimode models in the low-frequency fluctuation regime,” Phys. Rev. A 70, 053819 (2004).
[Crossref]

Matsuyama, T.

K. Wada, J. Fujita, J. Yamada, T. Matsuyama, and H. Horinaka, “Simple method for estimating shape functions of optical spectra,” Opt. Commun. 281, 368–373 (2008).
[Crossref]

K. Wada, H. Sato, H. Yoshioka, T. Matsuyama, and H. Horinaka, “Suppression of side fringes in low-coherence interferometric measurements using gain- or loss modulated multimode laser diodes,” Jpn. J. Appl. Phys. 44, 8484–8490 (2005).
[Crossref]

Ohtsubo, J.

J. Ohtsubo, Semiconductor Lasers –Stability, Instability and Chaos, Second Ed., (Springer-Verlag, 2007).
[PubMed]

Olshansky, R.

R. Olshansky, P. Hill, V. Lanzisera, and W. Powazinik, “Frequency response of 1.3 μm InGaAsP high speed semiconductor lasers,” IEEE J. Quantum Electron. 23, 1410–1418 (1987).
[Crossref]

C. B. Su, V. Lanzisera, and R. Olshansky, “Measurement of nonlinear gain from FM modulation index of In-GaAsP lasers,” Electron. Lett. 21, 893–895 (1985).
[Crossref]

Osinski, M.

M. Osinski and M. J. Adams, “Picosecond pulse analysis of gain-switched 1.55 μm InGaAsP lasers,” IEEE J. Quantum Electron. 21, 1929–1936 (1985).
[Crossref]

M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21, 981–982 (1985).
[Crossref]

M. Osinski and M. J. Adams, “Intrinsic manifestation of regular pulsations in time-averaged spectra of semiconductor lasers,” Electron. Lett. 20, 525–526 (1984).
[Crossref]

Otsuka, K.

S. Tarucha and K. Otsuka, “Response of semiconductor laser to deep sinusoidal injection current modulation,” IEEE J. Quantum Electron. 17, 810–816 (1981).
[Crossref]

Powazinik, W.

R. Olshansky, P. Hill, V. Lanzisera, and W. Powazinik, “Frequency response of 1.3 μm InGaAsP high speed semiconductor lasers,” IEEE J. Quantum Electron. 23, 1410–1418 (1987).
[Crossref]

Sargent, M.

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor-Laser Physics, (Springer-Verlag, 1994).
[Crossref]

Sato, H.

K. Wada, H. Sato, H. Yoshioka, T. Matsuyama, and H. Horinaka, “Suppression of side fringes in low-coherence interferometric measurements using gain- or loss modulated multimode laser diodes,” Jpn. J. Appl. Phys. 44, 8484–8490 (2005).
[Crossref]

Sermage, B.

B. Sermage, J. P. Heritage, and N. K. Dutta, “Temperature dependence of carrier lifetime and Auger recombination in 1.3 μm InGaAsP,” J. Appl. Phys. 57, 5443–5449 (1985).
[Crossref]

Siegman, A. E.

A. E. Siegman, Lasers (University science books, 1986), Chap. 26.

Stern, F.

F. Stern, “Band-tail model for optical absorption and for the mobility edge in amorphous silicon,” Phys. Rev. B 3, 2636–2645 (1971).
[Crossref]

G. Lasher and F. Stern, “Spontaneous and stimulated recombination radiation in semiconductors,” Phys. Rev. 133, A553–A563 (1964).
[Crossref]

Su, C. B.

C. B. Su, V. Lanzisera, and R. Olshansky, “Measurement of nonlinear gain from FM modulation index of In-GaAsP lasers,” Electron. Lett. 21, 893–895 (1985).
[Crossref]

Suematsu, Y.

T. Ikegami, K. Kobayashi, and Y. Suematsu, “Transient behaviour of semiconductor injection lasers,” Electron. Commun. Jpn. 53B, 82–89 (1970).

Suhara, T.

T. Suhara, Semiconductor laser fundamentals (Kyoritsu, 1998), Chap. 3. in Japanese.

Tarucha, S.

S. Tarucha and K. Otsuka, “Response of semiconductor laser to deep sinusoidal injection current modulation,” IEEE J. Quantum Electron. 17, 810–816 (1981).
[Crossref]

Tucker, R. S.

P. M. Downey, J. E. Bowers, R. S. Tucker, and E. Agyekum, “Picosecond dynamics of a gain-switched InGaAsP laser,” IEEE J. Quantum Electron. 23, 1039–1047 (1987).
[Crossref]

Wada, K.

K. Wada, J. Fujita, J. Yamada, T. Matsuyama, and H. Horinaka, “Simple method for estimating shape functions of optical spectra,” Opt. Commun. 281, 368–373 (2008).
[Crossref]

K. Wada, H. Sato, H. Yoshioka, T. Matsuyama, and H. Horinaka, “Suppression of side fringes in low-coherence interferometric measurements using gain- or loss modulated multimode laser diodes,” Jpn. J. Appl. Phys. 44, 8484–8490 (2005).
[Crossref]

White, I. H.

M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21, 981–982 (1985).
[Crossref]

Yamada, J.

K. Wada, J. Fujita, J. Yamada, T. Matsuyama, and H. Horinaka, “Simple method for estimating shape functions of optical spectra,” Opt. Commun. 281, 368–373 (2008).
[Crossref]

Yoshioka, H.

K. Wada, H. Sato, H. Yoshioka, T. Matsuyama, and H. Horinaka, “Suppression of side fringes in low-coherence interferometric measurements using gain- or loss modulated multimode laser diodes,” Jpn. J. Appl. Phys. 44, 8484–8490 (2005).
[Crossref]

Appl. Phys. Lett. (2)

K. Y. Lau, “Gain switching of semiconductor injection lasers,” Appl. Phys. Lett. 52, 257–259 (1988).
[Crossref]

W. B. Joyce and R. W. Dixon, “Analytic approximations for the Fermi energy of an ideal Fermi gas,” Appl. Phys. Lett. 31, 354–356 (1977).
[Crossref]

Electron. Commun. Jpn. (1)

T. Ikegami, K. Kobayashi, and Y. Suematsu, “Transient behaviour of semiconductor injection lasers,” Electron. Commun. Jpn. 53B, 82–89 (1970).

Electron. Lett. (4)

P. M. Boers and M. Danielsen, “Dynamic behaviour of semiconductor lasers,” Electron. Lett. 15, 206–208 (1975).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1

Experimentally observed power spectrum of the gain-switched pulse from an 800 nm Fabry-Perot laser diode.

Fig. 2
Fig. 2

Simulated power spectra of gain-switched pulses from multimode laser diodes; (a) is calculated with the direct bandgap model, whereas (b) and (c) are calculated with the conventional differential gain model with (b) k=0 and (c) k=20 nm. The numbers in (a) represent the mode numbers.

Fig. 3
Fig. 3

Gain spectra when the carrier density is varied from 1.25 × 1024m−3 to 1.73 × 1024m−3 in 0.04 × 1024m−3 steps. (a) is calculated with the direct bandgap model, and (b) and (c) are calculated with the conventional differential gain model with (b) k=0 and (c) k=20 nm.

Fig. 4
Fig. 4

The pulse intensity (blue) and the pulse width (red) of each pulse component of a gain-switched pulse with a multimode power spectrum.

Fig. 5
Fig. 5

Temporal waveforms of pulse components at −7th, −5th, −3rd, 0th, 3th, 5th, and 9th modes in the multimode oscillation, and a composite pulse of all pulse components, labeled “all modes”.

Fig. 6
Fig. 6

TBP–CBP plot for estimating pulse shape functions. Numbers in the figure correspond to the mode numbers in Fig. 2(a).

Fig. 7
Fig. 7

Examples of the modal gain (for −5th, 0th, and 5th modes) versus the carrier density in the direct bandgap model.

Fig. 8
Fig. 8

Estimated differential gain coefficient (red) and carrier density at transparency (blue) in each mode in the direct bandgap model.

Fig. 9
Fig. 9

Simulated power spectrum of the gain-switched pulse from a multimode laser diode in the linearized laser diode gain model.

Fig. 10
Fig. 10

Gain spectra using Eq. (23) when the carrier density is varied from 1.25×1024m−3 to 1.73 × 1024m−3 in 0.04 × 1024m−3 steps.

Fig. 11
Fig. 11

Variation of the threshold current as a function of the oscillation frequency for the single-mode case in the linearized laser diode gain model.

Fig. 12
Fig. 12

Simulated peak intensity (blue) and pulse width (red) of gain-switched pulses from a single-mode laser diode at each oscillation frequency in the linearized laser diode gain model.

Fig. 13
Fig. 13

Examples of simulated gain-switched pulse from a single-mode laser diode at different oscillation frequencies corresponding to the modes in the multimode oscillation in Fig. 2(a).

Fig. 14
Fig. 14

TBP–CBP plot for estimating shape functions of gain-switched pulses from a single-mode laser diode. Numbers in the figure correspond to the mode numbers in the multimode oscillation in Fig. 2(a).

Tables (3)

Tables Icon

Table 1 Notation and values of parameters used in the rate equations

Tables Icon

Table 2 Notation and values of parameters for the conventional differential gain model

Tables Icon

Table 3 Notation and values of parameters for the linearized laser diode gain model

Equations (27)

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d E n d t = 1 2 ( 1 + i α ) [ g n 1 + ɛ j S j 1 τ p + β C 2 N 2 S n ] E n + i n δ ω E n
d N d t = 1 e V 1 T 1 N n g n 1 + ɛ j S j S n
1 T 1 = C 1 + C 2 N + C 3 N 2
g n = Γ c n g π e 2 | M | 2 ( f b f a ) ρ r n r c ɛ 0 m 2 ω n
| M | 2 = m 2 E g ( E g + Δ ) 12 m n ( E g + 2 Δ / 3 )
ρ r = [ ( 2 m r ) 3 / 2 π 2 h ¯ 3 ] h ¯ ω n E g
f a ( b ) = 1 exp [ ( E a ( b ) F v ( c ) ) / k B T ] + 1
E a = E v ( m r m p ) ( h ¯ ω n E g )
E b = E c + ( m r m n ) ( h ¯ ω n E g )
1 m r = 1 m n + 1 m p
F v = E v k B T [ ln ( N N v ) + k = 1 4 A k ( N N v ) k ]
F c = E c + k B T [ ln ( N N c ) + k = 1 4 A k ( N N c ) k ]
N v ( c ) = 2 [ 2 π k B T m p ( n ) h 2 ] 3 / 2
g n = G 0 N [ 1 { 2 ( λ ( N ) λ n ) Δ λ g } 2 ] G 0 N 0
λ ( N ) = λ 0 + k [ N t h N N t h ]
λ n = λ 0 + n δ λ = λ 0 + n λ 0 2 2 n r L
N t h = N 0 + 1 G 0 τ p
I = I d c + I m w sin ( 2 π f m t )
C ( τ ) = | E ( t ) + E ( t + τ ) | 2 d t 2 | E ( t ) | 2 d t 1 ,
g n = G 0 n ( N N 0 n )
G 0 n = G 00 + n δ G 0
N 0 n = N 00 + n δ N 0
g n = δ G 0 δ N 0 [ { n 1 2 ( N N 00 δ N 0 G 00 δ G 0 ) } 2 1 4 ( N N 00 δ N 0 + G 00 δ G 0 ) 2 ]
Δ ω g = δ ω ( N N 00 δ N 0 + G 00 δ G 0 )
g m = 1 4 δ G 0 δ N 0 ( N N 00 δ N 0 + G 00 δ G 0 ) 2
I t h = e V ( C 1 N t h + C 2 N t h 2 )
N t h = N 0 + 1 G 0 τ p

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