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.

© 2011 Optical Society of America

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  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).
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    [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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  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).
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  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).
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  23. C. H. Henry, "Theory of the linewidth of semiconductor lasers," IEEE J. Quantum Electron. 18, 259-264 (1982).
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  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).
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  25. B. W. Hakki, "Optical and microwave instabilities in injection lasers," J. Appl. Phys. 51, 68-73 (1980).
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  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).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (1)

2008 (4)

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 Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62, 6487-6495 (2000).
[CrossRef]

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)

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]

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

1980 (2)

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

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]

Braun, H.

Channin, D. J.

D. J. Channin, "Effect of gain saturation on injection laser switching," J. Appl. Phys. 50, 3858-3860 (1979).
[CrossRef]

Chen, C.

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 Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 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]

Ding, G.

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 Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62, 6487-6495 (2000).
[CrossRef]

Helmy, A.

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, S. Takamatsu, H. Watanabe, T. Matsuyama, and H. Horinaka, "Pulse-shaping of gain-switched pulse from multimode laser diode using fiber Sagnac interferometer," Opt. Express 16, 19872-19881 (2008), http: //www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-24-19872.
[CrossRef] [PubMed]

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]

Hwang, J. C. M.

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.

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

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

Koch, T. L.

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]

Kuo, H.-C.

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]

Lester, L. F.

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]

Lin, C.-C.

Lin, G.-R.

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]

Lutgen, S.

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, S. Takamatsu, H. Watanabe, T. Matsuyama, and H. Horinaka, "Pulse-shaping of gain-switched pulse from multimode laser diode using fiber Sagnac interferometer," Opt. Express 16, 19872-19881 (2008), http: //www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-24-19872.
[CrossRef] [PubMed]

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]

Mayer, T.

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]

Ooi, B. S.

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]

Peng, P.-C.

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]

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]

Schillgalies, M.

Schwarz, U. T.

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]

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]

Strauss, U.

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).

Takamatsu, S.

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]

Tautz, S.

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, S. Takamatsu, H. Watanabe, T. Matsuyama, and H. Horinaka, "Pulse-shaping of gain-switched pulse from multimode laser diode using fiber Sagnac interferometer," Opt. Express 16, 19872-19881 (2008), http: //www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-24-19872.
[CrossRef] [PubMed]

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]

Watanabe, H.

White, I. H.

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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).
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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).
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[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)

Equations on this page are rendered with MathJax. Learn more.

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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