Simple form of multimode laser diode rate equations incorporating the band filling effect

doi:10.1364/OE.19.003019

Simple form of multimode laser diode rate equations incorporating the band filling effect

Kenji Wada, Hiroyuki Yoshioka, Jiaxun Zhu, Tetsuya Matsuyama, and Hiromichi Horinaka »View Author Affiliations

Optics Express, Vol. 19, Issue 4, pp. 3019-3036 (2011)
http://dx.doi.org/10.1364/OE.19.003019

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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.

OCIS Codes
(270.3430) Quantum optics : Laser theory
(300.6170) Spectroscopy : Spectra
(320.1590) Ultrafast optics : Chirping
(320.5390) Ultrafast optics : Picosecond phenomena
(320.5540) Ultrafast optics : Pulse shaping
(250.5960) Optoelectronics : Semiconductor lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: November 29, 2010
Revised Manuscript: January 21, 2011
Manuscript Accepted: January 30, 2011
Published: February 2, 2011

Citation
Kenji Wada, Hiroyuki Yoshioka, Jiaxun Zhu, Tetsuya Matsuyama, and Hiromichi Horinaka, "Simple form of multimode laser diode rate equations incorporating the band filling effect," Opt. Express 19, 3019-3036 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-3019

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References

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P. M. Boers, and M. Danielsen, "Dynamic behaviour of semiconductor lasers," Electron. Lett. 15, 206-208 (1975). [CrossRef]
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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]
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]
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K. Y. Lau, "Gain switching of semiconductor injection lasers," Appl. Phys. Lett. 52, 257-259 (1988). [CrossRef]
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]
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]
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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]
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]
C. H. Henry, "Theory of the linewidth of semiconductor lasers," IEEE J. Quantum Electron. 18, 259-264 (1982). [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]
B. W. Hakki, "Optical and microwave instabilities in injection lasers," J. Appl. Phys. 51, 68-73 (1980). [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]
G. Lasher, and F. Stern, "Spontaneous and stimulated recombination radiation in semiconductors," Phys. Rev. 133, A553-A563 (1964). [CrossRef]
T. Suhara, Semiconductor laser fundamentals (Kyoritsu, 1998), Chap. 3. in Japanese.
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]
A. E. Siegman, Lasers (University science books, 1986), Chap. 26.
R. A. Linke, "Modulation induced transient chirping in single frequency lasers," IEEE J. Quantum Electron. 21, 593-597 (1985). [CrossRef]
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]
F. Stern, "Band-tail model for optical absorption and for the mobility edge in amorphous silicon," Phys. Rev. B 3, 2636-2645 (1971). [CrossRef]

Appl. Phys. Lett.

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.

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

Electron. Lett.

P. M. Boers, and M. Danielsen, "Dynamic behaviour of semiconductor lasers," Electron. Lett. 15, 206-208 (1975). [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]
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]
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]

IEEE J. Quantum Electron.

C. H. Henry, "Theory of the linewidth of semiconductor lasers," IEEE J. Quantum Electron. 18, 259-264 (1982). [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]
R. A. Linke, "Modulation induced transient chirping in single frequency lasers," IEEE J. Quantum Electron. 21, 593-597 (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]
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]
R. Lang, and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980). [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]

J. Appl. Phys.

D. J. Channin, "Effect of gain saturation on injection laser switching," J. Appl. Phys. 50, 3858-3860 (1979). [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]
B. W. Hakki, "Optical and microwave instabilities in injection lasers," J. Appl. Phys. 51, 68-73 (1980). [CrossRef]

Jpn. J. Appl. Phys.

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]

Opt. Commun.

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]

Opt. Express

Phys. Rev.

G. Lasher, and F. Stern, "Spontaneous and stimulated recombination radiation in semiconductors," Phys. Rev. 133, A553-A563 (1964). [CrossRef]

Phys. Rev. A

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]

Phys. Rev. B

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

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

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]

Other

W. W. Chow, S. W. Koch, and M. SargentIII, Semiconductor-Laser Physics, (Springer-Verlag, 1994). [CrossRef]
W. W. Chow, and S. W. Koch, Semiconductor-Laser Fundamentals, (Springer-Verlag, 1999).
J. Ohtsubo, Semiconductor Lasers -Stability, Instability and Chaos, Second Ed., (Springer-Verlag, 2007). [PubMed]
T. Suhara, Semiconductor laser fundamentals (Kyoritsu, 1998), Chap. 3. in Japanese.
A. E. Siegman, Lasers (University science books, 1986), Chap. 26.

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