Abstract

Gain-switched pulses of InGaAs double-quantum-well lasers fabricated from identical epitaxial laser wafers were measured under both current injection and optical pumping conditions. The shortest output pulse widths were nearly identical (about 40 ps) both for current injection and optical pumping; this result attributed the dominant pulse-width limitation factor to the intrinsic gain properties of the lasers. We quantitatively compared the experimental results with theoretical calculations based on rate equations incorporating gain nonlinearities. Close consistency between the experimental data and the calculations was obtained only when we assumed a dynamically suppressed gain value deviated from the steady-state gain value supported by standard microscopic theories.

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  1. M. Ross, S. I. Green, and J. Brand, “Short-pulse optical communications experiments,” Proc. IEEE58(10), 1719–1726 (1970).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. N. Stelmakh, J. M. Lourtioz, G. Marquebielle, G. Volluet, and J. P. Hirtz, “Generation of high-energy (0.3 μJ) short pulses (<400 ps) from a gain-switched laser diode stack with subnanosecond electrical pump pulses,” IEEE J. Sel. Top. Quantum Electron.3(2), 245–249 (1997).
    [CrossRef]
  6. J. J. Zayhowski, J. Ochoa, and A. Mooradian, “Gain-switched pulsed operation of microchip lasers,” Opt. Lett.14(23), 1318–1320 (1989).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. P. Huai, H. Akiyama, Y. Tomio, and T. Ogawa, “Coulomb enhancement and suppression of peak gain in quantum wire lasers,” Jpn. J. Appl. Phys.46(44), L1071–L1073 (2007).
    [CrossRef]
  11. J. Huang and L. W. Casperson, “Gain and saturation in semiconductor lasers,” Opt. Quantum Electron.25(6), 369–390 (1993).
  12. S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys.51, 098001–098002 (2012).
    [CrossRef]
  13. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 5th edition (World Scientific Pub Co Inc., 2009).
  14. M. Asada, Y. Miyamoto, and Y. Suematsu, “Gain and the threshold of three-dimensional quantum-box lasers,” IEEE J. Quantum Electron.22(9), 1915–1921 (1986).
    [CrossRef]
  15. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer, 1999).
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  17. N. K. Dutta, “Temperature dependence of threshold current of GaAs quantum well lasers,” Electron. Lett.18(11), 451–453 (1982).
    [CrossRef]
  18. R. Frankenberger and R. Schimpe, “Origin of nonlinear gain saturation in index-guided InGaAsP laser diodes,” Appl. Phys. Lett.60(22), 2720–2722 (1992).
    [CrossRef]
  19. K. L. Hall, J. Mark, E. P Ippen, and G Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett.56, 1740–1742 (1990).
  20. M. Grupen and K. Hess, “Severe gain suppression due to dynamic carrier heating in quantum well lasers,” Appl. Phys. Lett.70(7), 808–810 (1997).
    [CrossRef]

2012 (1)

S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys.51, 098001–098002 (2012).
[CrossRef]

2011 (1)

M. Okano, P. Huai, M. Yoshita, S. Inada, H. Akiyama, K. Kamide, K. Asano, and T. Ogawa, “Robust carrier-induced suppression of peak gain inherent to quantum-wire lasers,” J. Phys. Soc. Jpn.80(11), 114716 (2011).
[CrossRef]

2010 (1)

2007 (1)

P. Huai, H. Akiyama, Y. Tomio, and T. Ogawa, “Coulomb enhancement and suppression of peak gain in quantum wire lasers,” Jpn. J. Appl. Phys.46(44), L1071–L1073 (2007).
[CrossRef]

2006 (1)

1997 (2)

M. Grupen and K. Hess, “Severe gain suppression due to dynamic carrier heating in quantum well lasers,” Appl. Phys. Lett.70(7), 808–810 (1997).
[CrossRef]

N. Stelmakh, J. M. Lourtioz, G. Marquebielle, G. Volluet, and J. P. Hirtz, “Generation of high-energy (0.3 μJ) short pulses (<400 ps) from a gain-switched laser diode stack with subnanosecond electrical pump pulses,” IEEE J. Sel. Top. Quantum Electron.3(2), 245–249 (1997).
[CrossRef]

1993 (1)

J. Huang and L. W. Casperson, “Gain and saturation in semiconductor lasers,” Opt. Quantum Electron.25(6), 369–390 (1993).

1992 (1)

R. Frankenberger and R. Schimpe, “Origin of nonlinear gain saturation in index-guided InGaAsP laser diodes,” Appl. Phys. Lett.60(22), 2720–2722 (1992).
[CrossRef]

1990 (1)

K. L. Hall, J. Mark, E. P Ippen, and G Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett.56, 1740–1742 (1990).

1989 (1)

1986 (2)

M. Asada, Y. Miyamoto, and Y. Suematsu, “Gain and the threshold of three-dimensional quantum-box lasers,” IEEE J. Quantum Electron.22(9), 1915–1921 (1986).
[CrossRef]

Y. Arakawa and A. Yariv, “Quantum well lasers–Gain, spectra, dynamics,” IEEE J. Quantum Electron.22(9), 1887–1899 (1986).
[CrossRef]

1982 (1)

N. K. Dutta, “Temperature dependence of threshold current of GaAs quantum well lasers,” Electron. Lett.18(11), 451–453 (1982).
[CrossRef]

1981 (1)

J. Auyeung, “Picosecond optical pulse generation at gigahertz rates by direct modulation of a semiconductor laser,” Appl. Phys. Lett.38(5), 308–310 (1981).
[CrossRef]

1979 (1)

D. J. Channin, “Effect of gain saturation on injection laser switching,” J. Appl. Phys.50(6), 3858–3860 (1979).
[CrossRef]

1970 (1)

M. Ross, S. I. Green, and J. Brand, “Short-pulse optical communications experiments,” Proc. IEEE58(10), 1719–1726 (1970).
[CrossRef]

Akiyama, H.

S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys.51, 098001–098002 (2012).
[CrossRef]

M. Okano, P. Huai, M. Yoshita, S. Inada, H. Akiyama, K. Kamide, K. Asano, and T. Ogawa, “Robust carrier-induced suppression of peak gain inherent to quantum-wire lasers,” J. Phys. Soc. Jpn.80(11), 114716 (2011).
[CrossRef]

P. Huai, H. Akiyama, Y. Tomio, and T. Ogawa, “Coulomb enhancement and suppression of peak gain in quantum wire lasers,” Jpn. J. Appl. Phys.46(44), L1071–L1073 (2007).
[CrossRef]

Arakawa, Y.

Y. Arakawa and A. Yariv, “Quantum well lasers–Gain, spectra, dynamics,” IEEE J. Quantum Electron.22(9), 1887–1899 (1986).
[CrossRef]

Asada, M.

M. Asada, Y. Miyamoto, and Y. Suematsu, “Gain and the threshold of three-dimensional quantum-box lasers,” IEEE J. Quantum Electron.22(9), 1915–1921 (1986).
[CrossRef]

Asano, K.

M. Okano, P. Huai, M. Yoshita, S. Inada, H. Akiyama, K. Kamide, K. Asano, and T. Ogawa, “Robust carrier-induced suppression of peak gain inherent to quantum-wire lasers,” J. Phys. Soc. Jpn.80(11), 114716 (2011).
[CrossRef]

Auyeung, J.

J. Auyeung, “Picosecond optical pulse generation at gigahertz rates by direct modulation of a semiconductor laser,” Appl. Phys. Lett.38(5), 308–310 (1981).
[CrossRef]

Brand, J.

M. Ross, S. I. Green, and J. Brand, “Short-pulse optical communications experiments,” Proc. IEEE58(10), 1719–1726 (1970).
[CrossRef]

Casperson, L. W.

J. Huang and L. W. Casperson, “Gain and saturation in semiconductor lasers,” Opt. Quantum Electron.25(6), 369–390 (1993).

Channin, D. J.

D. J. Channin, “Effect of gain saturation on injection laser switching,” J. Appl. Phys.50(6), 3858–3860 (1979).
[CrossRef]

Chen, S. Q.

S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys.51, 098001–098002 (2012).
[CrossRef]

Dutta, N. K.

N. K. Dutta, “Temperature dependence of threshold current of GaAs quantum well lasers,” Electron. Lett.18(11), 451–453 (1982).
[CrossRef]

Eisenstein, G

K. L. Hall, J. Mark, E. P Ippen, and G Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett.56, 1740–1742 (1990).

Frankenberger, R.

R. Frankenberger and R. Schimpe, “Origin of nonlinear gain saturation in index-guided InGaAsP laser diodes,” Appl. Phys. Lett.60(22), 2720–2722 (1992).
[CrossRef]

Green, S. I.

M. Ross, S. I. Green, and J. Brand, “Short-pulse optical communications experiments,” Proc. IEEE58(10), 1719–1726 (1970).
[CrossRef]

Grupen, M.

M. Grupen and K. Hess, “Severe gain suppression due to dynamic carrier heating in quantum well lasers,” Appl. Phys. Lett.70(7), 808–810 (1997).
[CrossRef]

Guo, H.

Hall, K. L.

K. L. Hall, J. Mark, E. P Ippen, and G Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett.56, 1740–1742 (1990).

Hess, K.

M. Grupen and K. Hess, “Severe gain suppression due to dynamic carrier heating in quantum well lasers,” Appl. Phys. Lett.70(7), 808–810 (1997).
[CrossRef]

Hirtz, J. P.

N. Stelmakh, J. M. Lourtioz, G. Marquebielle, G. Volluet, and J. P. Hirtz, “Generation of high-energy (0.3 μJ) short pulses (<400 ps) from a gain-switched laser diode stack with subnanosecond electrical pump pulses,” IEEE J. Sel. Top. Quantum Electron.3(2), 245–249 (1997).
[CrossRef]

Huai, P.

M. Okano, P. Huai, M. Yoshita, S. Inada, H. Akiyama, K. Kamide, K. Asano, and T. Ogawa, “Robust carrier-induced suppression of peak gain inherent to quantum-wire lasers,” J. Phys. Soc. Jpn.80(11), 114716 (2011).
[CrossRef]

P. Huai, H. Akiyama, Y. Tomio, and T. Ogawa, “Coulomb enhancement and suppression of peak gain in quantum wire lasers,” Jpn. J. Appl. Phys.46(44), L1071–L1073 (2007).
[CrossRef]

Huang, J.

J. Huang and L. W. Casperson, “Gain and saturation in semiconductor lasers,” Opt. Quantum Electron.25(6), 369–390 (1993).

Inada, S.

M. Okano, P. Huai, M. Yoshita, S. Inada, H. Akiyama, K. Kamide, K. Asano, and T. Ogawa, “Robust carrier-induced suppression of peak gain inherent to quantum-wire lasers,” J. Phys. Soc. Jpn.80(11), 114716 (2011).
[CrossRef]

Ippen, E. P

K. L. Hall, J. Mark, E. P Ippen, and G Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett.56, 1740–1742 (1990).

Ito, H.

Ito, T.

S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys.51, 098001–098002 (2012).
[CrossRef]

Kamide, K.

S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys.51, 098001–098002 (2012).
[CrossRef]

M. Okano, P. Huai, M. Yoshita, S. Inada, H. Akiyama, K. Kamide, K. Asano, and T. Ogawa, “Robust carrier-induced suppression of peak gain inherent to quantum-wire lasers,” J. Phys. Soc. Jpn.80(11), 114716 (2011).
[CrossRef]

Kono, S.

Lourtioz, J. M.

N. Stelmakh, J. M. Lourtioz, G. Marquebielle, G. Volluet, and J. P. Hirtz, “Generation of high-energy (0.3 μJ) short pulses (<400 ps) from a gain-switched laser diode stack with subnanosecond electrical pump pulses,” IEEE J. Sel. Top. Quantum Electron.3(2), 245–249 (1997).
[CrossRef]

Mark, J.

K. L. Hall, J. Mark, E. P Ippen, and G Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett.56, 1740–1742 (1990).

Marquebielle, G.

N. Stelmakh, J. M. Lourtioz, G. Marquebielle, G. Volluet, and J. P. Hirtz, “Generation of high-energy (0.3 μJ) short pulses (<400 ps) from a gain-switched laser diode stack with subnanosecond electrical pump pulses,” IEEE J. Sel. Top. Quantum Electron.3(2), 245–249 (1997).
[CrossRef]

Miyamoto, Y.

M. Asada, Y. Miyamoto, and Y. Suematsu, “Gain and the threshold of three-dimensional quantum-box lasers,” IEEE J. Quantum Electron.22(9), 1915–1921 (1986).
[CrossRef]

Mochizuki, T.

S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys.51, 098001–098002 (2012).
[CrossRef]

Mooradian, A.

Ochoa, J.

Ogawa, T.

S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys.51, 098001–098002 (2012).
[CrossRef]

M. Okano, P. Huai, M. Yoshita, S. Inada, H. Akiyama, K. Kamide, K. Asano, and T. Ogawa, “Robust carrier-induced suppression of peak gain inherent to quantum-wire lasers,” J. Phys. Soc. Jpn.80(11), 114716 (2011).
[CrossRef]

P. Huai, H. Akiyama, Y. Tomio, and T. Ogawa, “Coulomb enhancement and suppression of peak gain in quantum wire lasers,” Jpn. J. Appl. Phys.46(44), L1071–L1073 (2007).
[CrossRef]

Okano, M.

M. Okano, P. Huai, M. Yoshita, S. Inada, H. Akiyama, K. Kamide, K. Asano, and T. Ogawa, “Robust carrier-induced suppression of peak gain inherent to quantum-wire lasers,” J. Phys. Soc. Jpn.80(11), 114716 (2011).
[CrossRef]

Ross, M.

M. Ross, S. I. Green, and J. Brand, “Short-pulse optical communications experiments,” Proc. IEEE58(10), 1719–1726 (1970).
[CrossRef]

Saito, K.

Sato, A.

Sato, K.

Schimpe, R.

R. Frankenberger and R. Schimpe, “Origin of nonlinear gain saturation in index-guided InGaAsP laser diodes,” Appl. Phys. Lett.60(22), 2720–2722 (1992).
[CrossRef]

Stelmakh, N.

N. Stelmakh, J. M. Lourtioz, G. Marquebielle, G. Volluet, and J. P. Hirtz, “Generation of high-energy (0.3 μJ) short pulses (<400 ps) from a gain-switched laser diode stack with subnanosecond electrical pump pulses,” IEEE J. Sel. Top. Quantum Electron.3(2), 245–249 (1997).
[CrossRef]

Suematsu, Y.

M. Asada, Y. Miyamoto, and Y. Suematsu, “Gain and the threshold of three-dimensional quantum-box lasers,” IEEE J. Quantum Electron.22(9), 1915–1921 (1986).
[CrossRef]

Takashima, K.

Taniguchi, H.

Tomio, Y.

P. Huai, H. Akiyama, Y. Tomio, and T. Ogawa, “Coulomb enhancement and suppression of peak gain in quantum wire lasers,” Jpn. J. Appl. Phys.46(44), L1071–L1073 (2007).
[CrossRef]

Volluet, G.

N. Stelmakh, J. M. Lourtioz, G. Marquebielle, G. Volluet, and J. P. Hirtz, “Generation of high-energy (0.3 μJ) short pulses (<400 ps) from a gain-switched laser diode stack with subnanosecond electrical pump pulses,” IEEE J. Sel. Top. Quantum Electron.3(2), 245–249 (1997).
[CrossRef]

Yariv, A.

Y. Arakawa and A. Yariv, “Quantum well lasers–Gain, spectra, dynamics,” IEEE J. Quantum Electron.22(9), 1887–1899 (1986).
[CrossRef]

Yoda, T.

Yokoyama, H.

Yoshita, M.

S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys.51, 098001–098002 (2012).
[CrossRef]

M. Okano, P. Huai, M. Yoshita, S. Inada, H. Akiyama, K. Kamide, K. Asano, and T. Ogawa, “Robust carrier-induced suppression of peak gain inherent to quantum-wire lasers,” J. Phys. Soc. Jpn.80(11), 114716 (2011).
[CrossRef]

Zayhowski, J. J.

Appl. Phys. Lett. (4)

R. Frankenberger and R. Schimpe, “Origin of nonlinear gain saturation in index-guided InGaAsP laser diodes,” Appl. Phys. Lett.60(22), 2720–2722 (1992).
[CrossRef]

K. L. Hall, J. Mark, E. P Ippen, and G Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett.56, 1740–1742 (1990).

M. Grupen and K. Hess, “Severe gain suppression due to dynamic carrier heating in quantum well lasers,” Appl. Phys. Lett.70(7), 808–810 (1997).
[CrossRef]

J. Auyeung, “Picosecond optical pulse generation at gigahertz rates by direct modulation of a semiconductor laser,” Appl. Phys. Lett.38(5), 308–310 (1981).
[CrossRef]

Electron. Lett. (1)

N. K. Dutta, “Temperature dependence of threshold current of GaAs quantum well lasers,” Electron. Lett.18(11), 451–453 (1982).
[CrossRef]

IEEE J. Quantum Electron. (2)

Y. Arakawa and A. Yariv, “Quantum well lasers–Gain, spectra, dynamics,” IEEE J. Quantum Electron.22(9), 1887–1899 (1986).
[CrossRef]

M. Asada, Y. Miyamoto, and Y. Suematsu, “Gain and the threshold of three-dimensional quantum-box lasers,” IEEE J. Quantum Electron.22(9), 1915–1921 (1986).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

N. Stelmakh, J. M. Lourtioz, G. Marquebielle, G. Volluet, and J. P. Hirtz, “Generation of high-energy (0.3 μJ) short pulses (<400 ps) from a gain-switched laser diode stack with subnanosecond electrical pump pulses,” IEEE J. Sel. Top. Quantum Electron.3(2), 245–249 (1997).
[CrossRef]

J. Appl. Phys. (1)

D. J. Channin, “Effect of gain saturation on injection laser switching,” J. Appl. Phys.50(6), 3858–3860 (1979).
[CrossRef]

J. Phys. Soc. Jpn. (1)

M. Okano, P. Huai, M. Yoshita, S. Inada, H. Akiyama, K. Kamide, K. Asano, and T. Ogawa, “Robust carrier-induced suppression of peak gain inherent to quantum-wire lasers,” J. Phys. Soc. Jpn.80(11), 114716 (2011).
[CrossRef]

Jpn. J. Appl. Phys. (2)

P. Huai, H. Akiyama, Y. Tomio, and T. Ogawa, “Coulomb enhancement and suppression of peak gain in quantum wire lasers,” Jpn. J. Appl. Phys.46(44), L1071–L1073 (2007).
[CrossRef]

S. Q. Chen, M. Yoshita, T. Ito, T. Mochizuki, H. Akiyama, H. Yokoyama, K. Kamide, and T. Ogawa, “Analysis of gain-switching characteristics including strong gain saturation effects in low-dimensional semiconductor lasers,” Jpn. J. Appl. Phys.51, 098001–098002 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

J. Huang and L. W. Casperson, “Gain and saturation in semiconductor lasers,” Opt. Quantum Electron.25(6), 369–390 (1993).

Proc. IEEE (1)

M. Ross, S. I. Green, and J. Brand, “Short-pulse optical communications experiments,” Proc. IEEE58(10), 1719–1726 (1970).
[CrossRef]

Other (3)

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 5th edition (World Scientific Pub Co Inc., 2009).

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer, 1999).

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley-Interscience, 1995).

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Figures (4)

Fig. 1
Fig. 1

Schematic of (a) the structure of InGaAs double-QW lasers, and those of the experimental setups for (b) optical pumping and (c) current injection.

Fig. 2
Fig. 2

(a) Lasing spectra (left panel) and the corresponding waveforms (right panel) of the output pulses from the pulse-current-injected InGaAs double-QW laser with different bias current values. (b) Pulse-lasing spectra (left panel) and the corresponding waveforms (right panel) of the output pulses from the optically pumped InGaAs double-QW laser at room temperature for various values of the average pumping power.

Fig. 3
Fig. 3

Pulse characteristics of gain-switched InGaAs double-QW laser via optical pumping. (a) Experimental data for pulse width (circles), rise time (triangles), and relative delay time (squares). Quantitative simulation results are shown by dashed curves. For convenience in comparison of the experimentally obtained relative delay time and the simulated absolute delay time, an offset of 118 ps was set relative to the experimentally obtained relative delay time. (b) Experimental (solid) and simulation (dashed) curves of input vs. output average powers.

Fig. 4
Fig. 4

(a) Comparisons of carrier-density-dependent material gain calculated by the standard microscopic calculations, linear gain g = g0 × (n2D – n02D) and Eq. (3). A good agreement between the calculation and Eq. (3) was achieved when gs = 3700 cm−1 was used. (b) Simulation result of the dependence of pulse width on the saturation gain gs.

Equations (3)

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

d n 2D dt =η P(t) hνmwL Γ m v g g 1+ε s 2D s 2D n 2D τ r .
d s 2D dt =Γ v g g 1+ε s 2D s 2D s 2D τ p +mβ n 2D τ r .
g= g 0 ( n 2D n 0 2D )/[1+ g 0 ( n 2D n 0 2D ) g s ].

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