Abstract

In this paper, we analyze the dynamic characteristics of quantum dot (QD) photonic crystal lasers by solving Maxwell equations coupled to rate equations through linear susceptibility of QDs. Here, we study the effects of the quality factor of the microcavity and temperature on the delay, relaxation oscillation frequency, and output intensity of the lasers. Moreover, we investigate the dependence of the Purcell factor on temperature. We show that when the quality factor of the microcavity is so high that we can consider its linewidth as a delta function in comparison with QDs, the Purcell factor significantly drops with increasing temperature.

© 2014 Optical Society of America

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  1. T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Top. Quantum Electron. 3, 808–830 (1997).
    [CrossRef]
  2. D. Englund, H. Altug, B. Ellis, and J. Vuckovic, “Ultrafast photonic crystal lasers,” Laser Photon. Rev. 2, 264–274 (2008).
  3. T. Baba and D. Sano, “Low threshold lasing and Purcell effect in microdisk lasers at room temperature,” IEEE J. Sel. Top. Quantum Electron. 9, 1340–1346 (2003).
    [CrossRef]
  4. T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron. 27, 1347–1358 (1991).
    [CrossRef]
  5. Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [CrossRef]
  6. S. Noda, “Recent progresses and future prospects of two- and three-dimensional photonic crystals,” J. Lightwave Technol. 24, 4554–4567 (2006).
    [CrossRef]
  7. S. Noda, “Seeking the ultimate nanolaser,” Science 314, 260–261 (2006).
    [CrossRef]
  8. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
    [CrossRef]
  9. J. J. Coleman, J. D. Young, and A. Garg, “Semiconductor quantum dot lasers: a tutorial,” J. Lightwave Technol. 29, 499–510 (2011).
    [CrossRef]
  10. T. Yang, S. Lipson, J. D. O’Brien, and D. G. Deppe, “InAs quantum dot photonic crystal lasers and their temperature dependence,” IEEE Photon. Technol. Lett. 11, 2244–2246 (2005).
  11. M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express 14, 6308–6315 (2006).
    [CrossRef]
  12. B. Ellis, I. Fushman, D. Englund, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Dynamics of QD photonic crystal lasers,” Appl. Phys. Lett. 90, 151102 (2007).
  13. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  14. A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
    [CrossRef]
  15. S.-H. Chang and A. Taflove, “Finite-difference time-domain model of lasing action in a four-level two-electron atomic system,” Opt. Express 12, 3827–3833 (2004).
    [CrossRef]
  16. W. H. P. Pernice, F. P. Payne, and D. F. G. Gallagher, “A finite-difference time-domain method for the simulation of gain materials with carrier diffusion in photonic crystals,” J. Lightwave Technol. 25, 2306–2314 (2007).
    [CrossRef]
  17. Y. Zhang, W. Zheng, Q. Aiyi, H. Qu, H. Peng, S. Xie, and L. Chen, “Design of photonic crystal semiconductor optical amplifier with polarization independence,” J. Lightwave Technol. 22, 3207–3211 (2010).
  18. J. Schuster and R. Luebbers, “An accurate FDTD algorithm for dispersive media using a piecewise constant recursive convolution technique,” in IEEE Antennas And Propagation Society International Symposium (IEEE, 1998), pp. 2018–2021.
  19. M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004).
  20. M. Sugawara, K. Mukai, Y. Nakata, H. Ishikawa, and A. Sakamoto, “Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled InxGa1−xAs/GaAs quantum dot lasers,” Phys. Rev. B 61, 7595–7603 (2000).
  21. A. E. Siegman, Lasers (University Science, 1986).
  22. S. L. Chua, Y. Chong, A. D. Stone, M. Soljacic, and J. Bravo-Abad, “Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances,” Opt. Express 19, 1539–1562 (2011).
    [CrossRef]
  23. A. Meldrum, P. Bianucci, and F. Marsiglio, “Modification of ensemble emission rates and luminescence spectra for inhomogeneously broadened distributions of quantum dots coupled to optical microcavities,” Opt. Express 18, 10230–10239 (2010).
    [CrossRef]
  24. M. Sugawara, Self-Assembled InGaAs/GaAs Quantum Dots, M. Sugawara, ed., Vol. 60 of Semiconductors and Semimetals (Academic, 1999).
  25. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).
  26. H. Abbaspour, V. Ahmadi, and M. H. Yavari, “Analysis of QD VCSEL dynamic characteristics considering homogeneous and inhomogeneous broadening,” IEEE J. Sel. Top. Quantum Electron. 17, 1327–1333 (2011).
    [CrossRef]
  27. D. A. Neamen, Semiconductor Physics and Devices (McGraw-Hill, 2002).
  28. N. Tansu and L. J. Mawst, “Current injection efficiency of InGaAsN quantum-well lasers,” J. Appl. Phys. 97, 054502 (2005).
    [CrossRef]
  29. S. Shi and D. W. Prather, “Lasing dynamics of a silicon photonic crystal microcavity,” Opt. Express 15, 10294–10302 (2007).
    [CrossRef]
  30. G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
    [CrossRef]
  31. M. H. Yavari and V. Ahmadi, “Effects of carrier relaxation and homogeneous broadening on dynamic and modulation behavior of self-assembled quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 17, 1153–1157 (2011).
    [CrossRef]

2011 (4)

J. J. Coleman, J. D. Young, and A. Garg, “Semiconductor quantum dot lasers: a tutorial,” J. Lightwave Technol. 29, 499–510 (2011).
[CrossRef]

S. L. Chua, Y. Chong, A. D. Stone, M. Soljacic, and J. Bravo-Abad, “Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances,” Opt. Express 19, 1539–1562 (2011).
[CrossRef]

H. Abbaspour, V. Ahmadi, and M. H. Yavari, “Analysis of QD VCSEL dynamic characteristics considering homogeneous and inhomogeneous broadening,” IEEE J. Sel. Top. Quantum Electron. 17, 1327–1333 (2011).
[CrossRef]

M. H. Yavari and V. Ahmadi, “Effects of carrier relaxation and homogeneous broadening on dynamic and modulation behavior of self-assembled quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 17, 1153–1157 (2011).
[CrossRef]

2010 (2)

A. Meldrum, P. Bianucci, and F. Marsiglio, “Modification of ensemble emission rates and luminescence spectra for inhomogeneously broadened distributions of quantum dots coupled to optical microcavities,” Opt. Express 18, 10230–10239 (2010).
[CrossRef]

Y. Zhang, W. Zheng, Q. Aiyi, H. Qu, H. Peng, S. Xie, and L. Chen, “Design of photonic crystal semiconductor optical amplifier with polarization independence,” J. Lightwave Technol. 22, 3207–3211 (2010).

2008 (1)

D. Englund, H. Altug, B. Ellis, and J. Vuckovic, “Ultrafast photonic crystal lasers,” Laser Photon. Rev. 2, 264–274 (2008).

2007 (3)

2006 (3)

2005 (2)

T. Yang, S. Lipson, J. D. O’Brien, and D. G. Deppe, “InAs quantum dot photonic crystal lasers and their temperature dependence,” IEEE Photon. Technol. Lett. 11, 2244–2246 (2005).

N. Tansu and L. J. Mawst, “Current injection efficiency of InGaAsN quantum-well lasers,” J. Appl. Phys. 97, 054502 (2005).
[CrossRef]

2004 (2)

S.-H. Chang and A. Taflove, “Finite-difference time-domain model of lasing action in a four-level two-electron atomic system,” Opt. Express 12, 3827–3833 (2004).
[CrossRef]

M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004).

2003 (2)

T. Baba and D. Sano, “Low threshold lasing and Purcell effect in microdisk lasers at room temperature,” IEEE J. Sel. Top. Quantum Electron. 9, 1340–1346 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef]

2000 (1)

M. Sugawara, K. Mukai, Y. Nakata, H. Ishikawa, and A. Sakamoto, “Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled InxGa1−xAs/GaAs quantum dot lasers,” Phys. Rev. B 61, 7595–7603 (2000).

1998 (1)

A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[CrossRef]

1997 (1)

T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Top. Quantum Electron. 3, 808–830 (1997).
[CrossRef]

1994 (1)

G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[CrossRef]

1991 (1)

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron. 27, 1347–1358 (1991).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
[CrossRef]

Abbaspour, H.

H. Abbaspour, V. Ahmadi, and M. H. Yavari, “Analysis of QD VCSEL dynamic characteristics considering homogeneous and inhomogeneous broadening,” IEEE J. Sel. Top. Quantum Electron. 17, 1327–1333 (2011).
[CrossRef]

Ahmadi, V.

H. Abbaspour, V. Ahmadi, and M. H. Yavari, “Analysis of QD VCSEL dynamic characteristics considering homogeneous and inhomogeneous broadening,” IEEE J. Sel. Top. Quantum Electron. 17, 1327–1333 (2011).
[CrossRef]

M. H. Yavari and V. Ahmadi, “Effects of carrier relaxation and homogeneous broadening on dynamic and modulation behavior of self-assembled quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 17, 1153–1157 (2011).
[CrossRef]

Aiyi, Q.

Y. Zhang, W. Zheng, Q. Aiyi, H. Qu, H. Peng, S. Xie, and L. Chen, “Design of photonic crystal semiconductor optical amplifier with polarization independence,” J. Lightwave Technol. 22, 3207–3211 (2010).

Akahane, Y.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef]

Akiyama, T.

M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004).

Altug, H.

D. Englund, H. Altug, B. Ellis, and J. Vuckovic, “Ultrafast photonic crystal lasers,” Laser Photon. Rev. 2, 264–274 (2008).

Arakawa, Y.

M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express 14, 6308–6315 (2006).
[CrossRef]

M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004).

Asano, T.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef]

Baba, T.

T. Baba and D. Sano, “Low threshold lasing and Purcell effect in microdisk lasers at room temperature,” IEEE J. Sel. Top. Quantum Electron. 9, 1340–1346 (2003).
[CrossRef]

T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Top. Quantum Electron. 3, 808–830 (1997).
[CrossRef]

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron. 27, 1347–1358 (1991).
[CrossRef]

Bianucci, P.

Bjork, G.

G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[CrossRef]

Bravo-Abad, J.

Chang, S.-H.

Chen, L.

Y. Zhang, W. Zheng, Q. Aiyi, H. Qu, H. Peng, S. Xie, and L. Chen, “Design of photonic crystal semiconductor optical amplifier with polarization independence,” J. Lightwave Technol. 22, 3207–3211 (2010).

Chong, Y.

Chua, S. L.

Coldren, L. A.

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

Coleman, J. J.

Corzine, S. W.

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

Deppe, D. G.

T. Yang, S. Lipson, J. D. O’Brien, and D. G. Deppe, “InAs quantum dot photonic crystal lasers and their temperature dependence,” IEEE Photon. Technol. Lett. 11, 2244–2246 (2005).

Ebe, H.

M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004).

Ellis, B.

D. Englund, H. Altug, B. Ellis, and J. Vuckovic, “Ultrafast photonic crystal lasers,” Laser Photon. Rev. 2, 264–274 (2008).

B. Ellis, I. Fushman, D. Englund, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Dynamics of QD photonic crystal lasers,” Appl. Phys. Lett. 90, 151102 (2007).

Englund, D.

D. Englund, H. Altug, B. Ellis, and J. Vuckovic, “Ultrafast photonic crystal lasers,” Laser Photon. Rev. 2, 264–274 (2008).

B. Ellis, I. Fushman, D. Englund, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Dynamics of QD photonic crystal lasers,” Appl. Phys. Lett. 90, 151102 (2007).

Fushman, I.

B. Ellis, I. Fushman, D. Englund, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Dynamics of QD photonic crystal lasers,” Appl. Phys. Lett. 90, 151102 (2007).

Gallagher, D. F. G.

Garg, A.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Hamano, T.

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron. 27, 1347–1358 (1991).
[CrossRef]

Hatori, N.

M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004).

Iga, K.

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron. 27, 1347–1358 (1991).
[CrossRef]

Ishida, M.

M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004).

Ishida, S.

Ishikawa, H.

M. Sugawara, K. Mukai, Y. Nakata, H. Ishikawa, and A. Sakamoto, “Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled InxGa1−xAs/GaAs quantum dot lasers,” Phys. Rev. B 61, 7595–7603 (2000).

Iwamoto, S.

Karlsson, A.

G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[CrossRef]

Koyama, F.

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron. 27, 1347–1358 (1991).
[CrossRef]

Kumagai, N.

Lipson, S.

T. Yang, S. Lipson, J. D. O’Brien, and D. G. Deppe, “InAs quantum dot photonic crystal lasers and their temperature dependence,” IEEE Photon. Technol. Lett. 11, 2244–2246 (2005).

Luebbers, R.

J. Schuster and R. Luebbers, “An accurate FDTD algorithm for dispersive media using a piecewise constant recursive convolution technique,” in IEEE Antennas And Propagation Society International Symposium (IEEE, 1998), pp. 2018–2021.

Marsiglio, F.

Mawst, L. J.

N. Tansu and L. J. Mawst, “Current injection efficiency of InGaAsN quantum-well lasers,” J. Appl. Phys. 97, 054502 (2005).
[CrossRef]

Meldrum, A.

Mukai, K.

M. Sugawara, K. Mukai, Y. Nakata, H. Ishikawa, and A. Sakamoto, “Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled InxGa1−xAs/GaAs quantum dot lasers,” Phys. Rev. B 61, 7595–7603 (2000).

Nagra, A. S.

A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[CrossRef]

Nakata, Y.

M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express 14, 6308–6315 (2006).
[CrossRef]

M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004).

M. Sugawara, K. Mukai, Y. Nakata, H. Ishikawa, and A. Sakamoto, “Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled InxGa1−xAs/GaAs quantum dot lasers,” Phys. Rev. B 61, 7595–7603 (2000).

Neamen, D. A.

D. A. Neamen, Semiconductor Physics and Devices (McGraw-Hill, 2002).

Noda, S.

S. Noda, “Seeking the ultimate nanolaser,” Science 314, 260–261 (2006).
[CrossRef]

S. Noda, “Recent progresses and future prospects of two- and three-dimensional photonic crystals,” J. Lightwave Technol. 24, 4554–4567 (2006).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef]

Nomura, M.

O’Brien, J. D.

T. Yang, S. Lipson, J. D. O’Brien, and D. G. Deppe, “InAs quantum dot photonic crystal lasers and their temperature dependence,” IEEE Photon. Technol. Lett. 11, 2244–2246 (2005).

Otsubo, K.

M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004).

Payne, F. P.

Peng, H.

Y. Zhang, W. Zheng, Q. Aiyi, H. Qu, H. Peng, S. Xie, and L. Chen, “Design of photonic crystal semiconductor optical amplifier with polarization independence,” J. Lightwave Technol. 22, 3207–3211 (2010).

Pernice, W. H. P.

Prather, D. W.

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
[CrossRef]

Qu, H.

Y. Zhang, W. Zheng, Q. Aiyi, H. Qu, H. Peng, S. Xie, and L. Chen, “Design of photonic crystal semiconductor optical amplifier with polarization independence,” J. Lightwave Technol. 22, 3207–3211 (2010).

Sakamoto, A.

M. Sugawara, K. Mukai, Y. Nakata, H. Ishikawa, and A. Sakamoto, “Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled InxGa1−xAs/GaAs quantum dot lasers,” Phys. Rev. B 61, 7595–7603 (2000).

Sano, D.

T. Baba and D. Sano, “Low threshold lasing and Purcell effect in microdisk lasers at room temperature,” IEEE J. Sel. Top. Quantum Electron. 9, 1340–1346 (2003).
[CrossRef]

Schuster, J.

J. Schuster and R. Luebbers, “An accurate FDTD algorithm for dispersive media using a piecewise constant recursive convolution technique,” in IEEE Antennas And Propagation Society International Symposium (IEEE, 1998), pp. 2018–2021.

Shi, S.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Soljacic, M.

Song, B.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef]

Stone, A. D.

Sugawara, M.

M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004).

M. Sugawara, K. Mukai, Y. Nakata, H. Ishikawa, and A. Sakamoto, “Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled InxGa1−xAs/GaAs quantum dot lasers,” Phys. Rev. B 61, 7595–7603 (2000).

M. Sugawara, Self-Assembled InGaAs/GaAs Quantum Dots, M. Sugawara, ed., Vol. 60 of Semiconductors and Semimetals (Academic, 1999).

Taflove, A.

S.-H. Chang and A. Taflove, “Finite-difference time-domain model of lasing action in a four-level two-electron atomic system,” Opt. Express 12, 3827–3833 (2004).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Tansu, N.

N. Tansu and L. J. Mawst, “Current injection efficiency of InGaAsN quantum-well lasers,” J. Appl. Phys. 97, 054502 (2005).
[CrossRef]

Vuckovic, J.

D. Englund, H. Altug, B. Ellis, and J. Vuckovic, “Ultrafast photonic crystal lasers,” Laser Photon. Rev. 2, 264–274 (2008).

B. Ellis, I. Fushman, D. Englund, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Dynamics of QD photonic crystal lasers,” Appl. Phys. Lett. 90, 151102 (2007).

Watanabe, K.

Xie, S.

Y. Zhang, W. Zheng, Q. Aiyi, H. Qu, H. Peng, S. Xie, and L. Chen, “Design of photonic crystal semiconductor optical amplifier with polarization independence,” J. Lightwave Technol. 22, 3207–3211 (2010).

Yamamoto, Y.

B. Ellis, I. Fushman, D. Englund, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Dynamics of QD photonic crystal lasers,” Appl. Phys. Lett. 90, 151102 (2007).

G. Bjork, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[CrossRef]

Yang, T.

T. Yang, S. Lipson, J. D. O’Brien, and D. G. Deppe, “InAs quantum dot photonic crystal lasers and their temperature dependence,” IEEE Photon. Technol. Lett. 11, 2244–2246 (2005).

Yavari, M. H.

M. H. Yavari and V. Ahmadi, “Effects of carrier relaxation and homogeneous broadening on dynamic and modulation behavior of self-assembled quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 17, 1153–1157 (2011).
[CrossRef]

H. Abbaspour, V. Ahmadi, and M. H. Yavari, “Analysis of QD VCSEL dynamic characteristics considering homogeneous and inhomogeneous broadening,” IEEE J. Sel. Top. Quantum Electron. 17, 1327–1333 (2011).
[CrossRef]

York, R. A.

A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[CrossRef]

Young, J. D.

Zhang, B.

B. Ellis, I. Fushman, D. Englund, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Dynamics of QD photonic crystal lasers,” Appl. Phys. Lett. 90, 151102 (2007).

Zhang, Y.

Y. Zhang, W. Zheng, Q. Aiyi, H. Qu, H. Peng, S. Xie, and L. Chen, “Design of photonic crystal semiconductor optical amplifier with polarization independence,” J. Lightwave Technol. 22, 3207–3211 (2010).

Zheng, W.

Y. Zhang, W. Zheng, Q. Aiyi, H. Qu, H. Peng, S. Xie, and L. Chen, “Design of photonic crystal semiconductor optical amplifier with polarization independence,” J. Lightwave Technol. 22, 3207–3211 (2010).

Appl. Phys. Lett. (1)

B. Ellis, I. Fushman, D. Englund, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Dynamics of QD photonic crystal lasers,” Appl. Phys. Lett. 90, 151102 (2007).

IEEE J. Quantum Electron. (1)

T. Baba, T. Hamano, F. Koyama, and K. Iga, “Spontaneous emission factor of microcavity DBR surface-emitting laser,” IEEE J. Quantum Electron. 27, 1347–1358 (1991).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (4)

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Figures (7)

Fig. 1.
Fig. 1.

Schematic structure of PC QD laser with L3 microcavity. As shown by white arrows, the first air holes at both ends of the microcavity are shifted outward by 0.15a.

Fig. 2.
Fig. 2.

Four-level atomic system used for modeling transition of carriers in QDs. Levels 0 and 3 correspond to the valence band and conduction band of the GaAs wetting layer, and levels 1 and 2 correspond to ground states of the valence band and conduction band of InAs QDs.

Fig. 3.
Fig. 3.

Flowchart of the ADE-FDTD simulation.

Fig. 4.
Fig. 4.

Electric field distribution across the microcavity, calculated through ADE-FDTD.

Fig. 5.
Fig. 5.

Effect of temperature reduction (80 K) and reducing PC microcavity quality factor on (a) delay time, (b) population inversion, and (c) output intensity.

Fig. 6.
Fig. 6.

Carrier density of level 3 (N3) across the microcavity: (a) ignoring diffusion and (b) with diffusion of carriers.

Fig. 7.
Fig. 7.

(a) FWHM of HB of QDs, 2Γcv, (b) quality factor of QDs, and (c) Purcell factor for different temperatures.

Tables (1)

Tables Icon

Table 1. Parameters Used in the Simulation

Equations (29)

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Pm(1)(r,t)=ε0χσ(1)(r,t,ωm)Em,
χσ(1)(r,t,ωm)=c,v,k,sχσ(1)(t,ωm;cvks)δ(rrs)
χσ(1)(t,ωm;cvks)=2e2|Pcv,kσ|2ND(ρcc,k(0)(t;s)ρvv,k(0)(t;s))ε0m02ωmωcv,ks×[1ωmωcv,ksiΓcv,ks+1ωm+ωcv,ksiΓcv,ks],
|Pcv,kσ|2=m0212mn*Eg(E+Δ)Eg+2Δ/3.
ρcc(0)=N22ND
ρvv(0)=N12ND,
χ(1)(ω)2e2|Pcv|2(N1N2)ε0m02ωcv[1ω2+ωcv2+2iωΓcv]
P(1)(ω)=2e2|Pcv|2(N1N2)m02ωcv[1ω2+ωcv2+2iωΓcv]E.
d2P(1)dt2+2ΓcvdP(1)dt+ωcv2P(1)=2e2|Pcv|2(N1N2)m02ωcvE={2|Pcv|2m0ωcv}e2m0(N1N2)E.
d2P(1)dt2+2ΓcvdP(1)dt+ωcv2P(1)=e2m0(N1N2)E.
d2P(1)dt2+2ΓcvdP(1)dt+ωcv2P(1)={Fpurcell/τ21e2ωcv2/6πε0m0c3}×{2|Pcv|2m0ωcv}e2m0(N1N2)E.
dN3dt=WpN0N3τ32+Dxy2N3,
dN2dt=1ωcvE·dPdt+N3τ32N2Fpurcellτ21,
dN1dt=1ωcvE·dPdt+N2Fpurcellτ21N1τ10,
dN0dt=WpN0+N1τ10,
1τcav=2π20|f|H|i|2ρ(ω)Λ(ω)dω,
ρ(ω)=δ(ωωcav)
Λ(ω)=2πΔω04(ωω0)2+Δω02,
|f|H|i|2=ηω0μ22εVm,
1τfree=ω03μ23πεc3,
τfreeτcav=2π2ηω0μ22εVm3πεc3ω03μ22πΔω04(ωω0)2+Δω02.
τfreeτcav=η3(ω0/Δω0)(λ/n)34π2VmΔω024(ωω0)2+Δω02.
Bcv(ωωcv)=Γcv/π(ωωcv)2+Γcv2.
Γcv=1τc,
1τc=1τcp+1τcn,
τcp=mp*μpe
τcn=mn*μne.
μp(T)=μp300K(300KT)2.1
μn(T)=μn300K(300KT)2.1.

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