Abstract

Thresholdless lasing is an outstanding challenge in laser science and is achievable only in devices having near unity quantum efficiency even when not lasing. Such lasers are expected to exhibit featureless linear light output curves. However, such thresholdless behavior hinders identification of the laser transition, triggering a long-lasting argument on how to identify the lasing. Here, we demonstrate thresholdless lasing in a semiconductor quantum dot nanolaser with a photonic crystal nanocavity. We employ cavity resonant excitation for enabling the thresholdless operation via focused carrier injection into high cavity field regions. Under conventional (above bandgap) excitation, the same nanolaser exhibits a typical thresholded lasing transition, thereby facilitating a systematic comparison between the thresholdless and thresholded laser transitions in the single device. Our approach enables a clear verification of the thresholdless lasing and reveals core elements for its realization using quantum dots, paving the way to the development of ultimately energy-efficient nanolasers.

© 2017 Optical Society of America

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2016 (2)

2015 (1)

2014 (2)

W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light Sci. Appl. 3(8), e201 (2014).
[Crossref]

Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Measuring the second-order coherence of a nanolaser by intracavity frequency doubling,” Phys. Rev. A 89(2), 023824 (2014).
[Crossref]

2013 (2)

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

C. Z. Ning, “What is laser threshold?” IEEE J. Sel. Top. Quantum Electron. 19(4), 1503604 (2013).
[Crossref]

2012 (2)

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012).
[Crossref] [PubMed]

N. Takemura, J. Omachi, and M. Kuwata-Gonokami, “Fast periodic modulations in the photon correlation of single-mode vertical-cavity surface-emitting lasers,” Phys. Rev. A 85(5), 053811 (2012).
[Crossref]

2011 (1)

2009 (5)

U. Hohenester, A. Laucht, M. Kaniber, N. Hauke, A. Neumann, A. Mohtashami, M. Seliger, M. Bichler, and J. J. Finley, “Phonon-assisted transitions from quantum dot excitons to cavity photons,” Phys. Rev. B 80(20), 201311 (2009).
[Crossref]

J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[Crossref] [PubMed]

M. Winger, T. Volz, G. Tarel, S. Portolan, A. Badolato, K. J. Hennessy, E. L. Hu, A. Beveratos, J. Finley, V. Savona, and A. Imamoğlu, “Explanation of Photon Correlations in the Far-Off-Resonance Optical Emission from a Quantum-Dot-Cavity System,” Phys. Rev. Lett. 103(20), 207403 (2009).
[Crossref] [PubMed]

N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79(4), 041101 (2009).
[Crossref]

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Photonic crystal nanocavity laser with a single quantum dot gain,” Opt. Express 17(18), 15975–15982 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (4)

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[Crossref] [PubMed]

S. M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, and P. Michler, “Photon statistics of semiconductor microcavity lasers,” Phys. Rev. Lett. 98(4), 043906 (2007).
[Crossref] [PubMed]

Y.-S. Choi, M. T. Rakher, K. Hennessy, S. Strauf, A. Badolato, P. M. Petroff, D. Bouwmeester, and E. L. Hu, “Evolution of the onset of coherence in a family of photonic crystal nanolasers,” Appl. Phys. Lett. 91(3), 031108 (2007).
[Crossref]

Z. G. Xie, S. Götzinger, W. Fang, H. Cao, and G. S. Solomon, “Influence of a Single Quantum Dot State on the Characteristics of a Microdisk Laser,” Phys. Rev. Lett. 98(11), 117401 (2007).
[Crossref] [PubMed]

2006 (4)

S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-Tuned Quantum Dot Gain in Photonic Crystal Lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[Crossref] [PubMed]

M. Nomura, S. Iwamoto, M. Nishioka, S. Ishida, and Y. Arakawa, “Highly efficient optical pumping of photonic crystal nanocavity lasers using cavity resonant excitation,” Appl. Phys. Lett. 89(16), 161111 (2006).
[Crossref]

S. Noda, “Seeking the Ultimate Nanolaser,” Science(80-.).  314(5797), 260–261 (2006).
[Crossref] [PubMed]

S. Melnik, G. Huyet, and A. V. Uskov, “The linewidth enhancement factor α of quantum dot semiconductor lasers,” Opt. Express 14(7), 2950–2955 (2006).
[Crossref] [PubMed]

2005 (1)

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
[Crossref] [PubMed]

2003 (2)

M. Lončar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82(26), 4648–4650 (2003).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

2002 (1)

I. Wilson-Rae and A. Imamoglu, “Quantum dot cavity-QED in the presence of strong electron-phonon interactions,” Phys. Rev. B 65(23), 235311 (2002).
[Crossref]

1999 (1)

L. M. Pedrotti, M. Sokol, and P. R. Rice, “Linewidth of four-level microcavity lasers,” Phys. Rev. A 59(3), 2295–2301 (1999).
[Crossref]

1994 (3)

U. Mohideen, R. E. Slusher, F. Jahnke, and S. W. Koch, “Semiconductor Microlaser Linewidths,” Phys. Rev. Lett. 73(13), 1785–1788 (1994).
[Crossref] [PubMed]

P. R. Rice and H. J. Carmichael, “Photon statistics of a cavity-QED laser: A comment on the laser-phase-transition analogy,” Phys. Rev. A 50(5), 4318–4329 (1994).
[Crossref] [PubMed]

G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50(2), 1675–1680 (1994).
[Crossref] [PubMed]

1992 (3)

H. Yokoyama, “Physics and device applications of optical microcavities,” Science 256(5053), 66–70 (1992).
[Crossref] [PubMed]

G. Björk, A. Karlsson, and Y. Yamamoto, “On the linewidth of microcavity lasers,” Appl. Phys. Lett. 60(3), 304–306 (1992).
[Crossref]

G. Björk, A. Karlsson, and Y. Yamamoto, “On the linewidth of microcavity lasers,” Appl. Phys. Lett. 60(3), 304–306 (1992).
[Crossref]

1991 (1)

G. Bjork and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. 27(11), 2386–2396 (1991).
[Crossref]

1989 (1)

H. Yokoyama and S. D. Brorson, “Rate equation analysis of microcavity lasers,” J. Appl. Phys. 66(10), 4801–4805 (1989).
[Crossref]

1986 (1)

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

1982 (2)

C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

Y. Arakawa and H. Sakaki, “Multidimensional quantum well laser and temperature dependence of its threshold current,” Appl. Phys. Lett. 40(11), 939–941 (1982).
[Crossref]

Aboada, A. G. T.

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Akimov, I. A.

Amúñez, L. E. M. U.

Andreani, L. C.

S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-Tuned Quantum Dot Gain in Photonic Crystal Lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[Crossref] [PubMed]

Arakawa, Y.

Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Measuring the second-order coherence of a nanolaser by intracavity frequency doubling,” Phys. Rev. A 89(2), 023824 (2014).
[Crossref]

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Photonic crystal nanocavity laser with a single quantum dot gain,” Opt. Express 17(18), 15975–15982 (2009).
[Crossref] [PubMed]

Y. Ota, M. Nomura, N. Kumagai, K. Watanabe, S. Ishida, S. Iwamoto, and Y. Arakawa, “Enhanced photon emission and absorption of single quantum dot in resonance with two modes in photonic crystal nanocavity,” Appl. Phys. Lett. 93(18), 183114 (2008).
[Crossref]

M. Nomura, S. Iwamoto, M. Nishioka, S. Ishida, and Y. Arakawa, “Highly efficient optical pumping of photonic crystal nanocavity lasers using cavity resonant excitation,” Appl. Phys. Lett. 89(16), 161111 (2006).
[Crossref]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
[Crossref] [PubMed]

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

Y. Arakawa and H. Sakaki, “Multidimensional quantum well laser and temperature dependence of its threshold current,” Appl. Phys. Lett. 40(11), 939–941 (1982).
[Crossref]

Asano, T.

M. Yamaguchi, T. Asano, and S. Noda, “Photon emission by nanocavity-enhanced quantum anti-Zeno effect in solid-state cavity quantum-electrodynamics,” Opt. Express 16(22), 18067–18081 (2008).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Aßmann, M.

Assmann, M.

J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[Crossref] [PubMed]

Astor, J. P. M. A.

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[Crossref] [PubMed]

Ates, S.

S. M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, and P. Michler, “Photon statistics of semiconductor microcavity lasers,” Phys. Rev. Lett. 98(4), 043906 (2007).
[Crossref] [PubMed]

Atutano, G. M. U.

Baba, T.

Badolato, A.

M. Winger, T. Volz, G. Tarel, S. Portolan, A. Badolato, K. J. Hennessy, E. L. Hu, A. Beveratos, J. Finley, V. Savona, and A. Imamoğlu, “Explanation of Photon Correlations in the Far-Off-Resonance Optical Emission from a Quantum-Dot-Cavity System,” Phys. Rev. Lett. 103(20), 207403 (2009).
[Crossref] [PubMed]

Y.-S. Choi, M. T. Rakher, K. Hennessy, S. Strauf, A. Badolato, P. M. Petroff, D. Bouwmeester, and E. L. Hu, “Evolution of the onset of coherence in a family of photonic crystal nanolasers,” Appl. Phys. Lett. 91(3), 031108 (2007).
[Crossref]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[Crossref] [PubMed]

S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-Tuned Quantum Dot Gain in Photonic Crystal Lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[Crossref] [PubMed]

Bayer, M.

J.-S. Tempel, I. A. Akimov, M. Aßmann, C. Schneider, S. Höfling, C. Kistner, S. Reitzenstein, L. Worschech, A. Forchel, and M. Bayer, “Extrapolation of the intensity autocorrelation function of a quantum-dot micropillar laser into the thermal emission regime,” J. Opt. Soc. Am. B 28(6), 1404 (2011).
[Crossref]

J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
[Crossref] [PubMed]

Bazhenov, A.

Berstermann, T.

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W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light Sci. Appl. 3(8), e201 (2014).
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J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
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S. M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, and P. Michler, “Photon statistics of semiconductor microcavity lasers,” Phys. Rev. Lett. 98(4), 043906 (2007).
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Götzinger, S.

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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
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Hasebe, K.

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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
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S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-Tuned Quantum Dot Gain in Photonic Crystal Lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
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J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
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J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
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S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-Tuned Quantum Dot Gain in Photonic Crystal Lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
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Imamoglu, A.

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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
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W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light Sci. Appl. 3(8), e201 (2014).
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J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
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Kaniber, M.

U. Hohenester, A. Laucht, M. Kaniber, N. Hauke, A. Neumann, A. Mohtashami, M. Seliger, M. Bichler, and J. J. Finley, “Phonon-assisted transitions from quantum dot excitons to cavity photons,” Phys. Rev. B 80(20), 201311 (2009).
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G. Björk, A. Karlsson, and Y. Yamamoto, “On the linewidth of microcavity lasers,” Appl. Phys. Lett. 60(3), 304–306 (1992).
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M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012).
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M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012).
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J.-S. Tempel, I. A. Akimov, M. Aßmann, C. Schneider, S. Höfling, C. Kistner, S. Reitzenstein, L. Worschech, A. Forchel, and M. Bayer, “Extrapolation of the intensity autocorrelation function of a quantum-dot micropillar laser into the thermal emission regime,” J. Opt. Soc. Am. B 28(6), 1404 (2011).
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K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
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U. Mohideen, R. E. Slusher, F. Jahnke, and S. W. Koch, “Semiconductor Microlaser Linewidths,” Phys. Rev. Lett. 73(13), 1785–1788 (1994).
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J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009).
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Kumagai, N.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Photonic crystal nanocavity laser with a single quantum dot gain,” Opt. Express 17(18), 15975–15982 (2009).
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Kuwata-Gonokami, M.

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U. Hohenester, A. Laucht, M. Kaniber, N. Hauke, A. Neumann, A. Mohtashami, M. Seliger, M. Bichler, and J. J. Finley, “Phonon-assisted transitions from quantum dot excitons to cavity photons,” Phys. Rev. B 80(20), 201311 (2009).
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M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012).
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S. Reitzenstein, C. Böckler, A. Bazhenov, A. Gorbunov, A. Löffler, M. Kamp, V. D. Kulakovskii, and A. Forchel, “Single quantum dot controlled lasing effects in high-Q micropillar cavities,” Opt. Express 16(7), 4848–4857 (2008).
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M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012).
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Appl. Phys. Lett. (7)

M. Lončar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82(26), 4648–4650 (2003).
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Figures (7)

Fig. 1
Fig. 1

Structure of the PhC nanocavity QD lasers. (a) Schematic of the PhC nanocavity laser driven under the cavity resonant excitation. Carriers are injected only into the defect region of the nanocavity. (b,c) Electric field distributions of the fundamental (b) and the 5th order (c) cavity modes. The fundamental cavity mode is used for supporting the lasing oscillation while the 5th mode is for the cavity resonant excitation. It can be seen that the two mode has a large spatial overlap. The lattice constant of the PhC, a, is set to be 287 nm. (d) PL spectrum under above bandgap excitation at 50 K. The broad emission peak originated from QD ground state spontaneous emission and sharp peaks from cavity modes. Lasing and pumping modes are indicated by red arrows.

Fig. 2
Fig. 2

LL curves under the two excitation schemes at 15 K and their modeling. (a) Double logarithmic scale LL curves measured under the cavity resonant (red data points) and above bandgap (blue data points) excitation. Solid lines are obtained by fitting. (b) Laser model that contains two types of gain for describing our experiments. κ is the cavity leakage rate, βi is the spontaneous emission coupling factor of the i-th gain medium, N1T is the transparence carrier number, γi is the total spontaneous emission rate, Pi is the pump rate. The attached table summarizes the parameters used for the fitting to the data. (c), Linear scale LL curves measured under the two excitation schemes, clearly showing the disappearance of the threshold behavior under the cavity resonant excitation.

Fig. 3
Fig. 3

Comparison of emission spectra and linewidths under the two excitation schemes. (a,b), Emission spectra at 15 K at low injection rates about 17 GHz and (c,d) at high injection rates about 7700 GHz. Spectra under the above bandgap (a,c) are shown in blue while those under the cavity resonant excitation (b,d) are in red. (e) Linewidths plotted as a function of the injection rate. In particular for the low injection rates, linewidths for the cavity resonant excitation (red balls) exhibits faster narrowing than those for the above bandgap excitation (blue). Solid lines are of the calculation results using the simple linewidth model and the same parameter for simulating the LL curves.

Fig. 4
Fig. 4

Second order coherence measurement results. (a,b) g(2)(t) curves measured under various pump powers for the cavity resonant (a) and above bandgap (b) excitation. For the above bandgap excitation, PL intensity when P = ~100 GHz was too low to measure the corresponding g(2)(t) curve. (c) g(2)(t) curve showing the relaxation oscillation measured under the cavity resonant excitation at P = 760 GHz. Gray arrows indicate the peak positions of the oscillation. For (a)-(c), solid lines correspond to fitting results. (d) Evolution of g(2)(0) values as a function of the injection rate. The plot for the cavity resonant excitation (red points) exhibits faster decrease toward unity than that for the above bandgap excitation (blue points).

Fig. 5
Fig. 5

Temperature dependence of the laser transition (a) LL curves measured under the cavity resonant excitation at 4.5 K (magenta), 15 K (red) and 40 K (dark yellow). Solid lines are of fitting using a laser mode with a single gain medium. Dashed lines indicates the β = 1 straight lines. The 4.5 K and 40 K curves are offset by multiplication factors of 10 and 0.1, respectively. (b) Evolution of the extracted β value when changing the temperature. Error bars are determined by laser model fitting to the observed LL curves.

Fig. 6
Fig. 6

Jreso simulated for various β1 and N1T. The rest of parameters are the same with those used for fitting the LL curves. White line expresses Jreso = 1.08. The red star corresponds to the parameter found in the fitting to the experimental data (β1 = 0.973, N1T = 47).

Fig. 7
Fig. 7

Gain values simulated for the cavity resonant (red) and above bandgap (blue) excitation.

Equations (10)

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dn dt =κn+ i=1,2 β i γ i ( N i N i T )n + i=1,2 β i γ i N i , d N 1 dt = P 1 γ 1 N 1 γ nr N 1 β 1 γ 1 ( N 1 N 1 T )n d N 2 dt = P 2 γ 2 N 2 γ nr N 2 β 2 γ 2 ( N 2 N 2 T )n
J above = β ¯ 1 ( 1+ γ nr γ i + i=1,2 ( 1 β i + γ nr γ i ) β i γ i N i T κ ),
J reso = β 1 1 ( 1+ γ nr γ i + i=1,2 ( 1 β i + γ nr γ i ) β i γ i N i T κ ).
Δν=κ i=1,2 β i γ i ( N i N i T ) =κ( 1+ i=1,2 β i γ i N i T κ ( 1 N i N i T ) ).
Δ ν 0 =κ+ i=1,2 β i γ i N i T .
d dt [ δn δ N 1 δ N 2 ]=[ κ+ i=1,2 β i γ i ( N i 0 N i T ) β 1 γ 1 ( 1+ n 0 ) β 2 γ 2 ( 1+ n 0 ) β 1 γ 1 ( N 1 0 N 1 T ) γ 1 ( 1+ β 1 n 0 ) 0 β 2 γ 2 ( N 2 0 N 2 T ) 0 γ 2 ( 1+ β 2 n 0 ) ][ δn δ N 1 δ N 2 ]
d dt [ δn δN ]=[ κ+ i=1,2 β i γ i ( N i 0 N i T ) β 1 γ 1 ( 1+ n 0 ) i=1,2 β i γ i ( N i 0 N i T ) γ 1 ( 1+ β 1 n 0 ) ][ δn δN ].
δn(t)=δn(0) e γ R t cos( ω R t+ϕ)/cos(ϕ),
δn(t)=δn(0) e γ R t .
g (2) (|t|)=1+ δn(0)δn(|t|) n 0 2 .

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