## Lasing properties of non-resonant single quantum dot-cavity system under incoherent excitation |

Optics Express, Vol. 20, Issue 27, pp. 28437-28446 (2012)

http://dx.doi.org/10.1364/OE.20.028437

Acrobat PDF (1359 KB)

### Abstract

Single quantum dot laser has earned extensive interest due to its peculiar properties, however, most of works are focused on the resonant case. In this paper, the lasing oscillation based on off-resonant quantum dot (QD)-cavity system is investigated detailedly through two-electrons QD model. By gradually increasing the pump rate, the typical lasing signatures are shown with and without detuning, include the spectral transition from multiple peaks to single peak, and antibunching to Poissonian distribution. It is also demonstrated how detuning factor strongly influence photon statistics and emission properties, specially, the side peak of spectra induced by the exchange energy (named “sub-peak”) will go across the main peak from left to right when the detuning is gradually increased, and, furthermore, we find the “sub-peak cross of spectra” will facilitate the lasing oscillation because of the existence of exchange energy.

© 2012 OSA

## 1. Introduction

1. H. Mabuchi and A. Doherty, “Cavity quantum electrodynamics: Coherence in context,” Science **298**, 1372–1377 (2002). [CrossRef] [PubMed]

2. G. JP Reithmaier, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. Keldysh, V. Kulakovskii, and A. TL Reinecke, “Strong coupling in a single quantum dot–semiconductor microcavity system,” Nature **432**, 197–200 (2004). [CrossRef] [PubMed]

3. E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. **95**, 067401 (2005). [CrossRef] [PubMed]

4. S. Noda, “Seeking the Ultimate Nanolaser,” Science **314**, 260–261 (2006). [CrossRef] [PubMed]

5. E. Moreau, I. Robert, J. Gérard, I. Abram, L. Manin, and V. Thierry-Mieg, “Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities,” Appl. Phys. Lett. **79**, 2865–2867 (2001). [CrossRef]

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

8. P. Yao, P. Pathak, V. Rao, and S. Hughes, “Theory and design of chip-based quantum light sources using planar photonic crystals,” Proc. SPIE **7211**, 72110B (2009). [CrossRef]

*et al.*and Reithmaier

*et al.*experimentally realized vacuum Rabi splitting in the solid state system: a single QD strongly coupled to semiconductor micropillar and photonic crystal nanocavity respectively [2

2. G. JP Reithmaier, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. Keldysh, V. Kulakovskii, and A. TL Reinecke, “Strong coupling in a single quantum dot–semiconductor microcavity system,” Nature **432**, 197–200 (2004). [CrossRef] [PubMed]

9. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature **432**, 200–203 (2004). [CrossRef] [PubMed]

*et al.*precisely located the QD at the field antinode of single cavity mode by atomic force microscopy metrology, and validated the antibunching of generated photon stream in the strong coupling regime. All of these work pave the way to realize lasing oscillation with a single QD and a monolithic cavity of single mode. Almost at the same time, Xie

*et al.*investigate the influence of a Single QD State on the Characteristics of a Microdisk Laser [10

10. 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**, 117401 (2007). [CrossRef] [PubMed]

11. S. Reitzenstein, T. Heindel, C. Kistner, A. Rahimi-Iman, C. Schneider, S. Höfling, and A. Forchel, “Low threshold electrically pumped quantum dot-micropillar lasers,” Appl. Phys. Lett. **93**, 061104 (2008). [CrossRef]

*et al.*firstly realized the lasing oscillation from the real single QD in a photonic crystal cavity [12

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

13. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot–nanocavity system,” Nat. Phys. **6**, 279–283 (2010). [CrossRef]

13. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot–nanocavity system,” Nat. Phys. **6**, 279–283 (2010). [CrossRef]

16. P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, “Nonlinear photoluminescence spectra from a quantum-dot cavity system: Interplay of pump-induced stimulated emission and anharmonic cavity QED,” Phys. Rev. B **81**, 033309 (2010). [CrossRef]

*et al.*[17

17. S. Ritter, P. Gartner, C. Gies, and F. Jahnke, “Emission properties and photon statistics of a single quantum dot laser,” Opt. Express **18**, 9909–9921 (2010). [CrossRef] [PubMed]

*et al.*[18

18. C. Gies, M. Florian, P. Gartner, and F. Jahnke, “The single quantum dot-laser: lasing and strong coupling in the high-excitation regime,” Opt. Express **19**, 14370–14388 (2011). [CrossRef] [PubMed]

*et al.*discussed the range of validity of approximate theoretical scheme and found that the dimensionality of the dots has a crucial impact on the accuracy of the predicted addition spectra [19

19. M. Rontani, F. Rossi, F. Manghi, and E. Molinari, “Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality,” Phys. Rev. B **59**, 10165–10175 (1999). [CrossRef]

## 2. Theoretical model

17. S. Ritter, P. Gartner, C. Gies, and F. Jahnke, “Emission properties and photon statistics of a single quantum dot laser,” Opt. Express **18**, 9909–9921 (2010). [CrossRef] [PubMed]

*κ*; the coupling rate between the target QD exciton (s-exciton) and cavity is denoted as

*g*; the QD-cavity system is driven incoherently by exciton pump

*P*(

*γ*

_{41}) which pumps the QD level |1〉 → |4〉. Thus the dynamics of the whole system can be governed by a graceful master equation for the reduced density operator

*ρ*of the system, which can be derived using a Born-Markov and dipole approximation. In the interaction picture it reads with the system Hamiltonian where

*b*(

*b*

^{†}) represents the cavity mode annihilation (creation) operator,

*a*(

_{j}*j*= 1 ... 4) are the fermionic annihilation (creation) operators corresponding to the four states. The first term on the right-hand side of Eq. (2) is corresponding to the non-resonant Jaynes-Cummings Hamiltonian with the detuning between s-levels and the cavity mode (Δ =

*ω*−

_{x}*ω*) (here we introduce two definitions: the “bare” detuning and the “dressed” detuning, the former refers to the detuning between naked exciton and cavity mode while the latter corresponds to the detuning between cavity and QD energy levels dressed by the exchange energy). The second term is the exchange Coulomb interaction Hamiltonian (the direct Coulomb interaction Hamiltonian is negligible [20

_{c}20. N. Baer, P. Gartner, and F. Jahnke, “Coulomb effects in semiconductor quantum dots,” Eur. Phys. J. B **42**, 231–237 (2004). [CrossRef]

*γ*is the relaxation rate for the |

_{ij}*j*〉 → |

*i*〉 process with the subscript (

*i*,

*j*) = (1, 2), (3, 4), (2, 3), (1, 4), (4, 1) (the pump process

*γ*

_{41}=

*P*),

*κ*is the cavity decay rate, and Γ

*is the pure dephasing rate. It is noted, under incoherent excitation mechanism, the wetting layer (WL) population density varies as a function of the pump rates*

_{pd}*P*, and, due to the excitation-induced effects of the WL carriers, the scattering rates

*γ*

_{12}and

*γ*

_{34}and the sp-exchange energy

*E*is a function of the wetting layer population density, details are found in [17

_{sp}17. S. Ritter, P. Gartner, C. Gies, and F. Jahnke, “Emission properties and photon statistics of a single quantum dot laser,” Opt. Express **18**, 9909–9921 (2010). [CrossRef] [PubMed]

21. E. Peter, J. Hours, P. Senellart, A. Vasanelli, A. Cavanna, J. Bloch, and J. M. Gérard, “Phonon sidebands in exciton and biexciton emission from single GaAs quantum dots,” Phys. Rev. B **69**, 041307 (2004). [CrossRef]

23. M. Lorke, J. Seebeck, T. R. Nielsen, P. Gartner, and F. Jahnke, “Excitation dependence of the homogeneous linewidths in quantum dots,” Phys. Stat. Sol. (c) **3**, 2393–2396 (2006). [CrossRef]

13. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot–nanocavity system,” Nat. Phys. **6**, 279–283 (2010). [CrossRef]

15. A. Laucht, N. Hauke, J. M. Villas-Bôas, F. Hofbauer, G. Böhm, M. Kaniber, and J. J. Finley, “Dephasing of exciton polaritons in photoexcited InGaAs quantum dots in GaAs nanocavities,” Phys. Rev. Lett. **103**, 087405 (2009). [CrossRef] [PubMed]

24. T. Tawara, I. Suemune, and H. Kumano, “Strong coupling of CdS quantum dots to confined photonic modes in ZnSe-based microcavities,” Physica E **13**, 403–407 (2002). [CrossRef]

*κ*= 0.1/

*ps*, Γ

*= 0.035*

_{pd}*meV*and

*g*= 0.9/

*ps*respectively.

## 3. Simulation results and discussions

*ω*= ±1.4

*meV*) and the two weak peaks (at about Δ

*ω*= −0.06, 0.14

*meV*) are mainly ascribed to the next step of the Jaynes-Cummings ladder. The additional peak from the sp-biexciton transitions is positioned at twice the Coulomb exchange energy

*E*[17

_{sp}**18**, 9909–9921 (2010). [CrossRef] [PubMed]

*meV*, and it is completely pulled to the right side of the main peak for Δ = 6

*meV*, owing to the complex combined effect of detuning factor and pump rate.

*meV*is maximum in the medium pumping region (about 0.1 ∼ 1/

*ps*), while the mean photon number for detuning Δ = 2

*meV*is maximum in strong pumping region (approximately > 1/

*ps*). Generally, the smaller detuning the larger the mean photon number, and it is important to note that the detuning here is the “dressed” detuning. By directly solving the master equation, we find that the exchange energy is not monotonously changed with the pump rate and the detuning, and so evidently the complex appearance of the mean photon number is mainly from complex dependance of exchange energy on the pump and detuning. In addition, the mean photon number is approximately linearly increased with the pump rate in the strong pumping region, as we all know, the approximately linear increase of mean photon number usually means the generation of coherent light, to confirm it, we investigate the dependance of the second order correlation at zero delay

*g*

^{(2)}(0) on the pump rate [shown in Fig. 3(b)]. For all the cavity-s-exciton detunings,

*g*

^{(2)}(0) gradually approaches to 1 but at different speed when the pump rate is continuously increased. For detuning Δ = 2

*meV*,

*g*

^{(2)}(0) approaches to unity at about

*P*= 2.4/

*ps*, while for detuning Δ = 5

*meV*,

*g*

^{(2)}(0) approaches to unity only when

*P*> 1000/

*ps*, which is coincident with the variation of the mean photon number. However, it is not sufficient to judge coherent light only by

*g*

^{(2)}(0) = 1, instead the normalized second-order correlation function

*g*

^{(2)}(

*τ*) = 1 means coherent light, for example it is not a coherent light if

*γ*

_{12}=

*γ*

_{34}= 0.05

*meV*and

*E*= 3.3

_{sp}*meV*in our model [the grey line in inset of Fig. 3(c)] though

*g*

^{(2)}(0) = 1. Figure 3(c) shows

*g*

^{(2)}(

*τ*) for different detuning with

*P*= 1000/

*ps*, the normalized second-order correlation function

*g*

^{(2)}(

*τ*) is approximately stabilized at unity which indicates the output light is coherent, the tiny difference in

*g*

^{(2)}(

*τ*) among various detuning indicates the different laser threshold. Furthermore, Fig. 3(d) shows that the laser threshold varies as a function of detuning, here the threshold definition is proposed by Gunnar Bj

*ö*rk

*et al.*where the mean photon number in the mode at threshold is unity [25

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

*ps*when the QD is blue detuned with respect to the cavity by 4.36

*meV*. It is worth to clarify that the detuning case is the “bare” detuning, and in fact, it is exactly resonant with the dressed energy level dressed by exchange energy, to confirm it, the emission spectrum for the detuning Δ = 4.36

*meV*is calculated, and we find the “sub-peak” is completely overlapped with the main peak. Actually, the “sub-peak” in Fig. 2(c) is already very close to the main peak when detuning Δ = 4

*meV*. When the detuning is deviated from the optimum value, the threshold will grow rapidly because the energy exchange between the QD and cavity is very difficult when the “dressed” detuning is far larger than coupling constant

*g*. In order to compare the different definitions on the laser threshold, two more essential laser threshold definitions are taken into consideration: the first threshold definition is that the stimulated emission simply equals the spontaneous emission [26

26. G. Björk, A. Karlsson, and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. **27**, 2386–2396 (1991). [CrossRef]

26. G. Björk, A. Karlsson, and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. **27**, 2386–2396 (1991). [CrossRef]

27. Y. Mu and C. M. Savage, “One-atom lasers,” Phys. Rev. A **46**, 5944–5954 (1992). [CrossRef] [PubMed]

28. A. Auffèves, D. Gerace, J. M. Gérard, M. F. Santos, L. C. Andreani, and J.-P. Poizat, “Controlling the dynamics of a coupled atom-cavity system by pure dephasing,” Phys. Rev. B **81**, 245419 (2010). [CrossRef]

*P*= 0.1/

*ps*[Fig. 4(a)], the emission spectra show a multipeak structure which is coincident with

*g*

^{(2)}(0) ≠ 1, i.e. non-lasing, and the characteristic anti-crossing behavior between the cavity line and exciton line is observed in the detuning dependent emission spectra. The weak peaks (at about Δ

*ω*= ±1.4, −0.06, 0.14

*meV*for resonant case, see the black line in Fig. 4(a)) due to the next step of the Jaynes-Cummings ladder gradually fade out with increased detuning and disappear at Δ = ±2

*meV*. Unusually, the “sub-peak” from the sp-biexciton transitions is pulled to right along with blue detuning and left with red detuning, comparing with the resonant case under the same pump power, this pulling phenomenon depicts that the detuning factor will pronouncedly influence the sp-biexciton transitions and blue detuning of QD-cavity in some way enhances the coupling efficiency between QD and cavity mode. To bring evidences from experiments, we reproduce the PL emission with detuning Δ

*λ*= −0.03

*nm*in [7

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

*g*= 0.3

*meV*. From the inset of Fig. 4(a), we can see that the lineshape of the emission qualitatively agree with the experiment result: the two side peaks is mainly ascribed to the Rabi-splitting in the strong coupling regime, and the additional middle peak is due to the nonlinear effect of the Jaynes-Cummings ladder. It is noted that the horizontal ordinate in our manuscript is corresponding to frequency, and that in the reference wavelength, so the position of the peaks is inversed to the experiment result. For a high pump rate

*P*= 500/

*ps*as described in Fig. 4(b), the spectra becomes singlet and the linewidth shows significant reduction compared to the case of the weak pump rate, which indicates that strong coupling regime fades out and the whole system goes into weak coupling regime, especially, the resonant case doesn’t correspond to minimum linewidth and the dependence of linewidth on the detuning is not monotonic, which implies that “suitable detuning” will indeed facilitate lasing oscillation.

*E*. However, at strong pump rate, the mean photon number is declined with the increase of exchange energy. It is known that the biexciton emission will play a more and more important role in the emission process with the increase of pump rate, on the other hand, the emission of biexciton will be gradually out of resonance with the cavity mode due to the exchange energy, so the photon number shows a reduction with the increase of exchange energy. In this sense, the exchange energy is actually detrimental to the lasing oscillation, which is manifested by the second order correlation function. Just as we see from Fig. 5(b), for

_{sp}*E*= 0,

_{sp}*g*

^{(2)}(0) approaches to 1 more quickly than

*E*= 2.5, 5

_{sp}*meV*. Fortunately, the effect of exchange energy can be offset by cavity-s-exciton detuning, for example, just as we discussed above, for

*E*= 2.32

_{sp}*meV*at

*P*= 0.197/

*ps*, the detuning Δ = 4.36

*meV*will complete offset the exchange energy and the “sub-peak” will complete overlap the main peak.

## 4. Conclusion

*meV*will completely offset the energy shift of biexciton caused by

*E*= 2.32

_{sp}*meV*, therefore the laser threshold will reach its minimum

*P*= 0.197/

_{th}*ps*which is much lower than the resonant case. Finally, we would like to emphasize that the cavity resonance is only detuned from the s-exciton but exactly on-resonant with the QD configuration dressed by exchange energy.

## Acknowledgments

## References and links

1. | H. Mabuchi and A. Doherty, “Cavity quantum electrodynamics: Coherence in context,” Science |

2. | G. JP Reithmaier, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. Keldysh, V. Kulakovskii, and A. TL Reinecke, “Strong coupling in a single quantum dot–semiconductor microcavity system,” Nature |

3. | E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. |

4. | S. Noda, “Seeking the Ultimate Nanolaser,” Science |

5. | E. Moreau, I. Robert, J. Gérard, I. Abram, L. Manin, and V. Thierry-Mieg, “Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities,” Appl. Phys. Lett. |

6. | C. Santori, D. Fattal, J. Vuckovic, G. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature |

7. | K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature |

8. | P. Yao, P. Pathak, V. Rao, and S. Hughes, “Theory and design of chip-based quantum light sources using planar photonic crystals,” Proc. SPIE |

9. | T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature |

10. | 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. |

11. | S. Reitzenstein, T. Heindel, C. Kistner, A. Rahimi-Iman, C. Schneider, S. Höfling, and A. Forchel, “Low threshold electrically pumped quantum dot-micropillar lasers,” Appl. Phys. Lett. |

12. | M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Photonic crystal nanocavity laser with a single quantum dot gain,” Opt. Express |

13. | M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot–nanocavity system,” Nat. Phys. |

14. | F. P. Laussy, E. del Valle, and C. Tejedor, “Strong coupling of quantum dots in microcavities,” Phys. Rev. Lett. |

15. | A. Laucht, N. Hauke, J. M. Villas-Bôas, F. Hofbauer, G. Böhm, M. Kaniber, and J. J. Finley, “Dephasing of exciton polaritons in photoexcited InGaAs quantum dots in GaAs nanocavities,” Phys. Rev. Lett. |

16. | P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, “Nonlinear photoluminescence spectra from a quantum-dot cavity system: Interplay of pump-induced stimulated emission and anharmonic cavity QED,” Phys. Rev. B |

17. | S. Ritter, P. Gartner, C. Gies, and F. Jahnke, “Emission properties and photon statistics of a single quantum dot laser,” Opt. Express |

18. | C. Gies, M. Florian, P. Gartner, and F. Jahnke, “The single quantum dot-laser: lasing and strong coupling in the high-excitation regime,” Opt. Express |

19. | M. Rontani, F. Rossi, F. Manghi, and E. Molinari, “Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality,” Phys. Rev. B |

20. | N. Baer, P. Gartner, and F. Jahnke, “Coulomb effects in semiconductor quantum dots,” Eur. Phys. J. B |

21. | E. Peter, J. Hours, P. Senellart, A. Vasanelli, A. Cavanna, J. Bloch, and J. M. Gérard, “Phonon sidebands in exciton and biexciton emission from single GaAs quantum dots,” Phys. Rev. B |

22. | J. Y. Bigot, M. T. Portella, R. W. Schoenlein, J. E. Cunningham, and C. V. Shank, “Two-dimensional carrier-carrier screening in a quantum well,” Phys. Rev. Lett. |

23. | M. Lorke, J. Seebeck, T. R. Nielsen, P. Gartner, and F. Jahnke, “Excitation dependence of the homogeneous linewidths in quantum dots,” Phys. Stat. Sol. (c) |

24. | T. Tawara, I. Suemune, and H. Kumano, “Strong coupling of CdS quantum dots to confined photonic modes in ZnSe-based microcavities,” Physica E |

25. | G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A |

26. | G. Björk, A. Karlsson, and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. |

27. | Y. Mu and C. M. Savage, “One-atom lasers,” Phys. Rev. A |

28. | A. Auffèves, D. Gerace, J. M. Gérard, M. F. Santos, L. C. Andreani, and J.-P. Poizat, “Controlling the dynamics of a coupled atom-cavity system by pure dephasing,” Phys. Rev. B |

**OCIS Codes**

(140.3570) Lasers and laser optics : Lasers, single-mode

(270.5290) Quantum optics : Photon statistics

(140.3948) Lasers and laser optics : Microcavity devices

(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: September 26, 2012

Revised Manuscript: November 25, 2012

Manuscript Accepted: November 26, 2012

Published: December 7, 2012

**Citation**

Huan Guan, Peijun Yao, Wenhai Yu, Pei Wang, and Hai Ming, "Lasing properties of non-resonant single quantum dot-cavity system under incoherent excitation," Opt. Express **20**, 28437-28446 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-27-28437

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### References

- H. Mabuchi and A. Doherty, “Cavity quantum electrodynamics: Coherence in context,” Science298, 1372–1377 (2002). [CrossRef] [PubMed]
- G. JP Reithmaier, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. Keldysh, V. Kulakovskii, and A. TL Reinecke, “Strong coupling in a single quantum dot–semiconductor microcavity system,” Nature432, 197–200 (2004). [CrossRef] [PubMed]
- E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95, 067401 (2005). [CrossRef] [PubMed]
- S. Noda, “Seeking the Ultimate Nanolaser,” Science314, 260–261 (2006). [CrossRef] [PubMed]
- E. Moreau, I. Robert, J. Gérard, I. Abram, L. Manin, and V. Thierry-Mieg, “Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities,” Appl. Phys. Lett.79, 2865–2867 (2001). [CrossRef]
- C. Santori, D. Fattal, J. Vuckovic, G. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature419, 594–597 (2002). [CrossRef] [PubMed]
- K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445, 896–899 (2007). [CrossRef] [PubMed]
- P. Yao, P. Pathak, V. Rao, and S. Hughes, “Theory and design of chip-based quantum light sources using planar photonic crystals,” Proc. SPIE7211, 72110B (2009). [CrossRef]
- T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432, 200–203 (2004). [CrossRef] [PubMed]
- 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, 117401 (2007). [CrossRef] [PubMed]
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