## High-*Q* design of semiconductor-based ultrasmall photonic crystal nanocavity

Optics Express, Vol. 18, Issue 8, pp. 8144-8150 (2010)

http://dx.doi.org/10.1364/OE.18.008144

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### Abstract

We report a high-*Q* design for a semiconductor-based two-dimensional zero-cell photonic crystal (PhC) nanocavity with a small mode volume. The optimization of displacements of hexagonal-lattice air holes in the Γ-M direction, in addition to the Γ-K direction, resulted in a cavity quality factor *Q* of 2.8 × 10^{5} sustaining the small modal volume of 0.23(*λ*_{0}/*n*)^{3}. The momentum space consideration of out-of-plane radiation loss showed that the optimization of air hole displacements in both the in-plane *x* and *y* directions reduced FT components in the leaky region along the *k*_{x} and *k*_{y} axes, respectively. This high-*Q* cavity design is applicable to Si and GaAs semiconductor materials.

© 2010 OSA

## 1. Introduction

1. 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]

2. K. J. Vahala, “Optical microcavities,” Nature **424**(6950), 839–846 (2003). [CrossRef] [PubMed]

3. J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature **432**(7014), 197–200 (2004). [CrossRef] [PubMed]

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

7. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim I, “Two-dimensional photonic band-Gap defect mode laser,” Science **284**(5421), 1819–1821 (1999). [CrossRef] [PubMed]

15. 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]

*Q*) and the modal volume (

*V*

_{m}). In the weak-coupling regime, the artificial control of the radiation of photons, which is known as the Purcell effect, is determined by

*Q*/

*V*

_{m}. In the strong-coupling regime, the light-matter coupling strength

*g*is determined by

*V*

_{m}

^{-1/2}, which must be larger than

*γ*

_{QD}/4 and

*γ*

_{cav}/4, where

*γ*

_{QD}and

*γ*

_{cav}are the spectral linewidths of a QD and cavity mode, respectively. Therefore, a high-

*Q*cavity with smaller

*V*

_{m}is a better C-QED system.

16. E. del Valle, F. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B **79**(23), 235326 (2009). [CrossRef]

17. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys. (2010), doi:. [CrossRef]

18. 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]

20. M. Kaniber, A. Laucht, A. Neumann, J. Villas-Bôas, M. Bichler, M.-C. Amann, and J. Finley, “Investigation of the nonresonant dot-cavity coupling in two-dimensional photonic crystal nanocavities,” Phys. Rev. B **77**(16), 161303 (2008). [CrossRef]

*Q*and a small

*V*

_{m}is essential to enhance the light-matter interaction in the C-QED systems. A small

*V*

_{m}is the most important parameter in practical C-QED experiments, where the advantage of a high-

*Q*cavity is lost owing to the broad spectral linewidths of QDs.

21. Z. Zhang and M. Qiu, “Small-volume waveguide-section high *Q* microcavities in 2D photonic crystal slabs,” Opt. Express **12**(17), 3988–3995 (2004). [CrossRef] [PubMed]

28. J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express **17**(5), 3802–3817 (2009). [CrossRef] [PubMed]

21. Z. Zhang and M. Qiu, “Small-volume waveguide-section high *Q* microcavities in 2D photonic crystal slabs,” Opt. Express **12**(17), 3988–3995 (2004). [CrossRef] [PubMed]

29. K. Nozaki and T. Baba, “Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett. **88**(21), 211101 (2006). [CrossRef]

*Q*values that exceed 1 × 10

^{5}with a small

*V*

_{m}of 0.26-0.29(

*λ*

_{0}/

*n*)

^{3}, where

*λ*

_{0}and

*n*are the wavelength in vacuum and the refractive index of the material ( = 3.4), respectively. A square-lattice zero-cell PhC structure has been reported with a smaller

*V*

_{m}value of 0.21(

*λ*

_{0}/

*n*)

^{3}, but a moderate theoretical cavity

*Q*value of 4200 [27

27. H. S. Ee, K. Y. Jeong, M. K. Seo, Y. H. Lee, and H. G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett. **93**(1), 011104 (2008). [CrossRef]

*V*

_{m}and a high

*Q*.

*Q*design of a two-dimensional (2D) hexagonal-lattice zero-cell PhC nanocavity with a small

*V*

_{m}for semiconductor materials, such as Si and GaAs, with a refractive index of 3.4. Careful tuning of several air hole positions in both the Γ-K and Γ-M high-symmetry directions reduces the coupling of the cavity mode’s dominant Fourier components with radiating components and reduces the out-of-plane radiation loss. The tuning of the air hole positions increases

*Q*to a maximum value of 2.8 × 10

^{5}in zero-cell PhC nanocavities with a small

*V*

_{m}of 0.23(

*λ*

_{0}/

*n*)

^{3}. This result indicates the importance of the optimization of the air hole positions in the Γ-M direction that has not been adopted in previous works. These high-

*Q*nanocavities can be used to produce excellent solid-state C-QED systems with strong light–matter coupling that will enable further C-QED experiments to reach the multiquantum regime with high pumping.

## 2. Design of high-*Q* H0-type PhC nanocavity

*k*

_{//}= (

*ω*/

*c*)

^{2}defines a light cone [light blue region in Fig. 1(b)], where

*k*

_{//}is the in-plane momentum component,

*ω*is the angular frequency, and

*c*is the speed of light in air. Modes that lie within the light cone of air have small |

*k*

_{//}| and radiate vertically as leaky modes. Thus, designing cavities to reduce the out-of-plane radiation loss is the fundamental guideline [30

30. K. Srinivasan and O. Painter, “Momentum space design of high-*Q* photonic crystal optical cavitiers,” Opt. Express **10**(15), 670–684 (2002). [PubMed]

### 2.1 2D PhC H0-type nanocavity

*V*

_{m}than defect-type cavities produced via the removal of air holes. The cavity center is located at a

*C*

_{2}

*,*

_{v}*symmetry point in the hexagonal lattice. The shifts of on-axis air holes*

_{σv}*S*

_{ix}(

*i*= 1–3) in the

*x*-direction (Γ-K) and of

*S*

_{jy}(

*j*= 1, 2) in the

*y*-direction (Γ-M) are optimized in this study and are defined in Fig. 1(a). The band structure is calculated using the three-dimensional (3D) plane-wave expansion method. In the simulation, the thickness and

*n*of the slab are 0.6

*a*(where

*a*is the period of the lattice) and 3.4, respectively. The radius of the air hole

*r*is 0.26

*a*. The results indicate that the photonic band gap (PBG) region, colored light green in Fig. 1(b), ranges from 0.252 to 0.302 in units of normalized frequency (

*a*/

*λ*). The normalized frequencies of the fundamental modes of the cavities investigated in this study are in the range from 0.285 to 0.29, which lies within the PBG as shown by the orange line in Fig. 1(b).

*E*

_{x},

*E*

_{y}and

*H*

_{z}components are shown in Figs. 1(c)–1(e), respectively. The main electric field component is

*E*

_{y}, but

*E*

_{x}has comparable amplitude (~50%). The

*E*

_{x}component shows very strong localization in the cavity at two maxima. The calculated

*V*

_{m}slightly differs with a change in

*S*

_{ix,y}, but does not drastically change from a value of 0.24(

*λ*

_{0}/

*n*)

^{3}.

### 2.2 Optimization of Q by shifting multiple air holes

*S*

_{1x},

*S*

_{1y},

*S*

_{2x},

*S*

_{2y}, and

*S*

_{3x}so that

*Q*is a maximum. First,

*S*

_{1x}= 0.14

*a*gives the largest

*Q*of ~1.1 × 10

^{5}.

*S*

_{1x}is then fixed at 0.14

*a*and the value of

*S*

_{1y}is changed between 0 and 0.1

*a*to search for the local maximal value of

*Q*as shown in Fig. 2(a) . The cavity

*Q*is sensitive to the air-hole displacement in the

*y*-direction. In the series of calculations,

*S*

_{1y}= 0.04

*a*gives the maximum value of 2.1 × 10

^{5}and

*Q*decreases at larger

*S*

_{1y}. The same series of calculations are performed for the tuning parameters

*S*

_{2x},

*S*

_{2y}, and

*S*

_{3x}. The maximum value of

*Q*of 2.8 × 10

^{5}is found for

*S*

_{1x}= 0.14

*a*,

*S*

_{2x}= 0,

*S*

_{3x}= 0.06

*a*,

*S*

_{1y}= 0.04

*a*, and

*S*

_{2y}= 0.02

*a*(Cavity C). This value is more than twice the previously reported value for this type of cavity [11

11. K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express **15**(12), 7506–7514 (2007). [CrossRef] [PubMed]

21. Z. Zhang and M. Qiu, “Small-volume waveguide-section high *Q* microcavities in 2D photonic crystal slabs,” Opt. Express **12**(17), 3988–3995 (2004). [CrossRef] [PubMed]

*V*

_{m}increased by only 6% as compared with the initial design (Cavity A), whereas

*Q*is increased by more than twice. This is the most important point of cavity design in C-QED physics. In this study, the displacements of only on-axis air holes are optimized, and further improvement of

*Q*may be possible with the additional optimization for off-axis air holes.

## 3. Momentum space consideration of out-of-plane radiation loss

*k*values. When |

*k*

_{//}| lies within the range of 0–2π/

*λ*, the plane wave can escape to the air cladding because the total internal reflection condition is not fulfilled. On the other hand, the plane wave with |

*k*

_{//}| larger than 2π/

*λ*is strongly confined to the cavity. Therefore, we can investigate the out-of-plane radiation loss of the cavity mode by calculating the 2D spatial Fourier transformation (FT) of the in-plane electric field of the mode in the slab. Here, three cavities, referred to as Cavities A, B, and C and indicated in Figs. 2(a) and 2(b), are compared. The design of each cavity is presented in Table 1 . Cavity A is the initial design with a simple shift of the two closest air holes to create the cavity. Cavity B has an additional optimized shift of the air holes in the

*y*-direction. The design of Cavity C is optimized for both the

*x*- and

*y*-directions within

*i*= 1–3 and

*j*= 1–2, respectively.

*E*

_{x}for Cavities A, B, and C at the center of the slab. The FT spectra show

*E*

_{x}to be primarily composed of momentum components located around four

*M*points. The intensity increases, indicating a stronger confinement of light, as the cavities are more optimized. Figures 3(e), 3(f) show magnified FT spectra of Figs. 3(a)–3(c). The white circles indicate the cross section of the surface of the light cone for the cavity mode’s value of

*ω*. The electric field components inside the circle have small |

*k*

_{//}| that result in out-of-plane radiation loss. The ratio of integrated FT components inside the air light cone to the total of FT components at the middle of the slab for each cavity is 0.165%, 0.148%, and 0.146%. A better cavity has a reasonably smaller fraction of leaky modes.

*x*and

*y*axes. Figures 4(a) and 4(b) show the FT components of

*E*

_{x}for Cavities A (green), B (blue), and C (red) on the

*k*

_{x}and

*k*

_{y}axes, respectively. The gray region indicates the interior of the light cone, which corresponds to the leaky region. Cavity A has a large FT component at

*k*

_{x}= 0 and large integrated FT components in the leaky region. Cavity B has additional air-hole displacement along the

*y*axis and obviously smaller FT components along the

*k*

_{y}direction. The drastic reduction in the FT component at

*k*

_{x}= 0 is mainly due to the optimization of air-hole positions in the

*y*-direction. Therefore, the optimization of the air-hole displacement in the

*y*-direction is important in obtaining a high-

*Q*H0-type PhC nanocavity. The FT spectra of Cavities B and C are almost the same along the

*k*

_{y}axis [Fig. 4(b)] because there is no additional displacement of any air hole in the

*y*-direction. However, the FT components

*k*

_{y}~0 are reduced by the additional optimization of

*S*

_{3x}in the

*x*-direction. This improvement is clearly shown in the FT spectrum along the

*k*

_{x}direction in Fig. 4(a). These comparisons of FT components in the leaky region among the three cavities are consistent with the improvements in cavity

*Q*.

## 4. Aptitude of a zero-cell PhC nanocavity for C-QED experiments

_{QD}+ γ

_{cav})/2, where γ

_{QD}and γ

_{cav}are respectively the spectral linewidths of a QD and cavity mode. A state-of-the-art QD has γ

_{QD}~35 μeV in most C-QED experiments at cavity-mode photon energy of

*E*

_{cav}~1.35 eV [6

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

17. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys. (2010), doi:. [CrossRef]

_{QD}limits the spectral linewidth of each peak of the polariton doublets for a high-

*Q*cavity with

*Q*≥ 4 × 10

^{4}(~1.35 eV/35 μeV). However, γ

_{QD}can potentially be small at about 5 μeV, which corresponds to

*Q*~2.7 × 10

^{5}for the cavity mode, under an ideal pumping condition [31

31. S. Ates, S. M. Ulrich, A. Ulhaq, S. Reitzenstein, A. Loffler, S. Hofling, A. Forchel, and P. Michler, “Non-resonant dot-cavity coupling and its potential for resonant single-quantum-dot spectroscopy,” Nat. Photonics **3**(12), 724–728 (2009). [CrossRef]

*Q*values on the order of 10

^{8}, but this advantage is restricted by γ

_{QD}and strong light–matter coupling cannot be expected because of relatively large

*V*

_{m}> (

*λ*

_{0}/

*n*)

^{3}in the C-QED experiments. It is thus concluded that a smaller cavity has better performance in C-QED experiments if

*Q*is comparable to

*E*

_{cav}/γ

_{QD}. The proposed H0-type PhC nanocavity satisfies these essential requirements of an excellent cavity in C-QED experiments.

## 5. Summary

*Q*design of a two-dimensional hexagonal-lattice zero-cell (H0-type) PhC nanocavity was proposed. The optimization of the air-hole position in both Γ-K and Γ-M directions increased cavity

*Q*to a maximum value of 2.8 × 10

^{5}in zero-cell PhC nanocavities while maintaining a small mode volume of ~0.23(

*λ*

_{0}/

*n*)

^{3}. This result indicates the importance of the optimization of the air hole positions in the Γ-M direction, in addition to the Γ-K direction, that has not been adopted in previous works. The momentum space consideration of the out-of-plane radiation loss showed that the optimization of displacements of air holes around the cavity in the

*x*- and

*y*-directions reduced FT components in the leaky region along the

*k*

_{x}and

*k*

_{y}axes, respectively. This optimized design for a zero-cell PhC nanocavity is applicable to Si- and GaAs-based semiconductor materials.

## Acknowledgments

## References and links

1. | Y. Arakawa and H. Sakaki, “Multidimensional quantum well laser and temperature dependence of its threshold current,” Appl. Phys. Lett. |

2. | K. J. Vahala, “Optical microcavities,” Nature |

3. | J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature |

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

5. | 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. |

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

7. | O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim I, “Two-dimensional photonic band-Gap defect mode laser,” Science |

8. | H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science |

9. | 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. |

10. | 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 |

11. | K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express |

12. | 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. |

13. | 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 |

14. | K. A. Atlasov, M. Calic, K. F. Karlsson, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Photonic-crystal microcavity laser with site-controlled quantum-wire active medium,” Opt. Express |

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

16. | E. del Valle, F. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B |

17. | M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys. (2010), doi:. [CrossRef] |

18. | M. Yamaguchi, T. Asano, and S. Noda, “Photon emission by nanocavity-enhanced quantum anti-Zeno effect in solid-state cavity quantum-electrodynamics,” Opt. Express |

19. | Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” arXiv:0908.0788 (2009). |

20. | M. Kaniber, A. Laucht, A. Neumann, J. Villas-Bôas, M. Bichler, M.-C. Amann, and J. Finley, “Investigation of the nonresonant dot-cavity coupling in two-dimensional photonic crystal nanocavities,” Phys. Rev. B |

21. | Z. Zhang and M. Qiu, “Small-volume waveguide-section high |

22. | B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high- |

23. | Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high- |

24. | E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh- |

25. | C. Kreuzer, J. Riedrich-Möller, E. Neu, and C. Becher, “Design of photonic crystal microcavities in diamond films,” Opt. Express |

26. | M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh- |

27. | H. S. Ee, K. Y. Jeong, M. K. Seo, Y. H. Lee, and H. G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett. |

28. | J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express |

29. | K. Nozaki and T. Baba, “Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett. |

30. | K. Srinivasan and O. Painter, “Momentum space design of high- |

31. | S. Ates, S. M. Ulrich, A. Ulhaq, S. Reitzenstein, A. Loffler, S. Hofling, A. Forchel, and P. Michler, “Non-resonant dot-cavity coupling and its potential for resonant single-quantum-dot spectroscopy,” Nat. Photonics |

**OCIS Codes**

(270.5580) Quantum optics : Quantum electrodynamics

(050.5298) Diffraction and gratings : Photonic crystals

(130.3990) Integrated optics : Micro-optical devices

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: March 1, 2010

Revised Manuscript: March 26, 2010

Manuscript Accepted: March 26, 2010

Published: April 1, 2010

**Citation**

Masahiro Nomura, Katsuaki Tanabe, Satoshi Iwamoto, and Yasuhiko Arakawa, "High-Q design of semiconductor-based ultrasmall photonic crystal nanocavity," Opt. Express **18**, 8144-8150 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-8-8144

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### References

- 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]
- K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef] [PubMed]
- J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004). [CrossRef] [PubMed]
- T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (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(6), 067401 (2005). [CrossRef] [PubMed]
- K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]
- O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999). [CrossRef] [PubMed]
- H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004). [CrossRef] [PubMed]
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