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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 8 — Apr. 12, 2010
  • pp: 8144–8150
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High-Q design of semiconductor-based ultrasmall photonic crystal nanocavity

Masahiro Nomura, Katsuaki Tanabe, Satoshi Iwamoto, and Yasuhiko Arakawa  »View Author Affiliations


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 × 105 sustaining the small modal volume of 0.23(λ0/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 kx and ky axes, respectively. This high-Q cavity design is applicable to Si and GaAs semiconductor materials.

© 2010 OSA

1. Introduction

Recently, it has been theoretically predicted [16

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]

] and experimentally shown [17

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]

] that laser oscillations can occur even in the strong-coupling regime in excellent C-QED systems. In such solid state C-QED systems, fragile quantum physical interactions between a single QD and cavity field is hindered by several factors including the phonon-induced emission process, pure dephasing, and manifolds of the single QD near the cavity resonance [18

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

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]

]. Therefore, in C-QED experiments, a cavity design with both a high 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.

Many types of PhC cavity designs have been reported [21

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

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]

]. A hexagonal-lattice zero-cell PhC cavity, referred to as an H0-type or point-shift cavity, with air hole displacement in only the Γ-K direction has been proposed [21

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

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]

]. These designs have theoretical cavity Q values that exceed 1 × 105 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]

]. The main focus of this study is to develop a cavity design that has both a small V m and a high Q.

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

We investigate an air-clad 2D PhC nanocavity with a hexagonal air hole lattice [Fig. 1(a)
Fig. 1 (a) Schematic diagram of hexagonal-PhC H0-type nanocavity (top view). Band structure of fundamental TE-like mode calculated using 3D plane-wave expansion method. The air light cone (blue), PBG (light green), and typical cavity mode (orange) are shown. (c-e) 3D FDTD simulated profiles of E x, E y and H z components for fundamental mode.
]. In a 2D PhC slab, the distributed Bragg reflection due to the surrounding PhC structure results in the in-plane confinement of photons. On the other hand, standard wave guiding through total internal reflection determines the radiation loss into the out-of-plane direction. The energy-momentum dispersion relationship for this structure is 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

The studied optical cavity, which we refer to as the H0-type cavity in this work, comprises a defect created by shifting several air holes in a 2D PhC slab structure without removing any air holes as shown in Fig. 1(a). This cavity has much smaller V m than defect-type cavities produced via the removal of air holes. The cavity center is located at a C 2 v,σv symmetry point in the hexagonal lattice. The shifts of on-axis air holes 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 0.6a (where a is the period of the lattice) and 3.4, respectively. The radius of the air hole r is 0.26a. 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).

3D finite-difference time domain (FDTD) simulations are performed to obtain the frequency and profile of the fundamental mode of the example of an H0-type PhC nanocavity. The spatial distributions of 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

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

In this section, we discuss the change in the out-of-plane radiation loss in the optimization of the positions of the surrounding air holes. The light confined in the very small cavity consists of a significant number of plane wave components with various 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

Table 1. Cavity Q and shift of air holes for each type of cavity.

table-icon
View This Table
. 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.

Figures 3(a)
Fig. 3 (a–c) 2D spatial FT spectra of E x for Cavities A, B, and C at center of slab. (d–f) Magnified FT spectra of (a–c), respectively. The white circles indicate the cross section of the surface of the light cone for the cavity mode’s ω. The electric field components inside the circle are leaky components that result in out-of-plane radiation.
3(c) show the calculated 2D spatial FT spectra of 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.

Here, we individually discuss the changes in the out-of-plane radiation loss with the optimization of the displacements of air holes along the x and y axes. Figures 4(a)
Fig. 4 FT components of E x for Cavities A (green), B (blue), and C (red) on (a) k x and (b) k y axes. The gray region indicates the interior of the light cone. Smaller integrated components of FT(E x) in the light cone result in less out-of-plane radiation loss. The optimization of S ix and S iy reasonably lead to smaller integration components of FT(E x) in (a) and (b), respectively.
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

Finally, we discuss the importance of a smaller cavity in C-QED experiments. In the strong coupling regime, the spectral linewidth, which influences the clarity of photoluminescence spectra, of polariton doublets is given by (γQD + γcav)/2, where γQD and γcav are respectively the spectral linewidths of a QD and cavity mode. A state-of-the-art QD has γQD ~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

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]

]. Therefore, γQD limits the spectral linewidth of each peak of the polariton doublets for a high-Q cavity with Q ≥ 4 × 104 (~1.35 eV/35 μeV). However, γQD can potentially be small at about 5 μeV, which corresponds to Q ~2.7 × 105 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]

]. The proposed design can provide an H0-type PhC nanocavity that does not degrade the spectral clarity in C-QED experiments even under this ideal pumping case. There are cavity designs with extremely high Q values on the order of 108, but this advantage is restricted by γQD 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 cavQD. The proposed H0-type PhC nanocavity satisfies these essential requirements of an excellent cavity in C-QED experiments.

5. Summary

Acknowledgments

We thank A. Tandaechanurat for the fruitful discussions. This research was supported by the Special Coordination Funds for Promoting Science and Technology and Kakenhi20760030, from the Ministry of Education, Culture, Sports, Science and Technology, Japan.

References and links

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]

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 432(7014), 200–203 (2004). [CrossRef] [PubMed]

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. 95(6), 067401 (2005). [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]

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 305(5689), 1444–1447 (2004). [CrossRef] [PubMed]

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. 96(12), 127404 (2006). [CrossRef] [PubMed]

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 14(13), 6308–6315 (2006). [CrossRef] [PubMed]

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]

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. 98(4), 043906 (2007). [CrossRef] [PubMed]

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 16(7), 4848–4857 (2008). [CrossRef] [PubMed]

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 17(20), 18178–18183 (2009). [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]

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]

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 77(16), 161303 (2008). [CrossRef]

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]

22.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). [CrossRef]

23.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13(4), 1202–1214 (2005). [CrossRef] [PubMed]

24.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006). [CrossRef]

25.

C. Kreuzer, J. Riedrich-Möller, E. Neu, and C. Becher, “Design of photonic crystal microcavities in diamond films,” Opt. Express 16(3), 1632–1644 (2008). [CrossRef] [PubMed]

26.

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express 16(15), 11095–11102 (2008). [CrossRef] [PubMed]

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]

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]

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]

30.

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

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]

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

  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]
  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 432(7014), 200–203 (2004). [CrossRef] [PubMed]
  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. 95(6), 067401 (2005). [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, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999). [CrossRef] [PubMed]
  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 305(5689), 1444–1447 (2004). [CrossRef] [PubMed]
  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. 96(12), 127404 (2006). [CrossRef] [PubMed]
  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 14(13), 6308–6315 (2006). [CrossRef] [PubMed]
  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]
  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. 98(4), 043906 (2007). [CrossRef] [PubMed]
  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 16(7), 4848–4857 (2008). [CrossRef] [PubMed]
  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 17(20), 18178–18183 (2009). [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]
  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]
  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 77(16), 161303 (2008). [CrossRef]
  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]
  22. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). [CrossRef]
  23. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13(4), 1202–1214 (2005). [CrossRef] [PubMed]
  24. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006). [CrossRef]
  25. C. Kreuzer, J. Riedrich-Möller, E. Neu, and C. Becher, “Design of photonic crystal microcavities in diamond films,” Opt. Express 16(3), 1632–1644 (2008). [CrossRef] [PubMed]
  26. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express 16(15), 11095–11102 (2008). [CrossRef] [PubMed]
  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]
  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]
  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]
  30. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavitiers,” Opt. Express 10(15), 670–684 (2002). [PubMed]
  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]

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