## Vacuum Rabi splitting in a coupled system of single quantum dot and photonic crystal cavity: effect of local and propagation Green’s functions |

Optics Express, Vol. 21, Issue 20, pp. 23486-23497 (2013)

http://dx.doi.org/10.1364/OE.21.023486

Acrobat PDF (2888 KB)

### Abstract

We investigate the light emission characteristics for single two level quantum dot (QD) in a realistic photonic crystal (PC) L3 cavity based upon the local coupling strength between the QD and cavity together with the Green’s function in which the propagation function related to the position of the detector is taken into account. We find for a PC cavity that the line shape of the propagation function in frequency domain is identical to that of the cavity and independent on the detector's position. We confirm that this identity is not influenced by the horizontal decay of the cavity. Furthermore, it is revealed that the vacuum fluorescence spectrum of the coupled system never give the triplet in strong coupling regime. Our work demonstrates that the experimental spectral-triplet in coupled system of single QD and PC cavity cannot be individually understood by vacuum Rabi splitting without including other physics mechanism.

© 2013 Optical Society of America

1. H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science **298**(5597), 1372–1377 (2002). [CrossRef] [PubMed]

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

3. C. Monroe, “Quantum information processing with atoms and photons,” Nature **416**(6877), 238–246 (2002). [CrossRef] [PubMed]

4. J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics **3**(12), 687–695 (2009). [CrossRef]

5. 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]

9. D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature **450**(7171), 857–861 (2007). [CrossRef] [PubMed]

10. J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. **73**(3), 565–582 (2001). [CrossRef]

12. R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B **79**(15), 155317 (2009). [CrossRef]

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

14. 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**(4), 279–283 (2010). [CrossRef]

15. W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. **96**(11), 117401 (2006). [CrossRef] [PubMed]

16. D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett. **98**(11), 117402 (2007). [CrossRef] [PubMed]

17. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. **4**(11), 859–863 (2008). [CrossRef]

18. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics **1**(8), 449–458 (2007). [CrossRef]

6. 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]

*et al.*[8

8. 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]

19. M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett. **101**(22), 226808 (2008). [CrossRef] [PubMed]

21. M. Yamaguchi, T. Asano, and S. Noda, “Third emission mechanism in solid-state nanocavity quantum electrodynamics,” Rep. Prog. Phys. **75**(9), 096401 (2012). [CrossRef] [PubMed]

*et al.*[22

22. S. Hughes and P. Yao, “Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system,” Opt. Express **17**(5), 3322–3330 (2009). [CrossRef] [PubMed]

23. T. Ochiai, J.-i. Inoue, and K. Sakoda, “Spontaneous emission from a two-level atom in a bisphere microcavity,” Phys. Rev. A **74**(6), 063818 (2006). [CrossRef]

24. X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett. **91**(11), 113904 (2003). [CrossRef] [PubMed]

22. S. Hughes and P. Yao, “Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system,” Opt. Express **17**(5), 3322–3330 (2009). [CrossRef] [PubMed]

23. T. Ochiai, J.-i. Inoue, and K. Sakoda, “Spontaneous emission from a two-level atom in a bisphere microcavity,” Phys. Rev. A **74**(6), 063818 (2006). [CrossRef]

22. S. Hughes and P. Yao, “Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system,” Opt. Express **17**(5), 3322–3330 (2009). [CrossRef] [PubMed]

25. M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A **70**(5), 053823 (2004). [CrossRef]

27. H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A **40**(10), 5516–5519 (1989). [CrossRef] [PubMed]

28. L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B **60**(19), 13276–13279 (1999). [CrossRef]

24. X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett. **91**(11), 113904 (2003). [CrossRef] [PubMed]

*ab-initio*mapping [29

29. G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B **87**(19), 195138 (2013). [CrossRef]

6. 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]

*n*= 3.4. The spontaneous emission lifetime of the QD in GaAs is 1.82 ns.

*a*= 300nm,

*r*= 0.27

*a*,

*s*= 0.20

*a,*the thickness

*d*= 0.90

*a*, and 31 air holes in the x-direction and 29 air holes in the y-direction. There is thus 14 layers of air holes that surround the defect. For convenience, this slab PC L3 cavity is denoted as Sample#1. We find that the

29. G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B **87**(19), 195138 (2013). [CrossRef]

*Q*factor). From Eq. (12) we can determine the characteristic parameters of the cavity QED system, the normalized frequency of cavity mode is found to be 0.2433232, the decay rate in the unit of normalized frequency is

*Q*factor is thus 139,583, and the g factor is

*g*= 22.1GHz.

_{1}= (0, 0, 1.5)

*a*, B

_{1}= (0, 0, 5.5)

*a*and C

_{1}= (0, 0, 9.5)

*a*are also plotted in Figs. 2(b)-2(d). We can see that the propagation functions really have Lorentz line shape. Furthermore, the line widths

*Q*PC L3 cavity structure, the line width of the propagation function is identical to that of the PLDOS, i.e.,

*Q*PC L3 cavity, the detuning between these two wavelengths is set to be −0.06 nm, 0 nm and 0.06 nm, respectively. Figure 3(a) shows that, when the transition wavelength of the QD is resonant with the cavity mode, a symmetric Rabi splitting appears in the local dipole spectrum

_{1}= (0, 0, 9.5)

*a*. It can be seen clearly in Fig. 3(b) that the vacuum fluorescence spectrum is still double under on-resonance condition, the spectral triplet observed in [8

8. 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]

*Q*L3 cavity may be a special structure with horizontal decay

*Q*factor is still above 120,000; while if the number of air hole layers is decreased further, the decay rate

*Q*factor is reduced. This varying of the

*Q*factor is similar with the one in early work by O. Painter

*et al.*[30

30. O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B **16**(2), 275–285 (1999). [CrossRef]

**17**(5), 3322–3330 (2009). [CrossRef] [PubMed]

**17**(5), 3322–3330 (2009). [CrossRef] [PubMed]

**17**(5), 3322–3330 (2009). [CrossRef] [PubMed]

**17**(5), 3322–3330 (2009). [CrossRef] [PubMed]

30. O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B **16**(2), 275–285 (1999). [CrossRef]

## Acknowledgments

## References and links

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

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

3. | C. Monroe, “Quantum information processing with atoms and photons,” Nature |

4. | J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics |

5. | 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 |

6. | 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 |

7. | 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. |

8. | 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 |

9. | D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature |

10. | J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. |

11. | R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett. |

12. | R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B |

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

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

15. | W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. |

16. | D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett. |

17. | A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. |

18. | S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics |

19. | M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett. |

20. | M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B |

21. | M. Yamaguchi, T. Asano, and S. Noda, “Third emission mechanism in solid-state nanocavity quantum electrodynamics,” Rep. Prog. Phys. |

22. | S. Hughes and P. Yao, “Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system,” Opt. Express |

23. | T. Ochiai, J.-i. Inoue, and K. Sakoda, “Spontaneous emission from a two-level atom in a bisphere microcavity,” Phys. Rev. A |

24. | X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett. |

25. | M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A |

26. | C. T. Tai, |

27. | H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A |

28. | L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B |

29. | G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B |

30. | O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B |

**OCIS Codes**

(270.5580) Quantum optics : Quantum electrodynamics

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: March 5, 2013

Revised Manuscript: June 21, 2013

Manuscript Accepted: September 3, 2013

Published: September 26, 2013

**Citation**

Yi-Cong Yu, Jing-Feng Liu, Xiao-Lu Zhuo, Gengyan Chen, Chong-Jun Jin, and Xue-Hua Wang, "Vacuum Rabi splitting in a coupled system of single quantum dot and photonic crystal cavity: effect of local and propagation Green’s functions," Opt. Express **21**, 23486-23497 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23486

Sort: Year | Journal | Reset

### References

- H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science298(5597), 1372–1377 (2002). [CrossRef] [PubMed]
- K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003). [CrossRef] [PubMed]
- C. Monroe, “Quantum information processing with atoms and photons,” Nature416(6877), 238–246 (2002). [CrossRef] [PubMed]
- J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009). [CrossRef]
- 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,” Nature432(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,” Nature432(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,” Nature445(7130), 896–899 (2007). [CrossRef] [PubMed]
- D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007). [CrossRef] [PubMed]
- J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73(3), 565–582 (2001). [CrossRef]
- R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008). [CrossRef] [PubMed]
- R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B79(15), 155317 (2009). [CrossRef]
- E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B79(23), 235326 (2009). [CrossRef]
- 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(4), 279–283 (2010). [CrossRef]
- W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006). [CrossRef] [PubMed]
- D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007). [CrossRef] [PubMed]
- A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008). [CrossRef]
- S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007). [CrossRef]
- M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett.101(22), 226808 (2008). [CrossRef] [PubMed]
- M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B80(15), 155326 (2009). [CrossRef]
- M. Yamaguchi, T. Asano, and S. Noda, “Third emission mechanism in solid-state nanocavity quantum electrodynamics,” Rep. Prog. Phys.75(9), 096401 (2012). [CrossRef] [PubMed]
- S. Hughes and P. Yao, “Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system,” Opt. Express17(5), 3322–3330 (2009). [CrossRef] [PubMed]
- T. Ochiai, J.-i. Inoue, and K. Sakoda, “Spontaneous emission from a two-level atom in a bisphere microcavity,” Phys. Rev. A74(6), 063818 (2006). [CrossRef]
- X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003). [CrossRef] [PubMed]
- M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A70(5), 053823 (2004). [CrossRef]
- C. T. Tai, Dyadic Green Functions in Electromagnetic Theory (IEEE, 1993).
- H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A40(10), 5516–5519 (1989). [CrossRef] [PubMed]
- L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B60(19), 13276–13279 (1999). [CrossRef]
- G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013). [CrossRef]
- O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B16(2), 275–285 (1999). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.