Abstract

Spontaneous emission lifetime distribution in the basic unit cell or on a plane of the excited emitters embedded in woodpile photonics crystals with low refractive index contrast are investigated. It is found that the spontaneous emission lifetime distribution strongly depends on the position and transition frequency of the emitters, and has the same symmetry as that of the unit cell. The lifetimes of emitters near the upper gap edge are longer than that in the center of the pseudo-gap, which is quite a contrast to the conventional concept. Furthermore, it is revealed that the polarization orientation of the emitters has significant influence on the lifetime distribution, and may result in a high anisotropy factor (defined as the difference between the maximum and minimum values of the lifetime) up to 4.2. These results may be supplied in probing the lifetime distribution or orientation-dependent local density of states in future experiments.

© 2011 OSA

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    [PubMed]
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  4. M. Megens, J. E. G. J. Wijnhoven, A. Lagendijk, and W. L. Vos, “Fluorescence lifetimes and linewidths of dye in photonic crystals,” Phys. Rev. A 59(6), 4727–4731 (1999).
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  6. S. Bay, P. Lambropoulos, and K. Mølmer, “Fluorescence into flat and structured radiation continua: an atomic density matrix without a master equation,” Phys. Rev. Lett. 79(14), 2654–2657 (1997).
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  15. S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
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  20. S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
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  25. R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67(15), 155114 (2003).
  26. M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random photonic media,” Phys. Rev. Lett. 105(1), 013904 (2010).
    [PubMed]
  27. V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett. 105(18), 183901 (2010).
  28. K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(3), 3896–3908 (1998).
  29. I. S. Nikolaev, W. L. Vos, and A. F. Koenderink, “Accurate calculation of the local density of optical states in inverse-opal photonic crystals,” J. Opt. Soc. Am. B 26(5), 987–997 (2009).
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    [PubMed]
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2011

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).

2010

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random photonic media,” Phys. Rev. Lett. 105(1), 013904 (2010).
[PubMed]

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett. 105(18), 183901 (2010).

M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).

J.- Liu and X.-H. Wang, “Spontaneous emission in micro- and nano-structures,” Front. Phys. China 5(3), 245–259 (2010).

Q. Wang, S. Stobbe, H. Thyrrestrup, H. Hofmann, M. Kamp, T. W. Schlereth, S. Höfling, and P. Lodahl, “Highly anisotropic decay rates of single quantum dots in photonic crystal membranes,” Opt. Lett. 35(16), 2768–2770 (2010).
[PubMed]

L. Tang and T. Yoshie, “High-Q hybrid 3D-2D slab-3D photonic crystal microcavity,” Opt. Lett. 35(18), 3144–3146 (2010).
[PubMed]

2009

W. L. Vos, A. F. Koenderink, and I. S. Nikolaev, “Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment,” Phys. Rev. A 80(5), 053802 (2009).

I. S. Nikolaev, W. L. Vos, and A. F. Koenderink, “Accurate calculation of the local density of optical states in inverse-opal photonic crystals,” J. Opt. Soc. Am. B 26(5), 987–997 (2009).

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
[PubMed]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[PubMed]

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).

2008

M. J. Ventura and M. Gu, “Engineering spontaneous emission in a quantum-dot-doped polymer nanocomposite with three-dimensional photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(7), 1329–1332 (2008).

2007

J. Li, B. Jia, G. Zhou, C. Bullen, J. Serbin, and M. Gu, “Spectral redistribution in spontaneous emission from quantum-dot-infiltrated 3D woodpile photonic crystals for telecommunications,” Adv. Mater. (Deerfield Beach Fla.) 19(20), 3276–3280 (2007).

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).
[PubMed]

2004

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).
[PubMed]

2003

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[PubMed]

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).
[PubMed]

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67(15), 155114 (2003).

2002

X.-H. Wang, R. Wang, B.-Y. Gu, and G.-Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with pseudogaps,” Phys. Rev. Lett. 88(9), 093902 (2002).
[PubMed]

2000

Z.-Y. Li, L.-L. Lin, and Z.-Q. Zhang, “Spontaneous emission from photonic crystals: full vectorial calculations,” Phys. Rev. Lett. 84(19), 4341–4344 (2000).
[PubMed]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
[PubMed]

S.-Y. Zhu, Y. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84(10), 2136–2139 (2000).
[PubMed]

1999

M. Megens, J. E. G. J. Wijnhoven, A. Lagendijk, and W. L. Vos, “Fluorescence lifetimes and linewidths of dye in photonic crystals,” Phys. Rev. A 59(6), 4727–4731 (1999).

1998

E. P. Petrov, V. N. Bogomolov, I. I. Kalosha, and S. V. Gaponenko, “Spontaneous emission of organic molecules embedded in a photonic crystal,” Phys. Rev. Lett. 81(1), 77–80 (1998).

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(3), 3896–3908 (1998).

1997

S. Bay, P. Lambropoulos, and K. Mølmer, “Fluorescence into flat and structured radiation continua: an atomic density matrix without a master equation,” Phys. Rev. Lett. 79(14), 2654–2657 (1997).

1994

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89(5), 413–416 (1994).

1991

S. John and J. Wang, “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B Condens. Matter 43(16), 12772–12789 (1991).
[PubMed]

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[PubMed]

1976

H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13(12), 5188–5192 (1976).

Aoki, K.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[PubMed]

Aoyagi, Y.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[PubMed]

Arakawa, Y.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).

Atatüre, M.

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).
[PubMed]

Baba, T.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[PubMed]

Badolato, A.

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).
[PubMed]

Baek, J.-H.

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).
[PubMed]

Bay, S.

S. Bay, P. Lambropoulos, and K. Mølmer, “Fluorescence into flat and structured radiation continua: an atomic density matrix without a master equation,” Phys. Rev. Lett. 79(14), 2654–2657 (1997).

Birowosuto, M. D.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random photonic media,” Phys. Rev. Lett. 105(1), 013904 (2010).
[PubMed]

Biswas, R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89(5), 413–416 (1994).

Bogomolov, V. N.

E. P. Petrov, V. N. Bogomolov, I. I. Kalosha, and S. V. Gaponenko, “Spontaneous emission of organic molecules embedded in a photonic crystal,” Phys. Rev. Lett. 81(1), 77–80 (1998).

Bullen, C.

J. Li, B. Jia, G. Zhou, C. Bullen, J. Serbin, and M. Gu, “Spectral redistribution in spontaneous emission from quantum-dot-infiltrated 3D woodpile photonic crystals for telecommunications,” Adv. Mater. (Deerfield Beach Fla.) 19(20), 3276–3280 (2007).

Bur, J.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

Busch, K.

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(3), 3896–3908 (1998).

Carminati, R.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett. 105(18), 183901 (2010).

Castanié, E.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett. 105(18), 183901 (2010).

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89(5), 413–416 (1994).

Chen, H.

S.-Y. Zhu, Y. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84(10), 2136–2139 (2000).
[PubMed]

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
[PubMed]

David, A.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).

De Wilde, Y.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett. 105(18), 183901 (2010).

Fält, S.

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).
[PubMed]

Fleming, J. G.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

Gaponenko, S. V.

E. P. Petrov, V. N. Bogomolov, I. I. Kalosha, and S. V. Gaponenko, “Spontaneous emission of organic molecules embedded in a photonic crystal,” Phys. Rev. Lett. 81(1), 77–80 (1998).

Gerace, D.

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).
[PubMed]

Gu, B.-Y.

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).
[PubMed]

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67(15), 155114 (2003).

X.-H. Wang, R. Wang, B.-Y. Gu, and G.-Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with pseudogaps,” Phys. Rev. Lett. 88(9), 093902 (2002).
[PubMed]

Gu, M.

M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).

M. J. Ventura and M. Gu, “Engineering spontaneous emission in a quantum-dot-doped polymer nanocomposite with three-dimensional photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(7), 1329–1332 (2008).

J. Li, B. Jia, G. Zhou, C. Bullen, J. Serbin, and M. Gu, “Spectral redistribution in spontaneous emission from quantum-dot-infiltrated 3D woodpile photonic crystals for telecommunications,” Adv. Mater. (Deerfield Beach Fla.) 19(20), 3276–3280 (2007).

Guimard, D.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).

Gulde, S.

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).
[PubMed]

Hennessy, K.

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).
[PubMed]

Hetherington, D. L.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

Hirayama, H.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[PubMed]

Ho, K. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89(5), 413–416 (1994).

Höfling, S.

Hofmann, H.

Hu, E. L.

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).
[PubMed]

Imada, M.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
[PubMed]

Imamoglu, A.

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).
[PubMed]

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K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
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Ishizaki, K.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
[PubMed]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
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A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).

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M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).

J. Li, B. Jia, G. Zhou, C. Bullen, J. Serbin, and M. Gu, “Spectral redistribution in spontaneous emission from quantum-dot-infiltrated 3D woodpile photonic crystals for telecommunications,” Adv. Mater. (Deerfield Beach Fla.) 19(20), 3276–3280 (2007).

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Kamp, M.

Kim, S.-B.

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).
[PubMed]

Kim, S.-H.

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).
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Koenderink, A. F.

I. S. Nikolaev, W. L. Vos, and A. F. Koenderink, “Accurate calculation of the local density of optical states in inverse-opal photonic crystals,” J. Opt. Soc. Am. B 26(5), 987–997 (2009).

W. L. Vos, A. F. Koenderink, and I. S. Nikolaev, “Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment,” Phys. Rev. A 80(5), 053802 (2009).

Krachmalnicoff, V.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett. 105(18), 183901 (2010).

Kurtz, S. R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

Kwon, S.-H.

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).
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M. Megens, J. E. G. J. Wijnhoven, A. Lagendijk, and W. L. Vos, “Fluorescence lifetimes and linewidths of dye in photonic crystals,” Phys. Rev. A 59(6), 4727–4731 (1999).

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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).
[PubMed]

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M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).

J. Li, B. Jia, G. Zhou, C. Bullen, J. Serbin, and M. Gu, “Spectral redistribution in spontaneous emission from quantum-dot-infiltrated 3D woodpile photonic crystals for telecommunications,” Adv. Mater. (Deerfield Beach Fla.) 19(20), 3276–3280 (2007).

Li, Z.-Y.

Z.-Y. Li, L.-L. Lin, and Z.-Q. Zhang, “Spontaneous emission from photonic crystals: full vectorial calculations,” Phys. Rev. Lett. 84(19), 4341–4344 (2000).
[PubMed]

Lin, L.-L.

Z.-Y. Li, L.-L. Lin, and Z.-Q. Zhang, “Spontaneous emission from photonic crystals: full vectorial calculations,” Phys. Rev. Lett. 84(19), 4341–4344 (2000).
[PubMed]

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S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

Liu, J.-

J.- Liu and X.-H. Wang, “Spontaneous emission in micro- and nano-structures,” Front. Phys. China 5(3), 245–259 (2010).

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Megens, M.

M. Megens, J. E. G. J. Wijnhoven, A. Lagendijk, and W. L. Vos, “Fluorescence lifetimes and linewidths of dye in photonic crystals,” Phys. Rev. A 59(6), 4727–4731 (1999).

Megens, M. M.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).

Miyazaki, H. T.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[PubMed]

Mølmer, K.

S. Bay, P. Lambropoulos, and K. Mølmer, “Fluorescence into flat and structured radiation continua: an atomic density matrix without a master equation,” Phys. Rev. Lett. 79(14), 2654–2657 (1997).

Monkhorst, H. J.

H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13(12), 5188–5192 (1976).

Mosk, A. P.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random photonic media,” Phys. Rev. Lett. 105(1), 013904 (2010).
[PubMed]

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S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
[PubMed]

Nikolaev, I. S.

W. L. Vos, A. F. Koenderink, and I. S. Nikolaev, “Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment,” Phys. Rev. A 80(5), 053802 (2009).

I. S. Nikolaev, W. L. Vos, and A. F. Koenderink, “Accurate calculation of the local density of optical states in inverse-opal photonic crystals,” J. Opt. Soc. Am. B 26(5), 987–997 (2009).

Noda, S.

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[PubMed]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
[PubMed]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
[PubMed]

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A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).

Okano, M.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
[PubMed]

Ota, Y.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
[PubMed]

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H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13(12), 5188–5192 (1976).

Park, H.-G.

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).
[PubMed]

Petrov, E. P.

E. P. Petrov, V. N. Bogomolov, I. I. Kalosha, and S. V. Gaponenko, “Spontaneous emission of organic molecules embedded in a photonic crystal,” Phys. Rev. Lett. 81(1), 77–80 (1998).

Sakoda, K.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[PubMed]

Schlereth, T. W.

Serbin, J.

J. Li, B. Jia, G. Zhou, C. Bullen, J. Serbin, and M. Gu, “Spectral redistribution in spontaneous emission from quantum-dot-infiltrated 3D woodpile photonic crystals for telecommunications,” Adv. Mater. (Deerfield Beach Fla.) 19(20), 3276–3280 (2007).

Shinya, N.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
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Sigalas, M. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

Skipetrov, S. E.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random photonic media,” Phys. Rev. Lett. 105(1), 013904 (2010).
[PubMed]

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S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

Soukoulis, C. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89(5), 413–416 (1994).

Stobbe, S.

Suzuki, K.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
[PubMed]

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S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
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A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).

Tang, L.

Thyrrestrup, H.

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
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Ventura, M. J.

M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).

M. J. Ventura and M. Gu, “Engineering spontaneous emission in a quantum-dot-doped polymer nanocomposite with three-dimensional photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(7), 1329–1332 (2008).

Vos, W. L.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random photonic media,” Phys. Rev. Lett. 105(1), 013904 (2010).
[PubMed]

W. L. Vos, A. F. Koenderink, and I. S. Nikolaev, “Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment,” Phys. Rev. A 80(5), 053802 (2009).

I. S. Nikolaev, W. L. Vos, and A. F. Koenderink, “Accurate calculation of the local density of optical states in inverse-opal photonic crystals,” J. Opt. Soc. Am. B 26(5), 987–997 (2009).

M. Megens, J. E. G. J. Wijnhoven, A. Lagendijk, and W. L. Vos, “Fluorescence lifetimes and linewidths of dye in photonic crystals,” Phys. Rev. A 59(6), 4727–4731 (1999).

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S. John and J. Wang, “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B Condens. Matter 43(16), 12772–12789 (1991).
[PubMed]

Wang, Q.

Wang, R.

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).
[PubMed]

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67(15), 155114 (2003).

X.-H. Wang, R. Wang, B.-Y. Gu, and G.-Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with pseudogaps,” Phys. Rev. Lett. 88(9), 093902 (2002).
[PubMed]

Wang, X.-H.

J.- Liu and X.-H. Wang, “Spontaneous emission in micro- and nano-structures,” Front. Phys. China 5(3), 245–259 (2010).

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).
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R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67(15), 155114 (2003).

X.-H. Wang, R. Wang, B.-Y. Gu, and G.-Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with pseudogaps,” Phys. Rev. Lett. 88(9), 093902 (2002).
[PubMed]

Wierer, J. J.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).

Wijnhoven, J. E. G. J.

M. Megens, J. E. G. J. Wijnhoven, A. Lagendijk, and W. L. Vos, “Fluorescence lifetimes and linewidths of dye in photonic crystals,” Phys. Rev. A 59(6), 4727–4731 (1999).

Winger, M.

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).
[PubMed]

Xu, H.-Q.

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).
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S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
[PubMed]

Yang, G.-Z.

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67(15), 155114 (2003).

X.-H. Wang, R. Wang, B.-Y. Gu, and G.-Z. Yang, “Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with pseudogaps,” Phys. Rev. Lett. 88(9), 093902 (2002).
[PubMed]

Yang, J.-K.

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).
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Yang, Y.

S.-Y. Zhu, Y. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84(10), 2136–2139 (2000).
[PubMed]

Yoshie, T.

Zhang, Z.-Q.

Z.-Y. Li, L.-L. Lin, and Z.-Q. Zhang, “Spontaneous emission from photonic crystals: full vectorial calculations,” Phys. Rev. Lett. 84(19), 4341–4344 (2000).
[PubMed]

Zheng, H.

S.-Y. Zhu, Y. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84(10), 2136–2139 (2000).
[PubMed]

Zhou, G.

J. Li, B. Jia, G. Zhou, C. Bullen, J. Serbin, and M. Gu, “Spectral redistribution in spontaneous emission from quantum-dot-infiltrated 3D woodpile photonic crystals for telecommunications,” Adv. Mater. (Deerfield Beach Fla.) 19(20), 3276–3280 (2007).

Zhu, S.-Y.

S.-Y. Zhu, Y. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84(10), 2136–2139 (2000).
[PubMed]

Zubairy, M. S.

S.-Y. Zhu, Y. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84(10), 2136–2139 (2000).
[PubMed]

Zubrzycki, W.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

Adv. Mater. (Deerfield Beach Fla.)

J. Li, B. Jia, G. Zhou, C. Bullen, J. Serbin, and M. Gu, “Spectral redistribution in spontaneous emission from quantum-dot-infiltrated 3D woodpile photonic crystals for telecommunications,” Adv. Mater. (Deerfield Beach Fla.) 19(20), 3276–3280 (2007).

M. J. Ventura and M. Gu, “Engineering spontaneous emission in a quantum-dot-doped polymer nanocomposite with three-dimensional photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(7), 1329–1332 (2008).

Front. Phys. China

J.- Liu and X.-H. Wang, “Spontaneous emission in micro- and nano-structures,” Front. Phys. China 5(3), 245–259 (2010).

J. Opt. Soc. Am. B

Laser Photon. Rev.

M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).

Nat. Mater.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009).
[PubMed]

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[PubMed]

Nat. Photonics

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).

Nature

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[PubMed]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).

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).
[PubMed]

Opt. Lett.

Phys. Rev. A

W. L. Vos, A. F. Koenderink, and I. S. Nikolaev, “Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment,” Phys. Rev. A 80(5), 053802 (2009).

M. Megens, J. E. G. J. Wijnhoven, A. Lagendijk, and W. L. Vos, “Fluorescence lifetimes and linewidths of dye in photonic crystals,” Phys. Rev. A 59(6), 4727–4731 (1999).

Phys. Rev. B

H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13(12), 5188–5192 (1976).

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67(15), 155114 (2003).

Phys. Rev. B Condens. Matter

S. John and J. Wang, “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B Condens. Matter 43(16), 12772–12789 (1991).
[PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(3), 3896–3908 (1998).

Phys. Rev. Lett.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random photonic media,” Phys. Rev. Lett. 105(1), 013904 (2010).
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Figures (4)

Fig. 1
Fig. 1

Sketch of a woodpile structure and the Brillouin zone.

Fig. 2
Fig. 2

Averaged lifetime distributions of the emitters in woodpile PCs with different transition frequencies 0.905 ( 2 π c / a ) , 0.931 ( 2 π c / a ) and 0.956 ( 2 π c / a ) , respectively. (a) for the emitters located on the two surfaces far from the rod surface by 3nm and 6nm outside the elliptical rods, (b) for the emitters distributed on the surface far from the rod surface by 3nm outside the elliptical rods, and (c) for the emitters spread on the surface far from the rod surface by 3nm inside the elliptical rods. (d) The orange line corresponds to the emitters of transition frequency 0.732 ( 2 π c / a ) at the surface of the globules in the FCC structure. The black line is the same as that in Fig. 2(a) with the transition frequency 0.931 ( 2 π c / a ) .

Fig. 3
Fig. 3

Averaged lifetime distribution of emitters with a reduced transition frequency 0.658 and lying on the planes (a) z = 0; (b) z = a /4; (c) z = a /2; (d) z = 3a/4.

Fig. 4
Fig. 4

Orientation-dependent emission lifetime distributions for an emitter at a fixed position in woodpile PCs. (a) Curves (I) and (II) are emission lifetime distributions of an emitter located at the points (0.055a, 0, 0) and (0, 0.122a, 0.25a) at a frequency 0.931 ( 2 π c / a ) . Insets (I) and (II) are the relative emission lifetime surfaces versus the dipole orientation on the same points and at the same frequency as the curves (I) and (II). (b) Curves (III) and (IV) are emission lifetime distributions of an emitter located at the point (0.055a, 0, 0) at the frequency 0.658 ( 2 π c / a ) and 0.956 ( 2 π c / a ) , respectively. Insets (III) and (IV) are the relative emission lifetime surfaces versus the dipole orientation at the same point and the same frequency as the curves (III) and (IV).

Equations (6)

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ρ ( τ ˜ ) = i W i δ ( τ ˜ τ ˜ ( r i , ω , μ d ) ) ,
τ ( r , ω , μ d ) = [ π d 2 ω e g 2 3 ε 0 ω ρ L D O S O D ( r , ω , μ d ) ] 1 ,
ρ L D O S O D ( r , ω , μ d ) = 3 ( 2 π ) 3 n F B Z d k | μ d E n ( k , r ) | 2 δ ( ω ω n k ) ,
ρ L D O S O A ( r , ω ) = 1 ( 2 π ) 3 n F B Z d k | E n ( k , r ) | 2 δ ( ω ω n k ) .
ρ ( τ ˜ ) = i δ ( τ ˜ τ ˜ ( r i , ω ) ) .
ρ ( τ ˜ ) = θ , φ δ ( τ ˜ τ ˜ ( ω , μ d ( θ , φ ) ) ,

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