Abstract

Hybrid quantum information protocols are based on local qubits, such as trapped atoms, NV centers, and quantum dots, coupled to photons. The coupling is achieved through optical cavities. Here we demonstrate far-field optimized H1 photonic crystal membrane cavities combined with an additional back reflection mirror below the membrane that meet the optical requirements for implementing hybrid quantum information protocols. Using numerical optimization we find that 80% of the light can be radiated within an objective numerical aperture of 0.8, and the coupling to a single-mode fiber can be as high as 92%. We experimentally prove the unique external mode matching properties by resonant reflection spectroscopy with a cavity mode visibility above 50%.

© 2012 OSA

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    [CrossRef] [PubMed]
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  3. S. Strauf, N. G. Stoltz, M. T. Rakher, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “High-frequency single-photon source with polarization control,” Rep. Prog. Phys., vol. 68, p. 1129, 2005.
    [CrossRef]
  4. S. Reitzenstein and A. Forchel, “Quantum dot micropillars,” Journal of Physics D: Applied Physics, vol. 43, p. 033001, 2010.
    [CrossRef]
  5. M. Larqué, T. Karle, I. Robert-Philip, and A. Beveratos, “Optimizing H1 cavities for the generation of entangled photon pairs,” New Journal of Physics, vol. 11, p. 033022, 2009.
    [CrossRef]
  6. P. K. Pathak and S. Hughes, “Cavity-assisted fast generation of entangled photon pairs through the biexiton-exiton cascade,” Physical Review B, vol. 80, p. 155325, 2009.
    [CrossRef]
  7. S. M. de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyński, N. Dupuis, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Applied Physics Letters, vol. 99, p. 101103, 2011.
    [CrossRef]
  8. R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “Triggered polarization-entangled photon pairs from a single quantum dot up to 30 k,” New Journal of Physics, vol. 9, p. 315, 2007.
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    [CrossRef]
  13. C. Bonato, F. Haupt, S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Physical Review Letters, vol. 104, p. 160503, 2010.
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    [CrossRef]
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  22. D. Pinotsi, J. M. Sanchez, P. Fallahi, A. Badalato, and A. Imamog̃lu, “Charge controlled self-assembled quantum dots couple to photonic crystal nanocavities,” Photon. Nanostruct.: Fundam. Appl., p. doi:, 2011.
    [CrossRef]
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    [CrossRef] [PubMed]
  24. K. Hennessy, C. Högerle, E. Hu, A. Badalato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Applied Physics Letters, vol. 89, p. 041118, 2006.
    [CrossRef]
  25. I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,” Applied Physics Letters, vol. 100, p. 121116, 2012.
    [CrossRef]
  26. S.-H. Kim and Y.-H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE Journal of Quantum Electronics, vol. 39, p. 1081, 2003.
    [CrossRef]
  27. Lumerical Solutions, Inc.
    [CrossRef]
  28. J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE Journal of Quantum Electronics, vol. 38, p. 850, 2002.
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    [CrossRef]
  30. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A, vol. 20, p. 569, 2003.
    [CrossRef]

2012

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,” Applied Physics Letters, vol. 100, p. 121116, 2012.
[CrossRef]

2011

S. M. de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyński, N. Dupuis, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Applied Physics Letters, vol. 99, p. 101103, 2011.
[CrossRef]

2010

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature Letters, vol. 466, p. 217, 2010.
[CrossRef] [PubMed]

S. T. Yilmaz, P. Fallahi, and A. Imamoğlu, “Quantum-dot-spin single-photon interface,” Phys. Rev. Lett., vol. 105, p. 033601, 2010.
[CrossRef] [PubMed]

S. Reitzenstein and A. Forchel, “Quantum dot micropillars,” Journal of Physics D: Applied Physics, vol. 43, p. 033001, 2010.
[CrossRef]

C. Bonato, F. Haupt, S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Physical Review Letters, vol. 104, p. 160503, 2010.
[CrossRef] [PubMed]

N.-V.-Q. Tran, S. Combrié, P. Colman, T. Mei, and A. D. Rossi, “Vertical high emission in photonic crystal nanocavities by band-folding design,” Physical Review B, vol. 82, p. 075120, 2010.
[CrossRef]

S. L. Portalupi, M. Galli, C. Reardon, T. F. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Optics Express, vol. 18, p. 16064, 2010.
[CrossRef] [PubMed]

2009

M. T. Rakher, N. G. Stoltz, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “Externally mode-matched cavity quantum electrodynamics with charge-tunable quantum dots,” Physical Review Letters, vol. 102, p. 097403, 2009.
[CrossRef]

C. Y. Hu, W. J. Munro, J. L. O’Brien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B, vol. 80, p. 205326, 2009.
[CrossRef]

N.-V.-Q. Tran, S. Combrié, and A. D. Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Physical Review B, vol. 79, p. 041101, 2009.
[CrossRef]

M. Larqué, T. Karle, I. Robert-Philip, and A. Beveratos, “Optimizing H1 cavities for the generation of entangled photon pairs,” New Journal of Physics, vol. 11, p. 033022, 2009.
[CrossRef]

P. K. Pathak and S. Hughes, “Cavity-assisted fast generation of entangled photon pairs through the biexiton-exiton cascade,” Physical Review B, vol. 80, p. 155325, 2009.
[CrossRef]

2008

C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: applications to entangling remote spins via a single photon,” Phys. Rev. B, vol. 78, p. 085307, 2008.
[CrossRef]

2007

R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “Triggered polarization-entangled photon pairs from a single quantum dot up to 30 k,” New Journal of Physics, vol. 9, p. 315, 2007.
[CrossRef]

B. Lounis and M. Orrit, “Single-photon sources,” Nature Photonics, vol. 1, p. 704, 2007.
[CrossRef]

A. Auffèves-Garnier, C. Simon, J.-M. Gérard, and J.-P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,” Physical Review A, vol. 75, p. 053823, 2007.
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vučković, “Controlling cavity reflectivity with a single quantum dot,” Nature, vol. 450, p. 857, 2007.
[CrossRef] [PubMed]

M. Shirane, S. Kono, J. Ushida, S. Ohkouchi, N. Ikeda, Y. Sugimoto, and A. Tomita, “Mode identification of high-quality-factor single-defect nanocavities in quantum dot-embedded photonic crystals,” Journal of Applied Physics, vol. 101, p. 073107, 2007.
[CrossRef] [PubMed]

2006

K. Hennessy, C. Högerle, E. Hu, A. Badalato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Applied Physics Letters, vol. 89, p. 041118, 2006.
[CrossRef]

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Physical Review B, vol. 73, p. 235117, 2006.
[CrossRef]

E. Waks and J. Vučković, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Physical Review Letters, vol. 96, p. 153601, 2006.
[CrossRef] [PubMed]

2005

S. Strauf, N. G. Stoltz, M. T. Rakher, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “High-frequency single-photon source with polarization control,” Rep. Prog. Phys., vol. 68, p. 1129, 2005.
[CrossRef]

2003

K. Vahala, “Optical microcavities,” Nature424, 839 (2003).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature, vol. 425, p. 944, 2003.
[CrossRef] [PubMed]

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A, vol. 20, p. 569, 2003.
[CrossRef]

S.-H. Kim and Y.-H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE Journal of Quantum Electronics, vol. 39, p. 1081, 2003.
[CrossRef]

2002

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE Journal of Quantum Electronics, vol. 38, p. 850, 2002.

Ahmadi, E. D.

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,” Applied Physics Letters, vol. 100, p. 121116, 2012.
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature, vol. 425, p. 944, 2003.
[CrossRef] [PubMed]

Andreani, L. C.

S. L. Portalupi, M. Galli, C. Reardon, T. F. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Optics Express, vol. 18, p. 16064, 2010.
[CrossRef] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature, vol. 425, p. 944, 2003.
[CrossRef] [PubMed]

Auffèves-Garnier, A.

A. Auffèves-Garnier, C. Simon, J.-M. Gérard, and J.-P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,” Physical Review A, vol. 75, p. 053823, 2007.
[CrossRef]

Badalato, A.

K. Hennessy, C. Högerle, E. Hu, A. Badalato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Applied Physics Letters, vol. 89, p. 041118, 2006.
[CrossRef]

D. Pinotsi, J. M. Sanchez, P. Fallahi, A. Badalato, and A. Imamog̃lu, “Charge controlled self-assembled quantum dots couple to photonic crystal nanocavities,” Photon. Nanostruct.: Fundam. Appl., p. doi:, 2011.
[CrossRef]

Beveratos, A.

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature Letters, vol. 466, p. 217, 2010.
[CrossRef] [PubMed]

M. Larqué, T. Karle, I. Robert-Philip, and A. Beveratos, “Optimizing H1 cavities for the generation of entangled photon pairs,” New Journal of Physics, vol. 11, p. 033022, 2009.
[CrossRef]

Bloch, J.

S. M. de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyński, N. Dupuis, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Applied Physics Letters, vol. 99, p. 101103, 2011.
[CrossRef]

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature Letters, vol. 466, p. 217, 2010.
[CrossRef] [PubMed]

Bonato, C.

C. Bonato, F. Haupt, S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Physical Review Letters, vol. 104, p. 160503, 2010.
[CrossRef] [PubMed]

Bouwmeester, D.

C. Bonato, F. Haupt, S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Physical Review Letters, vol. 104, p. 160503, 2010.
[CrossRef] [PubMed]

M. T. Rakher, N. G. Stoltz, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “Externally mode-matched cavity quantum electrodynamics with charge-tunable quantum dots,” Physical Review Letters, vol. 102, p. 097403, 2009.
[CrossRef]

S. Strauf, N. G. Stoltz, M. T. Rakher, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “High-frequency single-photon source with polarization control,” Rep. Prog. Phys., vol. 68, p. 1129, 2005.
[CrossRef]

Calvar, A.

S. M. de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyński, N. Dupuis, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Applied Physics Letters, vol. 99, p. 101103, 2011.
[CrossRef]

Coldren, L. A.

M. T. Rakher, N. G. Stoltz, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “Externally mode-matched cavity quantum electrodynamics with charge-tunable quantum dots,” Physical Review Letters, vol. 102, p. 097403, 2009.
[CrossRef]

S. Strauf, N. G. Stoltz, M. T. Rakher, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “High-frequency single-photon source with polarization control,” Rep. Prog. Phys., vol. 68, p. 1129, 2005.
[CrossRef]

Colman, P.

N.-V.-Q. Tran, S. Combrié, P. Colman, T. Mei, and A. D. Rossi, “Vertical high emission in photonic crystal nanocavities by band-folding design,” Physical Review B, vol. 82, p. 075120, 2010.
[CrossRef]

Combrié, S.

N.-V.-Q. Tran, S. Combrié, P. Colman, T. Mei, and A. D. Rossi, “Vertical high emission in photonic crystal nanocavities by band-folding design,” Physical Review B, vol. 82, p. 075120, 2010.
[CrossRef]

N.-V.-Q. Tran, S. Combrié, and A. D. Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Physical Review B, vol. 79, p. 041101, 2009.
[CrossRef]

de Vasconcellos, S. M.

S. M. de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyński, N. Dupuis, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Applied Physics Letters, vol. 99, p. 101103, 2011.
[CrossRef]

Ding, D.

C. Bonato, F. Haupt, S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Physical Review Letters, vol. 104, p. 160503, 2010.
[CrossRef] [PubMed]

Dousse, A.

S. M. de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyński, N. Dupuis, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Applied Physics Letters, vol. 99, p. 101103, 2011.
[CrossRef]

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature Letters, vol. 466, p. 217, 2010.
[CrossRef] [PubMed]

Dupuis, N.

S. M. de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyński, N. Dupuis, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Applied Physics Letters, vol. 99, p. 101103, 2011.
[CrossRef]

Englund, D.

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vučković, “Controlling cavity reflectivity with a single quantum dot,” Nature, vol. 450, p. 857, 2007.
[CrossRef] [PubMed]

Fallahi, P.

S. T. Yilmaz, P. Fallahi, and A. Imamoğlu, “Quantum-dot-spin single-photon interface,” Phys. Rev. Lett., vol. 105, p. 033601, 2010.
[CrossRef] [PubMed]

D. Pinotsi, J. M. Sanchez, P. Fallahi, A. Badalato, and A. Imamog̃lu, “Charge controlled self-assembled quantum dots couple to photonic crystal nanocavities,” Photon. Nanostruct.: Fundam. Appl., p. doi:, 2011.
[CrossRef]

Fan, S.

Faraon, A.

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vučković, “Controlling cavity reflectivity with a single quantum dot,” Nature, vol. 450, p. 857, 2007.
[CrossRef] [PubMed]

Forchel, A.

S. Reitzenstein and A. Forchel, “Quantum dot micropillars,” Journal of Physics D: Applied Physics, vol. 43, p. 033001, 2010.
[CrossRef]

Fox, A. M.

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,” Applied Physics Letters, vol. 100, p. 121116, 2012.
[CrossRef]

Fushman, I.

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vučković, “Controlling cavity reflectivity with a single quantum dot,” Nature, vol. 450, p. 857, 2007.
[CrossRef] [PubMed]

Galli, M.

S. L. Portalupi, M. Galli, C. Reardon, T. F. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Optics Express, vol. 18, p. 16064, 2010.
[CrossRef] [PubMed]

Gerace, D.

S. L. Portalupi, M. Galli, C. Reardon, T. F. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Optics Express, vol. 18, p. 16064, 2010.
[CrossRef] [PubMed]

Gérard, J.-M.

A. Auffèves-Garnier, C. Simon, J.-M. Gérard, and J.-P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,” Physical Review A, vol. 75, p. 053823, 2007.
[CrossRef]

Gudat, J.

C. Bonato, F. Haupt, S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Physical Review Letters, vol. 104, p. 160503, 2010.
[CrossRef] [PubMed]

Hafenbrak, R.

R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “Triggered polarization-entangled photon pairs from a single quantum dot up to 30 k,” New Journal of Physics, vol. 9, p. 315, 2007.
[CrossRef]

Haupt, F.

C. Bonato, F. Haupt, S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Physical Review Letters, vol. 104, p. 160503, 2010.
[CrossRef] [PubMed]

Hennessy, K.

K. Hennessy, C. Högerle, E. Hu, A. Badalato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Applied Physics Letters, vol. 89, p. 041118, 2006.
[CrossRef]

Högerle, C.

K. Hennessy, C. Högerle, E. Hu, A. Badalato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Applied Physics Letters, vol. 89, p. 041118, 2006.
[CrossRef]

Hu, C. Y.

C. Y. Hu, W. J. Munro, J. L. O’Brien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B, vol. 80, p. 205326, 2009.
[CrossRef]

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Applied Physics Letters

S. M. de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyński, N. Dupuis, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Applied Physics Letters, vol. 99, p. 101103, 2011.
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I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,” Applied Physics Letters, vol. 100, p. 121116, 2012.
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IEEE Journal of Quantum Electronics

S.-H. Kim and Y.-H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE Journal of Quantum Electronics, vol. 39, p. 1081, 2003.
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J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE Journal of Quantum Electronics, vol. 38, p. 850, 2002.

J. Opt. Soc. Am. A

Journal of Applied Physics

M. Shirane, S. Kono, J. Ushida, S. Ohkouchi, N. Ikeda, Y. Sugimoto, and A. Tomita, “Mode identification of high-quality-factor single-defect nanocavities in quantum dot-embedded photonic crystals,” Journal of Applied Physics, vol. 101, p. 073107, 2007.
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Journal of Physics D: Applied Physics

S. Reitzenstein and A. Forchel, “Quantum dot micropillars,” Journal of Physics D: Applied Physics, vol. 43, p. 033001, 2010.
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Nature

K. Vahala, “Optical microcavities,” Nature424, 839 (2003).
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D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vučković, “Controlling cavity reflectivity with a single quantum dot,” Nature, vol. 450, p. 857, 2007.
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Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature, vol. 425, p. 944, 2003.
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Nature Letters

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature Letters, vol. 466, p. 217, 2010.
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Nature Photonics

B. Lounis and M. Orrit, “Single-photon sources,” Nature Photonics, vol. 1, p. 704, 2007.
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New Journal of Physics

M. Larqué, T. Karle, I. Robert-Philip, and A. Beveratos, “Optimizing H1 cavities for the generation of entangled photon pairs,” New Journal of Physics, vol. 11, p. 033022, 2009.
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R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “Triggered polarization-entangled photon pairs from a single quantum dot up to 30 k,” New Journal of Physics, vol. 9, p. 315, 2007.
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Optics Express

S. L. Portalupi, M. Galli, C. Reardon, T. F. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Optics Express, vol. 18, p. 16064, 2010.
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Phys. Rev. B

C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: applications to entangling remote spins via a single photon,” Phys. Rev. B, vol. 78, p. 085307, 2008.
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C. Y. Hu, W. J. Munro, J. L. O’Brien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B, vol. 80, p. 205326, 2009.
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Phys. Rev. Lett.

S. T. Yilmaz, P. Fallahi, and A. Imamoğlu, “Quantum-dot-spin single-photon interface,” Phys. Rev. Lett., vol. 105, p. 033601, 2010.
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Physical Review A

A. Auffèves-Garnier, C. Simon, J.-M. Gérard, and J.-P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,” Physical Review A, vol. 75, p. 053823, 2007.
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Physical Review B

P. K. Pathak and S. Hughes, “Cavity-assisted fast generation of entangled photon pairs through the biexiton-exiton cascade,” Physical Review B, vol. 80, p. 155325, 2009.
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S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Physical Review B, vol. 73, p. 235117, 2006.
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N.-V.-Q. Tran, S. Combrié, and A. D. Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Physical Review B, vol. 79, p. 041101, 2009.
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N.-V.-Q. Tran, S. Combrié, P. Colman, T. Mei, and A. D. Rossi, “Vertical high emission in photonic crystal nanocavities by band-folding design,” Physical Review B, vol. 82, p. 075120, 2010.
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Physical Review Letters

C. Bonato, F. Haupt, S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Physical Review Letters, vol. 104, p. 160503, 2010.
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E. Waks and J. Vučković, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Physical Review Letters, vol. 96, p. 153601, 2006.
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M. T. Rakher, N. G. Stoltz, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “Externally mode-matched cavity quantum electrodynamics with charge-tunable quantum dots,” Physical Review Letters, vol. 102, p. 097403, 2009.
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Rep. Prog. Phys.

S. Strauf, N. G. Stoltz, M. T. Rakher, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “High-frequency single-photon source with polarization control,” Rep. Prog. Phys., vol. 68, p. 1129, 2005.
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Other

D. Pinotsi, J. M. Sanchez, P. Fallahi, A. Badalato, and A. Imamog̃lu, “Charge controlled self-assembled quantum dots couple to photonic crystal nanocavities,” Photon. Nanostruct.: Fundam. Appl., p. doi:, 2011.
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Figures (11)

Fig. 1
Fig. 1

(a) Sketch of the H1 cavity, indicating the outward shift and reduced size of the six nearest air holes. (b) SEM image of a fabricated H1 cavity PhC device; scale bar: 2 μm. (c) Characteristic photoluminescence measurement of a fabricated device, illustrating the splitting of the H and V modes due to fabrication imperfections. (d) FDTD simulated near-field amplitude components for the H dipole mode (top row) and the V dipole mode (bottom row). Plotted for each mode are Re(Ex) and Re(Ey). Scale bar in all plots: 250 nm. (e) FDTD simulated far-field radiation intensities of Ex and Ey components for the H dipole mode (top row) and the V dipole mode (bottom row). The white concentric circles correspond to NA = 0.2, 0.4, 0.6, 0.8, and 1.0.

Fig. 2
Fig. 2

(a) Simulated Q of the H dipole mode as a function of s/a. Simulations without a bottom reflector are represented by the blue circles (labeled ‘no R’), and simulations with a bottom reflector separated by an air gap of L = 925 nm are represented by the red squares (labeled ‘with R’). (b) Simulated collection efficiency as a function of s/a for NA = 0.5 (in blue), 0.8 (in red), and 0.9 (in green). Simulations with (without) a bottom reflector are represented by squares (circles). For simulations without the bottom reflector, the collection efficiency maximum is 50%; however, with the bottom reflector, the maximum collection efficiency is 100%. The ideal compromise value, s/a = 0.115, is indicated by the cyan ellipse, where the Q is 15,000 and the coupling efficiency for an objective with NA of 0.8 is 80%.

Fig. 3
Fig. 3

Top: FDTD simulated Q (blue solid curve) and fiber mode-matching (green dashed curve) of the H dipole mode as a function of air gap separation L. The best compromise, indicated by the red ellipse, occurs for L = 925 nm. Bottom: Simulated far-field radiation patterns for devices of different L values. Each profile is normalized by its own maximum intensity, with a scale bar shown at the far right. As the air gap separation increases, the mode profiles become more Gaussian, which show better coupling to a single-mode fiber. The white concentric circles correspond to NA = 0.2, 0.4, 0.6, 0.8, and 1.0.

Fig. 4
Fig. 4

A plot of the total radiation intensity (W = |S +1|2) as a function of NA, for different values of L/λ. The calculation is done for the following paramaters: neff = 2.8, λ = 963 nm, d = 130 nm, and ε = π. In the bottom panel, line cuts are taken for L/λ = 0.93 (left, in pink), 0.96 (middle, in green), and 1.06 (right, in cyan). Plotted are a Gaussian (blue curve) and the Gaussian convolved with the function |S + 1|2 (red curve). The experimental air gap of L = 925 nm, for λ = 963 nm, is represented by the middle green curve.

Fig. 5
Fig. 5

Top row: FDTD simulated far-field profiles, considering the membrane only, for different values of s/a. The profiles are cut off at NA = 0.8 to allow for better comparison with experimental results. Middle row: FDTD simulations, including the air gap and DBR, for the same s/a values as above. For increasing shift values, the vertical beaming of the radiation clearly improves. Bottom row: Experimental far-field profiles, for one row of devices, showing a nice comparison with simulation results.

Fig. 6
Fig. 6

Reflection dips for cavities with different outward shift parameters, including s/a = 0.100, 0.115, 0.131, and 0.146. Data points are in blue, and the red curves are Fano line-shapes as predicted by our model, with rDBR = 0.95, and the mode-matching being the only free parameter. Larger dips are seen for cavities that were optimized for Gaussian-like far-field profiles. The measured far-field profiles (both H and V) for each of the cavities are shown below the reflection curves.

Fig. 7
Fig. 7

Model for asymmetric Fano lineshapes, using a temporal coupled-mode theory. (a) Representation of the PhC cavity, with two input/output ports. (b) Schematic of the full structure, including the PhC membrane, the air gap, the DBR mirror, and the substrate.

Fig. 8
Fig. 8

(a) Simulated Q of the H dipole mode as a function of rsm/r, where rsm represents the radius of the six nearest holes, and r represents the radius of the other holes in the PhC lattice. (b) Simulated collection efficiency as a function of rsm/r for NA = 0.5 (in blue), 0.8 (in red), and 0.9 (in green). The ideal compromise value, rsm/r = 0.64, is indicated by the red ellipse, where the Q is 17,000 and the coupling efficiency for an objective with NA of 0.8 is 40%.

Fig. 9
Fig. 9

Top row: FDTD simulated far-field profiles, considering the membrane only, for different values of rsm/r. The profiles are cut off at NA = 0.8 to allow for better comparison with experimental results. For decreasing small hole size, the radiation becomes more concentrated at small angles. Middle row: FDTD simulations, including the bottom reflector, for the same rsm/r values as above. Bottom row: Experimental far-field profiles, for row A of devices, showing a nice comparison with simulation results.

Fig. 10
Fig. 10

Top row: FDTD simulated far-field profiles, considering the membrane only, for different values of rsm/r. The profiles are cut off at NA = 0.8 to allow for better comparison with experimental results. For decreasing small hole size, the radiation becomes more concentrated at small angles. Middle row: FDTD simulations, including the bottom reflector, for the same rsm/r values as above. Bottom row: Experimental far-field profiles, for row B of devices, showing a nice comparison with simulation results.

Fig. 11
Fig. 11

Top row: FDTD simulated far-field profiles of the V dipole mode, considering the membrane only, for different values of s/a. The profiles are cut off at NA = 0.8 to allow for better comparison with experimental results. For increasing shift values, the vertical beaming of the signal improves. Middle row: FDTD simulations, including the bottom reflector, for the same s/a values as above. Bottom row: Experimental far-field profiles, for one row of devices, showing a nice comparison with simulation results.

Equations (11)

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ψ 2 ( r ) = 1 3 [ R 2 π / 3 ψ 1 ( r ) + R π / 3 ψ 1 ( r ) ]
ϕ = ( 2 π n eff λ ) d 1 ( 1 / n eff ) 2 sin 2 θ ,
φ = ( 2 π λ ) L cos θ .
S = t 0 2 e i ϕ ( 1 r 0 2 e 2 i ϕ ) ( r 0 + e 2 i φ e i ε ) r 0 t 0 2 e 2 i ϕ ,
W = | 1 + S | 2 .
[ E 1 E 2 ] = [ Σ 11 Σ 12 Σ 21 Σ 22 ] [ E 1 E 2 ]
Σ = [ r j t j t r ] ( r + j t ) / τ j ( ω ω 0 ) + 1 / τ [ 1 1 1 1 ]
R ( ω ) = r 2 ( ω ω 0 ) 2 + ( t / τ ) 2 + 2 r t ( ω ω 0 ) / τ ( ω ω 0 ) 2 + ( 1 / τ ) 2
E 2 = r D B R e 2 i ω L / c E 2
E 2 = r D B R e 2 i ω L / c Σ 21 ( ω ) 1 r D B R e 2 i ω L / c Σ 22 ( ω ) E 1
R eff ( ω ) = | Σ 11 ( ω ) + r D B R e 2 i ω L / c Σ 21 ( ω ) Σ 12 ( ω ) 1 r D B R e 2 i ω L / c Σ 22 ( ω ) | 2

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