Abstract

We present a method to analyze the suitability of particular photonic cavity designs for information exchange between arbitrary superposition states of a quantum emitter and the near-field photonic cavity mode. As an illustrative example, we consider whether quantum dot emitters embedded in “L3” and “H1” photonic crystal cavities are able to transfer a spin superposition state to a confined photonic superposition state for use in quantum information transfer. Using an established dyadic Green’s function (DGF) analysis, we describe methods to calculate coupling to arbitrary quantum emitter positions and orientations using the modified local density of states (LDOS) calculated using numerical finite-difference time-domain (FDTD) simulations. We find that while superposition states are not supported in L3 cavities, the double degeneracy of the H1 cavities supports superposition states of the two orthogonal modes that may be described as states on a Poincaré-like sphere. Methods are developed to comprehensively analyze the confined superposition state generated from an arbitrary emitter position and emitter dipole orientation.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
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  4. C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
    [CrossRef] [PubMed]
  5. 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 (London) 432, 200–203 (2004).
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    [CrossRef]
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  24. P. Biagioni, M. Savoini, J.-S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
    [CrossRef]
  25. Y. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18, 12489–12498 (2010).
    [CrossRef] [PubMed]
  26. T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study,” Phys. Rev. B 69, 045422 (2004).
    [CrossRef]
  27. A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
    [CrossRef]
  28. R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
    [CrossRef] [PubMed]
  29. S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
    [CrossRef]
  30. O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis,” Phys. Rev. B 68, 035110 (2003).
    [CrossRef]
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    [CrossRef]
  34. V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys. 107, 6756–6769 (1997).
    [CrossRef]
  35. S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M. Irvine, P. M. Petroff, and D. Bouwmeester, “Strong coupling through optical positioning of a quantum dot in a photonic crystal cavity,” Appl. Phys. Lett. 94, 111115 (2009).
    [CrossRef]

2012 (3)

I. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hughes, M. S. Skolnick, and A. M. Fox, “Restoring mode denegeracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett. 100, 121116 (2012).
[CrossRef]

C. H. Gan, J. P. Hugonin, and P. Lalanne, “Proposal for compact solid-state III–V single-plasmon source,” Phys. Rev. X 2, 021008 (2012).
[CrossRef]

P. T. Kristensen, C. Van Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
[CrossRef] [PubMed]

2011 (1)

P. T. Kristensen, J. Mørk, P. Lodahl, and S. Hughes, “Decay dynamics of radiatively coupled quantum dots in photonic crystal slabs,” Phys. Rev. B 83, 075305 (2011).
[CrossRef]

2010 (4)

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 (London) 466, 217–220 (2010).
[CrossRef]

Y. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18, 12489–12498 (2010).
[CrossRef] [PubMed]

S. Reizenstein, C. Böckler, A. Löffler, S. Höfling, L. Worschech, A. Forchel, P. Yao, and S. Hughes, “Polarization-dependent strong coupling in elliptical high-Q micropillar cavities,” Phys. Rev. B 82, 235313 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
[CrossRef]

2009 (6)

S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M. Irvine, P. M. Petroff, and D. Bouwmeester, “Strong coupling through optical positioning of a quantum dot in a photonic crystal cavity,” Appl. Phys. Lett. 94, 111115 (2009).
[CrossRef]

Y. Ota, M. Shirane, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Vacuum Rabi splitting with a single quantum dot embedded in a H1 photonic crystal nanocavity,” Appl. Phys. Lett. 94, 033102 (2009).
[CrossRef]

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

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

P. Biagioni, M. Savoini, J.-S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

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, 053802 (2009).
[CrossRef]

2008 (1)

C. Y. Hu, A. Young, J. L. OBrien, 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 78, 085307 (2008).
[CrossRef]

2007 (2)

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
[CrossRef] [PubMed]

2006 (2)

S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
[CrossRef]

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

2005 (3)

S. Hughes, “Modified spontaneous emission and qubit entanglement from dipole-coupled quantum dots in a photonic crystal nanocavity,” Phys. Rev. Lett. 94, 227402 (2005).
[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, 067401 (2005).
[CrossRef] [PubMed]

S. Hughes, “Quantum Emission dynamics from a single quantum dot in a planar photonic crystal nanocavity,” Opt. Lett. 30, 1393–1395 (2005).
[CrossRef] [PubMed]

2004 (3)

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study,” Phys. Rev. B 69, 045422 (2004).
[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 dotsemiconductor microcavity system,” Nature (London) 432, 197–200 (2004).
[CrossRef]

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

2003 (2)

A. R. Cowman and J. F. Young, “Optical bistability involving photonic crystal microcavities and Fano line shapes,” Phys. Rev. E 68, 046606 (2003).
[CrossRef]

O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis,” Phys. Rev. B 68, 035110 (2003).
[CrossRef]

1999 (1)

J. M. Gérard and B. Gayral, “Strong Purcell effect for InAs quantum boxes in three-dimensional solid-state microcavities,” J. Lightwave Tech. 17, 2089–2095 (1999).
[CrossRef]

1997 (1)

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys. 107, 6756–6769 (1997).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Ahmadi, E. D.

I. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hughes, M. S. Skolnick, and A. M. Fox, “Restoring mode denegeracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett. 100, 121116 (2012).
[CrossRef]

Arakawa, Y.

Y. Ota, M. Shirane, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Vacuum Rabi splitting with a single quantum dot embedded in a H1 photonic crystal nanocavity,” Appl. Phys. Lett. 94, 033102 (2009).
[CrossRef]

Badolato, A.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Benisty, H.

H. Benisty, J. M. Gérard, R. Houdré, J. Rarity, and C. Weisbuch, Confined Photon Systems (Springer, 1999).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
[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 (London) 466, 217–220 (2010).
[CrossRef]

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

Biagioni, P.

P. Biagioni, M. Savoini, J.-S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

Bloch, J.

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 (London) 466, 217–220 (2010).
[CrossRef]

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, 067401 (2005).
[CrossRef] [PubMed]

Böckler, C.

S. Reizenstein, C. Böckler, A. Löffler, S. Höfling, L. Worschech, A. Forchel, P. Yao, and S. Hughes, “Polarization-dependent strong coupling in elliptical high-Q micropillar cavities,” Phys. Rev. B 82, 235313 (2010).
[CrossRef]

Bouwmeester, D.

S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M. Irvine, P. M. Petroff, and D. Bouwmeester, “Strong coupling through optical positioning of a quantum dot in a photonic crystal cavity,” Appl. Phys. Lett. 94, 111115 (2009).
[CrossRef]

Bozhevolnyi, S. I.

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study,” Phys. Rev. B 69, 045422 (2004).
[CrossRef]

Chalcraft, A. R. A.

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
[CrossRef] [PubMed]

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Chen, Y.

Cowman, A. R.

A. R. Cowman and J. F. Young, “Optical bistability involving photonic crystal microcavities and Fano line shapes,” Phys. Rev. E 68, 046606 (2003).
[CrossRef]

Deppe, D. G.

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

Dousse, 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 (London) 466, 217–220 (2010).
[CrossRef]

Duo, L.

P. Biagioni, M. Savoini, J.-S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

Ell, C.

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

Finazzi, M.

P. Biagioni, M. Savoini, J.-S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

Forchel, A.

S. Reizenstein, C. Böckler, A. Löffler, S. Höfling, L. Worschech, A. Forchel, P. Yao, and S. Hughes, “Polarization-dependent strong coupling in elliptical high-Q micropillar cavities,” Phys. Rev. B 82, 235313 (2010).
[CrossRef]

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

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

Fox, A. M.

I. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hughes, M. S. Skolnick, and A. M. Fox, “Restoring mode denegeracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett. 100, 121116 (2012).
[CrossRef]

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
[CrossRef] [PubMed]

Gan, C. H.

C. H. Gan, J. P. Hugonin, and P. Lalanne, “Proposal for compact solid-state III–V single-plasmon source,” Phys. Rev. X 2, 021008 (2012).
[CrossRef]

Gayral, B.

J. M. Gérard and B. Gayral, “Strong Purcell effect for InAs quantum boxes in three-dimensional solid-state microcavities,” J. Lightwave Tech. 17, 2089–2095 (1999).
[CrossRef]

Gérard, J. M.

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, 067401 (2005).
[CrossRef] [PubMed]

J. M. Gérard and B. Gayral, “Strong Purcell effect for InAs quantum boxes in three-dimensional solid-state microcavities,” J. Lightwave Tech. 17, 2089–2095 (1999).
[CrossRef]

H. Benisty, J. M. Gérard, R. Houdré, J. Rarity, and C. Weisbuch, Confined Photon Systems (Springer, 1999).
[CrossRef]

Gibbs, H. M.

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 (London) 432, 200–203 (2004).
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C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

Gregersen, N.

Gudat, J.

S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M. Irvine, P. M. Petroff, and D. Bouwmeester, “Strong coupling through optical positioning of a quantum dot in a photonic crystal cavity,” Appl. Phys. Lett. 94, 111115 (2009).
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P. Biagioni, M. Savoini, J.-S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
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Heindel, T.

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

Hendrickson, J.

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 (London) 432, 200–203 (2004).
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K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Höfling, S.

S. Reizenstein, C. Böckler, A. Löffler, S. Höfling, L. Worschech, A. Forchel, P. Yao, and S. Hughes, “Polarization-dependent strong coupling in elliptical high-Q micropillar cavities,” Phys. Rev. B 82, 235313 (2010).
[CrossRef]

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
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Hofmann, C.

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 dotsemiconductor microcavity system,” Nature (London) 432, 197–200 (2004).
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K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
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Hopkinson, M.

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
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H. Benisty, J. M. Gérard, R. Houdré, J. Rarity, and C. Weisbuch, Confined Photon Systems (Springer, 1999).
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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, 067401 (2005).
[CrossRef] [PubMed]

Hu, C. Y.

C. Y. Hu, A. Young, J. L. OBrien, 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 78, 085307 (2008).
[CrossRef]

Hu, E.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Huang, J.-S.

P. Biagioni, M. Savoini, J.-S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

Huggenberger, A.

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

Hughes, M.

I. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hughes, M. S. Skolnick, and A. M. Fox, “Restoring mode denegeracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett. 100, 121116 (2012).
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Hughes, S.

P. T. Kristensen, C. Van Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
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P. T. Kristensen, J. Mørk, P. Lodahl, and S. Hughes, “Decay dynamics of radiatively coupled quantum dots in photonic crystal slabs,” Phys. Rev. B 83, 075305 (2011).
[CrossRef]

S. Reizenstein, C. Böckler, A. Löffler, S. Höfling, L. Worschech, A. Forchel, P. Yao, and S. Hughes, “Polarization-dependent strong coupling in elliptical high-Q micropillar cavities,” Phys. Rev. B 82, 235313 (2010).
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S. Hughes, “Quantum Emission dynamics from a single quantum dot in a planar photonic crystal nanocavity,” Opt. Lett. 30, 1393–1395 (2005).
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S. Hughes, “Modified spontaneous emission and qubit entanglement from dipole-coupled quantum dots in a photonic crystal nanocavity,” Phys. Rev. Lett. 94, 227402 (2005).
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C. H. Gan, J. P. Hugonin, and P. Lalanne, “Proposal for compact solid-state III–V single-plasmon source,” Phys. Rev. X 2, 021008 (2012).
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Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
[CrossRef]

Imamoglu, A.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Irvine, W. T. M.

S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M. Irvine, P. M. Petroff, and D. Bouwmeester, “Strong coupling through optical positioning of a quantum dot in a photonic crystal cavity,” Appl. Phys. Lett. 94, 111115 (2009).
[CrossRef]

Ishida, S.

Y. Ota, M. Shirane, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Vacuum Rabi splitting with a single quantum dot embedded in a H1 photonic crystal nanocavity,” Appl. Phys. Lett. 94, 033102 (2009).
[CrossRef]

Iwamoto, S.

Y. Ota, M. Shirane, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Vacuum Rabi splitting with a single quantum dot embedded in a H1 photonic crystal nanocavity,” Appl. Phys. Lett. 94, 033102 (2009).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

Jones, B. D.

Kamada, H.

S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to waveguide,” Phys. Rev. B 70, 195313 (2004).

Kamp, M.

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
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M. Larqué, T. Karle, I. Robert-Philip, and A. Beveratos, “Optimizing H1 cavities for the generation of entangled photon pairs,” New J. Phys. 11, 033022 (2009).
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Keldysh, L. V.

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 dotsemiconductor microcavity system,” Nature (London) 432, 197–200 (2004).
[CrossRef]

Khitrova, G.

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

Kim, H.

S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M. Irvine, P. M. Petroff, and D. Bouwmeester, “Strong coupling through optical positioning of a quantum dot in a photonic crystal cavity,” Appl. Phys. Lett. 94, 111115 (2009).
[CrossRef]

Kim, S. H.

S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
[CrossRef]

Kim, S. K.

S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
[CrossRef]

Koenderink, A. F.

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, 053802 (2009).
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Krauss, T. F.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
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Krebs, O.

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 (London) 466, 217–220 (2010).
[CrossRef]

Kristensen, P. T.

P. T. Kristensen, C. Van Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
[CrossRef] [PubMed]

P. T. Kristensen, J. Mørk, P. Lodahl, and S. Hughes, “Decay dynamics of radiatively coupled quantum dots in photonic crystal slabs,” Phys. Rev. B 83, 075305 (2011).
[CrossRef]

Kuhn, S.

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 dotsemiconductor microcavity system,” Nature (London) 432, 197–200 (2004).
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Kulakovskii, V. D.

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 dotsemiconductor microcavity system,” Nature (London) 432, 197–200 (2004).
[CrossRef]

Kumagai, N.

Y. Ota, M. Shirane, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Vacuum Rabi splitting with a single quantum dot embedded in a H1 photonic crystal nanocavity,” Appl. Phys. Lett. 94, 033102 (2009).
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Lalanne, P.

C. H. Gan, J. P. Hugonin, and P. Lalanne, “Proposal for compact solid-state III–V single-plasmon source,” Phys. Rev. X 2, 021008 (2012).
[CrossRef]

Lam, S.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
[CrossRef] [PubMed]

Larqué, M.

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

Lee, Y. H.

S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
[CrossRef]

Lemaître, 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 (London) 466, 217–220 (2010).
[CrossRef]

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, 067401 (2005).
[CrossRef] [PubMed]

Liu, H. Y.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Lodahl, P.

Löffler, A.

S. Reizenstein, C. Böckler, A. Löffler, S. Höfling, L. Worschech, A. Forchel, P. Yao, and S. Hughes, “Polarization-dependent strong coupling in elliptical high-Q micropillar cavities,” Phys. Rev. B 82, 235313 (2010).
[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 dotsemiconductor microcavity system,” Nature (London) 432, 197–200 (2004).
[CrossRef]

Luxmoore, B. J.

I. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hughes, M. S. Skolnick, and A. M. Fox, “Restoring mode denegeracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett. 100, 121116 (2012).
[CrossRef]

Luxmoore, I.

I. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hughes, M. S. Skolnick, and A. M. Fox, “Restoring mode denegeracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett. 100, 121116 (2012).
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V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys. 107, 6756–6769 (1997).
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Martrou, D.

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, 067401 (2005).
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Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

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Munro, W. J.

C. Y. Hu, A. Young, J. L. OBrien, 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 78, 085307 (2008).
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Nielsen, T. R.

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, 053802 (2009).
[CrossRef]

Nomura, M.

Y. Ota, M. Shirane, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Vacuum Rabi splitting with a single quantum dot embedded in a H1 photonic crystal nanocavity,” Appl. Phys. Lett. 94, 033102 (2009).
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L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University Press, 2007).

O’Brien, D.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
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OBrien, J. L.

C. Y. Hu, A. Young, J. L. OBrien, 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 78, 085307 (2008).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
[CrossRef]

Ota, Y.

Y. Ota, M. Shirane, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Vacuum Rabi splitting with a single quantum dot embedded in a H1 photonic crystal nanocavity,” Appl. Phys. Lett. 94, 033102 (2009).
[CrossRef]

Oulton, R.

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
[CrossRef] [PubMed]

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
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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, 067401 (2005).
[CrossRef] [PubMed]

Petroff, P. M.

S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M. Irvine, P. M. Petroff, and D. Bouwmeester, “Strong coupling through optical positioning of a quantum dot in a photonic crystal cavity,” Appl. Phys. Lett. 94, 111115 (2009).
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E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Rakher, M. T.

S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M. Irvine, P. M. Petroff, and D. Bouwmeester, “Strong coupling through optical positioning of a quantum dot in a photonic crystal cavity,” Appl. Phys. Lett. 94, 111115 (2009).
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Rarity, J.

H. Benisty, J. M. Gérard, R. Houdré, J. Rarity, and C. Weisbuch, Confined Photon Systems (Springer, 1999).
[CrossRef]

Rarity, J. G.

C. Y. Hu, A. Young, J. L. OBrien, 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 78, 085307 (2008).
[CrossRef]

Reinecke, T. L.

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 dotsemiconductor microcavity system,” Nature (London) 432, 197–200 (2004).
[CrossRef]

Reithmaier, J. P.

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 dotsemiconductor microcavity system,” Nature (London) 432, 197–200 (2004).
[CrossRef]

Reitzenstein, S.

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

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

Reizenstein, S.

S. Reizenstein, C. Böckler, A. Löffler, S. Höfling, L. Worschech, A. Forchel, P. Yao, and S. Hughes, “Polarization-dependent strong coupling in elliptical high-Q micropillar cavities,” Phys. Rev. B 82, 235313 (2010).
[CrossRef]

Robert-Philip, I.

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

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
[CrossRef]

Rupper, G.

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

Sagnes, I.

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 (London) 466, 217–220 (2010).
[CrossRef]

Sahin, M.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Sanvitto, D.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
[CrossRef] [PubMed]

Savoini, M.

P. Biagioni, M. Savoini, J.-S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

Scherer, A.

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

Schneider, C.

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

Sek, G.

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 dotsemiconductor microcavity system,” Nature (London) 432, 197–200 (2004).
[CrossRef]

Senellart, P.

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 (London) 466, 217–220 (2010).
[CrossRef]

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, 067401 (2005).
[CrossRef] [PubMed]

Shchekin, O. B.

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

Shirane, M.

Y. Ota, M. Shirane, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Vacuum Rabi splitting with a single quantum dot embedded in a H1 photonic crystal nanocavity,” Appl. Phys. Lett. 94, 033102 (2009).
[CrossRef]

Skolnick, M. S.

I. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hughes, M. S. Skolnick, and A. M. Fox, “Restoring mode denegeracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett. 100, 121116 (2012).
[CrossRef]

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
[CrossRef] [PubMed]

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Søndergaard, T.

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study,” Phys. Rev. B 69, 045422 (2004).
[CrossRef]

Srinivasan, K.

O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis,” Phys. Rev. B 68, 035110 (2003).
[CrossRef]

Strau, M.

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

Suffczynski, J.

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 (London) 466, 217–220 (2010).
[CrossRef]

Sünner, T.

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

Szymanski, D.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method (Artech House, 2005).

Tartakovskii, A. I.

I. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hughes, M. S. Skolnick, and A. M. Fox, “Restoring mode denegeracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett. 100, 121116 (2012).
[CrossRef]

Taylor, H. S.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys. 107, 6756–6769 (1997).
[CrossRef]

Thon, S. M.

S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M. Irvine, P. M. Petroff, and D. Bouwmeester, “Strong coupling through optical positioning of a quantum dot in a photonic crystal cavity,” Appl. Phys. Lett. 94, 111115 (2009).
[CrossRef]

Van Vlack, C.

Voisin, P.

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 (London) 466, 217–220 (2010).
[CrossRef]

Vos, W. L.

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, 053802 (2009).
[CrossRef]

Wasley, N. A.

I. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hughes, M. S. Skolnick, and A. M. Fox, “Restoring mode denegeracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett. 100, 121116 (2012).
[CrossRef]

Weinmann, P.

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

Weisbuch, C.

H. Benisty, J. M. Gérard, R. Houdré, J. Rarity, and C. Weisbuch, Confined Photon Systems (Springer, 1999).
[CrossRef]

Whittaker, D. M.

R. Oulton, B. D. Jones, S. Lam, A. R. A. Chalcraft, D. Szymanski, D. O’Brien, T. F. Krauss, D. Sanvitto, A. M. Fox, D. M. Whittaker, M. Hopkinson, and M. S. Skolnick, “Polarized quantum dot emission from photonic crystal nanocavities studied under mode-resonant excitation,” Opt. Express 15, 17221–17230 (2007).
[CrossRef] [PubMed]

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

Worschech, L.

S. Reizenstein, C. Böckler, A. Löffler, S. Höfling, L. Worschech, A. Forchel, P. Yao, and S. Hughes, “Polarization-dependent strong coupling in elliptical high-Q micropillar cavities,” Phys. Rev. B 82, 235313 (2010).
[CrossRef]

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

Yao, P.

S. Reizenstein, C. Böckler, A. Löffler, S. Höfling, L. Worschech, A. Forchel, P. Yao, and S. Hughes, “Polarization-dependent strong coupling in elliptical high-Q micropillar cavities,” Phys. Rev. B 82, 235313 (2010).
[CrossRef]

Yorozu, S.

Y. Ota, M. Shirane, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Vacuum Rabi splitting with a single quantum dot embedded in a H1 photonic crystal nanocavity,” Appl. Phys. Lett. 94, 033102 (2009).
[CrossRef]

Yoshie, T.

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

Young, A.

C. Y. Hu, A. Young, J. L. OBrien, 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 78, 085307 (2008).
[CrossRef]

Young, J. F.

A. R. Cowman and J. F. Young, “Optical bistability involving photonic crystal microcavities and Fano line shapes,” Phys. Rev. E 68, 046606 (2003).
[CrossRef]

Appl. Phys. Lett. (5)

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

I. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hughes, M. S. Skolnick, and A. M. Fox, “Restoring mode denegeracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett. 100, 121116 (2012).
[CrossRef]

Y. Ota, M. Shirane, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Vacuum Rabi splitting with a single quantum dot embedded in a H1 photonic crystal nanocavity,” Appl. Phys. Lett. 94, 033102 (2009).
[CrossRef]

S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M. Irvine, P. M. Petroff, and D. Bouwmeester, “Strong coupling through optical positioning of a quantum dot in a photonic crystal cavity,” Appl. Phys. Lett. 94, 111115 (2009).
[CrossRef]

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Comp. Phys. Comm. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
[CrossRef]

J. Chem. Phys. (1)

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys. 107, 6756–6769 (1997).
[CrossRef]

J. Lightwave Tech. (1)

J. M. Gérard and B. Gayral, “Strong Purcell effect for InAs quantum boxes in three-dimensional solid-state microcavities,” J. Lightwave Tech. 17, 2089–2095 (1999).
[CrossRef]

Nanotechnology (1)

C. Schneider, A. Huggenberger, T. Sünner, T. Heindel, M. Strau, S. Göpfert, P. Weinmann, S. Reitzenstein, L. Worschech, M. Kamp, S. Höfling, and A. Forchel, “Single site-controlled In(Ga)As/GaAs quantum dots: growth, properties and device integration,” Nanotechnology 20, 434012 (2009).
[CrossRef] [PubMed]

Nature (London) (3)

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 (London) 432, 200–203 (2004).
[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 (London) 466, 217–220 (2010).
[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 dotsemiconductor microcavity system,” Nature (London) 432, 197–200 (2004).
[CrossRef]

New J. Phys. (1)

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Phys. Rev. A (1)

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, 053802 (2009).
[CrossRef]

Phys. Rev. B (8)

S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to waveguide,” Phys. Rev. B 70, 195313 (2004).

S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
[CrossRef]

O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis,” Phys. Rev. B 68, 035110 (2003).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study,” Phys. Rev. B 69, 045422 (2004).
[CrossRef]

P. Biagioni, M. Savoini, J.-S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

S. Reizenstein, C. Böckler, A. Löffler, S. Höfling, L. Worschech, A. Forchel, P. Yao, and S. Hughes, “Polarization-dependent strong coupling in elliptical high-Q micropillar cavities,” Phys. Rev. B 82, 235313 (2010).
[CrossRef]

C. Y. Hu, A. Young, J. L. OBrien, 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 78, 085307 (2008).
[CrossRef]

P. T. Kristensen, J. Mørk, P. Lodahl, and S. Hughes, “Decay dynamics of radiatively coupled quantum dots in photonic crystal slabs,” Phys. Rev. B 83, 075305 (2011).
[CrossRef]

Phys. Rev. E (1)

A. R. Cowman and J. F. Young, “Optical bistability involving photonic crystal microcavities and Fano line shapes,” Phys. Rev. E 68, 046606 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

S. Hughes, “Modified spontaneous emission and qubit entanglement from dipole-coupled quantum dots in a photonic crystal nanocavity,” Phys. Rev. Lett. 94, 227402 (2005).
[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, 067401 (2005).
[CrossRef] [PubMed]

Phys. Rev. X (1)

C. H. Gan, J. P. Hugonin, and P. Lalanne, “Proposal for compact solid-state III–V single-plasmon source,” Phys. Rev. X 2, 021008 (2012).
[CrossRef]

Other (4)

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University Press, 2007).

H. Benisty, J. M. Gérard, R. Houdré, J. Rarity, and C. Weisbuch, Confined Photon Systems (Springer, 1999).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method (Artech House, 2005).

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Figures (9)

Fig. 1:
Fig. 1:

Schematic representation of the (a) L3 and (b) H1 photonic crystal cavities. The teal circle indicates the altered holes surrounding the cavity. The dotted circles indicate their unaltered size and position.

Fig. 2:
Fig. 2:

Cavity field distributions of the L3 [ 1 ] mode (a) |Hz|, (b) |Ex| and (c) |Ey|.

Fig. 3:
Fig. 3:

Cavity field distributions for the H1 cavity (a) |Ex| and (b) |Ey| field distributions of the χ dipole mode and (c) |Ex| and (d) |Ey| field distributions of the ψ dipole mode. (e) Poincaré–like sphere with different orientations of the |Hz| component of the H1 dipole mode.

Fig. 4:
Fig. 4:

Spatial map of the Purcell factor for L3 cavities for (a) a horizontal, x, dipole (b) a vertical, y, dipole (c) a diagonal, d, dipole (d) an anti-diagonal, a, dipole (e) a right, r, dipole and (f) a left, l, dipole. (g) Degree of polarization for an x and y dipole (h) degree of polarization for the d and a dipole and (i) degree of polarization for a r and l dipole (note that the DOP in (i) is almost zero).

Fig. 5:
Fig. 5:

(a) Angle of the dipole for which maximum enhancement is achieved. (b) Enhancement of the dipole when it is oriented at the optimal angle shown in (a).(c) Combination of plots (a) and (b), where the angles in (a) have been normalised to intensity using (b). This indicates that all areas of degenerate coupling do not show any enhanced emission.

Fig. 6:
Fig. 6:

Angles of the excited modes Eξ for a source placed at a specific location in the H1 cavity. (a) ξx(r) (b) ξy(r) (c) ξd (r) (d) ξa(r) and (e) Poincare-like sphere indicating the angle ξ

Fig. 7:
Fig. 7:

Spatial map of the Purcell factor for H1 cavities for (a) Fpx (b) Fpy (c) Fpd (d) Fpa (e) Fpr and (f) Fpl. (g–i) indicate the degrees of polarization for X/Y, D/A and R/L dipoles, where the hue shows the degree of polarization and the value (intensity) indicates the enhancement

Fig. 8:
Fig. 8:

(a) Angle of the dipole for which maximum enhancement is achieved. (b) Enhancement of the dipole when it is oriented at the angle shown in (a), (c) maximal degree of polarization and (d) a combination of (a) and (b) where the intensity of the plot is scaled by the enhancement.

Fig. 9:
Fig. 9:

(a) Contour plot of the minimum fidelity of the spin-photon interface. (b) Maximum fidelity when the QD is moved along the x-axis from the center of the cavity.

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

γ = 2 π h ¯ 2 | f | H i | i | 2 ρ ( ω )
F p = γ γ 0 = 3 Q ( λ c / n ) 3 4 π 2 V m η 2 1 1 + 4 Q 2 [ ( ω / ω c ) 1 ] 2
F p max = 3 Q ( λ c / n ) 3 4 π 2 V m
1 V m = Re { 1 v m } , v m = f c | f c ε ( r c ) f c 2 ( r c )
f x | f y = lim V V ε ( r ) f x ( r ) f y ( r ) d r + i ε c ω x + ω y δ V f x ( r ) f y ( r ) d r = δ x , y
d W d t = 1 2 V s Re { j * E } d r
d W d t = ω 2 Im { μ * E ( r 0 ) }
E ( r ) = ω 2 μ μ 0 G ( r , r 0 ; ω ) μ
× × G ( r , r 0 ; ω ) ω 2 c 2 ε ( r ) G ( r , r 0 ; ω ) = I δ ( r r 0 )
d W d t = ω 3 | μ | 2 2 c 2 ε ε 0 Im { μ ^ * G ( r 0 , r 0 ; ω ) μ ^ }
F p ( r 0 ) = Im { μ ^ * G ( r 0 , r 0 ; ω ) μ ^ } Im { μ ^ * G 0 ( r 0 , r 0 ; ω ) μ ^ }
G T ( r 0 , r 0 ; ω ) = c 2 e c ( r 0 ) e c * ( r 0 ) ω c 2 ω 2 i ω ω c / Q
e c ( r ) = E c ( r ) / V m max ( ε E c ( r ) )
F p ( r 0 ) = 6 π c 3 ω ε Im { μ ^ * e c ( r 0 ) e c * ( r 0 ) ω c 2 ω 2 i ω ω c / Q μ ^ }
G T ( r 0 , r 0 ; ω ) = c 2 n 1 , 2 e c n ( r 0 ) e c n * ( r 0 ) ω c n 2 ω 2 i ω ω c n / Q n
( H a , H b ) = V H a * ( r ) H b ( r ) d 3 r
D O P i , j ( x , y ) = F p i ( x , y ) F p j ( x , y ) F p i ( x , y ) + F p j ( x , y )
θ max ( r 0 ) = 1 2 arctan ( Im { G 1 , 2 ( r 0 , r 0 ) + G 2 , 1 ( r 0 , r 0 ) } Im { G 1 , 1 ( r 0 , r 0 ) + G 2 , 2 ( r 0 , r 0 ) } )
[ E ξ E ξ ] = [ cos ξ sin ξ sin ξ cos ξ ] [ E χ E ψ ]
ξ p ( r ) = arctan ( E p ψ ( r ) E p χ ( r ) )
= F P max F P min F P max + F P min + 1

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