Abstract

We design several single-photon-sources based on the emission of a quantum dot embedded in a semiconductor (GaAs) nanowire. Through various taper designs, we engineer the nanowire ends to realize efficient metallic-dielectric mirrors and to reduce the divergence of the far-field radiation diagram. Using fully-vectorial calculations and a comprehensive Fabry-Perot model, we show that various realistic nanowire geometries may act as nanoantennas (volume of ≈0.05 λ3) that assist funnelling the emitted photons into a single monomode channel. Typically, very high extraction efficiencies above 90% are predicted for a collection optics with a numerical aperture NA=0.85. In addition, since no frequency-selective effect is used in our design, this large efficiency is achieved over a remarkably broad spectral range, Δλ=70 nm at λ=950 nm.

© 2009 Optical Society of America

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2008 (9)

D. J. P. Ellis, A. J. Bennett, S. J. Dewhurst, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, "Cavity-enhanced radiative emission rate in a single-photon-emitting diode operating at 0.5 GHz," New J. Phys. 10, 043035 (2008).
[CrossRef]

V. Zwiller, N. Akopian, M. van Weert, M. van Kouwen, U. Perinetti, L. Kouwenhouwen, R. Algra, J. Gomez Rivas, E. Bakkers, G. Patriarche, L. Liu, J. C. Harmand, Y. Kobayashi, and J. Motohisa, "Optics with single nanowires," C. R. Physique 9, 804-815 (2008).
[CrossRef]

T. Lund-Handsen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, "Experimental realization of highly-efficient broadband coupling of single quantum dots to a photonic crystal waveguide," Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

Y. M. Niquet and D. C. Mojica, "Quantum dots and tunnel barriers in InAs/InP nanowire heterostructures: electronic and optical properties," Phys. Rev. B 77, 115316 (2008).
[CrossRef]

A. Dousse, L. Lanco, J. Suffczynski, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, "Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography," Phys. Rev. Lett. 101, 267404 (2008).
[CrossRef]

L. Ferrier, X. Letartre, P. Rojo-Romeo, E. Drouard, and P. Vicktorovitch, "Slow Bloch mode confinement in 2D photonic crystals for surface operating devices," Opt. Express 16, 3136-3145 (2008).
[CrossRef] [PubMed]

R. Sun, M. Beals, A. Pomerene, J. Cheng, C. Hong, L. Kimerling, and J. Michel, "Impedance matching vertical optical waveguide couplers for dense high index contrast circuits," Opt. Express 16, 11682-11690 (2008).
[CrossRef] [PubMed]

N. Gregersen, T. R. Nielsen, J. Claudon, J. M. Gérard, and J. Mørk, "Controlling the emission profile of a nanowire with a conical taper," Opt. Lett. 33, 1693-1695 (2008).
[CrossRef] [PubMed]

I. Friedler, P. Lalanne, J. P. Hugonin, J. Claudon, J. M. Gérard, A. Beveratos, and I. Robert-Philip, "Efficient photonic mirrors for semiconductor nanowires," Opt. Lett. 33, 2635-37 (2008).
[CrossRef] [PubMed]

2007 (13)

C. Grillet, C. Monat, C. L. C. Smith, B. J. Eggleton, D. J. Moss, S. Frederik, D. Dalacu, P. J. Poole, J. Lapointe, G. Aers, and R. L. Williams, "Nanowire coupling to photonic crystal nanocavities for single photon sources," Opt. Express 15, 1267-1276 (2007).
[CrossRef] [PubMed]

D. Englund, A. Faraon, B. Y. Zhang, Y. Yamamoto, and J. Vuckovic, "Generation and transfer of single photons on a photonic crystal chip," Opt. Express 15, 5550-5558 (2007).
[CrossRef] [PubMed]

G. Lecamp, J. P. Hugonin, and P. Lalanne, "Theoretical and computational concepts for periodic optical waveguides," Opt. Express 15, 11042-60 (2007).
[CrossRef] [PubMed]

G. Lecamp, J. P. Hugonin, P. Lalanne, R. Braive, S. Varoutsis, S. Laurent, A. Lemaître, I. Sagnes, G. Patriarche, I. Robert-Philip, and I. Abram, " Submicron-diameter semiconductor pillar microcavities with very high quality factors," Appl. Phys. Lett. 90, 091120 (2007).
[CrossRef]

Y. Alaverdyan, B. Sepulveda, L. Eurenius, E. Olsson, and M. Käll, "Optical antennas based on coupled nanoholes in thin metal films," Nature Phys.  3, 884-889 (2007).
[CrossRef]

M. T. Hill, Y. S. Oei, E. Smalbrugge, Y. Zhu, T. De Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. De Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, "Lasing in metallic-coated nanocavities," Nat. Photonics 1, 589-594 (2007).
[CrossRef]

G. Lecamp, P. Lalanne, and J. P. Hugonin, "Very large spontaneous emission β-factors in photonic crystal waveguides," Phys. Rev. Lett. 99, 023902 (2007).
[CrossRef] [PubMed]

V. S. C Manga Rao and S. Hughes, " Single quantum-dot Purcell factor and β-factor in photonic crystal waveguide," Phys. Rev. B 75, 205437 (2007).
[CrossRef]

B. Z. Tian, X. L. Zheng, T. J. Kempa, Y. Fang, N. F. Yu, G.H. Yu, J. L. Huang, and C. M. Lieber, "Coaxial silicon nanowires as solar cells and nanoelectronic power sources," Nature 449, 885-888 (2007).
[CrossRef] [PubMed]

Y. Nowicki-Bringuier, R. Hahner, J. Claudon, G. Lecamp, P. Lalanne, and J.M. Gérard, "A novel high-efficiency single mode single photon source," Ann. Phys. 32, 151-154 (2007).
[CrossRef]

M. B. Ward, T. Farrow, P. See, Z. L. Yuan, O. Z. Karimov, A. J. Bennett, A. J. Shields, P. Atkinson, K. Cooper, and D. A. Ritchie, "Electrically driven telecommunication wavelength single-photon source," Appl. Phys. Lett. 90, 063512 (2007).
[CrossRef]

C. Simon, Y. M. Niquet, X. Caillet, J. Eymery, J. P. Poizat, and J. M. Gérard, "Quantum communications with quantum dot spins," Phys. Rev. B 75, 081302(R) (2007).
[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," Nat. Photonics 1, 704-708 (2007).
[CrossRef]

2006 (6)

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

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]

P. J. Pauzauskie and P. Yang, "Nanowire photonics," Mater. Today 9, 36-45 (2006).
[CrossRef]

S. Kako, C. Santori, K. Hoshino, S. Götzinger, Y. Yamamoto, and Y. Arakawa, "A gallium nitride single-photon source operating at 200K," Nature Mater. 5, 887 (2006).
[CrossRef]

A. V. Maslov, M. I. Bukanov, and C. Z. Ning, "Distribution of optical emission between guided modes and free space in a semiconductor nanowire," J. Appl. Phys. 99, 024314 (2006).
[CrossRef]

L. Chen and E. Towe, "Nanowire lasers with distributed-Bragg-reflector mirrors," Appl. Phys. Lett. 89, 053125 (2006).
[CrossRef]

2005 (10)

Z. Y. Li and K. M. Ho, "Bloch mode reflection and lasing threshold in semiconductor nanowire laser arrays," Phys. Rev. B 71, 045315 (2005).
[CrossRef]

J. P. Hugonin and P. Lalanne, "Perfectly-matched-layers as nonlinear coordinate transforms: a generalized formalization," J. Opt. Soc. Am. A. 22, 1844-1849 (2005).
[CrossRef]

I. Favero, G. Cassabois, A. Jankovic, R. Ferreira, D. Darson, C. Voisin, C. Delalande, P. Roussignol, B. Gerardot, P. M. Petroff, and J. M. Gérard, "Giant optical anisotropy in a single quantum dot in a very dilute quantum dot ensemble," Appl. Phys. Lett. 86, 041904 (2005).
[CrossRef]

N. Bonod, E. Popov, and M. Nevière, "Differential theory of diffraction by finite cylindrical objects," J. Opt. Soc. Am. A. 22, 481-490 (2005).
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P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-09 (2005).
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A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, "Deterministic coupling of single quantum dots to single nanocavity modes," Science 308, 1158 (2005).
[CrossRef] [PubMed]

A. Kress, F. Hofbauer, N. Reinelt, M. Kaniber, H. J. Krenner, R. Meyer, G. Bohm, and J. J. Finley, "Manipulation of the spontaneous emission dynamics of quantum dots in two-dimensional photonic crystals," Phys. Rev. B 71, 241304(R) (2005).
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D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, "Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal," Phys. Rev. Lett. 95, 013904 (2005).
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M. T. Borgström, V. Zwiller, E. Müller, and A. Imamoglu, "Optically Bright Quantum Dots in Single Nanowires," Nano Lett. 5, 1439-1443 (2005).
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S.  Laurent, S.  Varoutsis, L.  Le Gratiet, A.  Lemaître, I.  Sagnes, F.  Raineri, A.  Levenson, I.  Robert-Philip, and I.  Abram, "Indistinguishable single photons from a single-quantum dot in a two-dimensional photonic crystal cavity," Appl. Phys. Lett.  87, 163107 (2005).
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2004 (4)

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically Driven Single-Cell Photonic Crystal Laser," Science 305, 1444-14447 (2004).
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W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, "Radiatively limited dephasing in InAs quantum dots," Phys. Rev. B 70, 033301 (2004).
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A. V. Maslov and C. Z. Ning, "Far-field emission of a semiconductor nanowire laser," Opt. Lett. 29, 572-574 (2004).
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Y. K. Lize, E. C. Magi, V. G. Ta'eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, "Microstructured optical fiber photonic wires with subwavelength core diameter," Opt. Express 12, 3209-3217 (2004).
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2003 (3)

X. F. Duang, Y. Huang, R. Agarwal, and C. M. Lieber, "Single-nanowire electrically driven lasers," Nature 421, 241-245 (2003).
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J. M. Gérard, "Solid-State Cavity-Quantum Electrodynamics with Self-Assembled Quantum Dots," Single quantum dots: Fundamentals, applications and new concepts 90, 269-314 (2003).

N. Panev, A. I. Persson, N. Sköld, and L. Samuelson, "Sharp exciton emission from single quantum dots in GaAs nanowires," Appl. Phys. Lett. 83, 2238 (2003).
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2002 (6)

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, "Indistinguishable photons from a single-photon device," Nature 419, 595 (2002).
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E. Moreau, I. Robert, L. Manin, V. Thierry-Mieg, J. M. Gérard, and I. Abram, "A single-mode solid-state source of single photons based on isolated quantum dots in a micropillar," Physica E 13, 418-422 (2002).

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. Wasey, P. Worthing, and V. Zwiller, "Solid-state single photon sources : light collection strategies," Eur. Phys. J. D 18, 197 (2002).
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T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, "Low loss mode size converter from 0.3 µm square Si wire waveguides to singlemode fibers," Electron. Lett. 38,1669-70 (2002).
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V. Almeida, R. Panepucci, and M. Lipson, "Nanotaper for compact mode conversion," Opt. Lett. 28, 1302-04 (2002).
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K. Sebald, P. Michler, T. Passow, D. Hommel, G. Bacher, and A. Forchel, "Single photon emission of CdSe quantum dots at temperatures up to 200K," Appl. Phys. Lett. 81, 2920 (2002).
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2001 (2)

C. Santori, M. Pelton, Y. Dale, and E. Yamamoto, "Triggered single photons from a quantum dot," Phys. Rev. Lett. 86, 1502-05 (2001).
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E. Knill, R. Laflamme and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
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2000 (4)

G. Brassard, N. Lutkenhaus, T. Mor, and B. C. Sanders, "Limitations on practical quantum cryptography," Phys. Rev. Lett. 85, 1330 (2000).
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P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A Imamoglu, "A quantum dot single photon turnstile device," Science 290, 2282-84 (2000).
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C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, "Stable solid-state source of single photons," Phys. Rev. Lett. 89, 290 (2000).
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R. Brouri, A. Beveratos, J. P. Poizat, and P. Grangier, "Photon antibunching in the fluorescence of individual color centers in diamond," Opt. Lett. 25, 1294 (2000).
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1998 (1)

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-13 (1998).
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1993 (1)

1992 (1)

C.H. Bennett, G. Brassard, and A. K. Eckert, "Quantum cryptography," Sci. Am. 267, 50-57 (1992).
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1989 (1)

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, "Efficient coupling of a semiconductor laser to an optical fiber by means of a tapered waveguide on silicon," Appl. Phys. Lett. 55, 2389 (1989).
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Abram, I.

G. Lecamp, J. P. Hugonin, P. Lalanne, R. Braive, S. Varoutsis, S. Laurent, A. Lemaître, I. Sagnes, G. Patriarche, I. Robert-Philip, and I. Abram, " Submicron-diameter semiconductor pillar microcavities with very high quality factors," Appl. Phys. Lett. 90, 091120 (2007).
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S.  Laurent, S.  Varoutsis, L.  Le Gratiet, A.  Lemaître, I.  Sagnes, F.  Raineri, A.  Levenson, I.  Robert-Philip, and I.  Abram, "Indistinguishable single photons from a single-quantum dot in a two-dimensional photonic crystal cavity," Appl. Phys. Lett.  87, 163107 (2005).
[CrossRef]

E. Moreau, I. Robert, L. Manin, V. Thierry-Mieg, J. M. Gérard, and I. Abram, "A single-mode solid-state source of single photons based on isolated quantum dots in a micropillar," Physica E 13, 418-422 (2002).

Ackerman, D. A.

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, "Efficient coupling of a semiconductor laser to an optical fiber by means of a tapered waveguide on silicon," Appl. Phys. Lett. 55, 2389 (1989).
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Aers, G.

Agarwal, R.

X. F. Duang, Y. Huang, R. Agarwal, and C. M. Lieber, "Single-nanowire electrically driven lasers," Nature 421, 241-245 (2003).
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Akopian, N.

V. Zwiller, N. Akopian, M. van Weert, M. van Kouwen, U. Perinetti, L. Kouwenhouwen, R. Algra, J. Gomez Rivas, E. Bakkers, G. Patriarche, L. Liu, J. C. Harmand, Y. Kobayashi, and J. Motohisa, "Optics with single nanowires," C. R. Physique 9, 804-815 (2008).
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Alaverdyan, Y.

Y. Alaverdyan, B. Sepulveda, L. Eurenius, E. Olsson, and M. Käll, "Optical antennas based on coupled nanoholes in thin metal films," Nature Phys.  3, 884-889 (2007).
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Algra, R.

V. Zwiller, N. Akopian, M. van Weert, M. van Kouwen, U. Perinetti, L. Kouwenhouwen, R. Algra, J. Gomez Rivas, E. Bakkers, G. Patriarche, L. Liu, J. C. Harmand, Y. Kobayashi, and J. Motohisa, "Optics with single nanowires," C. R. Physique 9, 804-815 (2008).
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Almeida, V.

Arakawa, Y.

S. Kako, C. Santori, K. Hoshino, S. Götzinger, Y. Yamamoto, and Y. Arakawa, "A gallium nitride single-photon source operating at 200K," Nature Mater. 5, 887 (2006).
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D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, "Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal," Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef] [PubMed]

Atature, M.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, "Deterministic coupling of single quantum dots to single nanocavity modes," Science 308, 1158 (2005).
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Atkinson, P.

M. B. Ward, T. Farrow, P. See, Z. L. Yuan, O. Z. Karimov, A. J. Bennett, A. J. Shields, P. Atkinson, K. Cooper, and D. A. Ritchie, "Electrically driven telecommunication wavelength single-photon source," Appl. Phys. Lett. 90, 063512 (2007).
[CrossRef]

Bacher, G.

K. Sebald, P. Michler, T. Passow, D. Hommel, G. Bacher, and A. Forchel, "Single photon emission of CdSe quantum dots at temperatures up to 200K," Appl. Phys. Lett. 81, 2920 (2002).
[CrossRef]

Badolato, A.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, "Deterministic coupling of single quantum dots to single nanocavity modes," Science 308, 1158 (2005).
[CrossRef] [PubMed]

Baek, J. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically Driven Single-Cell Photonic Crystal Laser," Science 305, 1444-14447 (2004).
[CrossRef] [PubMed]

Bakkers, E.

V. Zwiller, N. Akopian, M. van Weert, M. van Kouwen, U. Perinetti, L. Kouwenhouwen, R. Algra, J. Gomez Rivas, E. Bakkers, G. Patriarche, L. Liu, J. C. Harmand, Y. Kobayashi, and J. Motohisa, "Optics with single nanowires," C. R. Physique 9, 804-815 (2008).
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Barnes, W. L.

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. Wasey, P. Worthing, and V. Zwiller, "Solid-state single photon sources : light collection strategies," Eur. Phys. J. D 18, 197 (2002).
[CrossRef]

Beals, M.

Becher, C.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A Imamoglu, "A quantum dot single photon turnstile device," Science 290, 2282-84 (2000).
[CrossRef] [PubMed]

Bennett, A. J.

D. J. P. Ellis, A. J. Bennett, S. J. Dewhurst, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, "Cavity-enhanced radiative emission rate in a single-photon-emitting diode operating at 0.5 GHz," New J. Phys. 10, 043035 (2008).
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M. B. Ward, T. Farrow, P. See, Z. L. Yuan, O. Z. Karimov, A. J. Bennett, A. J. Shields, P. Atkinson, K. Cooper, and D. A. Ritchie, "Electrically driven telecommunication wavelength single-photon source," Appl. Phys. Lett. 90, 063512 (2007).
[CrossRef]

Bennett, C.H.

C.H. Bennett, G. Brassard, and A. K. Eckert, "Quantum cryptography," Sci. Am. 267, 50-57 (1992).
[CrossRef]

Beveratos, A.

Björk, G.

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. Wasey, P. Worthing, and V. Zwiller, "Solid-state single photon sources : light collection strategies," Eur. Phys. J. D 18, 197 (2002).
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Bloch, J.

A. Dousse, L. Lanco, J. Suffczynski, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, "Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography," Phys. Rev. Lett. 101, 267404 (2008).
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Bohm, G.

A. Kress, F. Hofbauer, N. Reinelt, M. Kaniber, H. J. Krenner, R. Meyer, G. Bohm, and J. J. Finley, "Manipulation of the spontaneous emission dynamics of quantum dots in two-dimensional photonic crystals," Phys. Rev. B 71, 241304(R) (2005).
[CrossRef]

Bolger, J. A.

Bonod, N.

N. Bonod, E. Popov, and M. Nevière, "Differential theory of diffraction by finite cylindrical objects," J. Opt. Soc. Am. A. 22, 481-490 (2005).
[CrossRef]

Borgström, M. T.

M. T. Borgström, V. Zwiller, E. Müller, and A. Imamoglu, "Optically Bright Quantum Dots in Single Nanowires," Nano Lett. 5, 1439-1443 (2005).
[CrossRef] [PubMed]

Borri, P.

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, "Radiatively limited dephasing in InAs quantum dots," Phys. Rev. B 70, 033301 (2004).
[CrossRef]

Bouwmeester, D.

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," Nat. Photonics 1, 704-708 (2007).
[CrossRef]

Braive, R.

G. Lecamp, J. P. Hugonin, P. Lalanne, R. Braive, S. Varoutsis, S. Laurent, A. Lemaître, I. Sagnes, G. Patriarche, I. Robert-Philip, and I. Abram, " Submicron-diameter semiconductor pillar microcavities with very high quality factors," Appl. Phys. Lett. 90, 091120 (2007).
[CrossRef]

Brassard, G.

G. Brassard, N. Lutkenhaus, T. Mor, and B. C. Sanders, "Limitations on practical quantum cryptography," Phys. Rev. Lett. 85, 1330 (2000).
[CrossRef] [PubMed]

C.H. Bennett, G. Brassard, and A. K. Eckert, "Quantum cryptography," Sci. Am. 267, 50-57 (1992).
[CrossRef]

Brouri, R.

Bukanov, M. I.

A. V. Maslov, M. I. Bukanov, and C. Z. Ning, "Distribution of optical emission between guided modes and free space in a semiconductor nanowire," J. Appl. Phys. 99, 024314 (2006).
[CrossRef]

Caillet, X.

C. Simon, Y. M. Niquet, X. Caillet, J. Eymery, J. P. Poizat, and J. M. Gérard, "Quantum communications with quantum dot spins," Phys. Rev. B 75, 081302(R) (2007).
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Cassabois, G.

I. Favero, G. Cassabois, A. Jankovic, R. Ferreira, D. Darson, C. Voisin, C. Delalande, P. Roussignol, B. Gerardot, P. M. Petroff, and J. M. Gérard, "Giant optical anisotropy in a single quantum dot in a very dilute quantum dot ensemble," Appl. Phys. Lett. 86, 041904 (2005).
[CrossRef]

Chang, H.S.

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

Chang, W. H.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, "Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities," Phys. Rev. Lett. 96, 117401 (2006).
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Chen, L.

L. Chen and E. Towe, "Nanowire lasers with distributed-Bragg-reflector mirrors," Appl. Phys. Lett. 89, 053125 (2006).
[CrossRef]

Chen, W.Y.

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

Cheng, J.

Chu, D. Y.

Chyi, J. I.

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

Claudon, J.

Coldren, L. A.

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," Nat. Photonics 1, 704-708 (2007).
[CrossRef]

Cooper, K.

M. B. Ward, T. Farrow, P. See, Z. L. Yuan, O. Z. Karimov, A. J. Bennett, A. J. Shields, P. Atkinson, K. Cooper, and D. A. Ritchie, "Electrically driven telecommunication wavelength single-photon source," Appl. Phys. Lett. 90, 063512 (2007).
[CrossRef]

Costard, E.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-13 (1998).
[CrossRef]

Dalacu, D.

Dale, Y.

C. Santori, M. Pelton, Y. Dale, and E. Yamamoto, "Triggered single photons from a quantum dot," Phys. Rev. Lett. 86, 1502-05 (2001).
[CrossRef] [PubMed]

Darson, D.

I. Favero, G. Cassabois, A. Jankovic, R. Ferreira, D. Darson, C. Voisin, C. Delalande, P. Roussignol, B. Gerardot, P. M. Petroff, and J. M. Gérard, "Giant optical anisotropy in a single quantum dot in a very dilute quantum dot ensemble," Appl. Phys. Lett. 86, 041904 (2005).
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De Vries, T.

M. T. Hill, Y. S. Oei, E. Smalbrugge, Y. Zhu, T. De Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. De Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, "Lasing in metallic-coated nanocavities," Nat. Photonics 1, 589-594 (2007).
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De Waardt, H.

M. T. Hill, Y. S. Oei, E. Smalbrugge, Y. Zhu, T. De Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. De Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, "Lasing in metallic-coated nanocavities," Nat. Photonics 1, 589-594 (2007).
[CrossRef]

Delalande, C.

I. Favero, G. Cassabois, A. Jankovic, R. Ferreira, D. Darson, C. Voisin, C. Delalande, P. Roussignol, B. Gerardot, P. M. Petroff, and J. M. Gérard, "Giant optical anisotropy in a single quantum dot in a very dilute quantum dot ensemble," Appl. Phys. Lett. 86, 041904 (2005).
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Dewhurst, S. J.

D. J. P. Ellis, A. J. Bennett, S. J. Dewhurst, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, "Cavity-enhanced radiative emission rate in a single-photon-emitting diode operating at 0.5 GHz," New J. Phys. 10, 043035 (2008).
[CrossRef]

Dousse, A.

A. Dousse, L. Lanco, J. Suffczynski, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, "Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography," Phys. Rev. Lett. 101, 267404 (2008).
[CrossRef]

Dreiser, J.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, "Deterministic coupling of single quantum dots to single nanocavity modes," Science 308, 1158 (2005).
[CrossRef] [PubMed]

Drouard, E.

Duang, X. F.

X. F. Duang, Y. Huang, R. Agarwal, and C. M. Lieber, "Single-nanowire electrically driven lasers," Nature 421, 241-245 (2003).
[CrossRef]

Eckert, A. K.

C.H. Bennett, G. Brassard, and A. K. Eckert, "Quantum cryptography," Sci. Am. 267, 50-57 (1992).
[CrossRef]

Eggleton, B. J.

Eijkemans, T. J.

M. T. Hill, Y. S. Oei, E. Smalbrugge, Y. Zhu, T. De Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. De Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, "Lasing in metallic-coated nanocavities," Nat. Photonics 1, 589-594 (2007).
[CrossRef]

Eisler, H. J.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-09 (2005).
[CrossRef] [PubMed]

Ellis, D. J. P.

D. J. P. Ellis, A. J. Bennett, S. J. Dewhurst, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, "Cavity-enhanced radiative emission rate in a single-photon-emitting diode operating at 0.5 GHz," New J. Phys. 10, 043035 (2008).
[CrossRef]

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Appl. Phys. Lett. (8)

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Figures (7)

Fig. 1
Fig. 1

(left). Normalized spontaneous emission rates of a radial dipole embedded in an infinite cylindrical GaAs (n=3.45) nanowire and located on the wire axis. Blue-solid curve: emission P M into the HE11 fundamental mode. Dashed-red curve: emission rate γ into the other modes including the radiative modes. Dotted-green curve: total emission rate, P M+γ. Dashed-dotted curve: β-factor for the HE11 fundamental mode, β=P M/(P M+γ). Right: Scanning electron micrograph obtained for a GaAs nanowire defined by e-beam lithography and reactive ion etching.

Fig. 2.
Fig. 2.

Fabry-Perot model for the emission of the dipole p in a nanowire of length L. A+ and A- are the amplitudes of the upward and backward-propagating HE11 guided mode; r t and r b are the reflection coefficients of the top and bottom facets. The emission rate in the continuum of radiation modes is denoted by γ. The transmitted intensity, T(θ), represents the fraction of the incident energy carried by the upward HE11 mode that is scattered by the top facet into a cone defined by the angle θ.

Fig. 3.
Fig. 3.

Optical properties of cleaved facets. (a) Dotted-blue curve: modal reflectivity Rm. Dashed-green curve: transmission T(θ=π/2) of the fundamental HE11 mode for a collection with a numerical aperture of 1. Solid-red curve: intensity Rs reflected into the radiation modes. All the coefficients are shown as a function of the normalized wire diameter D/λ. (b) T(θ) (in units of π) for different values of D/λ.

Fig. 4.
Fig. 4.

Right inset: tapered nanowire geometry with its physical parameters, h tip, D top and D. Left panel: (a) Transmission of the fundamental mode HE11 as a function of θ for a diameter of D=0.22λ. (b) Modal reflectivity Rm. (c) Transmission of the fundamental HE11 mode for θ=π/2 (NA=1). (d) Intensity Rs back-scattered into the radiation modes. All results are obtained for λ=0.95 μm and for D top=155 nm. The solid-blue and dashed-green curves are obtained for h tip=1 μm and htip=2 μm, respectively.

Fig. 5.
Fig. 5.

HE11 modal reflectance R of the three different mirror geometries as a function of the diameter D for λ=0.95 μm. The geometries are: a planar silver mirror covered by a 9-nm-thick dielectric (n=1.5) adlayer (solid-black curve), a post silver mirror covered by the same adlayer (green-dotted curve) and a 16-pair quarter-wave-thick GaAs/AlAs Bragg mirror connected to a GaAs substrate (dashed-blue curve).

Fig. 6.
Fig. 6.

HE11 modal reflectance R of the Bragg and Post geometries with a tapered section inserted between the wire end (diameter D) and the mirror section (diameter D M=0.35 μm), as a function of the diameter D. The calculations are performed for λ=0.95 μm. The solid-blue line shows the reflectance of a 16-pair quarter-wave GaAs/AlAs (n=3.45/2.95) Bragg mirror with a taper height of 0.6 μm. The dashed-green line shows the reflectance of a post silver mirror covered by a thin dielectric adlayer (n=1.5) of 9-nm thickness adlayer with a taper height of h=0.42 μm.

Fig. 7.
Fig. 7.

Intensity distribution ∣Ex2, normalized SE rate P T and extraction efficiency η for the three S4Ps built with the same top end but with different bottom mirrors. (a), (b) and (c) Planar S4P. (d), (e) and (f) Post S4P. (g), (h) and (i) Bragg S4P with 16 pairs in the dielectric mirror. The QD locations correspond to the intensity maximum (in the center of the white cloud). In (b), (e) and (h), the Fabry-Perot model predictions (red-solid line), the a-FMM calculation data (blue circles) and the Fabry-Perot model predictions with rt = 0 (black-dashed line) are shown. In (c), (f) and (i), the extraction efficiency has been calculated for θ=60° and θ=45° with the Fabry-Perot model (red- and black-solid curves) and with the a-FMM (red squares and black circles).

Equations (10)

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P M = 1 / 8 ω 2 p E M ( r 0 ) 2 ,
A + = A s + r b A exp ( ) ,
A = A s + r t A + exp ( ) ,
A + = A s 1 + r b exp ( ) 1 r t r b exp ( 2 ) , A = A s 1 + r t exp ( ) 1 r t r b exp ( 2 ) .
P T = ( 1 R t ) A + 2 + ( 1 R b ) A 2 + γ .
F p = ( 1 R t ) A + 2 + ( 1 R b ) A 2 .
η ( θ ) = T ( θ ) A + 2 / P T .
A + = A s [ 1 + r b exp ( ) ] and A = A s .
P T = P M [ 1 + r b cos ( ϕ + ϕ b ) ] + γ .
η ( θ ) = 0.5 T ( θ ) β ( 1 + r b ) 2 / ( 1 + β r b ) .

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