Abstract

We report coupling of the excitonic photon emission from photoexcited PbSe colloidal quantum dots (QDs) into an optical circuit that was fabricated in a silicon-on-insulator wafer using a CMOS-compatible process. The coupling between excitons and sub-μm sized silicon channel waveguides was mediated by a photonic crystal microcavity. The intensity of the coupled light saturates rapidly with the optical excitation power. The saturation behaviour was quantitatively studied using an isolated photonic crystal cavity with PbSe QDs site-selectively located at the cavity mode antinode position. Saturation occurs when a few μW of continuous wave HeNe pump power excites the QDs with a Gaussian spot size of 2 μm. By comparing the results with a master equation analysis that rigorously accounts for the complex dielectric environment of the QD excitons, the saturation is attributed to ground state depletion due to a non-radiative exciton decay channel with a trap state lifetime ∼ 3 μs.

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2012 (1)

2011 (10)

M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Fiber-based cryogenic and time-resolved spectroscopy of PbS quantum dots,” Opt. Express 19, 1786–1793 (2011).
[CrossRef] [PubMed]

T. S. Luk, S. Xiong, W. W. Chow, X. Miao, G. Subramania, P. J. Resnick, A. J. Fischer, and J. C. Brinker, “Anomalous enhanced emission from PbS quantum dots on a photonic-crystal microcavity,” J. Opt. Soc. Am. B 28, 1365–1373 (2011).
[CrossRef]

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
[CrossRef] [PubMed]

C. Roy and S. Hughes, “Phonon-dressed mollow triplet in the regime of cavity quantum electrodynamics: Excitation-induced dephasing and nonperturbative cavity feeding effects,” Phys. Rev. Lett. 106, 247403 (2011).
[CrossRef] [PubMed]

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, “Dephasing of triplet-sideband optical emission of a resonantly driven InAs/GaAs quantum dot inside a microcavity,” Phys. Rev. Lett. 106, 247402 (2011).
[CrossRef] [PubMed]

M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra, G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon, “Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities,” Phys. Rev. Lett. 106, 227402 (2011).
[CrossRef] [PubMed]

S. Hughes, P. Yao, F. Milde, A. Knorr, D. Dalacu, K. Mnaymneh, V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, R. Cheriton, and R. L. Williams, “Influence of electron-acoustic phonon scattering on off-resonant cavity feeding within a strongly coupled quantum-dot cavity system,” Phys. Rev. B 83, 165313 (2011).
[CrossRef]

A. Faraon, A. Majumdar, D. Englund, E. Kim, M. Bajcsy, and J. Vučković, “Integrated quantum optical networks based on quantum dots and photonic crystals,” New J. Phys. 13, 055025 (2011).
[CrossRef]

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
[CrossRef]

M. H. Hadj Alouane, R. Anufriev, N. Chauvin, H. Khmissi, K. Naji, B. Ilahi, H. Maaref, G. Patriarche, M. Gendry, and C. Bru-Chevallier, “Wurtzite InP/InAs/InP core-shell nanowires emitting at telecommunication wavelengths on Si substrate,” Nanotechnology 22, 405702 (2011).
[CrossRef]

2010 (10)

J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4, 527–534 (2010).
[CrossRef]

D. F. Logan, P. Velha, M. Sorel, R. M. De La Rue, A. P. Knights, and P. E. Jessop, “Defect-enhanced silicon-on-insulator waveguide resonant photodetector with high sensitivity at 1.55 μm,” IEEE Photonics Technol. Lett. 22, 1530–1532 (2010).
[CrossRef]

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4, 511–517 (2010).
[CrossRef]

B. De Geyter and Z. Hens, “The absorption coefficient of PbSe/CdSe core/shell colloidal quantum dots,” Appl. Phys. Lett. 97, 161908 (2010).
[CrossRef]

I. Moreels, G. Allan, B. De Geyter, L. Wirtz, C. Delerue, and Z. Hens, “Dielectric function of colloidal lead chalcogenide quantum dots obtained by a Kramers-Krönig analysis of the absorbance spectrum,” Phys. Rev. B 81, 235319 (2010).
[CrossRef]

H. Qiao, K. A. Abel, F. C. J. M. van Veggel, and J. F. Young, “Exciton thermalization and state broadening contributions to the photoluminescence of colloidal PbSe quantum dot films from 295 to 4.5 K,” Phys. Rev. B 82, 165435 (2010).
[CrossRef]

K. A. Abel, H. Qiao, J. F. Young, and F. C. J. M. van Veggel, “Four-fold enhancement of the activation energy for nonradiative decay of excitons in PbSe/CdSe core/shell versus PbSe colloidal quantum dots,” J. Phys. Chem. Lett. 1, 2334–2338 (2010).
[CrossRef]

T. Heindel, C. Schneider, M. Lermer, S. H. Kwon, T. Braun, S. Reitzenstein, S. Höfling, M. Kamp, and A. Forchel, “Electrically driven quantum dot-micropillar single photon source with 34% overall efficiency,” Appl. Phys. Lett. 96, 011107 (2010).
[CrossRef]

P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, “Nonlinear photoluminescence spectra from a quantum-dot-cavity system: Interplay of pump-induced stimulated emission and anharmonic cavity QED,” Phys. Rev. B 81, 033309 (2010).
[CrossRef]

J. Heo, T. Zhu, C. Zhang, J. Xu, and P. Bhattacharya, “Electroluminescence from silicon-based photonic crystal microcavities with PbSe quantum dots,” Opt. Lett. 35, 547–549 (2010).
[CrossRef] [PubMed]

2009 (9)

A. Laucht, N. Hauke, J. M. Villas-Bôas, F. Hofbauer, G. Böhm, M. Kaniber, and J. J. Finley, “Dephasing of exciton polaritons in photoexcited InGaAs quantum dots in GaAs nanocavities,” Phys. Rev. Lett. 103, 087405 (2009).
[CrossRef] [PubMed]

M. Toishi, D. Englund, A. Faraon, and J. Vučković, “High-brightness single photon source from a quantum dot in a directional-emission nanocavity,” Opt. Express 17, 14618–14626 (2009).
[CrossRef]

R. Bose, J. Gao, J. F. McMillan, A. D. Williams, and C. W. Wong, “Cryogenic spectroscopy of ultra-low density colloidal lead chalcogenide quantum dots on chip-scale optical cavities towards single quantum dot near-infrared cavity QED,” Opt. Express 17, 22474–22483 (2009).
[CrossRef]

U. Hohenester, A. Laucht, M. Kaniber, N. Hauke, A. Neumann, A. Mohtashami, M. Seliger, M. Bichler, and J. J. Finley, “Phonon-assisted transitions from quantum dot excitons to cavity photons,” Phys. Rev. B 80, 201311 (2009).

H. Bao, B. F. Habenicht, O. V. Prezhdo, and X. Ruan, “Temperature dependence of hot-carrier relaxation in PbSe nanocrystals: An ab initio study,” Phys. Rev. B 79, 235306 (2009).
[CrossRef]

L. Kong, Z. C. Feng, Z. Wu, and W. Lu, “Temperature dependent and time-resolved photoluminescence studies of InAs self-assembled quantum dots with InGaAs strain reducing layer structure,” J. Appl. Phys. 106, 013512 (2009).
[CrossRef]

A. G. Pattantyus-Abraham, H. Qiao, J. Shan, K. A. Abel, T.-S. Wang, F. C. J. M. van Veggel, and J. F. Young, “Site-selective optical coupling of PbSe nanocrystals to Si-based photonic crystal microcavities,” Nano Lett. 9, 2849–2854 (2009).
[CrossRef] [PubMed]

R. Bose, J. F. McMillan, J. Gao, and C. W. Wong, “Solution-processed cavity and slow-light quantum electrodynamics in near-infrared silicon photonic crystals,” Appl. Phys. Lett. 95, 131112 (2009).
[CrossRef]

I. Moreels, K. Lambert, D. Smeets, D. D. Muynck, T. Nollet, J. C. Martins, F. Vanhaecke, A. Vantomme, C. Delerue, G. Allan, and Z. Hens, “Size-dependent optical properties of colloidal PbS quantum dots,” ACS Nano 3, 3023–3030 (2009).
[CrossRef] [PubMed]

2008 (5)

J. M. An, M. Califano, A. Franceschetti, and A. Zunger, “Excited-state relaxation in PbSe quantum dots,” J. Chem. Phys. 128, 164720 (2008).
[CrossRef] [PubMed]

S. Vignolini, F. Riboli, F. Intonti, M. Belotti, M. Gurioli, Y. Chen, M. Colocci, L. C. Andreani, and D. S. Wiersma, “Local nanofluidic light sources in silicon photonic crystal microcavities,” Phys. Rev. E 78, 045603 (2008).
[CrossRef]

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
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S. N. Dorenbos, E. M. Reiger, U. Perinetti, V. Zwiller, T. Zijlstra, and T. M. Klapwijk, “Low noise superconducting single photon detectors on silicon,” Appl. Phys. Lett. 93, 131101 (2008).
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T. Lund-Hansen, 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).
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2007 (10)

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vučković, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90, 073102 (2007).
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V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: Proposal for an efficient “on chip” single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
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V. S. C. Manga Rao and S. Hughes, “Single quantum-dot purcell factor and β factor in a photonic crystal waveguide,” Phys. Rev. B 75, 205437 (2007).
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G. Lecamp, P. Lalanne, and J. P. Hugonin, “Very large spontaneous-emission β factors in photonic-crystal waveguides,” Phys. Rev. Lett. 99, 023902 (2007).
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R. Bose, X. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 μm at room temperature,” Appl. Phys. Lett. 90, 111117 (2007).
[CrossRef]

C. Bonati, A. Cannizzo, D. Tonti, A. Tortschanoff, F. van Mourik, and M. Chergui, “Subpicosecond near-infrared fluorescence upconversion study of relaxation processes in PbSe quantum dots,” Phys. Rev. B 76, 033304 (2007).
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J. W. Stouwdam, J. Shan, F. C. J. M. van Veggel, A. G. Pattantyus-Abraham, J. F. Young, and M. Raudsepp, “Photostability of colloidal PbSe and PbSe/PbS core/shell nanocrystals in solution and in the solid state,” J. Phys. Chem. C 111, 1086–1092 (2007).
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M. G. Banaee, A. G. Pattantyus-Abraham, M. W. McCutcheon, G. W. Rieger, and J. F. Young, “Efficient coupling of photonic crystal microcavity modes to a ridge waveguide,” Appl. Phys. Lett. 90, 19316 (2007).

J. M. Harbold and F. W. Wise, “Photoluminescence spectroscopy of PbSe nanocrystals,” Phys. Rev. B 76, 125304 (2007).
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I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, “Composition and size-dependent extinction coefficient of colloidal PbSe quantum dots,” Chem. Mater. 19, 6101–6106 (2007).
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2006 (2)

A. F. Koenderink, M. Kafesaki, C. M. Soukoulis, and V. Sandoghdar, “Spontaneous emission rates of dipoles in photonic crystal membranes,” J. Opt. Soc. Am. B 23, 1196–1206 (2006).
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A. L. Roest, M. A. Verheijen, O. Wunnicke, S. Serafin, H. Wondergem, and E. P. A. M. Bakkers, “Position-controlled epitaxial III–V nanowires on silicon,” Nanotechnology 17, S271–S275 (2006).
[CrossRef]

2005 (1)

J. M. Harbold, H. Du, T. D. Krauss, K. Cho, C. B. Murray, and F. W. Wise, “Time-resolved intraband relaxation of strongly confined electrons and holes in colloidal PbSe nanocrystals,” Phys. Rev. B 72,  195312 (2005).
[CrossRef]

2004 (2)

T. Mårtensson, C. P. T. Svensson, B. A. Wacaser, M. W. Larsson, W. Seifert, K. Deppert, A. Gustafsson, L. R. Wallenberg, and L. Samuelson, “Epitaxial III–V nanowires on silicon,” Nano Lett. 4, 1987–1990 (2004).
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D. A. Louderback, G. W. Pickrell, H. C. Lin, M. A. Fish, J. J. Hindi, and P. S. Guilfoyle, “VCSELs with monolithic coupling to internal horizontal waveguides using integrated diffraction gratings,” Electron. Lett. 40, 1064–1065 (2004).
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2003 (1)

K. L. Silverman, R. P. Mirin, S. T. Cundiff, and A. G. Norman, “Direct measurement of polarization resolved transition dipole moment in InGaAs/GaAs quantum dots,” Appl. Phys. Lett. 82, 4552–4554 (2003).
[CrossRef]

2002 (2)

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Rabi oscillations in the excitonic ground-state transition of InGaAs quantum dots,” Phys. Rev. B 66, 081306 (2002).
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H. Du, C. Chen, R. Krishnan, T. D. Krauss, J. M. Harbold, F. W. Wise, M. G. Thomas, and J. Silcox, “Optical properties of colloidal PbSe nanocrystals,” Nano Lett. 2, 1321–1324 (2002).
[CrossRef]

2001 (1)

C. B. Murray, S. Sun, W. Gaschler, H. Doyle, T. A. Betley, and C. R. Kagan, “Colloidal synthesis of nanocrystals and nanocrystal superlattices,” IBM J. Res. Dev. 45, 47–56 (2001).
[CrossRef]

2000 (3)

M. Paillard, X. Marie, E. Vanelle, T. Amand, V. K. Kalevich, A. R. Kovsh, A. E. Zhukov, and V. M. Ustinov, “Time-resolved photoluminescence in self-assembled InAs/GaAs quantum dots under strictly resonant excitation,” Appl. Phys. Lett. 76, 76–78 (2000).
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T. Okuno, Y. Masumoto, M. Ikezawa, T. Ogawa, and A. A. Lipovskii, “Size-dependent picosecond energy relaxation in PbSe quantum dots,” Appl. Phys. Lett. 77, 504–506 (2000).
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P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
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1999 (2)

M. Colocci, A. Vinattieri, L. Lippi, F. Bogani, M. Rosa-Clot, S. Taddei, A. Bosacchi, S. Franchi, and P. Frigeri, “Controlled tuning of the radiative lifetime in InAs self-assembled quantum dots through vertical ordering,” Appl. Phys. Lett. 74, 564–566 (1999).
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S. Scheel, L. Knöll, and D.-G. Welsch, “Spontaneous decay of an excited atom in an absorbing dielectric,” Phys. Rev. A 60, 4094–4104 (1999).
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1995 (1)

N. Suzuki, K. Sawai, and S. Adachi, “Optical properties of PbSe,” J. Appl. Phys. 77, 1249–1255 (1995).
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1992 (1)

S. M. Barnett, B. Huttner, and R. Loudon, “Spontaneous emission in absorbing dielectric media,” Phys. Rev. Lett. 68, 3698–3701 (1992).
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1988 (1)

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
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Abel, K. A.

K. A. Abel, H. Qiao, J. F. Young, and F. C. J. M. van Veggel, “Four-fold enhancement of the activation energy for nonradiative decay of excitons in PbSe/CdSe core/shell versus PbSe colloidal quantum dots,” J. Phys. Chem. Lett. 1, 2334–2338 (2010).
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H. Qiao, K. A. Abel, F. C. J. M. van Veggel, and J. F. Young, “Exciton thermalization and state broadening contributions to the photoluminescence of colloidal PbSe quantum dot films from 295 to 4.5 K,” Phys. Rev. B 82, 165435 (2010).
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A. G. Pattantyus-Abraham, H. Qiao, J. Shan, K. A. Abel, T.-S. Wang, F. C. J. M. van Veggel, and J. F. Young, “Site-selective optical coupling of PbSe nanocrystals to Si-based photonic crystal microcavities,” Nano Lett. 9, 2849–2854 (2009).
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Adachi, S.

N. Suzuki, K. Sawai, and S. Adachi, “Optical properties of PbSe,” J. Appl. Phys. 77, 1249–1255 (1995).
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Aers, G. C.

S. Hughes, P. Yao, F. Milde, A. Knorr, D. Dalacu, K. Mnaymneh, V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, R. Cheriton, and R. L. Williams, “Influence of electron-acoustic phonon scattering on off-resonant cavity feeding within a strongly coupled quantum-dot cavity system,” Phys. Rev. B 83, 165313 (2011).
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Allan, G.

I. Moreels, G. Allan, B. De Geyter, L. Wirtz, C. Delerue, and Z. Hens, “Dielectric function of colloidal lead chalcogenide quantum dots obtained by a Kramers-Krönig analysis of the absorbance spectrum,” Phys. Rev. B 81, 235319 (2010).
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I. Moreels, K. Lambert, D. Smeets, D. D. Muynck, T. Nollet, J. C. Martins, F. Vanhaecke, A. Vantomme, C. Delerue, G. Allan, and Z. Hens, “Size-dependent optical properties of colloidal PbS quantum dots,” ACS Nano 3, 3023–3030 (2009).
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I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, “Composition and size-dependent extinction coefficient of colloidal PbSe quantum dots,” Chem. Mater. 19, 6101–6106 (2007).
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Amand, T.

M. Paillard, X. Marie, E. Vanelle, T. Amand, V. K. Kalevich, A. R. Kovsh, A. E. Zhukov, and V. M. Ustinov, “Time-resolved photoluminescence in self-assembled InAs/GaAs quantum dots under strictly resonant excitation,” Appl. Phys. Lett. 76, 76–78 (2000).
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An, J. M.

J. M. An, M. Califano, A. Franceschetti, and A. Zunger, “Excited-state relaxation in PbSe quantum dots,” J. Chem. Phys. 128, 164720 (2008).
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Andreani, L. C.

S. Vignolini, F. Riboli, F. Intonti, M. Belotti, M. Gurioli, Y. Chen, M. Colocci, L. C. Andreani, and D. S. Wiersma, “Local nanofluidic light sources in silicon photonic crystal microcavities,” Phys. Rev. E 78, 045603 (2008).
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Anufriev, R.

M. H. Hadj Alouane, R. Anufriev, N. Chauvin, H. Khmissi, K. Naji, B. Ilahi, H. Maaref, G. Patriarche, M. Gendry, and C. Bru-Chevallier, “Wurtzite InP/InAs/InP core-shell nanowires emitting at telecommunication wavelengths on Si substrate,” Nanotechnology 22, 405702 (2011).
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Arakawa, Y.

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” E-print: arXiv:0908.0788v1.

Ates, S.

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, “Dephasing of triplet-sideband optical emission of a resonantly driven InAs/GaAs quantum dot inside a microcavity,” Phys. Rev. Lett. 106, 247402 (2011).
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Atlasov, K. A.

M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra, G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon, “Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities,” Phys. Rev. Lett. 106, 227402 (2011).
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Bajcsy, M.

A. Faraon, A. Majumdar, D. Englund, E. Kim, M. Bajcsy, and J. Vučković, “Integrated quantum optical networks based on quantum dots and photonic crystals,” New J. Phys. 13, 055025 (2011).
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Bakkers, E. P. A. M.

A. L. Roest, M. A. Verheijen, O. Wunnicke, S. Serafin, H. Wondergem, and E. P. A. M. Bakkers, “Position-controlled epitaxial III–V nanowires on silicon,” Nanotechnology 17, S271–S275 (2006).
[CrossRef]

Banaee, M. G.

M. G. Banaee, A. G. Pattantyus-Abraham, M. W. McCutcheon, G. W. Rieger, and J. F. Young, “Efficient coupling of photonic crystal microcavity modes to a ridge waveguide,” Appl. Phys. Lett. 90, 19316 (2007).

Bao, H.

H. Bao, B. F. Habenicht, O. V. Prezhdo, and X. Ruan, “Temperature dependence of hot-carrier relaxation in PbSe nanocrystals: An ab initio study,” Phys. Rev. B 79, 235306 (2009).
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Barnett, S. M.

S. M. Barnett, B. Huttner, and R. Loudon, “Spontaneous emission in absorbing dielectric media,” Phys. Rev. Lett. 68, 3698–3701 (1992).
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Belotti, M.

S. Vignolini, F. Riboli, F. Intonti, M. Belotti, M. Gurioli, Y. Chen, M. Colocci, L. C. Andreani, and D. S. Wiersma, “Local nanofluidic light sources in silicon photonic crystal microcavities,” Phys. Rev. E 78, 045603 (2008).
[CrossRef]

Betley, T. A.

C. B. Murray, S. Sun, W. Gaschler, H. Doyle, T. A. Betley, and C. R. Kagan, “Colloidal synthesis of nanocrystals and nanocrystal superlattices,” IBM J. Res. Dev. 45, 47–56 (2001).
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Bhattacharya, P.

J. Heo, T. Zhu, C. Zhang, J. Xu, and P. Bhattacharya, “Electroluminescence from silicon-based photonic crystal microcavities with PbSe quantum dots,” Opt. Lett. 35, 547–549 (2010).
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J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[CrossRef]

Biasiol, G.

M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra, G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon, “Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities,” Phys. Rev. Lett. 106, 227402 (2011).
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Bichler, M.

U. Hohenester, A. Laucht, M. Kaniber, N. Hauke, A. Neumann, A. Mohtashami, M. Seliger, M. Bichler, and J. J. Finley, “Phonon-assisted transitions from quantum dot excitons to cavity photons,” Phys. Rev. B 80, 201311 (2009).

Bimberg, D.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Rabi oscillations in the excitonic ground-state transition of InGaAs quantum dots,” Phys. Rev. B 66, 081306 (2002).
[CrossRef]

Bogani, F.

M. Colocci, A. Vinattieri, L. Lippi, F. Bogani, M. Rosa-Clot, S. Taddei, A. Bosacchi, S. Franchi, and P. Frigeri, “Controlled tuning of the radiative lifetime in InAs self-assembled quantum dots through vertical ordering,” Appl. Phys. Lett. 74, 564–566 (1999).
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A. Laucht, N. Hauke, J. M. Villas-Bôas, F. Hofbauer, G. Böhm, M. Kaniber, and J. J. Finley, “Dephasing of exciton polaritons in photoexcited InGaAs quantum dots in GaAs nanocavities,” Phys. Rev. Lett. 103, 087405 (2009).
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Bonati, C.

C. Bonati, A. Cannizzo, D. Tonti, A. Tortschanoff, F. van Mourik, and M. Chergui, “Subpicosecond near-infrared fluorescence upconversion study of relaxation processes in PbSe quantum dots,” Phys. Rev. B 76, 033304 (2007).
[CrossRef]

Borri, P.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Rabi oscillations in the excitonic ground-state transition of InGaAs quantum dots,” Phys. Rev. B 66, 081306 (2002).
[CrossRef]

Bosacchi, A.

M. Colocci, A. Vinattieri, L. Lippi, F. Bogani, M. Rosa-Clot, S. Taddei, A. Bosacchi, S. Franchi, and P. Frigeri, “Controlled tuning of the radiative lifetime in InAs self-assembled quantum dots through vertical ordering,” Appl. Phys. Lett. 74, 564–566 (1999).
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Bose, R.

M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Fiber-based cryogenic and time-resolved spectroscopy of PbS quantum dots,” Opt. Express 19, 1786–1793 (2011).
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R. Bose, J. Gao, J. F. McMillan, A. D. Williams, and C. W. Wong, “Cryogenic spectroscopy of ultra-low density colloidal lead chalcogenide quantum dots on chip-scale optical cavities towards single quantum dot near-infrared cavity QED,” Opt. Express 17, 22474–22483 (2009).
[CrossRef]

R. Bose, J. F. McMillan, J. Gao, and C. W. Wong, “Solution-processed cavity and slow-light quantum electrodynamics in near-infrared silicon photonic crystals,” Appl. Phys. Lett. 95, 131112 (2009).
[CrossRef]

R. Bose, X. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 μm at room temperature,” Appl. Phys. Lett. 90, 111117 (2007).
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Bowers, J. E.

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4, 511–517 (2010).
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Braun, T.

T. Heindel, C. Schneider, M. Lermer, S. H. Kwon, T. Braun, S. Reitzenstein, S. Höfling, M. Kamp, and A. Forchel, “Electrically driven quantum dot-micropillar single photon source with 34% overall efficiency,” Appl. Phys. Lett. 96, 011107 (2010).
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Brinker, J. C.

Bru-Chevallier, C.

M. H. Hadj Alouane, R. Anufriev, N. Chauvin, H. Khmissi, K. Naji, B. Ilahi, H. Maaref, G. Patriarche, M. Gendry, and C. Bru-Chevallier, “Wurtzite InP/InAs/InP core-shell nanowires emitting at telecommunication wavelengths on Si substrate,” Nanotechnology 22, 405702 (2011).
[CrossRef]

Calic, M.

M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra, G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon, “Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities,” Phys. Rev. Lett. 106, 227402 (2011).
[CrossRef] [PubMed]

Califano, M.

J. M. An, M. Califano, A. Franceschetti, and A. Zunger, “Excited-state relaxation in PbSe quantum dots,” J. Chem. Phys. 128, 164720 (2008).
[CrossRef] [PubMed]

Cannizzo, A.

C. Bonati, A. Cannizzo, D. Tonti, A. Tortschanoff, F. van Mourik, and M. Chergui, “Subpicosecond near-infrared fluorescence upconversion study of relaxation processes in PbSe quantum dots,” Phys. Rev. B 76, 033304 (2007).
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Chang, F. Y.

D. C. Wu, J. K. Kao, M. H. Mao, F. Y. Chang, and H. H. Lin, “Determination of interband transition dipole moment of InAs/InGaAs quantum dots from modal absorption spectra,” in “OSA Technical Digest Series (CD),” (Optical Society of America, 2007), p. JTuA111.

Chatterjee, R.

R. Bose, X. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 μm at room temperature,” Appl. Phys. Lett. 90, 111117 (2007).
[CrossRef]

Chauvin, N.

M. H. Hadj Alouane, R. Anufriev, N. Chauvin, H. Khmissi, K. Naji, B. Ilahi, H. Maaref, G. Patriarche, M. Gendry, and C. Bru-Chevallier, “Wurtzite InP/InAs/InP core-shell nanowires emitting at telecommunication wavelengths on Si substrate,” Nanotechnology 22, 405702 (2011).
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Chen, C.

H. Du, C. Chen, R. Krishnan, T. D. Krauss, J. M. Harbold, F. W. Wise, M. G. Thomas, and J. Silcox, “Optical properties of colloidal PbSe nanocrystals,” Nano Lett. 2, 1321–1324 (2002).
[CrossRef]

Chen, Y.

S. Vignolini, F. Riboli, F. Intonti, M. Belotti, M. Gurioli, Y. Chen, M. Colocci, L. C. Andreani, and D. S. Wiersma, “Local nanofluidic light sources in silicon photonic crystal microcavities,” Phys. Rev. E 78, 045603 (2008).
[CrossRef]

Chergui, M.

C. Bonati, A. Cannizzo, D. Tonti, A. Tortschanoff, F. van Mourik, and M. Chergui, “Subpicosecond near-infrared fluorescence upconversion study of relaxation processes in PbSe quantum dots,” Phys. Rev. B 76, 033304 (2007).
[CrossRef]

Cheriton, R.

S. Hughes, P. Yao, F. Milde, A. Knorr, D. Dalacu, K. Mnaymneh, V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, R. Cheriton, and R. L. Williams, “Influence of electron-acoustic phonon scattering on off-resonant cavity feeding within a strongly coupled quantum-dot cavity system,” Phys. Rev. B 83, 165313 (2011).
[CrossRef]

Chew, H.

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[CrossRef] [PubMed]

Cho, K.

J. M. Harbold, H. Du, T. D. Krauss, K. Cho, C. B. Murray, and F. W. Wise, “Time-resolved intraband relaxation of strongly confined electrons and holes in colloidal PbSe nanocrystals,” Phys. Rev. B 72,  195312 (2005).
[CrossRef]

Chow, W. W.

Colocci, M.

S. Vignolini, F. Riboli, F. Intonti, M. Belotti, M. Gurioli, Y. Chen, M. Colocci, L. C. Andreani, and D. S. Wiersma, “Local nanofluidic light sources in silicon photonic crystal microcavities,” Phys. Rev. E 78, 045603 (2008).
[CrossRef]

M. Colocci, A. Vinattieri, L. Lippi, F. Bogani, M. Rosa-Clot, S. Taddei, A. Bosacchi, S. Franchi, and P. Frigeri, “Controlled tuning of the radiative lifetime in InAs self-assembled quantum dots through vertical ordering,” Appl. Phys. Lett. 74, 564–566 (1999).
[CrossRef]

Cundiff, S. T.

K. L. Silverman, R. P. Mirin, S. T. Cundiff, and A. G. Norman, “Direct measurement of polarization resolved transition dipole moment in InGaAs/GaAs quantum dots,” Appl. Phys. Lett. 82, 4552–4554 (2003).
[CrossRef]

Dalacu, D.

S. Hughes, P. Yao, F. Milde, A. Knorr, D. Dalacu, K. Mnaymneh, V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, R. Cheriton, and R. L. Williams, “Influence of electron-acoustic phonon scattering on off-resonant cavity feeding within a strongly coupled quantum-dot cavity system,” Phys. Rev. B 83, 165313 (2011).
[CrossRef]

De Geyter, B.

I. Moreels, G. Allan, B. De Geyter, L. Wirtz, C. Delerue, and Z. Hens, “Dielectric function of colloidal lead chalcogenide quantum dots obtained by a Kramers-Krönig analysis of the absorbance spectrum,” Phys. Rev. B 81, 235319 (2010).
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B. De Geyter and Z. Hens, “The absorption coefficient of PbSe/CdSe core/shell colloidal quantum dots,” Appl. Phys. Lett. 97, 161908 (2010).
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De La Rue, R. M.

D. F. Logan, P. Velha, M. Sorel, R. M. De La Rue, A. P. Knights, and P. E. Jessop, “Defect-enhanced silicon-on-insulator waveguide resonant photodetector with high sensitivity at 1.55 μm,” IEEE Photonics Technol. Lett. 22, 1530–1532 (2010).
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De Muynck, D.

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, “Composition and size-dependent extinction coefficient of colloidal PbSe quantum dots,” Chem. Mater. 19, 6101–6106 (2007).
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D. A. Louderback, G. W. Pickrell, H. C. Lin, M. A. Fish, J. J. Hindi, and P. S. Guilfoyle, “VCSELs with monolithic coupling to internal horizontal waveguides using integrated diffraction gratings,” Electron. Lett. 40, 1064–1065 (2004).
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M. Paillard, X. Marie, E. Vanelle, T. Amand, V. K. Kalevich, A. R. Kovsh, A. E. Zhukov, and V. M. Ustinov, “Time-resolved photoluminescence in self-assembled InAs/GaAs quantum dots under strictly resonant excitation,” Appl. Phys. Lett. 76, 76–78 (2000).
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I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, “Composition and size-dependent extinction coefficient of colloidal PbSe quantum dots,” Chem. Mater. 19, 6101–6106 (2007).
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T. Okuno, Y. Masumoto, M. Ikezawa, T. Ogawa, and A. A. Lipovskii, “Size-dependent picosecond energy relaxation in PbSe quantum dots,” Appl. Phys. Lett. 77, 504–506 (2000).
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J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4, 527–534 (2010).
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S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, “Dephasing of triplet-sideband optical emission of a resonantly driven InAs/GaAs quantum dot inside a microcavity,” Phys. Rev. Lett. 106, 247402 (2011).
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S. Hughes, P. Yao, F. Milde, A. Knorr, D. Dalacu, K. Mnaymneh, V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, R. Cheriton, and R. L. Williams, “Influence of electron-acoustic phonon scattering on off-resonant cavity feeding within a strongly coupled quantum-dot cavity system,” Phys. Rev. B 83, 165313 (2011).
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K. L. Silverman, R. P. Mirin, S. T. Cundiff, and A. G. Norman, “Direct measurement of polarization resolved transition dipole moment in InGaAs/GaAs quantum dots,” Appl. Phys. Lett. 82, 4552–4554 (2003).
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S. Hughes, P. Yao, F. Milde, A. Knorr, D. Dalacu, K. Mnaymneh, V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, R. Cheriton, and R. L. Williams, “Influence of electron-acoustic phonon scattering on off-resonant cavity feeding within a strongly coupled quantum-dot cavity system,” Phys. Rev. B 83, 165313 (2011).
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U. Hohenester, A. Laucht, M. Kaniber, N. Hauke, A. Neumann, A. Mohtashami, M. Seliger, M. Bichler, and J. J. Finley, “Phonon-assisted transitions from quantum dot excitons to cavity photons,” Phys. Rev. B 80, 201311 (2009).

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I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, “Composition and size-dependent extinction coefficient of colloidal PbSe quantum dots,” Chem. Mater. 19, 6101–6106 (2007).
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U. Hohenester, A. Laucht, M. Kaniber, N. Hauke, A. Neumann, A. Mohtashami, M. Seliger, M. Bichler, and J. J. Finley, “Phonon-assisted transitions from quantum dot excitons to cavity photons,” Phys. Rev. B 80, 201311 (2009).

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P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
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I. Moreels, K. Lambert, D. Smeets, D. D. Muynck, T. Nollet, J. C. Martins, F. Vanhaecke, A. Vantomme, C. Delerue, G. Allan, and Z. Hens, “Size-dependent optical properties of colloidal PbS quantum dots,” ACS Nano 3, 3023–3030 (2009).
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K. L. Silverman, R. P. Mirin, S. T. Cundiff, and A. G. Norman, “Direct measurement of polarization resolved transition dipole moment in InGaAs/GaAs quantum dots,” Appl. Phys. Lett. 82, 4552–4554 (2003).
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T. Okuno, Y. Masumoto, M. Ikezawa, T. Ogawa, and A. A. Lipovskii, “Size-dependent picosecond energy relaxation in PbSe quantum dots,” Appl. Phys. Lett. 77, 504–506 (2000).
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P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Rabi oscillations in the excitonic ground-state transition of InGaAs quantum dots,” Phys. Rev. B 66, 081306 (2002).
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P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, “Nonlinear photoluminescence spectra from a quantum-dot-cavity system: Interplay of pump-induced stimulated emission and anharmonic cavity QED,” Phys. Rev. B 81, 033309 (2010).
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M. H. Hadj Alouane, R. Anufriev, N. Chauvin, H. Khmissi, K. Naji, B. Ilahi, H. Maaref, G. Patriarche, M. Gendry, and C. Bru-Chevallier, “Wurtzite InP/InAs/InP core-shell nanowires emitting at telecommunication wavelengths on Si substrate,” Nanotechnology 22, 405702 (2011).
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Perinetti, U.

S. N. Dorenbos, E. M. Reiger, U. Perinetti, V. Zwiller, T. Zijlstra, and T. M. Klapwijk, “Low noise superconducting single photon detectors on silicon,” Appl. Phys. Lett. 93, 131101 (2008).
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D. A. Louderback, G. W. Pickrell, H. C. Lin, M. A. Fish, J. J. Hindi, and P. S. Guilfoyle, “VCSELs with monolithic coupling to internal horizontal waveguides using integrated diffraction gratings,” Electron. Lett. 40, 1064–1065 (2004).
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J. W. Stouwdam, J. Shan, F. C. J. M. van Veggel, A. G. Pattantyus-Abraham, J. F. Young, and M. Raudsepp, “Photostability of colloidal PbSe and PbSe/PbS core/shell nanocrystals in solution and in the solid state,” J. Phys. Chem. C 111, 1086–1092 (2007).
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S. Vignolini, F. Riboli, F. Intonti, M. Belotti, M. Gurioli, Y. Chen, M. Colocci, L. C. Andreani, and D. S. Wiersma, “Local nanofluidic light sources in silicon photonic crystal microcavities,” Phys. Rev. E 78, 045603 (2008).
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S. Hughes, P. Yao, F. Milde, A. Knorr, D. Dalacu, K. Mnaymneh, V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, R. Cheriton, and R. L. Williams, “Influence of electron-acoustic phonon scattering on off-resonant cavity feeding within a strongly coupled quantum-dot cavity system,” Phys. Rev. B 83, 165313 (2011).
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[CrossRef]

H. Du, C. Chen, R. Krishnan, T. D. Krauss, J. M. Harbold, F. W. Wise, M. G. Thomas, and J. Silcox, “Optical properties of colloidal PbSe nanocrystals,” Nano Lett. 2, 1321–1324 (2002).
[CrossRef]

Woggon, U.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Rabi oscillations in the excitonic ground-state transition of InGaAs quantum dots,” Phys. Rev. B 66, 081306 (2002).
[CrossRef]

Wondergem, H.

A. L. Roest, M. A. Verheijen, O. Wunnicke, S. Serafin, H. Wondergem, and E. P. A. M. Bakkers, “Position-controlled epitaxial III–V nanowires on silicon,” Nanotechnology 17, S271–S275 (2006).
[CrossRef]

Wong, C. W.

M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Fiber-based cryogenic and time-resolved spectroscopy of PbS quantum dots,” Opt. Express 19, 1786–1793 (2011).
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[CrossRef]

R. Bose, J. F. McMillan, J. Gao, and C. W. Wong, “Solution-processed cavity and slow-light quantum electrodynamics in near-infrared silicon photonic crystals,” Appl. Phys. Lett. 95, 131112 (2009).
[CrossRef]

R. Bose, X. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 μm at room temperature,” Appl. Phys. Lett. 90, 111117 (2007).
[CrossRef]

Worschech, L.

P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, “Nonlinear photoluminescence spectra from a quantum-dot-cavity system: Interplay of pump-induced stimulated emission and anharmonic cavity QED,” Phys. Rev. B 81, 033309 (2010).
[CrossRef]

Wu, D. C.

D. C. Wu, J. K. Kao, M. H. Mao, F. Y. Chang, and H. H. Lin, “Determination of interband transition dipole moment of InAs/InGaAs quantum dots from modal absorption spectra,” in “OSA Technical Digest Series (CD),” (Optical Society of America, 2007), p. JTuA111.

Wu, Z.

L. Kong, Z. C. Feng, Z. Wu, and W. Lu, “Temperature dependent and time-resolved photoluminescence studies of InAs self-assembled quantum dots with InGaAs strain reducing layer structure,” J. Appl. Phys. 106, 013512 (2009).
[CrossRef]

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A. L. Roest, M. A. Verheijen, O. Wunnicke, S. Serafin, H. Wondergem, and E. P. A. M. Bakkers, “Position-controlled epitaxial III–V nanowires on silicon,” Nanotechnology 17, S271–S275 (2006).
[CrossRef]

Xiong, S.

Xu, J.

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[CrossRef]

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[CrossRef]

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R. Bose, X. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 μm at room temperature,” Appl. Phys. Lett. 90, 111117 (2007).
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P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, “Nonlinear photoluminescence spectra from a quantum-dot-cavity system: Interplay of pump-induced stimulated emission and anharmonic cavity QED,” Phys. Rev. B 81, 033309 (2010).
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Zhang, C.

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J. Heo, T. Zhu, C. Zhang, J. Xu, and P. Bhattacharya, “Electroluminescence from silicon-based photonic crystal microcavities with PbSe quantum dots,” Opt. Lett. 35, 547–549 (2010).
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J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
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M. Paillard, X. Marie, E. Vanelle, T. Amand, V. K. Kalevich, A. R. Kovsh, A. E. Zhukov, and V. M. Ustinov, “Time-resolved photoluminescence in self-assembled InAs/GaAs quantum dots under strictly resonant excitation,” Appl. Phys. Lett. 76, 76–78 (2000).
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Figures (9)

Fig. 1
Fig. 1

(A) Schematic and scanning electron micrograph of an “L3” microcavity. (B) Fundamental in-gap cavity mode electric field intensity at the silicon-air interface, with etched holes outlined. Axes originate at the L3 slab centroid, and is perpendicular to and ŷ.

Fig. 2
Fig. 2

(A) Close-up scanning electron micrograph of the photonic crystal cavity, photonic crystal waveguide, and channel waveguide region. (B) An optical image of the entire cavity, waveguides, and grating structure, with excitation spot (centered on the cavity) and collection spot (centered on the grating coupler) indicated. (C) Example ŷ-polarization-filtered PL spectrum for the excitation/collection geometry indicated in (B), and a plot of the cavity-enhanced, waveguide-coupled PL versus pump power.

Fig. 3
Fig. 3

Experimental setup and resulting data modeled in this article. (A) Schematic of excitation/collection geometry: excitation (at 633 nm) and collection performed with a common 100 X microscope objective. Red-filled circle indicates 1/e excitation spot intensity. Shaded square indicates span of grafted PbSe QDs. (B) Example PL spectrum with cavity-coupled emission indicated, and cavity-coupled PL versus pump power.

Fig. 4
Fig. 4

Minimal Hilbert space necessary to accommodate observed saturation behaviour: four states for the QD subspace and two for the cavity subspace. Significant decay paths indicated by solid blue arrows, of which squiggly lines are radiative and the remainder non-radiative. Laser field of Rabi coupling frequency Ω “pumps” the |P〉 state. The cavity is “fed” by coupling to the |X〉 ↔ |G〉 transition with electric-dipole coupling strength g.

Fig. 5
Fig. 5

Model dielectric environment ε(r,ω) = εL3(r,ω) +εQDs(r,ω). Nanocrystal array εQDs(r,ω) on left, centered on the L3 cavity surface. The computational volume for FDTD calculations (see text) is restricted to the 3 μm cube centered about the centroidal QD. The intrinsic “test” dipole is located at the center of centroidal QD, position rQD. The device silicon slab is surrounded by vacuum above and below, with backing silicon 1.2 μm below.

Fig. 6
Fig. 6

Spontaneous emission rate of a point dipole source of frequency ωcav + δω, for positions along the -axis of the L3 cavity, excluding the cavity mode and QD array, for electric dipole orientations along axes , ŷ, or (see text and orientation definitions in Fig. 1). All values normalized to the free-space spontaneous emission rate γXG,0.

Fig. 7
Fig. 7

Intensity profiles of HeNe excitation field, as modulated by the L3 cavity εL3(r). Gaussian laser field was injected along the axis towards increasingly negative z, indicated by black arrow. Air-silicon interfaces lined in black. (left) Profile several nanometers above the slab surface, the plane containing the PbSe QDs. (right) Profile in the x = 0 plane.

Fig. 8
Fig. 8

Best (minimum χ2) fits to cavity-enhanced photoluminescence for only three electronic levels (left), i.e. without a non-radiative state, and for four electronic levels (right), i.e. including a non-radiative “trap” state.

Fig. 9
Fig. 9

Trap state lifetime τ trap = γ YG 1 required to fit the data. Parameterization of τtrap is in terms of the “effective depolarization”, DPF, which is defined in-text (see Eq. (18)) and is equal to the laser field inside the QD in the full model dielectric environment relative to the laser field inside the same QD in vacuum. Variation of τtrap with DPF is dominated by uncertainties in parameters specific to our dielectric environment (photonic crystal cavity, QD array), whereas variation of τtrap for a particular DPF is dominated by parameter uncertainty not specific to our dielectric environment (e.g. solvent permittivity from solvent-based QD properties). Points are sampled from the model parameter space.

Equations (18)

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H 0 = h ¯ ω | | + h ¯ ω cav a a
H pump = h ¯ Ω ( | P G | + | G P | ) cos ( ω pump t )
H cav = h ¯ g ( | X G | + | G X | ) ( a + a )
H S = H 0 + H pump + H cav
d ρ dt = i h ¯ [ ρ , H S ] + j k [ D j k ρ D j k 1 2 ( D j k D j k ρ + ρ D j k D j k ) ] + γ cav [ a ρ a 1 2 ( a a ρ + ρ a a ) ] ,
D j k = γ j k | k j | quantum dot population   decay , | j | k
D j j = γ j | j j | quantum dot pure dephasing
γ XG , QD + sol = ε sol | 3 2 + ε QD , nr ( ω XG ) / ε sol | 2 γ XG , 0
= ε sol | 3 2 + ε QD , nr ( ω XG ) / ε sol | 2 ω XG 3 | μ XG , 0 | 2 3 π ε 0 h ¯ c 3
γ XG , ε ( r ) γ XG , 0 = P rad , ε ( r ) P rad , 0
γ XG = γ XG , ε ( r ) = P rad , ε ( r ) ( ω cav + δ ω ) orientation P rad , 0 ( ω cav + δ ω ) γ XG , 0 = 4 2 + 5 × 10 5 Hz
| E cav vac ( r QD ) | = h ¯ ω cav 2 ε 0 d r ε ( r ) ( | E cav ( r ) | | E cav ( r QD ) | ) 2 = 3 1 + 1 × 10 4 V / m ,
R Ω 2 γ P = | μ GP , 0 | 2 h ¯ 2 γ P | E pump ( r QD ) | 2
R = A 400 nm C Q PbSe A 633 nm A 400 nm h ¯ ω pump ε sol 2 η 0 | 2 + ε QD ( ω pump ) / ε sol 3 | 2 | E pump ( r QD ) | 2
Ω = γ P R
= 2 ε sol A 400 nm C Q PbSe A 633 nm A 400 nm γ P P 0 h ¯ ω pump π W 0 2 | 2 + ε QD ( ω pump ) / ε sol 3 | | E pump , ε ( r ) ( r QD ) | | E pump , 0 |
= 3 1 + 1 × 10 5 γ P P 0
DPF = | E pump , ε ( r ) ( r QD ) | | E pump , QD ( r QD ) | = | E pump , ε ( r ) ( r QD ) | | E pump , 0 | | 3 2 + ε QD ( ω pump ) | 1

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