Abstract

We present a universal method of determining the position, 3D orientation, and relative quantum yield ratio (RQYR) of fluorescent nanoemitters (ZnS coated CdSe quantum dots) in a glass slide by combining laser scanning microscopy (LSM) and polarization measurements. The quantum dots were located through LSM intensity maps using azimuthal, radial, and linear incident polarizations. LSM imaging was not sufficient to determine the orientation of the quantum dots due to the isotropic absorption dipole moment. The 3D orientation was obtained through polarization measurement. By combining LSM and polarization measurements, the RQYR of a single molecule was evaluated, allowing us to compare the quantum yield of the nanoemitters.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2015 (3)

A. M. Chizhik, L. Tarpani, L. Latterini, I. Gregor, J. Enderlein, and A. I. Chizhik, “Photoluminescence of a single quantum emitter in a strongly inhomogeneous chemical environment,” Phys. Chem. Chem. Phys. 17(22), 14994–15000 (2015).
[Crossref] [PubMed]

C. Würth, D. Geissler, T. Behnke, M. Kaiser, and U. Resch-Genger, “Critical review of the determination of photoluminescence quantum yields of luminescent reporters,” Anal. Bioanal. Chem. 407(1), 59–78 (2015).
[Crossref] [PubMed]

D. Kempe, A. Schöne, J. Fitter, and M. Gabba, “Accurate Fluorescence Quantum Yield Determination by Fluorescence Correlation Spectroscopy,” J. Phys. Chem. B 119(13), 4668–4672 (2015).
[Crossref] [PubMed]

2014 (2)

P. Holzmeister, E. Pibiri, J. J. Schmied, T. Sen, G. P. Acuna, and P. Tinnefeld, “Quantum yield and excitation rate of single molecules close to metallic nanostructures,” Nat. Commun. 5, 5356 (2014).
[Crossref] [PubMed]

C. Lethiec, J. Laverdant, H. Vallon, C. Javaux, B. Dubertret, J.-M. Frigerio, C. Schwob, L. Coolen, and A. Maître, “Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis,” Phys. Rev. X 4(2), 1–12 (2014).
[Crossref]

2013 (3)

C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Relative and absolute determination of fluorescence quantum yields of transparent samples,” Nat. Protoc. 8(8), 1535–1550 (2013).
[Crossref] [PubMed]

J. Hu and C. Y. Zhang, “Simple and accurate quantification of quantum yield at the single-molecule/particle level,” Anal. Chem. 85(4), 2000–2004 (2013).
[Crossref] [PubMed]

D. Punj, J. de Torres, H. Rigneault, and J. Wenger, “Gold nanoparticles for enhanced single molecule fluorescence analysis at micromolar concentration,” Opt. Express 21(22), 27338–27343 (2013).
[Crossref] [PubMed]

2012 (3)

A. Pillonnet, P. Fleury, A. I. Chizhik, A. M. Chizhik, D. Amans, G. Ledoux, F. Kulzer, A. J. Meixner, and C. Dujardin, “Local refractive index probed via the fluorescence decay of semiconductor quantum dots,” Opt. Express 20(3), 3200–3208 (2012).
[Crossref] [PubMed]

V. Pilla and E. Munin, “Fluorescence quantum efficiency of CdSe/ZnS quantum dots functionalized with amine or carboxyl groups,” J. Nanopart. Res. 14(10), 1147 (2012).
[Crossref]

D. Axelrod, “Fluorescence excitation and imaging of single molecules near dielectric-coated and bare surfaces: A theoretical study,” J. Microsc. 247(2), 147–160 (2012).
[Crossref] [PubMed]

2011 (2)

A. I. Chizhik, A. M. Chizhik, A. Huss, R. Jäger, and A. J. Meixner, “Nanoscale probing of dielectric interfaces with single-molecule excitation patterns and radially polarized illumination,” J. Phys. Chem. Lett. 2(17), 2152–2157 (2011).
[Crossref]

A. I. Chizhik, A. M. Chizhik, D. Khoptyar, S. Bär, and A. J. Meixner, “Excitation isotropy of single CdSe/ZnS nanocrystals,” Nano Lett. 11(3), 1131–1135 (2011).
[Crossref] [PubMed]

2010 (1)

H. Ishitobi, I. Nakamura, N. Hayazawa, Z. Sekkat, and S. Kawata, “Orientational Imaging of Single Molecules by Using Azimuthal and Radial Polarizations,” J. Phys. Chem. B 114(8), 2565–2571 (2010).
[Crossref] [PubMed]

2009 (2)

N. Hayazawa, K. Furusawa, A. Taguchi, and S. Kawata, “One-photon and two-photon excited fluorescence microscopies based on polarization-control: Applications to tip-enhanced microscopy,” J. Appl. Phys. 106(11), 113103 (2009).
[Crossref]

N. Hayazawa, K. Furusawa, A. Taguchi, S. Kawata, and H. Abe, “Tip-enhanced two-photon excited fluorescence microscopy with a silicon tip,” Appl. Phys. Lett. 94(19), 193112 (2009).
[Crossref]

2008 (2)

N. N. Horimoto, K. Imura, and H. Okamoto, “Dye fluorescence enhancement and quenching by gold nanoparticles: Direct near-field microscopic observation of shape dependence,” Chem. Phys. Lett. 467(1-3), 105–109 (2008).
[Crossref]

Z. Zhang, J. Pu, and X. Wang, “Tightly focusing of linearly polarized vortex beams through a dielectric interface,” Opt. Commun. 281(13), 3421–3426 (2008).
[Crossref]

2005 (2)

X. Brokmann, L. Coolen, J.-P. Hermier, and M. Dahan, “Emission properties of single CdSe/ZnS quantum dots close to a dielectric interface,” Chem. Phys. 318(1-2), 91–98 (2005).
[Crossref]

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

2004 (4)

J. Müller, J. M. Lupton, A. L. Rogach, J. Feldmann, D. V. Talapin, and H. Weller, “Air-induced fluorescence bursts from single semiconductor nanocrystals,” Appl. Phys. Lett. 85(3), 381–383 (2004).
[Crossref]

D. Patra, I. Gregor, and J. Enderlein, “Image analysis of defocused single molecule images for three dimensional molecular orientation studies,” J. Phys. Chem. A 108(33), 6836–6841 (2004).
[Crossref]

M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21(6), 1210 (2004).
[Crossref]

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
[Crossref]

2003 (1)

F. Koberling, U. Kolb, G. Philipp, I. Potapova, T. Basché, and A. Mews, “Fluorescence Anisotropy and Crystal Structure of Individual Semiconductor Nanocrystals,” J. Phys. Chem. B 107(30), 7463–7471 (2003).
[Crossref]

2002 (1)

W. G. J. H. M. van Sark, P. L. T. M. Frederix, A. A. Bol, H. C. Gerritsen, and A. Meijerink, “Blueing, Bleaching, and Blinking of Single CdSe/ZnS Quantum Dots,” ChemPhysChem 3(10), 871–879 (2002).
[Crossref]

2001 (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal Field Modes Probed by Single Molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

J. T. Fourkas, “Rapid Determination of the three-dimensional orientation of single molecules,” Opt. Lett. 26(4), 211–213 (2001).
[Crossref] [PubMed]

2000 (1)

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

1999 (1)

M. G. B. S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature 399(6732), 126–130 (1999).
[Crossref]

1996 (1)

A. L. Efros, M. Rosen, M. Kuno, M. Nirmal, D. J. Norris, and M. Bawendi, “Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states,” Phys. Rev. B Condens. Matter 54(7), 4843–4856 (1996).
[Crossref] [PubMed]

1992 (1)

A. L. Efros, “Luminescence polarization of CdSe microcrystals,” Phys. Rev. B Condens. Matter 46(12), 7448–7458 (1992).
[Crossref] [PubMed]

1987 (1)

1979 (1)

Abe, H.

N. Hayazawa, K. Furusawa, A. Taguchi, S. Kawata, and H. Abe, “Tip-enhanced two-photon excited fluorescence microscopy with a silicon tip,” Appl. Phys. Lett. 94(19), 193112 (2009).
[Crossref]

Acuna, G. P.

P. Holzmeister, E. Pibiri, J. J. Schmied, T. Sen, G. P. Acuna, and P. Tinnefeld, “Quantum yield and excitation rate of single molecules close to metallic nanostructures,” Nat. Commun. 5, 5356 (2014).
[Crossref] [PubMed]

Amans, D.

Axelrod, D.

D. Axelrod, “Fluorescence excitation and imaging of single molecules near dielectric-coated and bare surfaces: A theoretical study,” J. Microsc. 247(2), 147–160 (2012).
[Crossref] [PubMed]

E. H. Hellen and D. Axelrod, “Fluorescence emission at dielectric and metal-film interfaces,” J. Opt. Soc. Am. B 4(3), 337 (1987).
[Crossref]

Bär, S.

A. I. Chizhik, A. M. Chizhik, D. Khoptyar, S. Bär, and A. J. Meixner, “Excitation isotropy of single CdSe/ZnS nanocrystals,” Nano Lett. 11(3), 1131–1135 (2011).
[Crossref] [PubMed]

Basché, T.

F. Koberling, U. Kolb, G. Philipp, I. Potapova, T. Basché, and A. Mews, “Fluorescence Anisotropy and Crystal Structure of Individual Semiconductor Nanocrystals,” J. Phys. Chem. B 107(30), 7463–7471 (2003).
[Crossref]

Bawendi, M.

A. L. Efros, M. Rosen, M. Kuno, M. Nirmal, D. J. Norris, and M. Bawendi, “Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states,” Phys. Rev. B Condens. Matter 54(7), 4843–4856 (1996).
[Crossref] [PubMed]

Bawendi, M. G.

M. G. B. S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature 399(6732), 126–130 (1999).
[Crossref]

Behnke, T.

C. Würth, D. Geissler, T. Behnke, M. Kaiser, and U. Resch-Genger, “Critical review of the determination of photoluminescence quantum yields of luminescent reporters,” Anal. Bioanal. Chem. 407(1), 59–78 (2015).
[Crossref] [PubMed]

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal Field Modes Probed by Single Molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Bol, A. A.

W. G. J. H. M. van Sark, P. L. T. M. Frederix, A. A. Bol, H. C. Gerritsen, and A. Meijerink, “Blueing, Bleaching, and Blinking of Single CdSe/ZnS Quantum Dots,” ChemPhysChem 3(10), 871–879 (2002).
[Crossref]

Brokmann, X.

X. Brokmann, L. Coolen, J.-P. Hermier, and M. Dahan, “Emission properties of single CdSe/ZnS quantum dots close to a dielectric interface,” Chem. Phys. 318(1-2), 91–98 (2005).
[Crossref]

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal Field Modes Probed by Single Molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Chizhik, A. I.

A. M. Chizhik, L. Tarpani, L. Latterini, I. Gregor, J. Enderlein, and A. I. Chizhik, “Photoluminescence of a single quantum emitter in a strongly inhomogeneous chemical environment,” Phys. Chem. Chem. Phys. 17(22), 14994–15000 (2015).
[Crossref] [PubMed]

A. Pillonnet, P. Fleury, A. I. Chizhik, A. M. Chizhik, D. Amans, G. Ledoux, F. Kulzer, A. J. Meixner, and C. Dujardin, “Local refractive index probed via the fluorescence decay of semiconductor quantum dots,” Opt. Express 20(3), 3200–3208 (2012).
[Crossref] [PubMed]

A. I. Chizhik, A. M. Chizhik, D. Khoptyar, S. Bär, and A. J. Meixner, “Excitation isotropy of single CdSe/ZnS nanocrystals,” Nano Lett. 11(3), 1131–1135 (2011).
[Crossref] [PubMed]

A. I. Chizhik, A. M. Chizhik, A. Huss, R. Jäger, and A. J. Meixner, “Nanoscale probing of dielectric interfaces with single-molecule excitation patterns and radially polarized illumination,” J. Phys. Chem. Lett. 2(17), 2152–2157 (2011).
[Crossref]

Chizhik, A. M.

A. M. Chizhik, L. Tarpani, L. Latterini, I. Gregor, J. Enderlein, and A. I. Chizhik, “Photoluminescence of a single quantum emitter in a strongly inhomogeneous chemical environment,” Phys. Chem. Chem. Phys. 17(22), 14994–15000 (2015).
[Crossref] [PubMed]

A. Pillonnet, P. Fleury, A. I. Chizhik, A. M. Chizhik, D. Amans, G. Ledoux, F. Kulzer, A. J. Meixner, and C. Dujardin, “Local refractive index probed via the fluorescence decay of semiconductor quantum dots,” Opt. Express 20(3), 3200–3208 (2012).
[Crossref] [PubMed]

A. I. Chizhik, A. M. Chizhik, A. Huss, R. Jäger, and A. J. Meixner, “Nanoscale probing of dielectric interfaces with single-molecule excitation patterns and radially polarized illumination,” J. Phys. Chem. Lett. 2(17), 2152–2157 (2011).
[Crossref]

A. I. Chizhik, A. M. Chizhik, D. Khoptyar, S. Bär, and A. J. Meixner, “Excitation isotropy of single CdSe/ZnS nanocrystals,” Nano Lett. 11(3), 1131–1135 (2011).
[Crossref] [PubMed]

Coolen, L.

C. Lethiec, J. Laverdant, H. Vallon, C. Javaux, B. Dubertret, J.-M. Frigerio, C. Schwob, L. Coolen, and A. Maître, “Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis,” Phys. Rev. X 4(2), 1–12 (2014).
[Crossref]

X. Brokmann, L. Coolen, J.-P. Hermier, and M. Dahan, “Emission properties of single CdSe/ZnS quantum dots close to a dielectric interface,” Chem. Phys. 318(1-2), 91–98 (2005).
[Crossref]

Dahan, M.

X. Brokmann, L. Coolen, J.-P. Hermier, and M. Dahan, “Emission properties of single CdSe/ZnS quantum dots close to a dielectric interface,” Chem. Phys. 318(1-2), 91–98 (2005).
[Crossref]

de Torres, J.

Dubertret, B.

C. Lethiec, J. Laverdant, H. Vallon, C. Javaux, B. Dubertret, J.-M. Frigerio, C. Schwob, L. Coolen, and A. Maître, “Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis,” Phys. Rev. X 4(2), 1–12 (2014).
[Crossref]

Dujardin, C.

Efros, A. L.

A. L. Efros, M. Rosen, M. Kuno, M. Nirmal, D. J. Norris, and M. Bawendi, “Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states,” Phys. Rev. B Condens. Matter 54(7), 4843–4856 (1996).
[Crossref] [PubMed]

A. L. Efros, “Luminescence polarization of CdSe microcrystals,” Phys. Rev. B Condens. Matter 46(12), 7448–7458 (1992).
[Crossref] [PubMed]

Empedocles, M. G. B. S. A.

M. G. B. S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature 399(6732), 126–130 (1999).
[Crossref]

Enderlein, J.

A. M. Chizhik, L. Tarpani, L. Latterini, I. Gregor, J. Enderlein, and A. I. Chizhik, “Photoluminescence of a single quantum emitter in a strongly inhomogeneous chemical environment,” Phys. Chem. Chem. Phys. 17(22), 14994–15000 (2015).
[Crossref] [PubMed]

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

D. Patra, I. Gregor, and J. Enderlein, “Image analysis of defocused single molecule images for three dimensional molecular orientation studies,” J. Phys. Chem. A 108(33), 6836–6841 (2004).
[Crossref]

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J. Müller, J. M. Lupton, A. L. Rogach, J. Feldmann, D. V. Talapin, and H. Weller, “Air-induced fluorescence bursts from single semiconductor nanocrystals,” Appl. Phys. Lett. 85(3), 381–383 (2004).
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Fitter, J.

D. Kempe, A. Schöne, J. Fitter, and M. Gabba, “Accurate Fluorescence Quantum Yield Determination by Fluorescence Correlation Spectroscopy,” J. Phys. Chem. B 119(13), 4668–4672 (2015).
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Fourkas, J. T.

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W. G. J. H. M. van Sark, P. L. T. M. Frederix, A. A. Bol, H. C. Gerritsen, and A. Meijerink, “Blueing, Bleaching, and Blinking of Single CdSe/ZnS Quantum Dots,” ChemPhysChem 3(10), 871–879 (2002).
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C. Lethiec, J. Laverdant, H. Vallon, C. Javaux, B. Dubertret, J.-M. Frigerio, C. Schwob, L. Coolen, and A. Maître, “Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis,” Phys. Rev. X 4(2), 1–12 (2014).
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N. Hayazawa, K. Furusawa, A. Taguchi, and S. Kawata, “One-photon and two-photon excited fluorescence microscopies based on polarization-control: Applications to tip-enhanced microscopy,” J. Appl. Phys. 106(11), 113103 (2009).
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N. Hayazawa, K. Furusawa, A. Taguchi, S. Kawata, and H. Abe, “Tip-enhanced two-photon excited fluorescence microscopy with a silicon tip,” Appl. Phys. Lett. 94(19), 193112 (2009).
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D. Kempe, A. Schöne, J. Fitter, and M. Gabba, “Accurate Fluorescence Quantum Yield Determination by Fluorescence Correlation Spectroscopy,” J. Phys. Chem. B 119(13), 4668–4672 (2015).
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C. Würth, D. Geissler, T. Behnke, M. Kaiser, and U. Resch-Genger, “Critical review of the determination of photoluminescence quantum yields of luminescent reporters,” Anal. Bioanal. Chem. 407(1), 59–78 (2015).
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Gerritsen, H. C.

W. G. J. H. M. van Sark, P. L. T. M. Frederix, A. A. Bol, H. C. Gerritsen, and A. Meijerink, “Blueing, Bleaching, and Blinking of Single CdSe/ZnS Quantum Dots,” ChemPhysChem 3(10), 871–879 (2002).
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Grabolle, M.

C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Relative and absolute determination of fluorescence quantum yields of transparent samples,” Nat. Protoc. 8(8), 1535–1550 (2013).
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Gregor, I.

A. M. Chizhik, L. Tarpani, L. Latterini, I. Gregor, J. Enderlein, and A. I. Chizhik, “Photoluminescence of a single quantum emitter in a strongly inhomogeneous chemical environment,” Phys. Chem. Chem. Phys. 17(22), 14994–15000 (2015).
[Crossref] [PubMed]

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

D. Patra, I. Gregor, and J. Enderlein, “Image analysis of defocused single molecule images for three dimensional molecular orientation studies,” J. Phys. Chem. A 108(33), 6836–6841 (2004).
[Crossref]

Hayazawa, N.

H. Ishitobi, I. Nakamura, N. Hayazawa, Z. Sekkat, and S. Kawata, “Orientational Imaging of Single Molecules by Using Azimuthal and Radial Polarizations,” J. Phys. Chem. B 114(8), 2565–2571 (2010).
[Crossref] [PubMed]

N. Hayazawa, K. Furusawa, A. Taguchi, and S. Kawata, “One-photon and two-photon excited fluorescence microscopies based on polarization-control: Applications to tip-enhanced microscopy,” J. Appl. Phys. 106(11), 113103 (2009).
[Crossref]

N. Hayazawa, K. Furusawa, A. Taguchi, S. Kawata, and H. Abe, “Tip-enhanced two-photon excited fluorescence microscopy with a silicon tip,” Appl. Phys. Lett. 94(19), 193112 (2009).
[Crossref]

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
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Hecht, B.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
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Hellen, E. H.

Hermier, J.-P.

X. Brokmann, L. Coolen, J.-P. Hermier, and M. Dahan, “Emission properties of single CdSe/ZnS quantum dots close to a dielectric interface,” Chem. Phys. 318(1-2), 91–98 (2005).
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Holzmeister, P.

P. Holzmeister, E. Pibiri, J. J. Schmied, T. Sen, G. P. Acuna, and P. Tinnefeld, “Quantum yield and excitation rate of single molecules close to metallic nanostructures,” Nat. Commun. 5, 5356 (2014).
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Horimoto, N. N.

N. N. Horimoto, K. Imura, and H. Okamoto, “Dye fluorescence enhancement and quenching by gold nanoparticles: Direct near-field microscopic observation of shape dependence,” Chem. Phys. Lett. 467(1-3), 105–109 (2008).
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Hu, J.

J. Hu and C. Y. Zhang, “Simple and accurate quantification of quantum yield at the single-molecule/particle level,” Anal. Chem. 85(4), 2000–2004 (2013).
[Crossref] [PubMed]

Huss, A.

A. I. Chizhik, A. M. Chizhik, A. Huss, R. Jäger, and A. J. Meixner, “Nanoscale probing of dielectric interfaces with single-molecule excitation patterns and radially polarized illumination,” J. Phys. Chem. Lett. 2(17), 2152–2157 (2011).
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Imura, K.

N. N. Horimoto, K. Imura, and H. Okamoto, “Dye fluorescence enhancement and quenching by gold nanoparticles: Direct near-field microscopic observation of shape dependence,” Chem. Phys. Lett. 467(1-3), 105–109 (2008).
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H. Ishitobi, I. Nakamura, N. Hayazawa, Z. Sekkat, and S. Kawata, “Orientational Imaging of Single Molecules by Using Azimuthal and Radial Polarizations,” J. Phys. Chem. B 114(8), 2565–2571 (2010).
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Jäger, R.

A. I. Chizhik, A. M. Chizhik, A. Huss, R. Jäger, and A. J. Meixner, “Nanoscale probing of dielectric interfaces with single-molecule excitation patterns and radially polarized illumination,” J. Phys. Chem. Lett. 2(17), 2152–2157 (2011).
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Javaux, C.

C. Lethiec, J. Laverdant, H. Vallon, C. Javaux, B. Dubertret, J.-M. Frigerio, C. Schwob, L. Coolen, and A. Maître, “Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis,” Phys. Rev. X 4(2), 1–12 (2014).
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Kaiser, M.

C. Würth, D. Geissler, T. Behnke, M. Kaiser, and U. Resch-Genger, “Critical review of the determination of photoluminescence quantum yields of luminescent reporters,” Anal. Bioanal. Chem. 407(1), 59–78 (2015).
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Kawata, S.

H. Ishitobi, I. Nakamura, N. Hayazawa, Z. Sekkat, and S. Kawata, “Orientational Imaging of Single Molecules by Using Azimuthal and Radial Polarizations,” J. Phys. Chem. B 114(8), 2565–2571 (2010).
[Crossref] [PubMed]

N. Hayazawa, K. Furusawa, A. Taguchi, and S. Kawata, “One-photon and two-photon excited fluorescence microscopies based on polarization-control: Applications to tip-enhanced microscopy,” J. Appl. Phys. 106(11), 113103 (2009).
[Crossref]

N. Hayazawa, K. Furusawa, A. Taguchi, S. Kawata, and H. Abe, “Tip-enhanced two-photon excited fluorescence microscopy with a silicon tip,” Appl. Phys. Lett. 94(19), 193112 (2009).
[Crossref]

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
[Crossref]

Kempe, D.

D. Kempe, A. Schöne, J. Fitter, and M. Gabba, “Accurate Fluorescence Quantum Yield Determination by Fluorescence Correlation Spectroscopy,” J. Phys. Chem. B 119(13), 4668–4672 (2015).
[Crossref] [PubMed]

Khoptyar, D.

A. I. Chizhik, A. M. Chizhik, D. Khoptyar, S. Bär, and A. J. Meixner, “Excitation isotropy of single CdSe/ZnS nanocrystals,” Nano Lett. 11(3), 1131–1135 (2011).
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F. Koberling, U. Kolb, G. Philipp, I. Potapova, T. Basché, and A. Mews, “Fluorescence Anisotropy and Crystal Structure of Individual Semiconductor Nanocrystals,” J. Phys. Chem. B 107(30), 7463–7471 (2003).
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Kolb, U.

F. Koberling, U. Kolb, G. Philipp, I. Potapova, T. Basché, and A. Mews, “Fluorescence Anisotropy and Crystal Structure of Individual Semiconductor Nanocrystals,” J. Phys. Chem. B 107(30), 7463–7471 (2003).
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Kulzer, F.

Kuno, M.

A. L. Efros, M. Rosen, M. Kuno, M. Nirmal, D. J. Norris, and M. Bawendi, “Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states,” Phys. Rev. B Condens. Matter 54(7), 4843–4856 (1996).
[Crossref] [PubMed]

Latterini, L.

A. M. Chizhik, L. Tarpani, L. Latterini, I. Gregor, J. Enderlein, and A. I. Chizhik, “Photoluminescence of a single quantum emitter in a strongly inhomogeneous chemical environment,” Phys. Chem. Chem. Phys. 17(22), 14994–15000 (2015).
[Crossref] [PubMed]

Laverdant, J.

C. Lethiec, J. Laverdant, H. Vallon, C. Javaux, B. Dubertret, J.-M. Frigerio, C. Schwob, L. Coolen, and A. Maître, “Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis,” Phys. Rev. X 4(2), 1–12 (2014).
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Ledoux, G.

Lethiec, C.

C. Lethiec, J. Laverdant, H. Vallon, C. Javaux, B. Dubertret, J.-M. Frigerio, C. Schwob, L. Coolen, and A. Maître, “Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis,” Phys. Rev. X 4(2), 1–12 (2014).
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Lieb, M. A.

Lukosz, W.

Lupton, J. M.

J. Müller, J. M. Lupton, A. L. Rogach, J. Feldmann, D. V. Talapin, and H. Weller, “Air-induced fluorescence bursts from single semiconductor nanocrystals,” Appl. Phys. Lett. 85(3), 381–383 (2004).
[Crossref]

Maître, A.

C. Lethiec, J. Laverdant, H. Vallon, C. Javaux, B. Dubertret, J.-M. Frigerio, C. Schwob, L. Coolen, and A. Maître, “Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis,” Phys. Rev. X 4(2), 1–12 (2014).
[Crossref]

Meijerink, A.

W. G. J. H. M. van Sark, P. L. T. M. Frederix, A. A. Bol, H. C. Gerritsen, and A. Meijerink, “Blueing, Bleaching, and Blinking of Single CdSe/ZnS Quantum Dots,” ChemPhysChem 3(10), 871–879 (2002).
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Meixner, A. J.

A. Pillonnet, P. Fleury, A. I. Chizhik, A. M. Chizhik, D. Amans, G. Ledoux, F. Kulzer, A. J. Meixner, and C. Dujardin, “Local refractive index probed via the fluorescence decay of semiconductor quantum dots,” Opt. Express 20(3), 3200–3208 (2012).
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A. I. Chizhik, A. M. Chizhik, D. Khoptyar, S. Bär, and A. J. Meixner, “Excitation isotropy of single CdSe/ZnS nanocrystals,” Nano Lett. 11(3), 1131–1135 (2011).
[Crossref] [PubMed]

A. I. Chizhik, A. M. Chizhik, A. Huss, R. Jäger, and A. J. Meixner, “Nanoscale probing of dielectric interfaces with single-molecule excitation patterns and radially polarized illumination,” J. Phys. Chem. Lett. 2(17), 2152–2157 (2011).
[Crossref]

Mews, A.

F. Koberling, U. Kolb, G. Philipp, I. Potapova, T. Basché, and A. Mews, “Fluorescence Anisotropy and Crystal Structure of Individual Semiconductor Nanocrystals,” J. Phys. Chem. B 107(30), 7463–7471 (2003).
[Crossref]

Müller, J.

J. Müller, J. M. Lupton, A. L. Rogach, J. Feldmann, D. V. Talapin, and H. Weller, “Air-induced fluorescence bursts from single semiconductor nanocrystals,” Appl. Phys. Lett. 85(3), 381–383 (2004).
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Munin, E.

V. Pilla and E. Munin, “Fluorescence quantum efficiency of CdSe/ZnS quantum dots functionalized with amine or carboxyl groups,” J. Nanopart. Res. 14(10), 1147 (2012).
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Nakamura, I.

H. Ishitobi, I. Nakamura, N. Hayazawa, Z. Sekkat, and S. Kawata, “Orientational Imaging of Single Molecules by Using Azimuthal and Radial Polarizations,” J. Phys. Chem. B 114(8), 2565–2571 (2010).
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M. G. B. S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature 399(6732), 126–130 (1999).
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Nirmal, M.

A. L. Efros, M. Rosen, M. Kuno, M. Nirmal, D. J. Norris, and M. Bawendi, “Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states,” Phys. Rev. B Condens. Matter 54(7), 4843–4856 (1996).
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Norris, D. J.

A. L. Efros, M. Rosen, M. Kuno, M. Nirmal, D. J. Norris, and M. Bawendi, “Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states,” Phys. Rev. B Condens. Matter 54(7), 4843–4856 (1996).
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M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21(6), 1210 (2004).
[Crossref]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal Field Modes Probed by Single Molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

Okamoto, H.

N. N. Horimoto, K. Imura, and H. Okamoto, “Dye fluorescence enhancement and quenching by gold nanoparticles: Direct near-field microscopic observation of shape dependence,” Chem. Phys. Lett. 467(1-3), 105–109 (2008).
[Crossref]

Patra, D.

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

D. Patra, I. Gregor, and J. Enderlein, “Image analysis of defocused single molecule images for three dimensional molecular orientation studies,” J. Phys. Chem. A 108(33), 6836–6841 (2004).
[Crossref]

Pauli, J.

C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Relative and absolute determination of fluorescence quantum yields of transparent samples,” Nat. Protoc. 8(8), 1535–1550 (2013).
[Crossref] [PubMed]

Philipp, G.

F. Koberling, U. Kolb, G. Philipp, I. Potapova, T. Basché, and A. Mews, “Fluorescence Anisotropy and Crystal Structure of Individual Semiconductor Nanocrystals,” J. Phys. Chem. B 107(30), 7463–7471 (2003).
[Crossref]

Pibiri, E.

P. Holzmeister, E. Pibiri, J. J. Schmied, T. Sen, G. P. Acuna, and P. Tinnefeld, “Quantum yield and excitation rate of single molecules close to metallic nanostructures,” Nat. Commun. 5, 5356 (2014).
[Crossref] [PubMed]

Pilla, V.

V. Pilla and E. Munin, “Fluorescence quantum efficiency of CdSe/ZnS quantum dots functionalized with amine or carboxyl groups,” J. Nanopart. Res. 14(10), 1147 (2012).
[Crossref]

Pillonnet, A.

Potapova, I.

F. Koberling, U. Kolb, G. Philipp, I. Potapova, T. Basché, and A. Mews, “Fluorescence Anisotropy and Crystal Structure of Individual Semiconductor Nanocrystals,” J. Phys. Chem. B 107(30), 7463–7471 (2003).
[Crossref]

Pu, J.

Z. Zhang, J. Pu, and X. Wang, “Tightly focusing of linearly polarized vortex beams through a dielectric interface,” Opt. Commun. 281(13), 3421–3426 (2008).
[Crossref]

Punj, D.

Resch-Genger, U.

C. Würth, D. Geissler, T. Behnke, M. Kaiser, and U. Resch-Genger, “Critical review of the determination of photoluminescence quantum yields of luminescent reporters,” Anal. Bioanal. Chem. 407(1), 59–78 (2015).
[Crossref] [PubMed]

C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Relative and absolute determination of fluorescence quantum yields of transparent samples,” Nat. Protoc. 8(8), 1535–1550 (2013).
[Crossref] [PubMed]

Rigneault, H.

Rogach, A. L.

J. Müller, J. M. Lupton, A. L. Rogach, J. Feldmann, D. V. Talapin, and H. Weller, “Air-induced fluorescence bursts from single semiconductor nanocrystals,” Appl. Phys. Lett. 85(3), 381–383 (2004).
[Crossref]

Rosen, M.

A. L. Efros, M. Rosen, M. Kuno, M. Nirmal, D. J. Norris, and M. Bawendi, “Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states,” Phys. Rev. B Condens. Matter 54(7), 4843–4856 (1996).
[Crossref] [PubMed]

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
[Crossref]

Sauer, M.

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

Schmied, J. J.

P. Holzmeister, E. Pibiri, J. J. Schmied, T. Sen, G. P. Acuna, and P. Tinnefeld, “Quantum yield and excitation rate of single molecules close to metallic nanostructures,” Nat. Commun. 5, 5356 (2014).
[Crossref] [PubMed]

Schöne, A.

D. Kempe, A. Schöne, J. Fitter, and M. Gabba, “Accurate Fluorescence Quantum Yield Determination by Fluorescence Correlation Spectroscopy,” J. Phys. Chem. B 119(13), 4668–4672 (2015).
[Crossref] [PubMed]

Schwob, C.

C. Lethiec, J. Laverdant, H. Vallon, C. Javaux, B. Dubertret, J.-M. Frigerio, C. Schwob, L. Coolen, and A. Maître, “Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis,” Phys. Rev. X 4(2), 1–12 (2014).
[Crossref]

Sekkat, Z.

H. Ishitobi, I. Nakamura, N. Hayazawa, Z. Sekkat, and S. Kawata, “Orientational Imaging of Single Molecules by Using Azimuthal and Radial Polarizations,” J. Phys. Chem. B 114(8), 2565–2571 (2010).
[Crossref] [PubMed]

Sen, T.

P. Holzmeister, E. Pibiri, J. J. Schmied, T. Sen, G. P. Acuna, and P. Tinnefeld, “Quantum yield and excitation rate of single molecules close to metallic nanostructures,” Nat. Commun. 5, 5356 (2014).
[Crossref] [PubMed]

Sick, B.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

Spieles, M.

C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Relative and absolute determination of fluorescence quantum yields of transparent samples,” Nat. Protoc. 8(8), 1535–1550 (2013).
[Crossref] [PubMed]

Taguchi, A.

N. Hayazawa, K. Furusawa, A. Taguchi, S. Kawata, and H. Abe, “Tip-enhanced two-photon excited fluorescence microscopy with a silicon tip,” Appl. Phys. Lett. 94(19), 193112 (2009).
[Crossref]

N. Hayazawa, K. Furusawa, A. Taguchi, and S. Kawata, “One-photon and two-photon excited fluorescence microscopies based on polarization-control: Applications to tip-enhanced microscopy,” J. Appl. Phys. 106(11), 113103 (2009).
[Crossref]

Talapin, D. V.

J. Müller, J. M. Lupton, A. L. Rogach, J. Feldmann, D. V. Talapin, and H. Weller, “Air-induced fluorescence bursts from single semiconductor nanocrystals,” Appl. Phys. Lett. 85(3), 381–383 (2004).
[Crossref]

Tarpani, L.

A. M. Chizhik, L. Tarpani, L. Latterini, I. Gregor, J. Enderlein, and A. I. Chizhik, “Photoluminescence of a single quantum emitter in a strongly inhomogeneous chemical environment,” Phys. Chem. Chem. Phys. 17(22), 14994–15000 (2015).
[Crossref] [PubMed]

Tinnefeld, P.

P. Holzmeister, E. Pibiri, J. J. Schmied, T. Sen, G. P. Acuna, and P. Tinnefeld, “Quantum yield and excitation rate of single molecules close to metallic nanostructures,” Nat. Commun. 5, 5356 (2014).
[Crossref] [PubMed]

Vallon, H.

C. Lethiec, J. Laverdant, H. Vallon, C. Javaux, B. Dubertret, J.-M. Frigerio, C. Schwob, L. Coolen, and A. Maître, “Measurement of three-dimensional dipole orientation of a single fluorescent nanoemitter by emission polarization analysis,” Phys. Rev. X 4(2), 1–12 (2014).
[Crossref]

van Sark, W. G. J. H. M.

W. G. J. H. M. van Sark, P. L. T. M. Frederix, A. A. Bol, H. C. Gerritsen, and A. Meijerink, “Blueing, Bleaching, and Blinking of Single CdSe/ZnS Quantum Dots,” ChemPhysChem 3(10), 871–879 (2002).
[Crossref]

Wang, X.

Z. Zhang, J. Pu, and X. Wang, “Tightly focusing of linearly polarized vortex beams through a dielectric interface,” Opt. Commun. 281(13), 3421–3426 (2008).
[Crossref]

Weller, H.

J. Müller, J. M. Lupton, A. L. Rogach, J. Feldmann, D. V. Talapin, and H. Weller, “Air-induced fluorescence bursts from single semiconductor nanocrystals,” Appl. Phys. Lett. 85(3), 381–383 (2004).
[Crossref]

Wenger, J.

Würth, C.

C. Würth, D. Geissler, T. Behnke, M. Kaiser, and U. Resch-Genger, “Critical review of the determination of photoluminescence quantum yields of luminescent reporters,” Anal. Bioanal. Chem. 407(1), 59–78 (2015).
[Crossref] [PubMed]

C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Relative and absolute determination of fluorescence quantum yields of transparent samples,” Nat. Protoc. 8(8), 1535–1550 (2013).
[Crossref] [PubMed]

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal Field Modes Probed by Single Molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Zavislan, J. M.

Zhang, C. Y.

J. Hu and C. Y. Zhang, “Simple and accurate quantification of quantum yield at the single-molecule/particle level,” Anal. Chem. 85(4), 2000–2004 (2013).
[Crossref] [PubMed]

Zhang, Z.

Z. Zhang, J. Pu, and X. Wang, “Tightly focusing of linearly polarized vortex beams through a dielectric interface,” Opt. Commun. 281(13), 3421–3426 (2008).
[Crossref]

Anal. Bioanal. Chem. (1)

C. Würth, D. Geissler, T. Behnke, M. Kaiser, and U. Resch-Genger, “Critical review of the determination of photoluminescence quantum yields of luminescent reporters,” Anal. Bioanal. Chem. 407(1), 59–78 (2015).
[Crossref] [PubMed]

Anal. Chem. (1)

J. Hu and C. Y. Zhang, “Simple and accurate quantification of quantum yield at the single-molecule/particle level,” Anal. Chem. 85(4), 2000–2004 (2013).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
[Crossref]

N. Hayazawa, K. Furusawa, A. Taguchi, S. Kawata, and H. Abe, “Tip-enhanced two-photon excited fluorescence microscopy with a silicon tip,” Appl. Phys. Lett. 94(19), 193112 (2009).
[Crossref]

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

J. Müller, J. M. Lupton, A. L. Rogach, J. Feldmann, D. V. Talapin, and H. Weller, “Air-induced fluorescence bursts from single semiconductor nanocrystals,” Appl. Phys. Lett. 85(3), 381–383 (2004).
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Chem. Phys. (1)

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Figures (10)

Fig. 1
Fig. 1 Model used for (a) absorption and (b) emission dipole moment of CdSe/ZnS QD. The red dashed arrow in both (a) and (b) represents the QD c-axis aligned to the dark axis. The green solid arrow in (b) represents the degenerate dipole moment (bright plane) while the green dashed arrow is the projection of the bright plane on the sample plane.
Fig. 2
Fig. 2 (a) Schematic diagram of the experimental set-up. (P – polarizer, HWP – halfwave plate, BE – beam expander, Z-pol – polarization converter, OL – objective lens, XYZ-PZT – sample stage, NPBS – nonpolarizing beam splitter, A – analyzer, EF – long pass edge filter and L – lens) (b) Sample fluorescence signal of an individual QD nanoemitter..
Fig. 3
Fig. 3 LSM image profile of the QD’s using (a) azimuthal, (b) radial and (c) linear polarization excitation (along y – axis). The numbering of the QDs in (a) applies to (b) and (c) as well. (d), (e) and (f) corresponds to sample intensity line scans of QD5 comparing experimental and calculated intensity cross – section of the LSM image profile with azimuthal, radial and linear light excitation (along x – and y – axis).
Fig. 4
Fig. 4 Normalized intensity of 11 QDs selected on the LSM image profile at different analyzer angle with fittings.
Fig. 5
Fig. 5 (a) QD dark axis orientation (right) in relation to the LSM image profile (left). (b) Histogram of the out-of-plane orientation of the 11 QDs observed.
Fig. 6
Fig. 6 Intensity distribution of different electric field components at the tightly - focused spot in the air – glass interface with azimuthally, radially and linearly polarized light excitation (N.A. = 1.49).
Fig. 7
Fig. 7 (a) Absorption image profile of CdSe/ZnS QD for azimuthally (top row), radially (middle row) and linearly (bottom row) polarized light excitation at varying dark-axis orientation. (b) Emission image profile of QD placed in an interface at varying QD orientation.
Fig. 8
Fig. 8 Schematic representation of the model used to describe analyzer dependence of the dipole emission
Fig. 9
Fig. 9 Intensity of QD emission as a function of dark axis orientation and analyzer angle.
Fig. 10
Fig. 10 Collection efficiency of the CdSe/ZnS QD on an air – glass interface using high NA objective lens.

Tables (1)

Tables Icon

Table 1 CE, maximum intensity from LSM image profile (radial and linear) and relative quantum yield ratio (radial and linear) of the QDs. QD11 is the basis QD.

Equations (31)

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I= I max +( I min I max ) cos 2 (Φα)
M= I max I min I max + I min
I ems =(CE)(QY) | μ E exc | 2
CE= P coll P ems + P ems
RQY R i = RQ Y i RQ Y 0 = ( Q Y i Q Y R ) ( Q Y 0 Q Y R ) =( I ems, i C E i ) ( I ems, 0 C E 0 ) 1
E lin = 1 2 ( F 0 (θ)+ F 2 (θ) x 2 y 2 x 2 + y 2 ) x ^ + 1 2 ( F 2 (θ) 2xy x 2 + y 2 ) y ^ +i F 1 (θ) x x 2 + y 2 z ^
E rad =i G 0 (θ) x x 2 + y 2 x ^ +i G 0 (θ) y x 2 + y 2 y ^ + G 1 (θ) z ^
E azi =H(θ) y x 2 + y 2 x ^ +H(θ) x x 2 + y 2 y ^
F 0 (θ)= 0 θNA cosθ sinθ J 0 ( k x x 2 + y 2 )( t p (θ) 1 ( n 1 n 2 sinθ ) 2 + t s (θ) )dθ F 0 (θ)= 0 θNA cosθ sin 2 θ J 1 ( k x x 2 + y 2 )( n 1 n 2 t p (θ) )dθ F 0 (θ)= 0 θNA cosθ sinθ J 2 ( k x x 2 + y 2 )( t s (θ) t p (θ) 1 ( n 1 n 2 sinθ ) 2 )dθ
G 0 (θ)= 0 θNA cosθ sinθ J 1 ( k x x 2 + y 2 )( t p (θ) 1 ( n 1 n 2 sinθ ) 2 + )dθ G 0 (θ)= 0 θNA (cosθ) 1/2 sin 2 θ J 0 ( k x x 2 + y 2 ) n 1 n 2 t p (θ)dθ
H(θ)= 0 θNA cosθ sinθ J 1 ( k x x 2 + y 2 ) t p (θ)dθ
I ems =(CE)(QY) | μ abs E exc | 2
E =( E θ cosθcosφ E ϕ sinφ) x ^ +( E θ cosθsinφ+ E ϕ cosφ) y ^ +( E θ sinθ) z ^
E θ =f(r)[ C j 2 ( μ x cosφ+ μ y sinφ)cosθ C j 1 μ z sinθ ]
E φ =f(r)[ C j 3 ( μ x sinφ μ y cosφ ) ]
μ =sinΘcosΦ x ^ +sinΘsinΦ y ^ +cosΘ z ^
C 1 1 =1+ r p (θ)
C 1 2 =1+ r p (θ)
C 1 3 =1+ r s (θ)
C 2 1 = ( n 2 n 1 ) 2 cosθ s z (θ) t p (θ)
C 2 2 = n 2 n 1 t p (θ)
C 2 3 = n 2 n 1 cosθ s z (θ) t s (θ)
A =cosα x ^ +sinα y ^
I= 0 2π 0 Θ NA | E A (α) | 2 A(θ) r 2 sinθdθdφ.
S = 1 2 Re( E × H * )
P= r 2 S e r ^
P coll = 0 2π 0 θ NA p coll (Θ,Φ,θ,φ)sinθdθdφ, P ems = 0 2π π/2 π p ems (Θ,Φ,θ,φ)sinθdθdφ, P ems = 0 2π 0 π/2 p ems (Θ,Φ,θ,φ)sinθdθdφ.
p= 3 8π [ cosΘsinθ+sinΘcos(φΦ)cosθ ] 2 + 3 8π [ sinΘcos(φΦ) ] 2
p θ<θc = 3 2π { n 3 cos 2 θ [ cosΘsin θ 1 +sinΘcos(φΦ)cos θ 1 ] 2 n 2 1 + n 3 cos 2 θ sin 2 Θ sin 2 (φΦ) (cos θ 1 +ncosθ) 2 }
p θ<θc =( 3 2π n 3 cos 2 θ n 2 1 ) [ n 2 cos 2 Θ sin 2 θ ( n 2 1) sin 2 θ1 + sin 2 Θ cos 2 (φΦ)( n 2 sin 2 θ1) ( n 2 1) sin 2 θ1 + sin 2 Θ sin 2 (φΦ) ]
P coll = 0 2π 0 θc p θ<θc (Θ,Φ,θ,φ) sinθdθdφ + 0 2π θ c Θ NA P θ>θc (Θ,Φ,θ,φ)sinθdθdφ.

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