Abstract

Metallic nano-antennas provide strong field confinement and intensity enhancement in hotspots and thus can ultimately enhance fluorescence detection and provide ultra small detection volumes. In solution-based fluorescence measurements, the diffraction limited focus driving the nano-antenna can outshine the fluorescence originating from the hotspot and thus render the benefits of the hotspot negligible. We introduce a model to calculate the effect of a nano-antenna, or any other object creating a nontrivial intensity distribution, for fluorescence fluctuation measurements. Approximating the local field enhancement of the nano-antenna by a 3D Gaussian profile, we show which hotspot sizes and intensities are the most beneficial for an FCS measurement and compare it to realistic antenna parameters from literature.

© 2014 Optical Society of America

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    [CrossRef]
  24. J. Wenger, “Fluorescence Enhancement Factors on Optical Antennas: Enlarging the Experimental Values without Changing the Antenna Design,” Int. J. Opt.2012, 1–7 (2012).
    [CrossRef]
  25. G. Colas des Francs, A. Bouhelier, E. Finot, J. C. Weeber, A. Dereux, C. Girard, and E. Dujardin, “Fluorescence relaxation in the near-field of a mesoscopic metallic particle: distance dependence and role of plasmon modes,” Opt. Express16, 17654–17666 (2008).
    [CrossRef] [PubMed]
  26. J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
  28. I. Gregor, D. Patra, and J. Enderlein, “Optical saturation in fluorescence correlation spectroscopy under continuous-wave and pulsed excitation,” ChemPhysChem6, 164–170 (2005).
    [CrossRef] [PubMed]
  29. M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, “Two-beam cross-correlation: a method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem.71, 609–616 (1999).
    [CrossRef] [PubMed]
  30. T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem8, 433–443 (2007).
    [CrossRef] [PubMed]
  31. S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and Chemical Applications of Fluorescence Correlation Spectroscopy: A Review,” Biochemistry41, 697–705 (2002).
    [CrossRef] [PubMed]
  32. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.330, 377–445 (1908).
    [CrossRef]
  33. J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. García de Abajo, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B71, 235420 (2005).
    [CrossRef]

2014 (1)

S. Khatua, P. M. R. Paulo, H. Yuan, A. Gupta, P. Zijlstra, and M. Orrit, “Resonant plasmonic enhancement of single-molecule fluorescence by individual gold nanorods,” ACS Nano8, 4440–4449 (2014).
[CrossRef] [PubMed]

2013 (3)

D. Punj, J. de Torres, H. Rigneault, and J. Wenger, “Gold nanoparticles for enhanced single molecule fluorescence analysis at micromolar concentration,” Opt. Express21, 27338–27343 (2013).
[CrossRef] [PubMed]

H. Yuan, S. Khatua, P. Zijlstra, M. Yorulmaz, and M. Orrit, “Thousand-fold enhancement of single-molecule fluorescence near a single gold nanorod,” Angew. Chem. Int. Edit.52, 1217–1221 (2013).
[CrossRef]

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol.8, 512–516 (2013).
[CrossRef] [PubMed]

2012 (4)

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

S. Dutta Choudhury, K. Ray, and J. R. Lakowicz, “Silver Nanostructures for Fluorescence Correlation Spectroscopy: Reduced Volumes and Increased Signal Intensities,” J. Phys. Chem. Lett.3, 2915–2919 (2012).
[CrossRef]

J. Wenger, “Fluorescence Enhancement Factors on Optical Antennas: Enlarging the Experimental Values without Changing the Antenna Design,” Int. J. Opt.2012, 1–7 (2012).
[CrossRef]

A. Kinkhabwala, Z. Yu, S. Fan, and W. Moerner, “Fluorescence correlation spectroscopy at high concentrations using gold bowtie nanoantennas,” Chem. Phys.406, 3–8 (2012).
[CrossRef]

2011 (3)

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111, 3888–3912 (2011).
[CrossRef] [PubMed]

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett.11, 637–644 (2011).
[CrossRef] [PubMed]

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

2009 (1)

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

2008 (7)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7, 442–453 (2008).
[CrossRef] [PubMed]

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem.1, 601–626 (2008).
[CrossRef]

J. R. Lakowicz, K. Ray, M. Chowdhury, H. Szmacinski, Y. Fu, J. Zhang, and K. Nowaczyk, “Plasmon-controlled fluorescence: a new paradigm in fluorescence spectroscopy,” Analyst133, 1308–1346 (2008).
[CrossRef] [PubMed]

L. C. Estrada, P. F. Aramendía, and O. E. Martínez, “10000 times volume reduction for fluorescence correlation spectroscopy using nano-antennas,” Opt. Express16, 20597–20602 (2008).
[CrossRef] [PubMed]

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

J. Wenger, D. Gérard, J. Dintinger, O. Mahboub, N. Bonod, E. Popov, T. W. Ebbesen, and H. Rigneault, “Emission and excitation contributions to enhanced single molecule fluorescence by gold nanometric apertures,” Opt. Express16, 3008 (2008).
[CrossRef] [PubMed]

G. Colas des Francs, A. Bouhelier, E. Finot, J. C. Weeber, A. Dereux, C. Girard, and E. Dujardin, “Fluorescence relaxation in the near-field of a mesoscopic metallic particle: distance dependence and role of plasmon modes,” Opt. Express16, 17654–17666 (2008).
[CrossRef] [PubMed]

2007 (2)

J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
[CrossRef]

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem8, 433–443 (2007).
[CrossRef] [PubMed]

2006 (1)

J. Wenger, H. Rigneault, J. Dintinger, D. Marguet, and P.-F. Lenne, “Single-fluorophore diffusion in a lipid membrane over a subwavelength aperture,” J. Biol. Phys.32, SN1–4 (2006).
[CrossRef] [PubMed]

2005 (2)

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. García de Abajo, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B71, 235420 (2005).
[CrossRef]

I. Gregor, D. Patra, and J. Enderlein, “Optical saturation in fluorescence correlation spectroscopy under continuous-wave and pulsed excitation,” ChemPhysChem6, 164–170 (2005).
[CrossRef] [PubMed]

2003 (1)

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science299, 682–686 (2003).
[CrossRef] [PubMed]

2002 (1)

S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and Chemical Applications of Fluorescence Correlation Spectroscopy: A Review,” Biochemistry41, 697–705 (2002).
[CrossRef] [PubMed]

1999 (1)

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, “Two-beam cross-correlation: a method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem.71, 609–616 (1999).
[CrossRef] [PubMed]

1972 (1)

D. Magde, E. Elson, and W. Webb, “Thermodynamic Fluctuations in a Reacting System - Measurement by Fluorescence Correlation Spectroscopy,” Phys. Rev. Lett.29, 705–708 (1972).
[CrossRef]

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.330, 377–445 (1908).
[CrossRef]

Agio, M.

M. Agio and A. Alú, Optical Antennas (Cambridge University, 2013).

Aizpurua, J.

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. García de Abajo, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B71, 235420 (2005).
[CrossRef]

Alú, A.

M. Agio and A. Alú, Optical Antennas (Cambridge University, 2013).

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7, 442–453 (2008).
[CrossRef] [PubMed]

Aouani, H.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett.11, 637–644 (2011).
[CrossRef] [PubMed]

Aramendía, P. F.

Barbillon, G.

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Blair, S.

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

Bonod, N.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett.11, 637–644 (2011).
[CrossRef] [PubMed]

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

J. Wenger, D. Gérard, J. Dintinger, O. Mahboub, N. Bonod, E. Popov, T. W. Ebbesen, and H. Rigneault, “Emission and excitation contributions to enhanced single molecule fluorescence by gold nanometric apertures,” Opt. Express16, 3008 (2008).
[CrossRef] [PubMed]

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

Bouhelier, A.

Brinkmeier, M.

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, “Two-beam cross-correlation: a method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem.71, 609–616 (1999).
[CrossRef] [PubMed]

Bryant, G. W.

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. García de Abajo, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B71, 235420 (2005).
[CrossRef]

Chowdhury, M.

J. R. Lakowicz, K. Ray, M. Chowdhury, H. Szmacinski, Y. Fu, J. Zhang, and K. Nowaczyk, “Plasmon-controlled fluorescence: a new paradigm in fluorescence spectroscopy,” Analyst133, 1308–1346 (2008).
[CrossRef] [PubMed]

Colas des Francs, G.

Conchonaud, F.

J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
[CrossRef]

Craighead, H. G.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science299, 682–686 (2003).
[CrossRef] [PubMed]

de Torres, J.

D. Punj, J. de Torres, H. Rigneault, and J. Wenger, “Gold nanoparticles for enhanced single molecule fluorescence analysis at micromolar concentration,” Opt. Express21, 27338–27343 (2013).
[CrossRef] [PubMed]

D. Punj, P. Ghenuche, S. B. Moparthi, J. de Torres, V. Grigoriev, H. Rigneault, and J. Wenger, “Plasmonic antennas and zero-mode waveguides to enhance single molecule fluorescence detection and fluorescence correlation spectroscopy toward physiological concentrations,” Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol. (2014).

Dereux, A.

Dertinger, T.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem8, 433–443 (2007).
[CrossRef] [PubMed]

Devaux, E.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett.11, 637–644 (2011).
[CrossRef] [PubMed]

Dieringer, J. A.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem.1, 601–626 (2008).
[CrossRef]

Dintinger, J.

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

J. Wenger, D. Gérard, J. Dintinger, O. Mahboub, N. Bonod, E. Popov, T. W. Ebbesen, and H. Rigneault, “Emission and excitation contributions to enhanced single molecule fluorescence by gold nanometric apertures,” Opt. Express16, 3008 (2008).
[CrossRef] [PubMed]

J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
[CrossRef]

J. Wenger, H. Rigneault, J. Dintinger, D. Marguet, and P.-F. Lenne, “Single-fluorophore diffusion in a lipid membrane over a subwavelength aperture,” J. Biol. Phys.32, SN1–4 (2006).
[CrossRef] [PubMed]

Dörre, K.

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, “Two-beam cross-correlation: a method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem.71, 609–616 (1999).
[CrossRef] [PubMed]

Dujardin, E.

Dutta Choudhury, S.

S. Dutta Choudhury, K. Ray, and J. R. Lakowicz, “Silver Nanostructures for Fluorescence Correlation Spectroscopy: Reduced Volumes and Increased Signal Intensities,” J. Phys. Chem. Lett.3, 2915–2919 (2012).
[CrossRef]

Ebbesen, T. W.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett.11, 637–644 (2011).
[CrossRef] [PubMed]

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

J. Wenger, D. Gérard, J. Dintinger, O. Mahboub, N. Bonod, E. Popov, T. W. Ebbesen, and H. Rigneault, “Emission and excitation contributions to enhanced single molecule fluorescence by gold nanometric apertures,” Opt. Express16, 3008 (2008).
[CrossRef] [PubMed]

J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
[CrossRef]

Eigen, M.

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, “Two-beam cross-correlation: a method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem.71, 609–616 (1999).
[CrossRef] [PubMed]

Elson, E.

D. Magde, E. Elson, and W. Webb, “Thermodynamic Fluctuations in a Reacting System - Measurement by Fluorescence Correlation Spectroscopy,” Phys. Rev. Lett.29, 705–708 (1972).
[CrossRef]

Enderlein, J.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem8, 433–443 (2007).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, “Optical saturation in fluorescence correlation spectroscopy under continuous-wave and pulsed excitation,” ChemPhysChem6, 164–170 (2005).
[CrossRef] [PubMed]

Estrada, L. C.

Fan, S.

A. Kinkhabwala, Z. Yu, S. Fan, and W. Moerner, “Fluorescence correlation spectroscopy at high concentrations using gold bowtie nanoantennas,” Chem. Phys.406, 3–8 (2012).
[CrossRef]

Fernández-Domínguez, A. I.

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111, 3888–3912 (2011).
[CrossRef] [PubMed]

Finot, E.

Foquet, M.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science299, 682–686 (2003).
[CrossRef] [PubMed]

Fu, Y.

J. R. Lakowicz, K. Ray, M. Chowdhury, H. Szmacinski, Y. Fu, J. Zhang, and K. Nowaczyk, “Plasmon-controlled fluorescence: a new paradigm in fluorescence spectroscopy,” Analyst133, 1308–1346 (2008).
[CrossRef] [PubMed]

García de Abajo, F. J.

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. García de Abajo, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B71, 235420 (2005).
[CrossRef]

García-Parajó, M. F.

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol.8, 512–516 (2013).
[CrossRef] [PubMed]

Gerard, D.

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

Gérard, D.

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

J. Wenger, D. Gérard, J. Dintinger, O. Mahboub, N. Bonod, E. Popov, T. W. Ebbesen, and H. Rigneault, “Emission and excitation contributions to enhanced single molecule fluorescence by gold nanometric apertures,” Opt. Express16, 3008 (2008).
[CrossRef] [PubMed]

Ghenuche, P.

D. Punj, P. Ghenuche, S. B. Moparthi, J. de Torres, V. Grigoriev, H. Rigneault, and J. Wenger, “Plasmonic antennas and zero-mode waveguides to enhance single molecule fluorescence detection and fluorescence correlation spectroscopy toward physiological concentrations,” Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol. (2014).

Giannini, V.

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111, 3888–3912 (2011).
[CrossRef] [PubMed]

Girard, C.

Gong, Q.

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Gregor, I.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem8, 433–443 (2007).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, “Optical saturation in fluorescence correlation spectroscopy under continuous-wave and pulsed excitation,” ChemPhysChem6, 164–170 (2005).
[CrossRef] [PubMed]

Grigoriev, V.

D. Punj, P. Ghenuche, S. B. Moparthi, J. de Torres, V. Grigoriev, H. Rigneault, and J. Wenger, “Plasmonic antennas and zero-mode waveguides to enhance single molecule fluorescence detection and fluorescence correlation spectroscopy toward physiological concentrations,” Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol. (2014).

Gupta, A.

S. Khatua, P. M. R. Paulo, H. Yuan, A. Gupta, P. Zijlstra, and M. Orrit, “Resonant plasmonic enhancement of single-molecule fluorescence by individual gold nanorods,” ACS Nano8, 4440–4449 (2014).
[CrossRef] [PubMed]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7, 442–453 (2008).
[CrossRef] [PubMed]

Hartmann, R.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem8, 433–443 (2007).
[CrossRef] [PubMed]

Haustein, E.

P. Schwille and E. Haustein, Fluorescence Correlation Spectroscopy: An Introduction to Its Concepts and Applications (Biophysics Textbook Online 1(3), Göttingen, 2001).

Heck, S. C.

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111, 3888–3912 (2011).
[CrossRef] [PubMed]

Heikal, A. A.

S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and Chemical Applications of Fluorescence Correlation Spectroscopy: A Review,” Biochemistry41, 697–705 (2002).
[CrossRef] [PubMed]

Hess, S. T.

S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and Chemical Applications of Fluorescence Correlation Spectroscopy: A Review,” Biochemistry41, 697–705 (2002).
[CrossRef] [PubMed]

Hou, L.

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Huang, S.

S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and Chemical Applications of Fluorescence Correlation Spectroscopy: A Review,” Biochemistry41, 697–705 (2002).
[CrossRef] [PubMed]

Khatua, S.

S. Khatua, P. M. R. Paulo, H. Yuan, A. Gupta, P. Zijlstra, and M. Orrit, “Resonant plasmonic enhancement of single-molecule fluorescence by individual gold nanorods,” ACS Nano8, 4440–4449 (2014).
[CrossRef] [PubMed]

H. Yuan, S. Khatua, P. Zijlstra, M. Yorulmaz, and M. Orrit, “Thousand-fold enhancement of single-molecule fluorescence near a single gold nanorod,” Angew. Chem. Int. Edit.52, 1217–1221 (2013).
[CrossRef]

Kinkhabwala, A.

A. Kinkhabwala, Z. Yu, S. Fan, and W. Moerner, “Fluorescence correlation spectroscopy at high concentrations using gold bowtie nanoantennas,” Chem. Phys.406, 3–8 (2012).
[CrossRef]

Korlach, J.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science299, 682–686 (2003).
[CrossRef] [PubMed]

Lakowicz, J. R.

S. Dutta Choudhury, K. Ray, and J. R. Lakowicz, “Silver Nanostructures for Fluorescence Correlation Spectroscopy: Reduced Volumes and Increased Signal Intensities,” J. Phys. Chem. Lett.3, 2915–2919 (2012).
[CrossRef]

J. R. Lakowicz, K. Ray, M. Chowdhury, H. Szmacinski, Y. Fu, J. Zhang, and K. Nowaczyk, “Plasmon-controlled fluorescence: a new paradigm in fluorescence spectroscopy,” Analyst133, 1308–1346 (2008).
[CrossRef] [PubMed]

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2006), 3rd ed.
[CrossRef]

Lei, F.

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

Lei, F. H.

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Lenne, P. F.

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

Lenne, P.-F.

J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
[CrossRef]

J. Wenger, H. Rigneault, J. Dintinger, D. Marguet, and P.-F. Lenne, “Single-fluorophore diffusion in a lipid membrane over a subwavelength aperture,” J. Biol. Phys.32, SN1–4 (2006).
[CrossRef] [PubMed]

Levene, M. J.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science299, 682–686 (2003).
[CrossRef] [PubMed]

Li, W.

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

Liu, J.

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

Lu, G.

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Luo, C.

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7, 442–453 (2008).
[CrossRef] [PubMed]

Magde, D.

D. Magde, E. Elson, and W. Webb, “Thermodynamic Fluctuations in a Reacting System - Measurement by Fluorescence Correlation Spectroscopy,” Phys. Rev. Lett.29, 705–708 (1972).
[CrossRef]

Mahboub, O.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett.11, 637–644 (2011).
[CrossRef] [PubMed]

J. Wenger, D. Gérard, J. Dintinger, O. Mahboub, N. Bonod, E. Popov, T. W. Ebbesen, and H. Rigneault, “Emission and excitation contributions to enhanced single molecule fluorescence by gold nanometric apertures,” Opt. Express16, 3008 (2008).
[CrossRef] [PubMed]

Mahdavi, F.

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

Maier, S. A.

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111, 3888–3912 (2011).
[CrossRef] [PubMed]

Manfait, M.

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

Marguet, D.

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
[CrossRef]

J. Wenger, H. Rigneault, J. Dintinger, D. Marguet, and P.-F. Lenne, “Single-fluorophore diffusion in a lipid membrane over a subwavelength aperture,” J. Biol. Phys.32, SN1–4 (2006).
[CrossRef] [PubMed]

Marquette, C. A.

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Martínez, O. E.

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.330, 377–445 (1908).
[CrossRef]

Mivelle, M.

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol.8, 512–516 (2013).
[CrossRef] [PubMed]

Moerner, W.

A. Kinkhabwala, Z. Yu, S. Fan, and W. Moerner, “Fluorescence correlation spectroscopy at high concentrations using gold bowtie nanoantennas,” Chem. Phys.406, 3–8 (2012).
[CrossRef]

Moparthi, S. B.

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol.8, 512–516 (2013).
[CrossRef] [PubMed]

D. Punj, P. Ghenuche, S. B. Moparthi, J. de Torres, V. Grigoriev, H. Rigneault, and J. Wenger, “Plasmonic antennas and zero-mode waveguides to enhance single molecule fluorescence detection and fluorescence correlation spectroscopy toward physiological concentrations,” Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol. (2014).

Nelep, C.

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

Nowaczyk, K.

J. R. Lakowicz, K. Ray, M. Chowdhury, H. Szmacinski, Y. Fu, J. Zhang, and K. Nowaczyk, “Plasmon-controlled fluorescence: a new paradigm in fluorescence spectroscopy,” Analyst133, 1308–1346 (2008).
[CrossRef] [PubMed]

Orrit, M.

S. Khatua, P. M. R. Paulo, H. Yuan, A. Gupta, P. Zijlstra, and M. Orrit, “Resonant plasmonic enhancement of single-molecule fluorescence by individual gold nanorods,” ACS Nano8, 4440–4449 (2014).
[CrossRef] [PubMed]

H. Yuan, S. Khatua, P. Zijlstra, M. Yorulmaz, and M. Orrit, “Thousand-fold enhancement of single-molecule fluorescence near a single gold nanorod,” Angew. Chem. Int. Edit.52, 1217–1221 (2013).
[CrossRef]

Ouyang, Q.

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Pacheco, V.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem8, 433–443 (2007).
[CrossRef] [PubMed]

Patra, D.

I. Gregor, D. Patra, and J. Enderlein, “Optical saturation in fluorescence correlation spectroscopy under continuous-wave and pulsed excitation,” ChemPhysChem6, 164–170 (2005).
[CrossRef] [PubMed]

Paulo, P. M. R.

S. Khatua, P. M. R. Paulo, H. Yuan, A. Gupta, P. Zijlstra, and M. Orrit, “Resonant plasmonic enhancement of single-molecule fluorescence by individual gold nanorods,” ACS Nano8, 4440–4449 (2014).
[CrossRef] [PubMed]

Perriat, P.

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Popov, E.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett.11, 637–644 (2011).
[CrossRef] [PubMed]

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

J. Wenger, D. Gérard, J. Dintinger, O. Mahboub, N. Bonod, E. Popov, T. W. Ebbesen, and H. Rigneault, “Emission and excitation contributions to enhanced single molecule fluorescence by gold nanometric apertures,” Opt. Express16, 3008 (2008).
[CrossRef] [PubMed]

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

Punj, D.

D. Punj, J. de Torres, H. Rigneault, and J. Wenger, “Gold nanoparticles for enhanced single molecule fluorescence analysis at micromolar concentration,” Opt. Express21, 27338–27343 (2013).
[CrossRef] [PubMed]

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol.8, 512–516 (2013).
[CrossRef] [PubMed]

D. Punj, P. Ghenuche, S. B. Moparthi, J. de Torres, V. Grigoriev, H. Rigneault, and J. Wenger, “Plasmonic antennas and zero-mode waveguides to enhance single molecule fluorescence detection and fluorescence correlation spectroscopy toward physiological concentrations,” Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol. (2014).

Ray, K.

S. Dutta Choudhury, K. Ray, and J. R. Lakowicz, “Silver Nanostructures for Fluorescence Correlation Spectroscopy: Reduced Volumes and Increased Signal Intensities,” J. Phys. Chem. Lett.3, 2915–2919 (2012).
[CrossRef]

J. R. Lakowicz, K. Ray, M. Chowdhury, H. Szmacinski, Y. Fu, J. Zhang, and K. Nowaczyk, “Plasmon-controlled fluorescence: a new paradigm in fluorescence spectroscopy,” Analyst133, 1308–1346 (2008).
[CrossRef] [PubMed]

Richter, L. J.

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. García de Abajo, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B71, 235420 (2005).
[CrossRef]

Rigneault, H.

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol.8, 512–516 (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. Express21, 27338–27343 (2013).
[CrossRef] [PubMed]

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett.11, 637–644 (2011).
[CrossRef] [PubMed]

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

J. Wenger, D. Gérard, J. Dintinger, O. Mahboub, N. Bonod, E. Popov, T. W. Ebbesen, and H. Rigneault, “Emission and excitation contributions to enhanced single molecule fluorescence by gold nanometric apertures,” Opt. Express16, 3008 (2008).
[CrossRef] [PubMed]

J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
[CrossRef]

J. Wenger, H. Rigneault, J. Dintinger, D. Marguet, and P.-F. Lenne, “Single-fluorophore diffusion in a lipid membrane over a subwavelength aperture,” J. Biol. Phys.32, SN1–4 (2006).
[CrossRef] [PubMed]

D. Punj, P. Ghenuche, S. B. Moparthi, J. de Torres, V. Grigoriev, H. Rigneault, and J. Wenger, “Plasmonic antennas and zero-mode waveguides to enhance single molecule fluorescence detection and fluorescence correlation spectroscopy toward physiological concentrations,” Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol. (2014).

Roux, S.

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Schwille, P.

P. Schwille and E. Haustein, Fluorescence Correlation Spectroscopy: An Introduction to Its Concepts and Applications (Biophysics Textbook Online 1(3), Göttingen, 2001).

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7, 442–453 (2008).
[CrossRef] [PubMed]

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem.1, 601–626 (2008).
[CrossRef]

Stephan, J.

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, “Two-beam cross-correlation: a method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem.71, 609–616 (1999).
[CrossRef] [PubMed]

Stiles, P. L.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem.1, 601–626 (2008).
[CrossRef]

Szmacinski, H.

J. R. Lakowicz, K. Ray, M. Chowdhury, H. Szmacinski, Y. Fu, J. Zhang, and K. Nowaczyk, “Plasmon-controlled fluorescence: a new paradigm in fluorescence spectroscopy,” Analyst133, 1308–1346 (2008).
[CrossRef] [PubMed]

Tillement, O.

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Turner, S. W.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science299, 682–686 (2003).
[CrossRef] [PubMed]

Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7, 442–453 (2008).
[CrossRef] [PubMed]

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem.1, 601–626 (2008).
[CrossRef]

van Hulst, N. F.

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol.8, 512–516 (2013).
[CrossRef] [PubMed]

van Zanten, T. S.

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol.8, 512–516 (2013).
[CrossRef] [PubMed]

von der Hocht, I.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem8, 433–443 (2007).
[CrossRef] [PubMed]

Wang, Q.

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Wawrezinieck, L.

J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
[CrossRef]

Webb, W.

D. Magde, E. Elson, and W. Webb, “Thermodynamic Fluctuations in a Reacting System - Measurement by Fluorescence Correlation Spectroscopy,” Phys. Rev. Lett.29, 705–708 (1972).
[CrossRef]

Webb, W. W.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science299, 682–686 (2003).
[CrossRef] [PubMed]

S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and Chemical Applications of Fluorescence Correlation Spectroscopy: A Review,” Biochemistry41, 697–705 (2002).
[CrossRef] [PubMed]

Weeber, J. C.

Wenger, J.

D. Punj, J. de Torres, H. Rigneault, and J. Wenger, “Gold nanoparticles for enhanced single molecule fluorescence analysis at micromolar concentration,” Opt. Express21, 27338–27343 (2013).
[CrossRef] [PubMed]

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol.8, 512–516 (2013).
[CrossRef] [PubMed]

J. Wenger, “Fluorescence Enhancement Factors on Optical Antennas: Enlarging the Experimental Values without Changing the Antenna Design,” Int. J. Opt.2012, 1–7 (2012).
[CrossRef]

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett.11, 637–644 (2011).
[CrossRef] [PubMed]

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

J. Wenger, D. Gérard, J. Dintinger, O. Mahboub, N. Bonod, E. Popov, T. W. Ebbesen, and H. Rigneault, “Emission and excitation contributions to enhanced single molecule fluorescence by gold nanometric apertures,” Opt. Express16, 3008 (2008).
[CrossRef] [PubMed]

J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
[CrossRef]

J. Wenger, H. Rigneault, J. Dintinger, D. Marguet, and P.-F. Lenne, “Single-fluorophore diffusion in a lipid membrane over a subwavelength aperture,” J. Biol. Phys.32, SN1–4 (2006).
[CrossRef] [PubMed]

D. Punj, P. Ghenuche, S. B. Moparthi, J. de Torres, V. Grigoriev, H. Rigneault, and J. Wenger, “Plasmonic antennas and zero-mode waveguides to enhance single molecule fluorescence detection and fluorescence correlation spectroscopy toward physiological concentrations,” Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol. (2014).

Yang, H.

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Yorulmaz, M.

H. Yuan, S. Khatua, P. Zijlstra, M. Yorulmaz, and M. Orrit, “Thousand-fold enhancement of single-molecule fluorescence near a single gold nanorod,” Angew. Chem. Int. Edit.52, 1217–1221 (2013).
[CrossRef]

Yu, Z.

A. Kinkhabwala, Z. Yu, S. Fan, and W. Moerner, “Fluorescence correlation spectroscopy at high concentrations using gold bowtie nanoantennas,” Chem. Phys.406, 3–8 (2012).
[CrossRef]

Yuan, H.

S. Khatua, P. M. R. Paulo, H. Yuan, A. Gupta, P. Zijlstra, and M. Orrit, “Resonant plasmonic enhancement of single-molecule fluorescence by individual gold nanorods,” ACS Nano8, 4440–4449 (2014).
[CrossRef] [PubMed]

H. Yuan, S. Khatua, P. Zijlstra, M. Yorulmaz, and M. Orrit, “Thousand-fold enhancement of single-molecule fluorescence near a single gold nanorod,” Angew. Chem. Int. Edit.52, 1217–1221 (2013).
[CrossRef]

Zhang, J.

J. R. Lakowicz, K. Ray, M. Chowdhury, H. Szmacinski, Y. Fu, J. Zhang, and K. Nowaczyk, “Plasmon-controlled fluorescence: a new paradigm in fluorescence spectroscopy,” Analyst133, 1308–1346 (2008).
[CrossRef] [PubMed]

Zhang, T.

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Zhao, J.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7, 442–453 (2008).
[CrossRef] [PubMed]

Zijlstra, P.

S. Khatua, P. M. R. Paulo, H. Yuan, A. Gupta, P. Zijlstra, and M. Orrit, “Resonant plasmonic enhancement of single-molecule fluorescence by individual gold nanorods,” ACS Nano8, 4440–4449 (2014).
[CrossRef] [PubMed]

H. Yuan, S. Khatua, P. Zijlstra, M. Yorulmaz, and M. Orrit, “Thousand-fold enhancement of single-molecule fluorescence near a single gold nanorod,” Angew. Chem. Int. Edit.52, 1217–1221 (2013).
[CrossRef]

ACS Nano (1)

S. Khatua, P. M. R. Paulo, H. Yuan, A. Gupta, P. Zijlstra, and M. Orrit, “Resonant plasmonic enhancement of single-molecule fluorescence by individual gold nanorods,” ACS Nano8, 4440–4449 (2014).
[CrossRef] [PubMed]

Anal. Chem. (1)

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, “Two-beam cross-correlation: a method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem.71, 609–616 (1999).
[CrossRef] [PubMed]

Analyst (1)

J. R. Lakowicz, K. Ray, M. Chowdhury, H. Szmacinski, Y. Fu, J. Zhang, and K. Nowaczyk, “Plasmon-controlled fluorescence: a new paradigm in fluorescence spectroscopy,” Analyst133, 1308–1346 (2008).
[CrossRef] [PubMed]

Angew. Chem. Int. Edit. (1)

H. Yuan, S. Khatua, P. Zijlstra, M. Yorulmaz, and M. Orrit, “Thousand-fold enhancement of single-molecule fluorescence near a single gold nanorod,” Angew. Chem. Int. Edit.52, 1217–1221 (2013).
[CrossRef]

Ann. Phys. (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.330, 377–445 (1908).
[CrossRef]

Annu. Rev. Anal. Chem. (1)

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem.1, 601–626 (2008).
[CrossRef]

Biochemistry (1)

S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and Chemical Applications of Fluorescence Correlation Spectroscopy: A Review,” Biochemistry41, 697–705 (2002).
[CrossRef] [PubMed]

Biophys. J. (1)

J. Wenger, F. Conchonaud, J. Dintinger, L. Wawrezinieck, T. W. Ebbesen, H. Rigneault, D. Marguet, and P.-F. Lenne, “Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization,” Biophys. J.92, 913–919 (2007).
[CrossRef]

Chem. Phys. (1)

A. Kinkhabwala, Z. Yu, S. Fan, and W. Moerner, “Fluorescence correlation spectroscopy at high concentrations using gold bowtie nanoantennas,” Chem. Phys.406, 3–8 (2012).
[CrossRef]

Chem. Phys. Lett. (1)

Q. Wang, G. Lu, L. Hou, T. Zhang, C. Luo, H. Yang, G. Barbillon, F. H. Lei, C. A. Marquette, P. Perriat, O. Tillement, S. Roux, Q. Ouyang, and Q. Gong, “Fluorescence correlation spectroscopy near individual gold nanoparticle,” Chem. Phys. Lett.503, 256–261 (2011).
[CrossRef]

Chem. Rev. (1)

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111, 3888–3912 (2011).
[CrossRef] [PubMed]

ChemPhysChem (2)

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem8, 433–443 (2007).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, “Optical saturation in fluorescence correlation spectroscopy under continuous-wave and pulsed excitation,” ChemPhysChem6, 164–170 (2005).
[CrossRef] [PubMed]

Int. J. Mater. Prod. Tec. (1)

J. Wenger, D. Gerard, P. F. Lenne, H. Rigneault, N. Bonod, E. Popov, D. Marguet, C. Nelep, and T. W. Ebbesen, “Biophotonics applications of nanometric apertures,” Int. J. Mater. Prod. Tec.34, 488–506 (2009).
[CrossRef]

Int. J. Opt. (1)

J. Wenger, “Fluorescence Enhancement Factors on Optical Antennas: Enlarging the Experimental Values without Changing the Antenna Design,” Int. J. Opt.2012, 1–7 (2012).
[CrossRef]

J. Biol. Phys. (1)

J. Wenger, H. Rigneault, J. Dintinger, D. Marguet, and P.-F. Lenne, “Single-fluorophore diffusion in a lipid membrane over a subwavelength aperture,” J. Biol. Phys.32, SN1–4 (2006).
[CrossRef] [PubMed]

J. Phys. Chem. Lett. (1)

S. Dutta Choudhury, K. Ray, and J. R. Lakowicz, “Silver Nanostructures for Fluorescence Correlation Spectroscopy: Reduced Volumes and Increased Signal Intensities,” J. Phys. Chem. Lett.3, 2915–2919 (2012).
[CrossRef]

Nano Lett. (1)

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett.11, 637–644 (2011).
[CrossRef] [PubMed]

Nanoscale (1)

G. Lu, J. Liu, T. Zhang, W. Li, L. Hou, C. Luo, F. Lei, M. Manfait, and Q. Gong, “Plasmonic near-field in the vicinity of a single gold nanoparticle investigated with fluorescence correlation spectroscopy,” Nanoscale4, 3359–3364 (2012).
[CrossRef] [PubMed]

Nat. Mater. (1)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7, 442–453 (2008).
[CrossRef] [PubMed]

Nat. Nanotechnol. (1)

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol.8, 512–516 (2013).
[CrossRef] [PubMed]

Opt. Express (4)

Phys. Rev. B (2)

D. Gérard, J. Wenger, N. Bonod, E. Popov, H. Rigneault, F. Mahdavi, S. Blair, J. Dintinger, and T. W. Ebbesen, “Nanoaperture-enhanced fluorescence: Towards higher detection rates with plasmonic metals,” Phys. Rev. B77, 045413 (2008).
[CrossRef]

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. García de Abajo, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B71, 235420 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

D. Magde, E. Elson, and W. Webb, “Thermodynamic Fluctuations in a Reacting System - Measurement by Fluorescence Correlation Spectroscopy,” Phys. Rev. Lett.29, 705–708 (1972).
[CrossRef]

Science (1)

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science299, 682–686 (2003).
[CrossRef] [PubMed]

Other (4)

D. Punj, P. Ghenuche, S. B. Moparthi, J. de Torres, V. Grigoriev, H. Rigneault, and J. Wenger, “Plasmonic antennas and zero-mode waveguides to enhance single molecule fluorescence detection and fluorescence correlation spectroscopy toward physiological concentrations,” Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol. (2014).

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2006), 3rd ed.
[CrossRef]

P. Schwille and E. Haustein, Fluorescence Correlation Spectroscopy: An Introduction to Its Concepts and Applications (Biophysics Textbook Online 1(3), Göttingen, 2001).

M. Agio and A. Alú, Optical Antennas (Cambridge University, 2013).

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Figures (4)

Fig. 1
Fig. 1

Schematic of a non-Gaussian MDF: a focused laser beam (green) illuminates a metallic nano-particle (center) which gives rise to field enhancement in its vicinity (orange).

Fig. 2
Fig. 2

a) crosscut though a MDF (red line) constructed of two Gaussians: a wide Gaussian (blue dashed line, width: σ1 = 500 nm; peak height: P1 = 1; integral: S1 = 0.7μm3), representing a diffraction limited focus and a narrow Gaussian (green dashed line; σ2 = 50nm; P2 = 31; S2 = 0.023μm3) mimicking a ‘hot spot’ of a plasmonic nanoparticle. b) Calculated autocorrelation function for the entire MDF (red solid line) and its constituents: the autocorrelation of background focus A1,1 (blue dashed line), the hotspot A2,2 (green dashed line) and the sum of the identical cross-terms 2 A1,2 (magenta dashed line).

Fig. 3
Fig. 3

The background focus is kept constant at σ1 = 500 nm and P1 = 1 whereas the parameters of the hotspot are varied. a) The total correlation contrast G′(0) (solid lines) for three different peak to peak ratios. For the red curve (P2/P1 = 32) we additionally show its constituents: A1,1 (dashed line), A2,2 (dotted line) and 2 A1,2 (dash-dotted line). In the range of ideal correlation contrast enhancement for a given peak intensity enhancement, the cross term A1,2 can have a stronger influence on the total correlation function than the background focus A1,1 itself. The time dependence of the red curves at σ2/σ1 = 10−1 is shown in Fig. 2(b).

Fig. 4
Fig. 4

a) Shows how the effective diffusion time τ* of the total correlation function depends on the hotspot size and amplitude. The apparent diffusion coefficient D* was extracted from G′(0), τ* and known concentration assuming a single focus FCS experiment. b) Shows the ratio D*/D0 of the apparent divided by the real diffusion coefficient, showing a possible misjudging of 1000× in the calculated parameter range. The cyan lines (from Fig. 3(b)) shows the parameters for which the total correlation contrast in enhanced 10×.

Tables (1)

Tables Icon

Table 1 Properties of gold nano-antennas in literature: A) Gold Mie sphere (∅100 nm); near field intensity enhancement was calculated and σ2 was approximated by the cubic root of the calculated effective mode volume; B) single nanorod ( [33], Fig. 2(b) inset), hotspot diameter approximated by rod diameter; C) Bow tie antenna [18], hotspot diameter approximated by the gap size. All hotspot diameters were put into ratio to the extend of the background focus given by a diffraction limited focus of σ1 = λ/(2 NA) assuming a NA=1 objective.

Equations (10)

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

G ( τ ) = B 2 MDF ( r ) MDF ( r ) δ C ( r , 0 ) δ C ( r , τ ) d 3 r d 3 r [ B C MDF ( r ) d 3 r ] 2
G ( τ ) = MDF ( r ) { MDF ( r ) * ( 4 π D τ ) 3 2 exp [ ( r r ) 2 / ( 4 D τ ) ] } d 3 r C [ MDF ( r ) d 3 r ] 2 ,
Γ ( r , S , R , σ ) = ( 2 π ) 3 2 S σ 1 σ 2 σ 3 exp [ 2 k = 1 , 2 , 3 ( r k R k σ k ) 2 ] .
G ( τ ) = [ C k = 1 , 2 , 3 π 4 D τ + σ k 2 ] 1 .
MDF ( r ) = i = 1 N Γ i ( r ) = i = 1 N Γ ( r , S i , R i , σ i ) .
G ( τ ) = 1 C S M D F 2 [ Σ n A n , n ( τ ) + Σ n m A n , m ( τ ) ]
Γ m D ( r , τ ) = Γ ( r , S m , R m , σ m D ( τ ) ) = Γ m ( r ) * ( 4 π D τ ) 3 2 exp [ ( r r ) 2 / ( 4 D τ ) ]
A n , m ( τ ) = S n S m k = 1 , 2 , 3 [ 2 π [ σ n , k ] 2 + [ σ m , k D ( τ ) ] 2 exp ( 2 ( R n , k R m , k ) 2 [ σ n , k ] 2 + [ σ m , k D ( τ ) ] 2 ) ] .
A n , m ( 0 ) = S n S m k = 1 , 2 , 3 2 π σ n , k 2 + σ m , k 2 .
A n , n ( 0 ) = S n 2 π 3 / 2 σ n , 1 σ n , 2 σ n , 3 = S n 2 V n * .

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