Abstract

Fluorescence correlation spectroscopy when fluorescent nanoemitters are diffusing in the vicinity of a dielectric mirror is studied both theoretically and experimentally. We demonstrate that two important effects occur when the confocal detection volume is located on the mirror’s surface. First, the count rate per emitter is significantly enhanced owing to control of spontaneous emission and enhancement of the excitation field. Second, interference fringes in the excitation beam give rise to a new characteristic time in the photocurrent’s autocorrelation function. This new time is found to be independent of the transverse excitation field’s beam waist and permits accurate measurement of diffusion coefficients without any a priori knowledge of the confocal volume geometry.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  51. R. Rigler, U. Mets, J. Widengren, and P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
    [CrossRef]
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    [CrossRef]

2002 (5)

R. A. Keller, W. P. Ambrose, A. A. Arias, H. Cai, S. R. Emory, P. M. Goodwin, and J. H. Jett, “Analytical applications of single-molecule detection,” Anal. Chem. 74, 316A–324A (2002).
[CrossRef] [PubMed]

Y. Chen, J. D. Muller, Q. Ruan, and E. Gratton, “Molecular brightness characterization of EGFP in vivo by fluorescence fluctuation spectroscopy,” Biophys. J. 82, 133–144 (2002).
[CrossRef]

F. Lemarchand and H. Rigneault, “Light emission from europium chelates located in crossed grating structures,” J. Opt. 4, S115–S118 (2002).

P. F. Lenne, E. Etienne, and H. Rigneault, “Subwavelength patterns and high detection efficiency in fluorescence correlation spectroscopy using photonic structures,” Appl. Phys. Lett. 80, 4106–4108 (2002).
[CrossRef]

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83, 2300–2317 (2002).
[CrossRef] [PubMed]

2001 (4)

A. Belarouci, B. Jacquier, P. Moretti, S. Robert, and H. Rigneault, “Praseodymium-doped planar multidielectric microcavities: induced lifetime changes over the emission spectrum,” J. Opt. Soc. Am. B 18, 832–838 (2001).
[CrossRef]

E. Moreau, I. Robert, L. Manin, V. Thierry-Mieg, J. M. Gérard, and I. Abram, “Quantum cascade of photons in semiconductor quantum dots,” Phys. Rev. Lett. 87, 183601 (2001).
[CrossRef]

A. Beveratos, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Non-classical radiation from diamond nonocrystals,” Phys. Rev. A 64, 061802 (2001).
[CrossRef]

P. Schwille, “Fluorescence correlation spectroscopy and its potential for intracellular applications,” Cell. Biochem. Biophys. 34, 383–408 (2001).
[CrossRef]

2000 (7)

K. Palo, U. Mets, S. Jager, P. Kask, and K. Gall, “Fluorescence intensity multiple distribution analysis: concurrent determination of diffusion times and molecular brightness,” Biophys. J. 79, 2858–2866 (2000).
[CrossRef] [PubMed]

Y. Ishii and T. Yaganida, “Single molecule detection in life science,” Single Molec. 1, 5–14 (2000).
[CrossRef]

B. Lounis and W. E. Moerner, “Single photons on demand from a single molecule at room temperature,” Nature 407, 491–493 (2000).
[CrossRef] [PubMed]

T. Ruckstuhl, J. Enderlein, S. Jung, and S. Seeger, “Forbidden light detection from singles molecules,” Anal. Chem. 72, 2117–2123 (2000).
[CrossRef] [PubMed]

C. Begon, H. Rigneault, P. Jonsson, and J. G. Rarity, “Spontaneous emission control with planar dielectric structures: an asset for ultrasensitive fluorescence analysis,” Single Molec. 1, 207–214 (2000).
[CrossRef]

H. Rigneault, F. Lemarchand, and A. Sentenac, “Dipole ra-diation into grating structures,” J. Opt. Soc. Am. A 17, 1048–1058 (2000).
[CrossRef]

J. Enderlein, “Theoretical study of detection of a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).
[CrossRef]

1999 (7)

P. Schwille, U. Haupts, S. Maiti, and W. W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

C. Brunel, B. Lounis, P. Tamarat, and M. Orrit, “Triggered source of single photons based on controlled single molecule fluorescence,” Phys. Rev. Lett. 83, 2722–2725 (1999).
[CrossRef]

S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science 283, 1676–1683 (1999).
[CrossRef] [PubMed]

W. P. Ambrose, P. M. Goodwin, J. H. Jett, A. Van Orden, J. H. Werner, and R. A. Keller, “Single molecule fluorescence spectroscopy at ambient temperature,” Chem. Rev. (Washington, D.C.) 99, 2929–2956 (1999).
[CrossRef]

W. E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
[CrossRef] [PubMed]

Y. Chen, J. D. Muller, P. T. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

P. Kask, K. Palo, D. Ullman, and K. Gall, “Fluorescence intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. U.S.A. 96, 13, 756–13, 761 (1999).
[CrossRef]

1998 (3)

A. J. Meixner, “Optical single-molecule detection at room temperature,” Adv. Photochem. 24, 1–59 (1998).

X. S. Xie and J. K. Trautman, “Optical studies of single molecule at room temperature,” Annu. Rev. Phys. Chem. 49, 441–480 (1998).
[CrossRef]

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

1997 (3)

P. Schwille, F. J. Meyer-Almes, and R. Rigler, “Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution,” Biophys. J. 72, 1878–1886 (1997).
[CrossRef] [PubMed]

N. F. van Hulst, M. F. Garcia-Parajo, M. H. Moers, J. A. Veerman, and A. G. Ruiter, “Near-field fluorescence imaging of genetic material: toward the molecular limit,” J. Struct. Biol. 119, 222–231 (1997).
[CrossRef] [PubMed]

S. Nie and R. N. Zare, “Optical detection of single molecules,” Annu. Rev. Biophys. Biomol. Struct. 26, 567–596 (1997).
[CrossRef] [PubMed]

1996 (1)

H. Rigneault and S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54, 2356–2368 (1996).
[CrossRef] [PubMed]

1994 (2)

M. Eigen and R. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. U.S.A. 91, 5740–5747 (1994).
[CrossRef] [PubMed]

D. G. Deppe, C. Lei, C. C. Lin, and D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
[CrossRef]

1993 (3)

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

P. M. Goodwin, M. E. Johnson, J. C. Martin, W. P. Ambrose, B. L. Marrone, J. H. Jett, and R. A. Keller, “Rapid sizing of individual fluorescently stained DNA fragments by flow cytometry,” Nucleic Acids Res. 21, 803–806 (1993).
[CrossRef] [PubMed]

R. Rigler, U. Mets, J. Widengren, and P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

1992 (1)

C. H. Bennett, G. Brassard, and A. K. Eckert, “Quantum cryptography,” Sci. Am. 267, 26 (1992).
[CrossRef]

1991 (1)

1990 (1)

M. Orrit and J. Bernard, “Single pentacene molecules detected by fluorescence excitation in a p-terphenyl crystal,” Phys. Rev. Lett. 65, 2716–2719 (1990).
[CrossRef] [PubMed]

1989 (1)

W. E. Moerner and L. Kador, “Optical detection and spectroscopy of single molecules in a solid,” Phys. Rev. Lett. 62, 2535–2538 (1989).
[CrossRef] [PubMed]

1976 (3)

W. W. Webb, “Applications of fluorescence correlation spectroscopy,” Q. Rev. Biophys. 9, 49–68 (1976).
[CrossRef] [PubMed]

H. Asai and T. Ando, “Fluorescence correlation spectroscopy illuminated by standing exciting light waves,” J. Phys. Soc. Jpn. 40, 1527–1528 (1976).
[CrossRef]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, and W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

1974 (1)

E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
[CrossRef]

1946 (1)

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

Abram, I.

E. Moreau, I. Robert, L. Manin, V. Thierry-Mieg, J. M. Gérard, and I. Abram, “Quantum cascade of photons in semiconductor quantum dots,” Phys. Rev. Lett. 87, 183601 (2001).
[CrossRef]

Ambrose, W. P.

R. A. Keller, W. P. Ambrose, A. A. Arias, H. Cai, S. R. Emory, P. M. Goodwin, and J. H. Jett, “Analytical applications of single-molecule detection,” Anal. Chem. 74, 316A–324A (2002).
[CrossRef] [PubMed]

W. P. Ambrose, P. M. Goodwin, J. H. Jett, A. Van Orden, J. H. Werner, and R. A. Keller, “Single molecule fluorescence spectroscopy at ambient temperature,” Chem. Rev. (Washington, D.C.) 99, 2929–2956 (1999).
[CrossRef]

P. M. Goodwin, M. E. Johnson, J. C. Martin, W. P. Ambrose, B. L. Marrone, J. H. Jett, and R. A. Keller, “Rapid sizing of individual fluorescently stained DNA fragments by flow cytometry,” Nucleic Acids Res. 21, 803–806 (1993).
[CrossRef] [PubMed]

Ando, T.

H. Asai and T. Ando, “Fluorescence correlation spectroscopy illuminated by standing exciting light waves,” J. Phys. Soc. Jpn. 40, 1527–1528 (1976).
[CrossRef]

Arias, A. A.

R. A. Keller, W. P. Ambrose, A. A. Arias, H. Cai, S. R. Emory, P. M. Goodwin, and J. H. Jett, “Analytical applications of single-molecule detection,” Anal. Chem. 74, 316A–324A (2002).
[CrossRef] [PubMed]

Asai, H.

H. Asai and T. Ando, “Fluorescence correlation spectroscopy illuminated by standing exciting light waves,” J. Phys. Soc. Jpn. 40, 1527–1528 (1976).
[CrossRef]

Axelrod, D.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, and W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

Begon, C.

C. Begon, H. Rigneault, P. Jonsson, and J. G. Rarity, “Spontaneous emission control with planar dielectric structures: an asset for ultrasensitive fluorescence analysis,” Single Molec. 1, 207–214 (2000).
[CrossRef]

Belarouci, A.

Bennett, C. H.

C. H. Bennett, G. Brassard, and A. K. Eckert, “Quantum cryptography,” Sci. Am. 267, 26 (1992).
[CrossRef]

Bernard, J.

M. Orrit and J. Bernard, “Single pentacene molecules detected by fluorescence excitation in a p-terphenyl crystal,” Phys. Rev. Lett. 65, 2716–2719 (1990).
[CrossRef] [PubMed]

Beveratos, A.

A. Beveratos, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Non-classical radiation from diamond nonocrystals,” Phys. Rev. A 64, 061802 (2001).
[CrossRef]

Brassard, G.

C. H. Bennett, G. Brassard, and A. K. Eckert, “Quantum cryptography,” Sci. Am. 267, 26 (1992).
[CrossRef]

Brouri, R.

A. Beveratos, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Non-classical radiation from diamond nonocrystals,” Phys. Rev. A 64, 061802 (2001).
[CrossRef]

Brunel, C.

C. Brunel, B. Lounis, P. Tamarat, and M. Orrit, “Triggered source of single photons based on controlled single molecule fluorescence,” Phys. Rev. Lett. 83, 2722–2725 (1999).
[CrossRef]

Cai, H.

R. A. Keller, W. P. Ambrose, A. A. Arias, H. Cai, S. R. Emory, P. M. Goodwin, and J. H. Jett, “Analytical applications of single-molecule detection,” Anal. Chem. 74, 316A–324A (2002).
[CrossRef] [PubMed]

Caneau, C.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

Chen, Y.

Y. Chen, J. D. Muller, Q. Ruan, and E. Gratton, “Molecular brightness characterization of EGFP in vivo by fluorescence fluctuation spectroscopy,” Biophys. J. 82, 133–144 (2002).
[CrossRef]

Y. Chen, J. D. Muller, P. T. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

Costard, E.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Deppe, D. G.

D. G. Deppe, C. Lei, C. C. Lin, and D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
[CrossRef]

Eckert, A. K.

C. H. Bennett, G. Brassard, and A. K. Eckert, “Quantum cryptography,” Sci. Am. 267, 26 (1992).
[CrossRef]

Eigen, M.

M. Eigen and R. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. U.S.A. 91, 5740–5747 (1994).
[CrossRef] [PubMed]

Elson, E. L.

H. Quian and E. L. Elson, “Analysis of confocal laser-microscope optics for 3-D fluorescence correlation spectroscopy,” Appl. Opt. 30, 1185–1195 (1991).
[CrossRef]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, and W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
[CrossRef]

Emory, S. R.

R. A. Keller, W. P. Ambrose, A. A. Arias, H. Cai, S. R. Emory, P. M. Goodwin, and J. H. Jett, “Analytical applications of single-molecule detection,” Anal. Chem. 74, 316A–324A (2002).
[CrossRef] [PubMed]

Enderlein, J.

J. Enderlein, “Theoretical study of detection of a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).
[CrossRef]

T. Ruckstuhl, J. Enderlein, S. Jung, and S. Seeger, “Forbidden light detection from singles molecules,” Anal. Chem. 72, 2117–2123 (2000).
[CrossRef] [PubMed]

Etienne, E.

P. F. Lenne, E. Etienne, and H. Rigneault, “Subwavelength patterns and high detection efficiency in fluorescence correlation spectroscopy using photonic structures,” Appl. Phys. Lett. 80, 4106–4108 (2002).
[CrossRef]

Gacoin, T.

A. Beveratos, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Non-classical radiation from diamond nonocrystals,” Phys. Rev. A 64, 061802 (2001).
[CrossRef]

Gall, K.

K. Palo, U. Mets, S. Jager, P. Kask, and K. Gall, “Fluorescence intensity multiple distribution analysis: concurrent determination of diffusion times and molecular brightness,” Biophys. J. 79, 2858–2866 (2000).
[CrossRef] [PubMed]

P. Kask, K. Palo, D. Ullman, and K. Gall, “Fluorescence intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. U.S.A. 96, 13, 756–13, 761 (1999).
[CrossRef]

Garcia-Parajo, M. F.

N. F. van Hulst, M. F. Garcia-Parajo, M. H. Moers, J. A. Veerman, and A. G. Ruiter, “Near-field fluorescence imaging of genetic material: toward the molecular limit,” J. Struct. Biol. 119, 222–231 (1997).
[CrossRef] [PubMed]

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J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Gérard, J. M.

E. Moreau, I. Robert, L. Manin, V. Thierry-Mieg, J. M. Gérard, and I. Abram, “Quantum cascade of photons in semiconductor quantum dots,” Phys. Rev. Lett. 87, 183601 (2001).
[CrossRef]

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Gmitter, T. J.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

Goodwin, P. M.

R. A. Keller, W. P. Ambrose, A. A. Arias, H. Cai, S. R. Emory, P. M. Goodwin, and J. H. Jett, “Analytical applications of single-molecule detection,” Anal. Chem. 74, 316A–324A (2002).
[CrossRef] [PubMed]

W. P. Ambrose, P. M. Goodwin, J. H. Jett, A. Van Orden, J. H. Werner, and R. A. Keller, “Single molecule fluorescence spectroscopy at ambient temperature,” Chem. Rev. (Washington, D.C.) 99, 2929–2956 (1999).
[CrossRef]

P. M. Goodwin, M. E. Johnson, J. C. Martin, W. P. Ambrose, B. L. Marrone, J. H. Jett, and R. A. Keller, “Rapid sizing of individual fluorescently stained DNA fragments by flow cytometry,” Nucleic Acids Res. 21, 803–806 (1993).
[CrossRef] [PubMed]

Grangier, P.

A. Beveratos, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Non-classical radiation from diamond nonocrystals,” Phys. Rev. A 64, 061802 (2001).
[CrossRef]

Gratton, E.

Y. Chen, J. D. Muller, Q. Ruan, and E. Gratton, “Molecular brightness characterization of EGFP in vivo by fluorescence fluctuation spectroscopy,” Biophys. J. 82, 133–144 (2002).
[CrossRef]

Y. Chen, J. D. Muller, P. T. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

Haupts, U.

P. Schwille, U. Haupts, S. Maiti, and W. W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

Hess, S. T.

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83, 2300–2317 (2002).
[CrossRef] [PubMed]

Huffaker, D. L.

D. G. Deppe, C. Lei, C. C. Lin, and D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
[CrossRef]

Ishii, Y.

Y. Ishii and T. Yaganida, “Single molecule detection in life science,” Single Molec. 1, 5–14 (2000).
[CrossRef]

Jacquier, B.

Jager, S.

K. Palo, U. Mets, S. Jager, P. Kask, and K. Gall, “Fluorescence intensity multiple distribution analysis: concurrent determination of diffusion times and molecular brightness,” Biophys. J. 79, 2858–2866 (2000).
[CrossRef] [PubMed]

Jett, J. H.

R. A. Keller, W. P. Ambrose, A. A. Arias, H. Cai, S. R. Emory, P. M. Goodwin, and J. H. Jett, “Analytical applications of single-molecule detection,” Anal. Chem. 74, 316A–324A (2002).
[CrossRef] [PubMed]

W. P. Ambrose, P. M. Goodwin, J. H. Jett, A. Van Orden, J. H. Werner, and R. A. Keller, “Single molecule fluorescence spectroscopy at ambient temperature,” Chem. Rev. (Washington, D.C.) 99, 2929–2956 (1999).
[CrossRef]

P. M. Goodwin, M. E. Johnson, J. C. Martin, W. P. Ambrose, B. L. Marrone, J. H. Jett, and R. A. Keller, “Rapid sizing of individual fluorescently stained DNA fragments by flow cytometry,” Nucleic Acids Res. 21, 803–806 (1993).
[CrossRef] [PubMed]

Johnson, M. E.

P. M. Goodwin, M. E. Johnson, J. C. Martin, W. P. Ambrose, B. L. Marrone, J. H. Jett, and R. A. Keller, “Rapid sizing of individual fluorescently stained DNA fragments by flow cytometry,” Nucleic Acids Res. 21, 803–806 (1993).
[CrossRef] [PubMed]

Jonsson, P.

C. Begon, H. Rigneault, P. Jonsson, and J. G. Rarity, “Spontaneous emission control with planar dielectric structures: an asset for ultrasensitive fluorescence analysis,” Single Molec. 1, 207–214 (2000).
[CrossRef]

Jung, S.

T. Ruckstuhl, J. Enderlein, S. Jung, and S. Seeger, “Forbidden light detection from singles molecules,” Anal. Chem. 72, 2117–2123 (2000).
[CrossRef] [PubMed]

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W. E. Moerner and L. Kador, “Optical detection and spectroscopy of single molecules in a solid,” Phys. Rev. Lett. 62, 2535–2538 (1989).
[CrossRef] [PubMed]

Kask, P.

K. Palo, U. Mets, S. Jager, P. Kask, and K. Gall, “Fluorescence intensity multiple distribution analysis: concurrent determination of diffusion times and molecular brightness,” Biophys. J. 79, 2858–2866 (2000).
[CrossRef] [PubMed]

P. Kask, K. Palo, D. Ullman, and K. Gall, “Fluorescence intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. U.S.A. 96, 13, 756–13, 761 (1999).
[CrossRef]

R. Rigler, U. Mets, J. Widengren, and P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Keller, R. A.

R. A. Keller, W. P. Ambrose, A. A. Arias, H. Cai, S. R. Emory, P. M. Goodwin, and J. H. Jett, “Analytical applications of single-molecule detection,” Anal. Chem. 74, 316A–324A (2002).
[CrossRef] [PubMed]

W. P. Ambrose, P. M. Goodwin, J. H. Jett, A. Van Orden, J. H. Werner, and R. A. Keller, “Single molecule fluorescence spectroscopy at ambient temperature,” Chem. Rev. (Washington, D.C.) 99, 2929–2956 (1999).
[CrossRef]

P. M. Goodwin, M. E. Johnson, J. C. Martin, W. P. Ambrose, B. L. Marrone, J. H. Jett, and R. A. Keller, “Rapid sizing of individual fluorescently stained DNA fragments by flow cytometry,” Nucleic Acids Res. 21, 803–806 (1993).
[CrossRef] [PubMed]

Koppel, D. E.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, and W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

Legrand, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Lei, C.

D. G. Deppe, C. Lei, C. C. Lin, and D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
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Lemarchand, F.

F. Lemarchand and H. Rigneault, “Light emission from europium chelates located in crossed grating structures,” J. Opt. 4, S115–S118 (2002).

H. Rigneault, F. Lemarchand, and A. Sentenac, “Dipole ra-diation into grating structures,” J. Opt. Soc. Am. A 17, 1048–1058 (2000).
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P. F. Lenne, E. Etienne, and H. Rigneault, “Subwavelength patterns and high detection efficiency in fluorescence correlation spectroscopy using photonic structures,” Appl. Phys. Lett. 80, 4106–4108 (2002).
[CrossRef]

Lin, C. C.

D. G. Deppe, C. Lei, C. C. Lin, and D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
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B. Lounis and W. E. Moerner, “Single photons on demand from a single molecule at room temperature,” Nature 407, 491–493 (2000).
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C. Brunel, B. Lounis, P. Tamarat, and M. Orrit, “Triggered source of single photons based on controlled single molecule fluorescence,” Phys. Rev. Lett. 83, 2722–2725 (1999).
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E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
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P. Schwille, U. Haupts, S. Maiti, and W. W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

Manin, L.

E. Moreau, I. Robert, L. Manin, V. Thierry-Mieg, J. M. Gérard, and I. Abram, “Quantum cascade of photons in semiconductor quantum dots,” Phys. Rev. Lett. 87, 183601 (2001).
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Marrone, B. L.

P. M. Goodwin, M. E. Johnson, J. C. Martin, W. P. Ambrose, B. L. Marrone, J. H. Jett, and R. A. Keller, “Rapid sizing of individual fluorescently stained DNA fragments by flow cytometry,” Nucleic Acids Res. 21, 803–806 (1993).
[CrossRef] [PubMed]

Martin, J. C.

P. M. Goodwin, M. E. Johnson, J. C. Martin, W. P. Ambrose, B. L. Marrone, J. H. Jett, and R. A. Keller, “Rapid sizing of individual fluorescently stained DNA fragments by flow cytometry,” Nucleic Acids Res. 21, 803–806 (1993).
[CrossRef] [PubMed]

Meixner, A. J.

A. J. Meixner, “Optical single-molecule detection at room temperature,” Adv. Photochem. 24, 1–59 (1998).

Mets, U.

K. Palo, U. Mets, S. Jager, P. Kask, and K. Gall, “Fluorescence intensity multiple distribution analysis: concurrent determination of diffusion times and molecular brightness,” Biophys. J. 79, 2858–2866 (2000).
[CrossRef] [PubMed]

R. Rigler, U. Mets, J. Widengren, and P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Meyer-Almes, F. J.

P. Schwille, F. J. Meyer-Almes, and R. Rigler, “Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution,” Biophys. J. 72, 1878–1886 (1997).
[CrossRef] [PubMed]

Moerner, W. E.

B. Lounis and W. E. Moerner, “Single photons on demand from a single molecule at room temperature,” Nature 407, 491–493 (2000).
[CrossRef] [PubMed]

W. E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
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W. E. Moerner and L. Kador, “Optical detection and spectroscopy of single molecules in a solid,” Phys. Rev. Lett. 62, 2535–2538 (1989).
[CrossRef] [PubMed]

Moers, M. H.

N. F. van Hulst, M. F. Garcia-Parajo, M. H. Moers, J. A. Veerman, and A. G. Ruiter, “Near-field fluorescence imaging of genetic material: toward the molecular limit,” J. Struct. Biol. 119, 222–231 (1997).
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Monneret, S.

H. Rigneault and S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54, 2356–2368 (1996).
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E. Moreau, I. Robert, L. Manin, V. Thierry-Mieg, J. M. Gérard, and I. Abram, “Quantum cascade of photons in semiconductor quantum dots,” Phys. Rev. Lett. 87, 183601 (2001).
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Moretti, P.

Muller, J. D.

Y. Chen, J. D. Muller, Q. Ruan, and E. Gratton, “Molecular brightness characterization of EGFP in vivo by fluorescence fluctuation spectroscopy,” Biophys. J. 82, 133–144 (2002).
[CrossRef]

Y. Chen, J. D. Muller, P. T. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

Nie, S.

S. Nie and R. N. Zare, “Optical detection of single molecules,” Annu. Rev. Biophys. Biomol. Struct. 26, 567–596 (1997).
[CrossRef] [PubMed]

Orrit, M.

C. Brunel, B. Lounis, P. Tamarat, and M. Orrit, “Triggered source of single photons based on controlled single molecule fluorescence,” Phys. Rev. Lett. 83, 2722–2725 (1999).
[CrossRef]

W. E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
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M. Orrit and J. Bernard, “Single pentacene molecules detected by fluorescence excitation in a p-terphenyl crystal,” Phys. Rev. Lett. 65, 2716–2719 (1990).
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Palo, K.

K. Palo, U. Mets, S. Jager, P. Kask, and K. Gall, “Fluorescence intensity multiple distribution analysis: concurrent determination of diffusion times and molecular brightness,” Biophys. J. 79, 2858–2866 (2000).
[CrossRef] [PubMed]

P. Kask, K. Palo, D. Ullman, and K. Gall, “Fluorescence intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. U.S.A. 96, 13, 756–13, 761 (1999).
[CrossRef]

Poizat, J. P.

A. Beveratos, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Non-classical radiation from diamond nonocrystals,” Phys. Rev. A 64, 061802 (2001).
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Purcell, E. M.

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

Quian, H.

Rarity, J. G.

C. Begon, H. Rigneault, P. Jonsson, and J. G. Rarity, “Spontaneous emission control with planar dielectric structures: an asset for ultrasensitive fluorescence analysis,” Single Molec. 1, 207–214 (2000).
[CrossRef]

Rigler, R.

P. Schwille, F. J. Meyer-Almes, and R. Rigler, “Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution,” Biophys. J. 72, 1878–1886 (1997).
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M. Eigen and R. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. U.S.A. 91, 5740–5747 (1994).
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R. Rigler, U. Mets, J. Widengren, and P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Rigneault, H.

P. F. Lenne, E. Etienne, and H. Rigneault, “Subwavelength patterns and high detection efficiency in fluorescence correlation spectroscopy using photonic structures,” Appl. Phys. Lett. 80, 4106–4108 (2002).
[CrossRef]

F. Lemarchand and H. Rigneault, “Light emission from europium chelates located in crossed grating structures,” J. Opt. 4, S115–S118 (2002).

A. Belarouci, B. Jacquier, P. Moretti, S. Robert, and H. Rigneault, “Praseodymium-doped planar multidielectric microcavities: induced lifetime changes over the emission spectrum,” J. Opt. Soc. Am. B 18, 832–838 (2001).
[CrossRef]

C. Begon, H. Rigneault, P. Jonsson, and J. G. Rarity, “Spontaneous emission control with planar dielectric structures: an asset for ultrasensitive fluorescence analysis,” Single Molec. 1, 207–214 (2000).
[CrossRef]

H. Rigneault, F. Lemarchand, and A. Sentenac, “Dipole ra-diation into grating structures,” J. Opt. Soc. Am. A 17, 1048–1058 (2000).
[CrossRef]

H. Rigneault and S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54, 2356–2368 (1996).
[CrossRef] [PubMed]

Robert, I.

E. Moreau, I. Robert, L. Manin, V. Thierry-Mieg, J. M. Gérard, and I. Abram, “Quantum cascade of photons in semiconductor quantum dots,” Phys. Rev. Lett. 87, 183601 (2001).
[CrossRef]

Robert, S.

Ruan, Q.

Y. Chen, J. D. Muller, Q. Ruan, and E. Gratton, “Molecular brightness characterization of EGFP in vivo by fluorescence fluctuation spectroscopy,” Biophys. J. 82, 133–144 (2002).
[CrossRef]

Ruckstuhl, T.

T. Ruckstuhl, J. Enderlein, S. Jung, and S. Seeger, “Forbidden light detection from singles molecules,” Anal. Chem. 72, 2117–2123 (2000).
[CrossRef] [PubMed]

Ruiter, A. G.

N. F. van Hulst, M. F. Garcia-Parajo, M. H. Moers, J. A. Veerman, and A. G. Ruiter, “Near-field fluorescence imaging of genetic material: toward the molecular limit,” J. Struct. Biol. 119, 222–231 (1997).
[CrossRef] [PubMed]

Scherer, A.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

Schlessinger, J.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, and W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

Schnitzer, I.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

Schwille, P.

P. Schwille, “Fluorescence correlation spectroscopy and its potential for intracellular applications,” Cell. Biochem. Biophys. 34, 383–408 (2001).
[CrossRef]

P. Schwille, U. Haupts, S. Maiti, and W. W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

P. Schwille, F. J. Meyer-Almes, and R. Rigler, “Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution,” Biophys. J. 72, 1878–1886 (1997).
[CrossRef] [PubMed]

Seeger, S.

T. Ruckstuhl, J. Enderlein, S. Jung, and S. Seeger, “Forbidden light detection from singles molecules,” Anal. Chem. 72, 2117–2123 (2000).
[CrossRef] [PubMed]

Sentenac, A.

Sermage, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

So, P. T.

Y. Chen, J. D. Muller, P. T. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

Tamarat, P.

C. Brunel, B. Lounis, P. Tamarat, and M. Orrit, “Triggered source of single photons based on controlled single molecule fluorescence,” Phys. Rev. Lett. 83, 2722–2725 (1999).
[CrossRef]

Thierry-Mieg, V.

E. Moreau, I. Robert, L. Manin, V. Thierry-Mieg, J. M. Gérard, and I. Abram, “Quantum cascade of photons in semiconductor quantum dots,” Phys. Rev. Lett. 87, 183601 (2001).
[CrossRef]

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Trautman, J. K.

X. S. Xie and J. K. Trautman, “Optical studies of single molecule at room temperature,” Annu. Rev. Phys. Chem. 49, 441–480 (1998).
[CrossRef]

Ullman, D.

P. Kask, K. Palo, D. Ullman, and K. Gall, “Fluorescence intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. U.S.A. 96, 13, 756–13, 761 (1999).
[CrossRef]

van Hulst, N. F.

N. F. van Hulst, M. F. Garcia-Parajo, M. H. Moers, J. A. Veerman, and A. G. Ruiter, “Near-field fluorescence imaging of genetic material: toward the molecular limit,” J. Struct. Biol. 119, 222–231 (1997).
[CrossRef] [PubMed]

Van Orden, A.

W. P. Ambrose, P. M. Goodwin, J. H. Jett, A. Van Orden, J. H. Werner, and R. A. Keller, “Single molecule fluorescence spectroscopy at ambient temperature,” Chem. Rev. (Washington, D.C.) 99, 2929–2956 (1999).
[CrossRef]

Veerman, J. A.

N. F. van Hulst, M. F. Garcia-Parajo, M. H. Moers, J. A. Veerman, and A. G. Ruiter, “Near-field fluorescence imaging of genetic material: toward the molecular limit,” J. Struct. Biol. 119, 222–231 (1997).
[CrossRef] [PubMed]

Webb, W. W.

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83, 2300–2317 (2002).
[CrossRef] [PubMed]

P. Schwille, U. Haupts, S. Maiti, and W. W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

W. W. Webb, “Applications of fluorescence correlation spectroscopy,” Q. Rev. Biophys. 9, 49–68 (1976).
[CrossRef] [PubMed]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, and W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

Weiss, S.

S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science 283, 1676–1683 (1999).
[CrossRef] [PubMed]

Werner, J. H.

W. P. Ambrose, P. M. Goodwin, J. H. Jett, A. Van Orden, J. H. Werner, and R. A. Keller, “Single molecule fluorescence spectroscopy at ambient temperature,” Chem. Rev. (Washington, D.C.) 99, 2929–2956 (1999).
[CrossRef]

Widengren, J.

R. Rigler, U. Mets, J. Widengren, and P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Xie, X. S.

X. S. Xie and J. K. Trautman, “Optical studies of single molecule at room temperature,” Annu. Rev. Phys. Chem. 49, 441–480 (1998).
[CrossRef]

Yablonovitch, E.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

Yaganida, T.

Y. Ishii and T. Yaganida, “Single molecule detection in life science,” Single Molec. 1, 5–14 (2000).
[CrossRef]

Zare, R. N.

S. Nie and R. N. Zare, “Optical detection of single molecules,” Annu. Rev. Biophys. Biomol. Struct. 26, 567–596 (1997).
[CrossRef] [PubMed]

Adv. Photochem. (1)

A. J. Meixner, “Optical single-molecule detection at room temperature,” Adv. Photochem. 24, 1–59 (1998).

Anal. Chem. (2)

R. A. Keller, W. P. Ambrose, A. A. Arias, H. Cai, S. R. Emory, P. M. Goodwin, and J. H. Jett, “Analytical applications of single-molecule detection,” Anal. Chem. 74, 316A–324A (2002).
[CrossRef] [PubMed]

T. Ruckstuhl, J. Enderlein, S. Jung, and S. Seeger, “Forbidden light detection from singles molecules,” Anal. Chem. 72, 2117–2123 (2000).
[CrossRef] [PubMed]

Annu. Rev. Biophys. Biomol. Struct. (1)

S. Nie and R. N. Zare, “Optical detection of single molecules,” Annu. Rev. Biophys. Biomol. Struct. 26, 567–596 (1997).
[CrossRef] [PubMed]

Annu. Rev. Phys. Chem. (1)

X. S. Xie and J. K. Trautman, “Optical studies of single molecule at room temperature,” Annu. Rev. Phys. Chem. 49, 441–480 (1998).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

P. F. Lenne, E. Etienne, and H. Rigneault, “Subwavelength patterns and high detection efficiency in fluorescence correlation spectroscopy using photonic structures,” Appl. Phys. Lett. 80, 4106–4108 (2002).
[CrossRef]

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
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Figures (13)

Fig. 1
Fig. 1

Setup for confocal detection of fluorescent dye molecules diffusing in a liquid slab located upon a dielectric mirror, M.

Fig. 2
Fig. 2

(A) Full radiative mode (0<Neff<next), (B) substrate’s radiative mode (next<Neff<ns), (C) guided mode (ns<Neff<nH).

Fig. 3
Fig. 3

Reflectance of mirror M together with Cy5 emission spectrum and excitation laser line.

Fig. 4
Fig. 4

CEF(0, 0, z) for a collection volume located on mirror surface M and 5 μm above surface M.

Fig. 5
Fig. 5

Ie(x=0, y=0, z) for a collection volume located on the mirror surface M and 5 μm above surface M. The fringe visibility is maximum on surface M.

Fig. 6
Fig. 6

MDE(x=0, y=0, z) for a collection volume located 5 μm above surface M on surface M, and on a simple cover glass. Hatched area, mirror M (curves A and B) and cover glass (curve C).

Fig. 7
Fig. 7

MDE(x, 0, z) for a collection volume located A, on surface M and B, on a simple cover glass. The gray scales are not comparable in A and B, and one must refer to curves B and C of Fig. 6 for the correct relative intensity.

Fig. 8
Fig. 8

Computed photocurrent autocorrelation function for a collection volume located on mirror M and on a cover glass. Also plotted are the fitting curves given by Eq. (35) (for a cover glass) and Eq. (36) (for a mirror).

Fig. 9
Fig. 9

Bottom, experimental and theoretical radiation patterns for Cy5 molecules located on mirror M [silica substrate/(HL)15L, where H and L stand for high- and low-refractive-index quarter-wavelength layers, respectively, at λM=660 nm-nH=2.2; nL=1.46]. Top, schematic of the experimental setup.

Fig. 10
Fig. 10

Experimental (crosses) and theoretical (solid curves) autocorrelation functions obtained for fluorescent nanospheres (A) in the absence and (B) in the presence of mirror M.

Fig. 11
Fig. 11

Photocount autocorrelation functions obtained in the presence of mirror M with 1, underfilling and 2, overfilling of the objective NA with the excitation beam. Fringe time τf is unaffected.

Fig. 12
Fig. 12

Number of molecules and coefficient A as a function of the fringe visibility.

Fig. 13
Fig. 13

Photocurrent autocorrelation function g(2)(τ) obtained for a Cy5–septravidine complex diffusing (A) in the absence and (B) in the presence of mirror M. In (B) the fringe fluctuation time τf is clearly separated from fast isomerization time τe and slow diffusion time τd.

Tables (2)

Tables Icon

Table 1 Parameters Used to Fit the Photocurrent Correlation Functions of Fig. 8

Tables Icon

Table 2 Results Extracted from the Photocount Autocorrelation Function Plotted in Fig. 10

Equations (43)

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F(r, kp)=E(z, kp)exp i(kpr)u(kp),
rFi(r, kp)Fi*(r, kp)dr=(2π)3δ(kp-kp)
(i=fr, sr, g),
E(r, t)=γgOgcg(t, kpg)Fg(r, kpg)dkpg+Ofr[cfr-(t, kp)Ffr-(r, kp)+cfr+(t, kp)Ffr+(r, kp)]dkp+Osrcsr(t, kp)Fsr(r, kp)dkp+TMterm,
ΔE(r, t)-(z)μ02E(r, t)t2=μ02p(r, t)t2+μ0j(r, t)t,
2a(t)t2+ω02a(t)=qm [eE(r0, t)].
P(r0)=04πdP(r0, Ω)dΩdΩ.
CEF(r0)=Min[Ωp(r0),ΩNA(r0)]dP(r0, Ω)dΩdΩ.
CEF(r0)=ΔλdλMin[Ωp(r0),ΩNA(r0)]dP(r0, λ, Ω)dΩdΩ.
Ee(x, y, z0)=E0exp-x2w2exp-y2w2,
Ee(x, y, z0)=exp-y2w2-+W(σ)exp(2iπσx)dσ,
E02=4Pπw2Y0,Y0=0μ0.
Ee(x, y, z)=exp-y2w2-+A(σ, z)exp(2iπσx)dσ,
Ie(r)= |Ee(r)|2.
MDE(r)=CEF(r)Ie(r).
i(t)=sMDE(r)C(r, t)dr,
δC(r, t)=C(r, t)-C¯,
ϕ(r, r, τ)=δC(r, t)δC(r, t+τ),
ϕ(r, r, τ)=δC(r, 0)δC(r, τ).
C(r, τ)τ=D2δC(r, t),
ϕ(r, r, τ)=C¯(4πDτ)3/2exp-|r-r|24Dτ.
δi(t)=i(t)-i¯=qMDE(r)δC(r, t)dr,
G(τ)=δi(0)δi(τ)=q2MDE(r)MDE(r)×δC(r, 0)δC(r, τ)drdr=q2MDE(r)MDE(r)ϕ(r, r, τ)drdr,
g(2)(τ)=i(0)i(τ)i(t)2=1+δi(0)δi(τ)i(t)2=1+G(τ)i(t)2,
i(t)=i¯=sC¯MDE(r)dr.
ϕ(r, r, 0)=δC(r, 0)δC(r, 0)=C¯δ(r-r),
g(2)(0)=δi(0)2i(t)2=1+q2C¯[MDE(r)]2drq2C¯2MDE(r)dr2=1+1C¯Veq,
Veq=MDE(r)dr2[MDE(r)]2dr.
MDE(r)=M(z)exp-2 (x2+y2)w2,
i(t)=sC¯π2 w2M(z)dz,
Veq=πw2M(z)dz2[M(z)]2dz.
x,x,y,yexp-2 (x2+y2)w2exp-2 (x2+y2w2×exp-[(x-x)2+(y-y)2]4Dτdxdxdydy
=π2Dτw44Dτ+w2.
J=z,zM(z)M(z)exp-(z-z)24Dτdzdz
G(τ)=s2πC¯w28[1+(τ/τd)]1πDτ J,
M(z)=M0exp-2 z2wl2,
J=M02π2wl24Dτ(4Dτ+wl2)1/2,
g(2)(τ)=1+1M1[1+(τ/τd)][1+s2(τ/τd)]1/2,
gf(2)(τ)=g(2)(τ)1+A exp-ττf,
τf=λp216π2nwD,
M(z)=M0exp-2 z2wl2cos2(kz),
D=kT6πηR=24μm2 s-1,
M(z)=M0exp-2 z2wl2[1+V cos(2kz)],

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