Abstract

The luminescence of dye molecules depends on their position in a layered optical system. Conversely, the luminescence can be applied to measure the position of dye molecules above an interface. We formulate the electromagnetic theory of stationary fluorescence in a layered optical system—of light absorption, light detection, and fluorescence lifetime—computing the angular dependence of dipole interaction with all plane waves by a classical Sommerfeld approach. The theory is checked by experiments with stained lipid membranes on silicon with 256 terraces of silicon dioxide. We apply the electromagnetic theory to fluorescence micrographs of living cells on oxidized silicon chips and evaluate distances between the cell membrane and the substrate in a range of 1–150 nm.

© 2002 Optical Society of America

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2001 (2)

Y. Iwanaga, D. Braun, and P. Fromherz, “No correlation of focal contacts and close adhesion by comparing GFP-vinculin and fluorescence interference of DiI,” Eur. Biophys. J. 30, 17–26 (2001).
[CrossRef]

A. Lambacher and P. Fromherz, “Orientation of hemicyanine dye in lipid membrane measured by fluorescence interferometry on a silicon chip,” J. Phys. Chem. 105, 343–346 (2001).
[CrossRef]

2000 (2)

J. Enderlein, “A theoretical investigation of single-molecule fluorescence detection on thin metallic layers,” Biophys. J. 78, 2151–2158 (2000).
[CrossRef] [PubMed]

J. Mertz, “Radiative absorption, fluorescence, and scattering of a classical dipole near a lossless interface: a unified description,” J. Opt. Soc. Am. B 17, 1906–1913 (2000).
[CrossRef]

1999 (3)

P. Fromherz, V. Kiessling, K. Kottig, and G. Zeck, “Membrane-transistor with giant lipid vesicle touching a silicon chip,” Appl. Phys. A 69, 571–576 (1999).
[CrossRef]

P. Geggier and G. Fuhr, “A time-resolved total internal reflection aqueous fluorescence (TIRAF) microscope for the investigation of cell adhesion dynamics,” Appl. Phys. A 68, 505–513 (1999).
[CrossRef]

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, and M. Bastmeyer, “Imaging of cell/substrate contacts of living cells with surface plasmon resonance microscopy,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

1998 (2)

J. S. Burmeister, L. A. Olivier, W. M. Reichert, and G. A. Truskey, “Application of total internal reflection fluorescence microscopy to study cell adhesion to biomaterials,” Biomaterials 19, 307–325 (1998).
[CrossRef] [PubMed]

D. Braun and P. Fromherz, “Fluorescence interferometry of neuronal cell adhesion on microstructured silicon,” Phys. Rev. Lett. 81, 5241–5244 (1998).
[CrossRef]

1997 (3)

D. Braun and P. Fromherz, “Fluorescence interference contrast microscopy of cell adhesion on silicon,” Appl. Phys. A 65, 341–348 (1997).
[CrossRef]

R. Weis and P. Fromherz, “Frequency dependent signal-transfer in neuron-transistors,” Phys. Rev. E 55, 877–889 (1997).
[CrossRef]

K. G. Sullivan and D. G. Hall, “Enhancement and inhibition of electromagnetic radiation in plane-layered media. I. Plane-wave spectrum approach to modeling classical effects,” J. Opt. Soc. Am. B 14, 1149–1159 (1997).
[CrossRef]

1996 (2)

L. M. Loew, “Potentiometric dyes: imaging electrical activity of cell membranes,” Pure Appl. Chem. 68, 1405–1409 (1996).
[CrossRef]

A. Lambacher and P. Fromherz, “Fluorescence interference contrast microscopy on oxidized silicon using a monomolecular dye layer,” Appl. Phys. A 63, 207–216 (1996).
[CrossRef]

1995 (1)

J. O. Rädler, T. J. Feder, H. H. Strey, and E. Sackmann, “Fluctuation analysis of tension controlled undulation forces between giant vesicles and solid substrates,” Phys. Rev. E 51, 4526 (1995).
[CrossRef]

1993 (1)

M. Krieg, M. B. Srichai, and R. W. Redmond, “Photophysical properties of 3,2-dialkylthiacarbocyanine dyes in organized media: unilamellar liposomes and thin polymer films,” Biochim. Biophys. Acta 1151, 168–174 (1993).
[CrossRef] [PubMed]

1988 (1)

P. Fromherz and G. Reinbold, “Energy transfer between fluorescent dyes spaced by multilayers of Cd-salts of fatty acids,” Thin Solid Films 160, 347–353 (1988).
[CrossRef]

1985 (1)

M. Stavola, D. L. Dexter, and R. S. Knox, “Electron–hole pair excitation in semiconductors via energy transfer from an external sensitizer,” Phys. Rev. B 31, 2277–2289 (1985).
[CrossRef]

1984 (1)

P. Fromherz and R. Kotulla, “Fluorescent dye in soap lamella as a probe of the electrical potential,” Ber. Bunsenges. Phys. Chem. 88, 1106–1112 (1984).
[CrossRef]

1982 (1)

G. E. Jellison, Jr., and F. A. Modine, “Optical constants for silicon at 300 K and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

1979 (1)

D. Gingell and I. Todd, “Interference reflection microscopy: a quantitative theory for image interpretation and its application to cell–substratum separation measurement,” Biophys. J. 26, 507–526 (1979).
[CrossRef] [PubMed]

1977 (1)

1975 (3)

P. Fromherz, “Instrumentation for handling monomolecular films at an air–water interface,” Rev. Sci. Instrum. 46, 1380–1385 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Fluorescence and energy transfer near interfaces: the complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

1974 (3)

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt. 12, 163–232 (1974).
[CrossRef]

O. J. Sims, A. S. Waggoner, C. H. Wang, and J. F. Hoffmann, “Studies on the mechanism by which cyanine dyes measure membrane potential in red blood cells and phosphatidylcholine vesicles,” Biochemistry 13, 3315–3330 (1974).
[CrossRef] [PubMed]

1973 (1)

K. H. Tews, “Zur Variation von Lumineszenz-Lebensdauern,” Ann. Phys. (Leipzig) 29, 97–120 (1973).
[CrossRef]

1971 (1)

J. Sondermann, “Darstellung oberflächenaktiver Polymethincyanin-Farbstoffe mit langen N-Alkyl-Ketten,” Liebigs Ann. Chem. 749, 183–197 (1971).
[CrossRef]

1970 (1)

H. Kuhn, “Classical aspects of energy transfer in molecular systems,” J. Chem. Phys. 53, 1071–108 (1970).
[CrossRef]

1969 (1)

R. J. Cherry and D. Chapman, “Optical properties of black lecithin films,” J. Mol. Biol. 40, 19–32 (1969).
[CrossRef] [PubMed]

1968 (1)

K. H. Drexhage, H. Kuhn, and F. P. Schäfer, “Variation of fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsenges. Phys. Chem. 72, 329 (1968).

1967 (1)

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

1964 (1)

A. S. Curtis, “The mechanism of adhesion of cells to glass. A study by interference reflection microscopy,” J. Cell Biol. 20, 199–215 (1964).
[CrossRef] [PubMed]

1938 (1)

I. Langmuir and V. J. Schaefer, “Activities of urease and pepsin monolayers,” J. Am. Chem. Soc. 60, 1351–1360 (1938).
[CrossRef]

1937 (1)

K. B. Blodgett and I. Langmuir, “Built-up films of barium stearate and their optical properties,” Phys. Rev. 51, 964–982 (1937).
[CrossRef]

1919 (1)

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. (Leipzig) 60, 481–500 (1919).
[CrossRef]

1909 (1)

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–736 (1909).
[CrossRef]

Bastmeyer, M.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, and M. Bastmeyer, “Imaging of cell/substrate contacts of living cells with surface plasmon resonance microscopy,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Bechinger, C.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, and M. Bastmeyer, “Imaging of cell/substrate contacts of living cells with surface plasmon resonance microscopy,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Blodgett, K. B.

K. B. Blodgett and I. Langmuir, “Built-up films of barium stearate and their optical properties,” Phys. Rev. 51, 964–982 (1937).
[CrossRef]

Braun, D.

Y. Iwanaga, D. Braun, and P. Fromherz, “No correlation of focal contacts and close adhesion by comparing GFP-vinculin and fluorescence interference of DiI,” Eur. Biophys. J. 30, 17–26 (2001).
[CrossRef]

D. Braun and P. Fromherz, “Fluorescence interferometry of neuronal cell adhesion on microstructured silicon,” Phys. Rev. Lett. 81, 5241–5244 (1998).
[CrossRef]

D. Braun and P. Fromherz, “Fluorescence interference contrast microscopy of cell adhesion on silicon,” Appl. Phys. A 65, 341–348 (1997).
[CrossRef]

Bücher, H.

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Burmeister, J. S.

J. S. Burmeister, L. A. Olivier, W. M. Reichert, and G. A. Truskey, “Application of total internal reflection fluorescence microscopy to study cell adhesion to biomaterials,” Biomaterials 19, 307–325 (1998).
[CrossRef] [PubMed]

Chance, R. R.

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Fluorescence and energy transfer near interfaces: the complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

Chapman, D.

R. J. Cherry and D. Chapman, “Optical properties of black lecithin films,” J. Mol. Biol. 40, 19–32 (1969).
[CrossRef] [PubMed]

Cherry, R. J.

R. J. Cherry and D. Chapman, “Optical properties of black lecithin films,” J. Mol. Biol. 40, 19–32 (1969).
[CrossRef] [PubMed]

Curtis, A. S.

A. S. Curtis, “The mechanism of adhesion of cells to glass. A study by interference reflection microscopy,” J. Cell Biol. 20, 199–215 (1964).
[CrossRef] [PubMed]

Dexter, D. L.

M. Stavola, D. L. Dexter, and R. S. Knox, “Electron–hole pair excitation in semiconductors via energy transfer from an external sensitizer,” Phys. Rev. B 31, 2277–2289 (1985).
[CrossRef]

Drexhage, K. H.

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt. 12, 163–232 (1974).
[CrossRef]

K. H. Drexhage, H. Kuhn, and F. P. Schäfer, “Variation of fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsenges. Phys. Chem. 72, 329 (1968).

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Enderlein, J.

J. Enderlein, “A theoretical investigation of single-molecule fluorescence detection on thin metallic layers,” Biophys. J. 78, 2151–2158 (2000).
[CrossRef] [PubMed]

Feder, T. J.

J. O. Rädler, T. J. Feder, H. H. Strey, and E. Sackmann, “Fluctuation analysis of tension controlled undulation forces between giant vesicles and solid substrates,” Phys. Rev. E 51, 4526 (1995).
[CrossRef]

Fleck, M.

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Fromherz, P.

A. Lambacher and P. Fromherz, “Orientation of hemicyanine dye in lipid membrane measured by fluorescence interferometry on a silicon chip,” J. Phys. Chem. 105, 343–346 (2001).
[CrossRef]

Y. Iwanaga, D. Braun, and P. Fromherz, “No correlation of focal contacts and close adhesion by comparing GFP-vinculin and fluorescence interference of DiI,” Eur. Biophys. J. 30, 17–26 (2001).
[CrossRef]

P. Fromherz, V. Kiessling, K. Kottig, and G. Zeck, “Membrane-transistor with giant lipid vesicle touching a silicon chip,” Appl. Phys. A 69, 571–576 (1999).
[CrossRef]

D. Braun and P. Fromherz, “Fluorescence interferometry of neuronal cell adhesion on microstructured silicon,” Phys. Rev. Lett. 81, 5241–5244 (1998).
[CrossRef]

D. Braun and P. Fromherz, “Fluorescence interference contrast microscopy of cell adhesion on silicon,” Appl. Phys. A 65, 341–348 (1997).
[CrossRef]

R. Weis and P. Fromherz, “Frequency dependent signal-transfer in neuron-transistors,” Phys. Rev. E 55, 877–889 (1997).
[CrossRef]

A. Lambacher and P. Fromherz, “Fluorescence interference contrast microscopy on oxidized silicon using a monomolecular dye layer,” Appl. Phys. A 63, 207–216 (1996).
[CrossRef]

P. Fromherz and G. Reinbold, “Energy transfer between fluorescent dyes spaced by multilayers of Cd-salts of fatty acids,” Thin Solid Films 160, 347–353 (1988).
[CrossRef]

P. Fromherz and R. Kotulla, “Fluorescent dye in soap lamella as a probe of the electrical potential,” Ber. Bunsenges. Phys. Chem. 88, 1106–1112 (1984).
[CrossRef]

P. Fromherz, “Instrumentation for handling monomolecular films at an air–water interface,” Rev. Sci. Instrum. 46, 1380–1385 (1975).
[CrossRef]

Fuhr, G.

P. Geggier and G. Fuhr, “A time-resolved total internal reflection aqueous fluorescence (TIRAF) microscope for the investigation of cell adhesion dynamics,” Appl. Phys. A 68, 505–513 (1999).
[CrossRef]

Geggier, P.

P. Geggier and G. Fuhr, “A time-resolved total internal reflection aqueous fluorescence (TIRAF) microscope for the investigation of cell adhesion dynamics,” Appl. Phys. A 68, 505–513 (1999).
[CrossRef]

Giebel, K. F.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, and M. Bastmeyer, “Imaging of cell/substrate contacts of living cells with surface plasmon resonance microscopy,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Gingell, D.

D. Gingell and I. Todd, “Interference reflection microscopy: a quantitative theory for image interpretation and its application to cell–substratum separation measurement,” Biophys. J. 26, 507–526 (1979).
[CrossRef] [PubMed]

Hall, D. G.

Herminghaus, S.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, and M. Bastmeyer, “Imaging of cell/substrate contacts of living cells with surface plasmon resonance microscopy,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Hoffmann, J. F.

O. J. Sims, A. S. Waggoner, C. H. Wang, and J. F. Hoffmann, “Studies on the mechanism by which cyanine dyes measure membrane potential in red blood cells and phosphatidylcholine vesicles,” Biochemistry 13, 3315–3330 (1974).
[CrossRef] [PubMed]

Iwanaga, Y.

Y. Iwanaga, D. Braun, and P. Fromherz, “No correlation of focal contacts and close adhesion by comparing GFP-vinculin and fluorescence interference of DiI,” Eur. Biophys. J. 30, 17–26 (2001).
[CrossRef]

Jellison Jr., G. E.

G. E. Jellison, Jr., and F. A. Modine, “Optical constants for silicon at 300 K and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

Kiessling, V.

P. Fromherz, V. Kiessling, K. Kottig, and G. Zeck, “Membrane-transistor with giant lipid vesicle touching a silicon chip,” Appl. Phys. A 69, 571–576 (1999).
[CrossRef]

Knox, R. S.

M. Stavola, D. L. Dexter, and R. S. Knox, “Electron–hole pair excitation in semiconductors via energy transfer from an external sensitizer,” Phys. Rev. B 31, 2277–2289 (1985).
[CrossRef]

Kottig, K.

P. Fromherz, V. Kiessling, K. Kottig, and G. Zeck, “Membrane-transistor with giant lipid vesicle touching a silicon chip,” Appl. Phys. A 69, 571–576 (1999).
[CrossRef]

Kotulla, R.

P. Fromherz and R. Kotulla, “Fluorescent dye in soap lamella as a probe of the electrical potential,” Ber. Bunsenges. Phys. Chem. 88, 1106–1112 (1984).
[CrossRef]

Krieg, M.

M. Krieg, M. B. Srichai, and R. W. Redmond, “Photophysical properties of 3,2-dialkylthiacarbocyanine dyes in organized media: unilamellar liposomes and thin polymer films,” Biochim. Biophys. Acta 1151, 168–174 (1993).
[CrossRef] [PubMed]

Kuhn, H.

H. Kuhn, “Classical aspects of energy transfer in molecular systems,” J. Chem. Phys. 53, 1071–108 (1970).
[CrossRef]

K. H. Drexhage, H. Kuhn, and F. P. Schäfer, “Variation of fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsenges. Phys. Chem. 72, 329 (1968).

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Kunz, R. E.

Lambacher, A.

A. Lambacher and P. Fromherz, “Orientation of hemicyanine dye in lipid membrane measured by fluorescence interferometry on a silicon chip,” J. Phys. Chem. 105, 343–346 (2001).
[CrossRef]

A. Lambacher and P. Fromherz, “Fluorescence interference contrast microscopy on oxidized silicon using a monomolecular dye layer,” Appl. Phys. A 63, 207–216 (1996).
[CrossRef]

Langmuir, I.

I. Langmuir and V. J. Schaefer, “Activities of urease and pepsin monolayers,” J. Am. Chem. Soc. 60, 1351–1360 (1938).
[CrossRef]

K. B. Blodgett and I. Langmuir, “Built-up films of barium stearate and their optical properties,” Phys. Rev. 51, 964–982 (1937).
[CrossRef]

Leiderer, P.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, and M. Bastmeyer, “Imaging of cell/substrate contacts of living cells with surface plasmon resonance microscopy,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Loew, L. M.

L. M. Loew, “Potentiometric dyes: imaging electrical activity of cell membranes,” Pure Appl. Chem. 68, 1405–1409 (1996).
[CrossRef]

Lukosz, W.

Mertz, J.

Möbius, D.

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Modine, F. A.

G. E. Jellison, Jr., and F. A. Modine, “Optical constants for silicon at 300 K and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

Olivier, L. A.

J. S. Burmeister, L. A. Olivier, W. M. Reichert, and G. A. Truskey, “Application of total internal reflection fluorescence microscopy to study cell adhesion to biomaterials,” Biomaterials 19, 307–325 (1998).
[CrossRef] [PubMed]

Prock, A.

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Fluorescence and energy transfer near interfaces: the complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

Rädler, J. O.

J. O. Rädler, T. J. Feder, H. H. Strey, and E. Sackmann, “Fluctuation analysis of tension controlled undulation forces between giant vesicles and solid substrates,” Phys. Rev. E 51, 4526 (1995).
[CrossRef]

Redmond, R. W.

M. Krieg, M. B. Srichai, and R. W. Redmond, “Photophysical properties of 3,2-dialkylthiacarbocyanine dyes in organized media: unilamellar liposomes and thin polymer films,” Biochim. Biophys. Acta 1151, 168–174 (1993).
[CrossRef] [PubMed]

Reichert, W. M.

J. S. Burmeister, L. A. Olivier, W. M. Reichert, and G. A. Truskey, “Application of total internal reflection fluorescence microscopy to study cell adhesion to biomaterials,” Biomaterials 19, 307–325 (1998).
[CrossRef] [PubMed]

Reinbold, G.

P. Fromherz and G. Reinbold, “Energy transfer between fluorescent dyes spaced by multilayers of Cd-salts of fatty acids,” Thin Solid Films 160, 347–353 (1988).
[CrossRef]

Riedel, M.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, and M. Bastmeyer, “Imaging of cell/substrate contacts of living cells with surface plasmon resonance microscopy,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Sackmann, E.

J. O. Rädler, T. J. Feder, H. H. Strey, and E. Sackmann, “Fluctuation analysis of tension controlled undulation forces between giant vesicles and solid substrates,” Phys. Rev. E 51, 4526 (1995).
[CrossRef]

Schaefer, V. J.

I. Langmuir and V. J. Schaefer, “Activities of urease and pepsin monolayers,” J. Am. Chem. Soc. 60, 1351–1360 (1938).
[CrossRef]

Schäfer, F. P.

K. H. Drexhage, H. Kuhn, and F. P. Schäfer, “Variation of fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsenges. Phys. Chem. 72, 329 (1968).

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Silbey, R.

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Fluorescence and energy transfer near interfaces: the complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

Sims, O. J.

O. J. Sims, A. S. Waggoner, C. H. Wang, and J. F. Hoffmann, “Studies on the mechanism by which cyanine dyes measure membrane potential in red blood cells and phosphatidylcholine vesicles,” Biochemistry 13, 3315–3330 (1974).
[CrossRef] [PubMed]

Sommerfeld, A.

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–736 (1909).
[CrossRef]

Sondermann, J.

J. Sondermann, “Darstellung oberflächenaktiver Polymethincyanin-Farbstoffe mit langen N-Alkyl-Ketten,” Liebigs Ann. Chem. 749, 183–197 (1971).
[CrossRef]

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Sperling, W.

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Srichai, M. B.

M. Krieg, M. B. Srichai, and R. W. Redmond, “Photophysical properties of 3,2-dialkylthiacarbocyanine dyes in organized media: unilamellar liposomes and thin polymer films,” Biochim. Biophys. Acta 1151, 168–174 (1993).
[CrossRef] [PubMed]

Stavola, M.

M. Stavola, D. L. Dexter, and R. S. Knox, “Electron–hole pair excitation in semiconductors via energy transfer from an external sensitizer,” Phys. Rev. B 31, 2277–2289 (1985).
[CrossRef]

Strey, H. H.

J. O. Rädler, T. J. Feder, H. H. Strey, and E. Sackmann, “Fluctuation analysis of tension controlled undulation forces between giant vesicles and solid substrates,” Phys. Rev. E 51, 4526 (1995).
[CrossRef]

Sullivan, K. G.

Tews, K. H.

K. H. Tews, “Zur Variation von Lumineszenz-Lebensdauern,” Ann. Phys. (Leipzig) 29, 97–120 (1973).
[CrossRef]

Tillmann, P.

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Todd, I.

D. Gingell and I. Todd, “Interference reflection microscopy: a quantitative theory for image interpretation and its application to cell–substratum separation measurement,” Biophys. J. 26, 507–526 (1979).
[CrossRef] [PubMed]

Truskey, G. A.

J. S. Burmeister, L. A. Olivier, W. M. Reichert, and G. A. Truskey, “Application of total internal reflection fluorescence microscopy to study cell adhesion to biomaterials,” Biomaterials 19, 307–325 (1998).
[CrossRef] [PubMed]

Waggoner, A. S.

O. J. Sims, A. S. Waggoner, C. H. Wang, and J. F. Hoffmann, “Studies on the mechanism by which cyanine dyes measure membrane potential in red blood cells and phosphatidylcholine vesicles,” Biochemistry 13, 3315–3330 (1974).
[CrossRef] [PubMed]

Wang, C. H.

O. J. Sims, A. S. Waggoner, C. H. Wang, and J. F. Hoffmann, “Studies on the mechanism by which cyanine dyes measure membrane potential in red blood cells and phosphatidylcholine vesicles,” Biochemistry 13, 3315–3330 (1974).
[CrossRef] [PubMed]

Weiland, U.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, and M. Bastmeyer, “Imaging of cell/substrate contacts of living cells with surface plasmon resonance microscopy,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Weis, R.

R. Weis and P. Fromherz, “Frequency dependent signal-transfer in neuron-transistors,” Phys. Rev. E 55, 877–889 (1997).
[CrossRef]

Weyl, H.

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. (Leipzig) 60, 481–500 (1919).
[CrossRef]

Wiegand, J.

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Zeck, G.

P. Fromherz, V. Kiessling, K. Kottig, and G. Zeck, “Membrane-transistor with giant lipid vesicle touching a silicon chip,” Appl. Phys. A 69, 571–576 (1999).
[CrossRef]

Ann. Phys. (Leipzig) (3)

K. H. Tews, “Zur Variation von Lumineszenz-Lebensdauern,” Ann. Phys. (Leipzig) 29, 97–120 (1973).
[CrossRef]

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–736 (1909).
[CrossRef]

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. (Leipzig) 60, 481–500 (1919).
[CrossRef]

Appl. Phys. A (4)

P. Geggier and G. Fuhr, “A time-resolved total internal reflection aqueous fluorescence (TIRAF) microscope for the investigation of cell adhesion dynamics,” Appl. Phys. A 68, 505–513 (1999).
[CrossRef]

P. Fromherz, V. Kiessling, K. Kottig, and G. Zeck, “Membrane-transistor with giant lipid vesicle touching a silicon chip,” Appl. Phys. A 69, 571–576 (1999).
[CrossRef]

A. Lambacher and P. Fromherz, “Fluorescence interference contrast microscopy on oxidized silicon using a monomolecular dye layer,” Appl. Phys. A 63, 207–216 (1996).
[CrossRef]

D. Braun and P. Fromherz, “Fluorescence interference contrast microscopy of cell adhesion on silicon,” Appl. Phys. A 65, 341–348 (1997).
[CrossRef]

Ber. Bunsenges. Phys. Chem. (2)

K. H. Drexhage, H. Kuhn, and F. P. Schäfer, “Variation of fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsenges. Phys. Chem. 72, 329 (1968).

P. Fromherz and R. Kotulla, “Fluorescent dye in soap lamella as a probe of the electrical potential,” Ber. Bunsenges. Phys. Chem. 88, 1106–1112 (1984).
[CrossRef]

Biochemistry (1)

O. J. Sims, A. S. Waggoner, C. H. Wang, and J. F. Hoffmann, “Studies on the mechanism by which cyanine dyes measure membrane potential in red blood cells and phosphatidylcholine vesicles,” Biochemistry 13, 3315–3330 (1974).
[CrossRef] [PubMed]

Biochim. Biophys. Acta (1)

M. Krieg, M. B. Srichai, and R. W. Redmond, “Photophysical properties of 3,2-dialkylthiacarbocyanine dyes in organized media: unilamellar liposomes and thin polymer films,” Biochim. Biophys. Acta 1151, 168–174 (1993).
[CrossRef] [PubMed]

Biomaterials (1)

J. S. Burmeister, L. A. Olivier, W. M. Reichert, and G. A. Truskey, “Application of total internal reflection fluorescence microscopy to study cell adhesion to biomaterials,” Biomaterials 19, 307–325 (1998).
[CrossRef] [PubMed]

Biophys. J. (3)

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, and M. Bastmeyer, “Imaging of cell/substrate contacts of living cells with surface plasmon resonance microscopy,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

D. Gingell and I. Todd, “Interference reflection microscopy: a quantitative theory for image interpretation and its application to cell–substratum separation measurement,” Biophys. J. 26, 507–526 (1979).
[CrossRef] [PubMed]

J. Enderlein, “A theoretical investigation of single-molecule fluorescence detection on thin metallic layers,” Biophys. J. 78, 2151–2158 (2000).
[CrossRef] [PubMed]

Eur. Biophys. J. (1)

Y. Iwanaga, D. Braun, and P. Fromherz, “No correlation of focal contacts and close adhesion by comparing GFP-vinculin and fluorescence interference of DiI,” Eur. Biophys. J. 30, 17–26 (2001).
[CrossRef]

J. Am. Chem. Soc. (1)

I. Langmuir and V. J. Schaefer, “Activities of urease and pepsin monolayers,” J. Am. Chem. Soc. 60, 1351–1360 (1938).
[CrossRef]

J. Appl. Phys. (1)

G. E. Jellison, Jr., and F. A. Modine, “Optical constants for silicon at 300 K and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

J. Cell Biol. (1)

A. S. Curtis, “The mechanism of adhesion of cells to glass. A study by interference reflection microscopy,” J. Cell Biol. 20, 199–215 (1964).
[CrossRef] [PubMed]

J. Chem. Phys. (4)

H. Kuhn, “Classical aspects of energy transfer in molecular systems,” J. Chem. Phys. 53, 1071–108 (1970).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” J. Chem. Phys. 62, 2245–2253 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Fluorescence and energy transfer near interfaces: the complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

J. Mol. Biol. (1)

R. J. Cherry and D. Chapman, “Optical properties of black lecithin films,” J. Mol. Biol. 40, 19–32 (1969).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

J. Phys. Chem. (1)

A. Lambacher and P. Fromherz, “Orientation of hemicyanine dye in lipid membrane measured by fluorescence interferometry on a silicon chip,” J. Phys. Chem. 105, 343–346 (2001).
[CrossRef]

Liebigs Ann. Chem. (1)

J. Sondermann, “Darstellung oberflächenaktiver Polymethincyanin-Farbstoffe mit langen N-Alkyl-Ketten,” Liebigs Ann. Chem. 749, 183–197 (1971).
[CrossRef]

Mol. Cryst. (1)

H. Bücher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schäfer, J. Sondermann, W. Sperling, P. Tillmann, and J. Wiegand, “Controlled transfer of excitation energy through thin layers,” Mol. Cryst. 2, 199–230 (1967).
[CrossRef]

Phys. Rev. (1)

K. B. Blodgett and I. Langmuir, “Built-up films of barium stearate and their optical properties,” Phys. Rev. 51, 964–982 (1937).
[CrossRef]

Phys. Rev. B (1)

M. Stavola, D. L. Dexter, and R. S. Knox, “Electron–hole pair excitation in semiconductors via energy transfer from an external sensitizer,” Phys. Rev. B 31, 2277–2289 (1985).
[CrossRef]

Phys. Rev. E (2)

R. Weis and P. Fromherz, “Frequency dependent signal-transfer in neuron-transistors,” Phys. Rev. E 55, 877–889 (1997).
[CrossRef]

J. O. Rädler, T. J. Feder, H. H. Strey, and E. Sackmann, “Fluctuation analysis of tension controlled undulation forces between giant vesicles and solid substrates,” Phys. Rev. E 51, 4526 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

D. Braun and P. Fromherz, “Fluorescence interferometry of neuronal cell adhesion on microstructured silicon,” Phys. Rev. Lett. 81, 5241–5244 (1998).
[CrossRef]

Prog. Opt. (1)

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt. 12, 163–232 (1974).
[CrossRef]

Pure Appl. Chem. (1)

L. M. Loew, “Potentiometric dyes: imaging electrical activity of cell membranes,” Pure Appl. Chem. 68, 1405–1409 (1996).
[CrossRef]

Rev. Sci. Instrum. (1)

P. Fromherz, “Instrumentation for handling monomolecular films at an air–water interface,” Rev. Sci. Instrum. 46, 1380–1385 (1975).
[CrossRef]

Thin Solid Films (1)

P. Fromherz and G. Reinbold, “Energy transfer between fluorescent dyes spaced by multilayers of Cd-salts of fatty acids,” Thin Solid Films 160, 347–353 (1988).
[CrossRef]

Other (9)

K. H. Hellwege, ed., Landolt-Börnstein, 6th Ed. (Springer, Berlin, 1962), Vol. II, Part 8.

A. Sommerfeld, Electrodynamics: Lectures on Theoretical Physics (Academic, San Diego, Calif., 1964), Vol. 3.

L. D. Landau and E. M. Lifschitz, Theoretical Physics (Butterworth-Heineman, Oxford, UK, 1982).

T. Förster, Fluoreszenz Organischer Verbindungen (Vandenhoeck & Ruprecht, Göttingen, Germany, 1982).

M. Born and E. Wolf, Principles of Optics 6th ed. (Pergamon, London, 1980).

G. Zeck and P. Fromherz are preparing a manuscript to be called “Steric repulsion of laminin with sedimented giant lipid vesicles and in cell adhesion.”

A. Sommerfeld, Partial Differential Equations in Physics: Lectures on Theoretical Physics (Academic, San Diego, Calif., 1964), Vol. 6.

J. A. Stratton, Electromagnetic theory (McGraw-Hill, New York, 1941).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C, 2nd ed. (Cambridge University, Cambridge, England, 1997).

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Figures (12)

Fig. 1
Fig. 1

Fluorescence interference contrast (FLIC) microscopy. A living cell grows across shallow terraces of silicon dioxide on silicon. (Width of a terrace is 2.5–5 µm; height is ∼50 nm. Note that the lateral and vertical dimensions are not on scale.) The cell membrane is stained with a fluorescent dye. Its light absorption and light emission depend on the structure of the standing modes of light in front of the reflecting and absorbing substrates. The fluorescence intensity of the attached membrane is determined by the height of the terraces and by the unknown gap between membrane and chip. The width of the gap is evaluated by a comparison of the pattern of fluorescence with the electromagnetic theory of light absorption and light emission in the stratified system.

Fig. 2
Fig. 2

Optical system. (a) Structure of a multilayer system of silicon, silicon dioxide (thickness dox), an electrolyte film (thickness dgap), a cell membrane (thickness dm), and bulk electrolyte (cytoplasm). Dye molecules are located in both monolayers of the membrane (black dots). (b) Reduced optical system obtained by transfer matrices. Medium 1 (refractive index n1) corresponds to the cell membrane. It is sandwiched between the medium 2 of bulk electrolyte (refractive index n2) and medium 0 (refractive index n0), which comprises electrolyte film, silicon dioxide, and silicon. The transition dipole of a molecule is located in medium 1 at distances d0 from medium 0 and d2 from medium 2. Incident (left) and outgoing rays (right) with polar angles θ2in and θ2out in medium 2 are indicated Multireflection is omitted for the sake of clarity. (c) Cartesian coordinate system located at the transition dipole with a polar angle θem for emission (θex for excitation). The z axis points in the direction of medium 2, the x axis into the direction of the dipole. The directions of the light waves are defined by the polar and azimuthal angles. The electrical field is decomposed into the transverse electric and transverse magnetic components with respect to the plane of incidence.

Fig. 3
Fig. 3

Theoretical fluorescence intensity on oxidized silicon, effects of excitation, detected emission, and lifetime. Dye molecules are in a lipid bilayer on oxidized silicon with transition moments parallel to the surface with random azimuthal angle. Small-aperture, monochromatic illumination is at 18 320 cm-1 (546 nm), and monochromatic detection is at 17 000 cm-1 (588 nm). Fluorescence intensities are relative to the intensity in infinite medium 1 without silicon. (a) Relative intensity due to excitation alone versus thickness of silicon dioxide. (b) Relative intensity due to the effects of excitation and of detected emission at constant lifetime. (c) Relative intensity computed by the complete electromagnetic theory with the effects of excitation, detected emission, and lifetime.

Fig. 4
Fig. 4

Theoretical fluorescence intensity on oxidized silicon, effect of broad-band detection, and large aperture. Dye molecules are in a lipid bilayer on oxidized silicon with transition moments parallel to the surface with random azimuthal angle. Fluorescence intensity is relative to the intensity in infinite medium 1 without silicon versus thickness of silicon dioxide. Monochromatic illumination at 18 320 cm-1 and broadband detection with a width (2σ) of 1000 cm-1 at 17 000 cm-1. (a) Small aperture NA=10-4. (b) Large aperture NA=1.0.

Fig. 5
Fig. 5

Effect of lifetime modulation. (a) Theoretical fluorescence intensity versus thickness of silicon dioxide for large aperture NA=1.0, monochromatic illumination at 18 320 cm-1, and broadband detection with a width (2σ) of 1000 cm at 17 000 cm-1. The Complete theory is relative to infinite medium 1 without silicon (solid curve) and theory with constant lifetime kelmag=kfl (dashed curve). (b) Relative change of the intensity due to modulation of lifetime with respect to the approximation kelmag=kfl, by the full electrodynamic interaction (solid curve), by the near field only (dashed curve) and the far field only (dotted curve).

Fig. 6
Fig. 6

Theoretical fluorescence intensity on oxidized silicon and effect of orientation. The polar angle of the transition dipole at random azimuthal angle is indicated. Numerical aperture NA=1.0, monochromatic illumination is at 18 320 cm-1, and broadband detection is with a width (2σ) of 1000 cm at 17 000 cm-1. All intensities are normalized to one at infinite thickness of silicon dioxide on silicon.

Fig. 7
Fig. 7

Microstructured silicon chip. (a) Arrangement of the 256 terraces of silicon dioxide in the order of their height. The size of each terrace is 250 µm×250 µm. The height varies from 3 nm to 987 nm. (b) Reflection colors of the dry chip in white light. Note the bright-white reflectance in the left-upper corner for thin oxide. (c) Fluorescence of a dry monolayer of cyanine dye DiIC18 in a lipid monolayer of POPC. Illumination is at 546 nm; detection is at 570–650 nm. Note the dark fluorescence in the left-upper corner for thin oxide.

Fig. 8
Fig. 8

Relative experimental fluorescence intensity of the cyanine dye DiIC18 in a dry lipid monolayer on oxidized silicon measured at an aperture NA=0.075. Excitation is at 546 nm; detection is from 545 to 645 nm. The data are plotted versus the thickness of silicon dioxide. The electromagnetic theory is fitted with transition dipoles in the layer plane (θex=θem=90°). For details, see text. The residuals are shown at the bottom.

Fig. 9
Fig. 9

Relative experimental fluorescence intensity of the cyanine dye DiIC18 in a lipid bilayer on oxidized silicon in water at an aperture NA=1.0. Excitation is at 546 nm; detection is from 545 to 645 nm. The data are plotted versus the thickness of silicon dioxide. The electromagnetic theory is fitted with an inclination angle θex=θem=62° of the transition dipoles to the normal. For details of the fit, see text. The residuals are shown at the bottom.

Fig. 10
Fig. 10

Relative experimental fluorescence intensity of the hemicyanine dye Di8ANEPPS in a lipid bilayer on oxidized silicon in water at an aperture NA=0.9. Excitation is at 436 nm; detection is from 455 to 575 nm. The data points are plotted versus the thickness of silicon dioxide. The electromagnetic theory is fitted with an inclination θex=θem=36° of the transition dipoles to the normal. For details, see text. The residuals are shown at the bottom.

Fig. 11
Fig. 11

Distance measurements by FLIC microscopy using the cyanine dye DiIC18 as a probe. Top: fluorescence micrographs of (a) giant lipid vesicle on poly-L-lysine, (b) erythrocyte ghost on poly-L-lysine, and (c) astrocyte from rat brain on laminin. The scale bar is 10 µm. Bottom: Relative experimental fluorescence intensities versus height of oxide terraces. Excitation is at 546 nm; detection is from 545 to 645 nm. The electromagnetic theory is fitted with the distance dgap between membrane and chip as a free parameter as indicated, with an inclination angle θex=θem=62° of the transition dipoles.

Fig. 12
Fig. 12

Focal adhesion of GD25-β1A cell cultured for three hours on a chip with 5 µm×5 µm oxide terraces coated with fibronectin. (a) Fluorescence micrograph of vinculin-GFP (green fluorescent protein). (b) FLIC micrograph with DiIC18. (c) Blowup of one terrace of a vinculin-GFP picture. (d) Color-coded distance map on the same terrace evaluated from the FLIC micrograph.

Equations (113)

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dn*dt=kex,ill(1-n*)-(kelmag+kmol)n*.
J=kem,det 1kelmag+kmolkex,ill.
Pem(ω)=2n1ω33ε0hc3|Mem|2.
dPemdΩ=PemΛΩ(θ, ϕ)ΛΩ=38π|κ×μ|2.
dPexdΩ=dIωQdΩ 8π3c2n12ω2 dPemdΩ.
Pelmag=Pem0alldΩΛΩ(θ, ϕ),
Pem,det=Pem0aperturedΩΛΩ(θ, ϕ),
Pex,ill=dIωQ(ω)dΩ 8π3c2n12ω2Pem0aperturedΩΛΩ(θ, ϕ).
kflfω(ω)=Pem(ω)gωS0(ω).
ε(ω)=8π3c2n12ω2 Pem8πgωS1(ω).
kelmag(d0, d2)=kfldωfω(ω)×0alldΩΛΩlayer(θ, ϕ),
kem,det(d0, d2)=kfldωfω(ω)×0aperturedΩΛΩlayer(θ, ϕ),
kex,ill(d0, d2)=8πdωε(ω) dIωQ(ω)dΩ×0aperturedΩΛΩlayer(θ, ϕ).
kelmag(d0, d2)
= sin θemdθemO(θem)kelmag(d0, d2, θem),
kem,det(d0, d2)
= sin θemdθemO(θem)kem,det(d0, d2, θem),
kex,ill(d0, d2)
= sin θexdθexO(θex)kex,ill(d0, d2, θex).
J=kex,illkem,det/kfl(kelmag/kfl-1)+(Φfl)-1.
JΦflkem,detkex,illkfl.
Jexp=a dλIλQ(λ)ε(λ)0aperturedkρΛkρlayer(kρ)dλT(λ)fλ(λ)0aperturedkρΛkρlayer(kρ)dλfλ(λ)0dkρΛkρlayer(kρ)-1+(Φfl)-1+b,
Jexp=adλIλQ(λ)ε(λ)0aperturedkρΛkρlayer(kρ)dλT(λ)fλ(λ)0aperturedkρΛkρlayer(kρ)+b.
Iem(ω)=n1ω4Mem212πε0c3,
dIemdΩ=IemΛΩ(θ, ϕ),
ΛΩ(θ, ϕ)=38π sin2 θ.
Ielmag=Iem0alldΩΛΩlayer(θ, ϕ).
Π(r)=eemMem4π exp(ik1r)r.
Π(r)=eemMem4π ik12π 02πdϕ10π/2-i sin θ1dθ1 exp(ik1r),
k1r=k1(x sin θ1 cos ϕ1+y sin θ1 sin ϕ1+|z|cos θ1).
Π(r)=ieemMem4π 0dkρJ0(kρρ) kρk1z exp(ik1z|z|).
Π2(r)=iezMem4π 0dkρJ0(kρρ)f2×exp[ik2z(z-d2)+ik1zd2],
Π1(r)=iezMem4π 0dkρJ0(kρρ)kρk1z×exp(ik1z|z|)+f1up exp[ik1z(z+d0)]+f1down exp[-ik1z(z-d2)],
Π0(r)=iezMem4π 0dkρJ0(kρρ)f0×exp[-ik0z(z+d0)+ik1zd0].
E(r)=1n12ε0[Π(r)+k2Π(r)],
H(r)=-iω[×Π(r)].
Eφ=Hρ=0,
Eρ=1n12ε0 2zρz,Hφ=iω zρ,
1n12 1zzz=d2=1n22 2zzz=d2,
1n12 1zzz=-d0=1n02 0zzz=-d0,
|1z|z=d2=|2z|z=d2,
|1z|z=-d0=|0z|z=-d0.
Π2z(r)=iezMem cos ϕ4π 0dkρJ1(kρρ)f2z×exp[ik2z(z-d2)+ik1zd2],
Π1z(r)=iezMem cos ϕ4π 0dkρJ1(kρρ)×{f1zup exp[ik1z(z+d0)]+f1zdown exp[-ik1z(z-d2)]},
Π0z(r)=iezMem cos ϕ4π 0dkρJ1(kρρ)f0z×exp[-ik0z(z+d0)+ik1zd0],
Π2x(r)=iexMem4π 0dkρ(kρρ)f2x×exp[ik2z(z-d2)+ik1zd2],
Π1x(r)=iexMem4π 0dkρJ0(kρρ)×kρk1z exp(ik1z|z|)+f1xup exp[ik1z(z+d0)]+f1xdown exp[-ik1z(z-d2)],
Π0x(r)=iexMem4π 0dkρJ0(kρρ)f0x×exp[-ik0z(z+d0)+ik1zd0].
1z|z=d2=2z|z=d2,
1z|z=-d0=0z|z=-d0,
1x|z=d2=2x|z=d2,
|1x|z=-d0=0x|z=-d0,
1xzz=d2=2xzz=d2
1xzz=-d0=0xzz=-d0,
1n12 1xx+1zzz=d2
=1n22 2xx+2zzz=d2,
1n12 1xx+1zzz=-d0
=1n02 0xx+0zzz=-d0.
S=12 E×H*,
Sz=12(EρHφ*-EφHρ*),
Iplane= Re{Sz}dA.
Eρ=14πε0n1n2Mem0J1(kρρ)kρ2 k2zk1za2TM,ndkρ,
Hφ*=ω4π n2*n1Mem0J1(kρρ) kρ2k1z*(a2TM,n)*dkρ,
Eφ=Hρ=0.
Iplane=ωMem216πε0n12 0 ρdρ×Ren2*n2 0 J1(kρρ)kρ2 k2zk1za2TM,ndkρ×0J1(kρρ) kρ2k1z*(a2TM,n)*dkρ,
Iplane=ωMem216πε0n12×Ren2*n2 0 kρ2 k2zk1za2TM,ndkρ×0 kρ2k1z*(a2TM,n)*dkρ 0ρdρJ1(kρρ)J1(kρρ),
Iplane=ωMem216πε0n12 0dkρ Rekρ3 k2zk1zk1z* n2*n2|a2TM,n|2.
In(k1, d0, d2)=Iem0dkρRe34k13 kρ3k1zk1z*×k0z n0*n0|a0TM,n|2+k2z n2*n2|a2TM,n|2,
Ip(k1, d0, d2)=I(k1)0dkρ×Re38k13kρk0z n0*n0|a0TM,p|2+k2z n2*n2|a2TM,p|2+k12k1zk1z*(k0z|a0TE|2+k2z|a2TE|2).
Ielmag(d0, d2, k1)
=Ip(k1, d0, d2)cos2 θem+In(k1, d0, d2)sin2 θem,
Ielmag(d0, d2, k1)
=Iem0dkρ 3kρ8k13×Re2 kρ2k1zk1z* k0z n0*n0|a0TM, n|2+k2z n2*n2|a2TM, n|2cos2 θem+k0z n0*n0|a0TM, p|2+k2z n2*n2|a2TM, p|2+k12k1zk1z*(k0z|a0TE|2+k2z|a2TE|2)sin2 θem,
Ielmag(d0, d2, k1)
=Iem0dkρΛkρlayer(kρ).
Iem,det(d0, d2, k1)
=Iem0aperturedkρ 3kρ8k13Re2 kρ2k1zk1z*k2z n2*n2×|a2TM, n|2 cos2 θem+k2z n2*n2|a2TM, p|2+k12k1zk1z*k2z|a2TE|2sin2 θem,
Iem, det(d0, d2, k1)
=Iem0aperturedkρΛkρlayer(kρ).
f0=kρk1z n0n1 exp(-ik1zd0)a0TM,n,
f1up=kρk1z r10TMt10TMa0TM,n,
f1down=kρk1z r12TMt12TMa2TM,n,
f2=kρk1z n2n1 exp(-ik1zd2)a2TM,n,
a0TM,n=t10TM exp(ik1zd0)×1+r12TM exp(2ik1zd2)1-r10TMr12TM exp(2ik1zd),
a2TM,n=t12TM exp(ik1zd2)×1+r10TM exp(2ik1zd0)1-r10TMr12TM exp(2ik1zd).
f0x=kρk1z exp(-ik1zd0)a0TE,
f1xup=kρk1z r10TEt10TEa0TE,
f1xdown=kρk1z r12TEt12TEa2TE,
f2x=kρk1z exp(-ik1zd2)a2TE,
f1zup=i1-r10TMr12TM exp(2ik1zd) kρ2k1z×a2TE n22-n12n22k1z+n12k2zr10TM exp(ik1zd)-a0TE n02-n12n02k1z+n12k0z,
f1zdown=i1-r10TMr12TM exp(2ik1zd) kρ2k1z×a2TE n22-n12n22k1z+n12k2z-a0TE n02-n12n02k1z+n12k0zr12TM exp(ik1zd),
f0z=f1zup exp(-ik1zd0)+f1zdown exp(ik1zd2),
f2z=f1zup exp(ik1zd0)+f1zdown exp(-ik1zd2),
a0TE=t10TE exp(ik1zd0)×1+r12TE exp(2ik1zdz)1-r10TEr12TE exp(2ik1zd),
a2TE=t12TE exp(ik1zd2)×1+r10TE exp(2ik1zd0)1-r10TEr12TE(2ik1zd),
a0TM,p=t10TM exp(ik1zd0)×1-r12TM exp(2ik1zd2)1-r10TMr12TM exp(2ik1zd),
a2TM,p=t12TM exp(ik1zd2)×1-r10TM exp(2ik1zd0)1-r10TMr12TM exp(2ik1zd).
rijTE=ni cos θi-nj cos θjni cos θi+nj cos θj,rijTM=nj cos θi-ni cos θjnj cos θi+ni cos θj,
tijTE=2ni cos θini cos θi+nj cos θj,tijTM=2ni cos θinj cos θi+ni cos θj.
MiTE=m11TEm12TEm21TEm22TE=cos(kidi cos θi)-ipi sin(kidi cos θi)-ipi sin(kidi cos θi)cos(kidi cos θi),
MiTM=m11TMm12TMm21TMm22TM=cos(kidi cos θi)-iqi sin(kidi cos θi)-iqi sin(kidi cos θi)cos(kidi cos θi).
M=M1×M2××Mn.
rTE=(m11TE+m12TEp2)p0-(m21TE+m22TEp2)(m11TE+m12TEp2)p0+(m21TE+m22TEp2),
rTM=(m11TM+m12TMq2)q0-(m21TM+m22TMq2)(m11TM+m12TMq2)q0+(m21TM+m22TMq2),
tTE=2p0(m11TE+m12TEp2)p0+(m21TE+m22TEp2),
tTM=2q0(m11TE+m12TEq2)q0+(m21TE+m22TEq2).
Iem,det0aperture kρdkρk13 Re2 kρ2k2zk1zk1z* n2*n2|a2TM,n|2 cos2 θem+k2z n2*n2|a2TM,p|2+k12k2zk1zk1z*|a2TE|2sin2 θem.
Iem,det0aperture sin θ1dθ1 n2 cos θ2n1 cos θ1×[2 sin2 θ1|a2TM,n|2 cos2 θem+(cos2 θ1|a2TM,p|2+|a2TE|2)sin2 θem].
|a2TM,p|2=t13TM 1+r10TM exp(iΦout)1-r10TMr13TM exp(iΦout)2=|ifoutTM,p|2,
|a2TM,n|2=t13TM 1-r10TM exp(iΦout)1-r10TMr13TM exp(iΦout)2=|ifoutTM,n|2,
|a2TE|2=t13TE 1+r10TE exp(iΦout)1-r10TEr13TE exp(iΦout)2=|ifoutTE|2.
Aout(θ1)=n2 cos θ2n1 cos θ1.
Iem,det0aperturesinθ1dθ1Aout(θ1)[sin2θem(|ifoutTE|2+cos2θ1|ifoutTM,p|2)+2cos2θem sin2θ1|ifoutTM,n|2].

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