Abstract

The problem of the retrieval of the complex dielectric function of nanoparticles having multiple spectral features is addressed. It is shown that the complex dielectric function of nanoparticles that are in a water matrix can be obtained with a maximum entropy model along with surface-plasmon resonance spectroscopy. The present analysis provides means to identify nanoparticles and to gain information on their concentration, which are important factors in the monitoring of nanoparticles in liquid phase.

© 2005 Optical Society of America

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References

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  1. J. Räty, K.-E. Peiponen, and T. Asakura, UV-Visible Reflection Spectroscopy of Liquids (Springer, Heidelberg, Germany, 2004).
    [Crossref]
  2. H. Räther, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, Germany, 1988).
  3. C. Nylander, B. Liendberg, and T. Lind, "Gas detection by means of surface plasmon resonance," Sens. Actuators 3, 79-88 (1982).
    [Crossref]
  4. R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies,C. J. Roberts, and S. J. B. Tendler, "Surface plasmon resonance analysis of dynamic biological interactions with biomaterials," Biomaterials 21, 1823-1835 (2000).
    [Crossref] [PubMed]
  5. S. Aldridge, "Surface plasmon resonance finds use across broad range of biomolecular-interaction studies," Genet. Eng. News 24, 25-25 (2004).
  6. J. Räty, K.-E. Peiponen, A. Jääskeläinen, and M. O. A. Mäkinen, "Measurement of wavelength-dependent complex refractive index of transparent and absorbing liquids by a multifunction reflectometer," Appl. Spectrosc. 56, 935-941 (2002).
    [Crossref]
  7. K. Matsubara, S. Kawata, and S. Minami, "Optical chemical sensor based on surface plasmon measurement," Appl. Opt. 27, 1160-1163 (1988).
    [Crossref] [PubMed]
  8. K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, Heidelberg, Germany, 1999).
  9. J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, "Simulation on wavelength-dependent complex refractive index of liquids obtained by phase retrieval from reflectance dip due to surface plasmon resonance," Appl. Spectrosc. 57, 288-292 (2003).
    [Crossref] [PubMed]
  10. J. J. Saarinen, E. M. Vartiainen, and K.-E. Peiponen, "Retrieval of the complex permittivity of spherical nanoparticles in a liquid host material from a spectral surface plasmon resonance measurement," Appl. Phys. Lett. 83, 893-895 (2003).
    [Crossref]
  11. M. N. V. Ravi Kumar, "Nano and microparticles as controlled drug delivery devices," J. Pharm. Pharmaceut. Sci. 3, 234-258 (2000).
  12. J. E. Sipe, "New Green-function formalism for surface optics," J. Opt. Soc. Am. B 4, 481-489 (1987).
    [Crossref]
  13. J. E. Sipe, "Surface plasmon-enhanced absorption of light by adsorbed molecules," Solid State Commun. 33, 7-9 (1980).
    [Crossref]
  14. M. Zangeneh, N. Doa, E. Sambriski, and R. H. Terrill, "Surface plasmon spectral finger-printing of adsorbed magnesium phthalocyanine by angle and wavelength modulation," Appl. Spectrosc. 58, 10-17 (2004).
    [Crossref] [PubMed]
  15. P. Grosse and V. Offermann, "Analysis of reflectance data using the Kramers-Kronig relations," Appl. Phys. A 52, 138-144 (1991).
    [Crossref]
  16. E. M. Vartiainen, T. Asakura, and K.-E. Peiponen, "Generalized noniterative maximum entropy procedure for phase retrieval problems in optical spectroscopy," Opt. Commun. 104, 149-156 (1993).
    [Crossref]
  17. E. M. Vartiainen and K.-E. Peiponen, "Meromorphic degenerate nonlinear susceptibility: phase retrieval from the amplitude spectrum," Phys. Rev. B 50, 1941-1944 (1994).
    [Crossref]
  18. E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, "Phase retrieval in optical spectroscopy: resolving optical constants from power spectra," Appl. Spectrosc. 50, 1283-1289 (1996).
    [Crossref]
  19. K. F. Palmer, M. Z. Williams, and B. A. Budde, "Multiply subtractive Kramers-Kronig analysis of optical data," Appl. Opt. 37, 2660-2673 (1998).
    [Crossref]
  20. S. Haykin and S. Kesler, "Prediction-error filtering and maximum entropy spectral estimation," in Nonlinear Methods of Spectral Analysis, 2nd ed., S.Haykin, ed. (Springer, Berlin, Germany, 1983), pp. 9-72.
  21. J.-F. Brun, D. D. S. Meneses, B. Rousseau, and P. Echegut, "Dispersion relations and phase retrieval in infrared reflection spectra analysis," Appl. Spectrosc. 55, 774-780 (2001).
    [Crossref]
  22. J. C. Maxwell Garnett, "Colours in metal glasses and in metallic films," Philos. Trans. R. Soc. London 203, 385-420 (1904).
    [Crossref]
  23. J. E. Sipe and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614-1629 (1992).
    [Crossref] [PubMed]
  24. D. A. G. Bruggeman, "Berechnung verschiedener physicalischer konstanten von heterogenen substanten. i. dielektizittskonstanten und leitfhigkeiten der mischkrper aus isotropen substanten," Ann. Phys. 24, 636-679 (1935).
    [Crossref]
  25. R. J. Gehr, G. L. Fischer, and R. W. Boyd, "Nonlinear-optical response of porous-glass-based composite materials," J. Opt. Soc. Am. B 14, 2310-2314 (1997).
    [Crossref]
  26. R. W. Boyd and J. E. Sipe, "Nonlinear optical susceptibilities of layered composite materials," J. Opt. Soc. Am. B 11, 297-303 (1994).
    [Crossref]
  27. J. R. Partington, An Advanced Treatise on Physical Chemistry (Longmans, Green, New York, 1960), Vol. 4.
  28. D. W. Lynch and W. R. Hunter, "Comments on the optical constants of metals and an introduction to the data for several metals," in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, Boston, Mass., 1985), pp. 275-367.
    [Crossref]

2004 (2)

2003 (2)

J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, "Simulation on wavelength-dependent complex refractive index of liquids obtained by phase retrieval from reflectance dip due to surface plasmon resonance," Appl. Spectrosc. 57, 288-292 (2003).
[Crossref] [PubMed]

J. J. Saarinen, E. M. Vartiainen, and K.-E. Peiponen, "Retrieval of the complex permittivity of spherical nanoparticles in a liquid host material from a spectral surface plasmon resonance measurement," Appl. Phys. Lett. 83, 893-895 (2003).
[Crossref]

2002 (1)

2001 (1)

2000 (2)

R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies,C. J. Roberts, and S. J. B. Tendler, "Surface plasmon resonance analysis of dynamic biological interactions with biomaterials," Biomaterials 21, 1823-1835 (2000).
[Crossref] [PubMed]

M. N. V. Ravi Kumar, "Nano and microparticles as controlled drug delivery devices," J. Pharm. Pharmaceut. Sci. 3, 234-258 (2000).

1998 (1)

1997 (1)

1996 (1)

1994 (2)

E. M. Vartiainen and K.-E. Peiponen, "Meromorphic degenerate nonlinear susceptibility: phase retrieval from the amplitude spectrum," Phys. Rev. B 50, 1941-1944 (1994).
[Crossref]

R. W. Boyd and J. E. Sipe, "Nonlinear optical susceptibilities of layered composite materials," J. Opt. Soc. Am. B 11, 297-303 (1994).
[Crossref]

1993 (1)

E. M. Vartiainen, T. Asakura, and K.-E. Peiponen, "Generalized noniterative maximum entropy procedure for phase retrieval problems in optical spectroscopy," Opt. Commun. 104, 149-156 (1993).
[Crossref]

1992 (1)

J. E. Sipe and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614-1629 (1992).
[Crossref] [PubMed]

1991 (1)

P. Grosse and V. Offermann, "Analysis of reflectance data using the Kramers-Kronig relations," Appl. Phys. A 52, 138-144 (1991).
[Crossref]

1988 (1)

1987 (1)

1982 (1)

C. Nylander, B. Liendberg, and T. Lind, "Gas detection by means of surface plasmon resonance," Sens. Actuators 3, 79-88 (1982).
[Crossref]

1980 (1)

J. E. Sipe, "Surface plasmon-enhanced absorption of light by adsorbed molecules," Solid State Commun. 33, 7-9 (1980).
[Crossref]

1935 (1)

D. A. G. Bruggeman, "Berechnung verschiedener physicalischer konstanten von heterogenen substanten. i. dielektizittskonstanten und leitfhigkeiten der mischkrper aus isotropen substanten," Ann. Phys. 24, 636-679 (1935).
[Crossref]

1904 (1)

J. C. Maxwell Garnett, "Colours in metal glasses and in metallic films," Philos. Trans. R. Soc. London 203, 385-420 (1904).
[Crossref]

Aldridge, S.

S. Aldridge, "Surface plasmon resonance finds use across broad range of biomolecular-interaction studies," Genet. Eng. News 24, 25-25 (2004).

Asakura, T.

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, "Phase retrieval in optical spectroscopy: resolving optical constants from power spectra," Appl. Spectrosc. 50, 1283-1289 (1996).
[Crossref]

E. M. Vartiainen, T. Asakura, and K.-E. Peiponen, "Generalized noniterative maximum entropy procedure for phase retrieval problems in optical spectroscopy," Opt. Commun. 104, 149-156 (1993).
[Crossref]

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, Heidelberg, Germany, 1999).

J. Räty, K.-E. Peiponen, and T. Asakura, UV-Visible Reflection Spectroscopy of Liquids (Springer, Heidelberg, Germany, 2004).
[Crossref]

Boyd, R. W.

Bruggeman, D. A. G.

D. A. G. Bruggeman, "Berechnung verschiedener physicalischer konstanten von heterogenen substanten. i. dielektizittskonstanten und leitfhigkeiten der mischkrper aus isotropen substanten," Ann. Phys. 24, 636-679 (1935).
[Crossref]

Brun, J.-F.

Budde, B. A.

Davies, M. C.

R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies,C. J. Roberts, and S. J. B. Tendler, "Surface plasmon resonance analysis of dynamic biological interactions with biomaterials," Biomaterials 21, 1823-1835 (2000).
[Crossref] [PubMed]

Doa, N.

Echegut, P.

Fischer, G. L.

Frazier, R. A.

R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies,C. J. Roberts, and S. J. B. Tendler, "Surface plasmon resonance analysis of dynamic biological interactions with biomaterials," Biomaterials 21, 1823-1835 (2000).
[Crossref] [PubMed]

Gehr, R. J.

Green, R. J.

R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies,C. J. Roberts, and S. J. B. Tendler, "Surface plasmon resonance analysis of dynamic biological interactions with biomaterials," Biomaterials 21, 1823-1835 (2000).
[Crossref] [PubMed]

Grosse, P.

P. Grosse and V. Offermann, "Analysis of reflectance data using the Kramers-Kronig relations," Appl. Phys. A 52, 138-144 (1991).
[Crossref]

Haykin, S.

S. Haykin and S. Kesler, "Prediction-error filtering and maximum entropy spectral estimation," in Nonlinear Methods of Spectral Analysis, 2nd ed., S.Haykin, ed. (Springer, Berlin, Germany, 1983), pp. 9-72.

Hunter, W. R.

D. W. Lynch and W. R. Hunter, "Comments on the optical constants of metals and an introduction to the data for several metals," in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, Boston, Mass., 1985), pp. 275-367.
[Crossref]

Jääskeläinen, A.

Kawata, S.

Kesler, S.

S. Haykin and S. Kesler, "Prediction-error filtering and maximum entropy spectral estimation," in Nonlinear Methods of Spectral Analysis, 2nd ed., S.Haykin, ed. (Springer, Berlin, Germany, 1983), pp. 9-72.

Liendberg, B.

C. Nylander, B. Liendberg, and T. Lind, "Gas detection by means of surface plasmon resonance," Sens. Actuators 3, 79-88 (1982).
[Crossref]

Lind, T.

C. Nylander, B. Liendberg, and T. Lind, "Gas detection by means of surface plasmon resonance," Sens. Actuators 3, 79-88 (1982).
[Crossref]

Lynch, D. W.

D. W. Lynch and W. R. Hunter, "Comments on the optical constants of metals and an introduction to the data for several metals," in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, Boston, Mass., 1985), pp. 275-367.
[Crossref]

Mäkinen, M. O. A.

Matsubara, K.

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, "Colours in metal glasses and in metallic films," Philos. Trans. R. Soc. London 203, 385-420 (1904).
[Crossref]

Meneses, D. D. S.

Minami, S.

Nylander, C.

C. Nylander, B. Liendberg, and T. Lind, "Gas detection by means of surface plasmon resonance," Sens. Actuators 3, 79-88 (1982).
[Crossref]

Offermann, V.

P. Grosse and V. Offermann, "Analysis of reflectance data using the Kramers-Kronig relations," Appl. Phys. A 52, 138-144 (1991).
[Crossref]

Palmer, K. F.

Partington, J. R.

J. R. Partington, An Advanced Treatise on Physical Chemistry (Longmans, Green, New York, 1960), Vol. 4.

Peiponen, K.-E.

J. J. Saarinen, E. M. Vartiainen, and K.-E. Peiponen, "Retrieval of the complex permittivity of spherical nanoparticles in a liquid host material from a spectral surface plasmon resonance measurement," Appl. Phys. Lett. 83, 893-895 (2003).
[Crossref]

J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, "Simulation on wavelength-dependent complex refractive index of liquids obtained by phase retrieval from reflectance dip due to surface plasmon resonance," Appl. Spectrosc. 57, 288-292 (2003).
[Crossref] [PubMed]

J. Räty, K.-E. Peiponen, A. Jääskeläinen, and M. O. A. Mäkinen, "Measurement of wavelength-dependent complex refractive index of transparent and absorbing liquids by a multifunction reflectometer," Appl. Spectrosc. 56, 935-941 (2002).
[Crossref]

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, "Phase retrieval in optical spectroscopy: resolving optical constants from power spectra," Appl. Spectrosc. 50, 1283-1289 (1996).
[Crossref]

E. M. Vartiainen and K.-E. Peiponen, "Meromorphic degenerate nonlinear susceptibility: phase retrieval from the amplitude spectrum," Phys. Rev. B 50, 1941-1944 (1994).
[Crossref]

E. M. Vartiainen, T. Asakura, and K.-E. Peiponen, "Generalized noniterative maximum entropy procedure for phase retrieval problems in optical spectroscopy," Opt. Commun. 104, 149-156 (1993).
[Crossref]

J. Räty, K.-E. Peiponen, and T. Asakura, UV-Visible Reflection Spectroscopy of Liquids (Springer, Heidelberg, Germany, 2004).
[Crossref]

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, Heidelberg, Germany, 1999).

Räther, H.

H. Räther, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, Germany, 1988).

Räty, J.

Ravi Kumar, M. N. V.

M. N. V. Ravi Kumar, "Nano and microparticles as controlled drug delivery devices," J. Pharm. Pharmaceut. Sci. 3, 234-258 (2000).

Roberts, C. J.

R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies,C. J. Roberts, and S. J. B. Tendler, "Surface plasmon resonance analysis of dynamic biological interactions with biomaterials," Biomaterials 21, 1823-1835 (2000).
[Crossref] [PubMed]

Rousseau, B.

Saarinen, J. J.

J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, "Simulation on wavelength-dependent complex refractive index of liquids obtained by phase retrieval from reflectance dip due to surface plasmon resonance," Appl. Spectrosc. 57, 288-292 (2003).
[Crossref] [PubMed]

J. J. Saarinen, E. M. Vartiainen, and K.-E. Peiponen, "Retrieval of the complex permittivity of spherical nanoparticles in a liquid host material from a spectral surface plasmon resonance measurement," Appl. Phys. Lett. 83, 893-895 (2003).
[Crossref]

Sambriski, E.

Sipe, J. E.

R. W. Boyd and J. E. Sipe, "Nonlinear optical susceptibilities of layered composite materials," J. Opt. Soc. Am. B 11, 297-303 (1994).
[Crossref]

J. E. Sipe and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614-1629 (1992).
[Crossref] [PubMed]

J. E. Sipe, "New Green-function formalism for surface optics," J. Opt. Soc. Am. B 4, 481-489 (1987).
[Crossref]

J. E. Sipe, "Surface plasmon-enhanced absorption of light by adsorbed molecules," Solid State Commun. 33, 7-9 (1980).
[Crossref]

Skakesheff, K. M.

R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies,C. J. Roberts, and S. J. B. Tendler, "Surface plasmon resonance analysis of dynamic biological interactions with biomaterials," Biomaterials 21, 1823-1835 (2000).
[Crossref] [PubMed]

Tendler, S. J. B.

R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies,C. J. Roberts, and S. J. B. Tendler, "Surface plasmon resonance analysis of dynamic biological interactions with biomaterials," Biomaterials 21, 1823-1835 (2000).
[Crossref] [PubMed]

Terrill, R. H.

Vartiainen, E. M.

J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, "Simulation on wavelength-dependent complex refractive index of liquids obtained by phase retrieval from reflectance dip due to surface plasmon resonance," Appl. Spectrosc. 57, 288-292 (2003).
[Crossref] [PubMed]

J. J. Saarinen, E. M. Vartiainen, and K.-E. Peiponen, "Retrieval of the complex permittivity of spherical nanoparticles in a liquid host material from a spectral surface plasmon resonance measurement," Appl. Phys. Lett. 83, 893-895 (2003).
[Crossref]

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, "Phase retrieval in optical spectroscopy: resolving optical constants from power spectra," Appl. Spectrosc. 50, 1283-1289 (1996).
[Crossref]

E. M. Vartiainen and K.-E. Peiponen, "Meromorphic degenerate nonlinear susceptibility: phase retrieval from the amplitude spectrum," Phys. Rev. B 50, 1941-1944 (1994).
[Crossref]

E. M. Vartiainen, T. Asakura, and K.-E. Peiponen, "Generalized noniterative maximum entropy procedure for phase retrieval problems in optical spectroscopy," Opt. Commun. 104, 149-156 (1993).
[Crossref]

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, Heidelberg, Germany, 1999).

Williams, M. Z.

Zangeneh, M.

Ann. Phys. (1)

D. A. G. Bruggeman, "Berechnung verschiedener physicalischer konstanten von heterogenen substanten. i. dielektizittskonstanten und leitfhigkeiten der mischkrper aus isotropen substanten," Ann. Phys. 24, 636-679 (1935).
[Crossref]

Appl. Opt. (2)

Appl. Phys. A (1)

P. Grosse and V. Offermann, "Analysis of reflectance data using the Kramers-Kronig relations," Appl. Phys. A 52, 138-144 (1991).
[Crossref]

Appl. Phys. Lett. (1)

J. J. Saarinen, E. M. Vartiainen, and K.-E. Peiponen, "Retrieval of the complex permittivity of spherical nanoparticles in a liquid host material from a spectral surface plasmon resonance measurement," Appl. Phys. Lett. 83, 893-895 (2003).
[Crossref]

Appl. Spectrosc. (5)

Biomaterials (1)

R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies,C. J. Roberts, and S. J. B. Tendler, "Surface plasmon resonance analysis of dynamic biological interactions with biomaterials," Biomaterials 21, 1823-1835 (2000).
[Crossref] [PubMed]

Genet. Eng. News (1)

S. Aldridge, "Surface plasmon resonance finds use across broad range of biomolecular-interaction studies," Genet. Eng. News 24, 25-25 (2004).

J. Opt. Soc. Am. B (3)

J. Pharm. Pharmaceut. Sci. (1)

M. N. V. Ravi Kumar, "Nano and microparticles as controlled drug delivery devices," J. Pharm. Pharmaceut. Sci. 3, 234-258 (2000).

Opt. Commun. (1)

E. M. Vartiainen, T. Asakura, and K.-E. Peiponen, "Generalized noniterative maximum entropy procedure for phase retrieval problems in optical spectroscopy," Opt. Commun. 104, 149-156 (1993).
[Crossref]

Philos. Trans. R. Soc. London (1)

J. C. Maxwell Garnett, "Colours in metal glasses and in metallic films," Philos. Trans. R. Soc. London 203, 385-420 (1904).
[Crossref]

Phys. Rev. A (1)

J. E. Sipe and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614-1629 (1992).
[Crossref] [PubMed]

Phys. Rev. B (1)

E. M. Vartiainen and K.-E. Peiponen, "Meromorphic degenerate nonlinear susceptibility: phase retrieval from the amplitude spectrum," Phys. Rev. B 50, 1941-1944 (1994).
[Crossref]

Sens. Actuators (1)

C. Nylander, B. Liendberg, and T. Lind, "Gas detection by means of surface plasmon resonance," Sens. Actuators 3, 79-88 (1982).
[Crossref]

Solid State Commun. (1)

J. E. Sipe, "Surface plasmon-enhanced absorption of light by adsorbed molecules," Solid State Commun. 33, 7-9 (1980).
[Crossref]

Other (6)

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, Heidelberg, Germany, 1999).

J. Räty, K.-E. Peiponen, and T. Asakura, UV-Visible Reflection Spectroscopy of Liquids (Springer, Heidelberg, Germany, 2004).
[Crossref]

H. Räther, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, Germany, 1988).

S. Haykin and S. Kesler, "Prediction-error filtering and maximum entropy spectral estimation," in Nonlinear Methods of Spectral Analysis, 2nd ed., S.Haykin, ed. (Springer, Berlin, Germany, 1983), pp. 9-72.

J. R. Partington, An Advanced Treatise on Physical Chemistry (Longmans, Green, New York, 1960), Vol. 4.

D. W. Lynch and W. R. Hunter, "Comments on the optical constants of metals and an introduction to the data for several metals," in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, Boston, Mass., 1985), pp. 275-367.
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

A schematic diagram of the investigated Kretschmann’s structure. The wave vector of the incident light is divided into parallel κ ( ω ) and perpendicular w ( ω ) pieces with ω ̃ = ω c .

Fig. 2
Fig. 2

(a) The SPR reflectance from 3 dip resonance nanoparticle solution with particle volume fraction f i = 0.1 . The parameters are: θ = 70 ° , ϵ = 2.5 , ω 01 = 1.65 eV , ω 02 = 1.8 eV , ω 03 = 1.95 eV , ω p 1 2 = 0.07 eV 2 , ω p 2 2 = ω p 3 2 = 0.1 eV 2 , and Γ 1 = Γ 2 = Γ 3 = 0.1 eV . The ME parameters are: K = 4 , M ( K ) = 1000 [ M ( K ) N ( K ) 2 , where N ( 0 ) and N ( K ) are the number of data points of the reflectance before and after the squeezing procedure, respectively; here N ( 0 ) = 201 ].

Fig. 3
Fig. 3

(a) The real and (b) imaginary parts of the effective dielectric function of the nanoparticle solution. Solid lines are the exact values and retrieved values are shown by open circles. The parameters are as shown in Fig. 2.

Tables (1)

Tables Icon

Table 1 rms Deviation between ϕ MG ( ν ; K ) and ϕ h ( ν ; K )

Equations (18)

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

w i ( ω ) = [ ω ̃ 2 ϵ i ( ω ) κ 2 ( ω ) ] 1 2 ,
r i j ( ω ) = w i ( ω ) ϵ j ( ω ) w j ( ω ) ϵ i ( ω ) w i ( ω ) ϵ j ( ω ) + w j ( ω ) ϵ i ( ω ) .
r ( ω ) = r 31 ( ω ) + t 31 ( ω ) r 12 ( ω ) t 13 ( ω ) exp [ i 2 w 1 ( ω ) d ] 1 r 12 ( ω ) r 13 ( ω ) exp [ i 2 w 1 ( ω ) d ] ,
R ( ω ) = r ( ω ) 2 = r 31 ( ω ) + r 12 ( ω ) exp [ i 2 w 1 ( ω ) d ] 1 + r 12 ( ω ) r 31 ( ω ) exp [ i 2 w 1 ( ω ) d ] 2 .
κ sp ( ω ) = ω ̃ [ ϵ 1 ( ω ) ϵ 2 ( ω ) ϵ 1 ( ω ) + ϵ 2 ( ω ) ] 1 2 .
ω ̃ n 3 ( ω ) sin θ = ω ̃ [ ϵ 1 ( ω ) ϵ 2 ( ω ) ϵ 1 ( ω ) + ϵ 2 ( ω ) ] 1 2 .
ϵ 2 ( ω ) = 1 2 { B ( ω ) + [ B 2 ( ω ) 4 B ( ω ) n 3 2 ( ω ) sin 2 θ ] 1 2 } ,
B ( ω ) = { n 3 ( ω ) [ 1 r 31 ( ω ) ] [ 1 r 12 ( ω ) ] cos θ [ 1 + r 31 ( ω ) ] [ 1 + r 12 ( ω ) ] } 2 ,
r 12 ( ω ) = r 31 ( ω ) R 1 2 ( ω ) exp [ i φ ( ω ) ] { r 31 ( ω ) R 1 2 ( ω ) exp [ i φ ( ω ) 1 ] } exp [ i 2 w 1 ( ω ) d ] .
R ( ν ) = β 2 A M ( ν ) 2 ,
( C ( 0 ) C ( 1 ) C ( M ) C ( 1 ) C ( 0 ) C ( 1 M ) C ( M ) C ( M 1 ) C ( 0 ) ) ( 1 a 1 a M ) = ( β 2 0 0 ) ,
C ( t ) = 0 1 R ( ν ) exp ( i 2 π t ν ) d ν .
r ( ν ) = β exp [ i φ ( ν ) ] A M ( ν ) = β exp [ i { φ ( ν ) ψ ( ν ) } ] A M ( ν ) exp [ i ψ ( ν ) ] = β exp [ i ϕ ( ν ) ] [ A M ( ν ) ] * ,
ϕ ̂ ( ν ) = B 0 + B 1 ν + + B L ν L = l = 0 L B l ν l .
R ( ν ) R ( ν ; K ) = { R ( ω 1 ) ; 0 ν < K 2 K + 1 R ( ω ) ; K 2 K + 1 ν K + 1 2 K + 1 R ( ω 2 ) ; K + 1 2 K + 1 ν < 1 } ,
ϵ eff ( ω ) ϵ h ( ω ) ϵ eff ( ω ) + 2 ϵ h ( ω ) = f i ϵ i ( ω ) ϵ h ( ω ) ϵ i ( ω ) + 2 ϵ h ( ω ) ,
ϵ i ( ω ) = ϵ + m ω p m 2 ω 0 m 2 ω 2 i Γ m ω .
n 3 2 ( ω ) = 1 + 266.387 256.237 ω 2 + 17.804 76.811 ω 2 + 0.0150 0.0148 ω 2 .

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