Abstract

By employing a modified Otto’s configuration for measuring surface plasmon resonance that has been proposed by Bliokh and his coworkers [Appl. Phys. Lett. 89, 021908 (2006)] we have obtained complex refractive indices of metals at several wavelengths. We demonstrate that the configuration has high potential for obtaining dispersion relations of metal conductors in bulk samples as well as in thin films from the visible to the near-infrared wavelength region. Furthermore, we show that the configuration enables us to obtain the complex refractive indices of metals or a thickness or refractive index of a dielectric layer on the metal at different points simultaneously. We have constructed a measurement system and carried out basic experiments. The experimental results agreed well with numerically simulated values or published ones.

© 2008 Optical Society of America

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References

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  1. Yu. P. Bliokh, R. Vander, S. G. Lipson, and J. Felsteiner, “Visualization of the complex refractive index of a conductor by frustrated total internal reflection,” Appl. Phys. Lett. 89, 021908 (2006).
    [CrossRef]
  2. W. Lukosz and H. Wahlen, “Total absorption of p-polarized light by surface plasma waves,” Opt. Lett. 3, 88-90 (1978).
    [CrossRef] [PubMed]
  3. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, 1988).
  4. A. Otto, “Excitation of nonradiative surface waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398-410 (1968).
    [CrossRef]
  5. E. Z. Kretschmann, “Die Bestimmung Optischer Konstanten von Mettlen duch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313-324 (1971).
    [CrossRef]
  6. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Willey-VCH Verlag, 2004).
  7. K. Yamamoto, A. Masui, and H. Ishida, “Kramers-Kronig analysis of infrared reflection spectra with perpendicular polarization,” Appl. Opt. 33, 6285-6293 (1994).
    [CrossRef] [PubMed]
  8. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1989).
  9. http//www.sigma-koki.com/index.html.
  10. E. D. Patrik, ed., Handbook of Optical Constants of Solids, (Academic, 1985).
  11. C. M. Herzinger, B. Johs, W. A. McGahan, and J. A. Woolam, “Ellipsometric determination of optical constant for silicon and thermally grown silicon dioxide via a multi-stage, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323-3336 (1998).
    [CrossRef]
  12. G. E. Jellison, Jr., L. A. Boatner, J. D. Budai, B.-S. Jeong, and D. P. Norton, “Spectroscopic ellipsometry of thin film and bulk anatasee (TiO2),” J. Appl. Phys. 93, 9357-9541 (2003).
    [CrossRef]
  13. H. Kano and W. Knoll, “Locally excited surface-plasmom-polaritons for thickness measurement of LBK films,” Opt. Commun. 153, 235-239 (1998).
    [CrossRef]
  14. H. Kano and W. Knoll, “A scanning microscope employing localized surface-plasmon-polaritons as a sensing probe,” Opt. Commun. 182, 11-15 (2000).
    [CrossRef]
  15. R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter , 13, 1811 (2001).
    [CrossRef]
  16. T. Iwata and S. Maeda, “Simulation of an absorption-based surface-plasmon resonance sensor by means of ellipsometry,” Appl. Opt. 46, 1575-1582 (2007).
    [CrossRef] [PubMed]

2007 (1)

2006 (1)

Yu. P. Bliokh, R. Vander, S. G. Lipson, and J. Felsteiner, “Visualization of the complex refractive index of a conductor by frustrated total internal reflection,” Appl. Phys. Lett. 89, 021908 (2006).
[CrossRef]

2004 (1)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Willey-VCH Verlag, 2004).

2003 (1)

G. E. Jellison, Jr., L. A. Boatner, J. D. Budai, B.-S. Jeong, and D. P. Norton, “Spectroscopic ellipsometry of thin film and bulk anatasee (TiO2),” J. Appl. Phys. 93, 9357-9541 (2003).
[CrossRef]

2001 (1)

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter , 13, 1811 (2001).
[CrossRef]

2000 (1)

H. Kano and W. Knoll, “A scanning microscope employing localized surface-plasmon-polaritons as a sensing probe,” Opt. Commun. 182, 11-15 (2000).
[CrossRef]

1998 (2)

H. Kano and W. Knoll, “Locally excited surface-plasmom-polaritons for thickness measurement of LBK films,” Opt. Commun. 153, 235-239 (1998).
[CrossRef]

C. M. Herzinger, B. Johs, W. A. McGahan, and J. A. Woolam, “Ellipsometric determination of optical constant for silicon and thermally grown silicon dioxide via a multi-stage, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

1994 (1)

1989 (1)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1989).

1988 (1)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, 1988).

1985 (1)

E. D. Patrik, ed., Handbook of Optical Constants of Solids, (Academic, 1985).

1978 (1)

1971 (1)

E. Z. Kretschmann, “Die Bestimmung Optischer Konstanten von Mettlen duch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313-324 (1971).
[CrossRef]

1968 (1)

A. Otto, “Excitation of nonradiative surface waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398-410 (1968).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1989).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1989).

Bliokh, Yu. P.

Yu. P. Bliokh, R. Vander, S. G. Lipson, and J. Felsteiner, “Visualization of the complex refractive index of a conductor by frustrated total internal reflection,” Appl. Phys. Lett. 89, 021908 (2006).
[CrossRef]

Boatner, L. A.

G. E. Jellison, Jr., L. A. Boatner, J. D. Budai, B.-S. Jeong, and D. P. Norton, “Spectroscopic ellipsometry of thin film and bulk anatasee (TiO2),” J. Appl. Phys. 93, 9357-9541 (2003).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Willey-VCH Verlag, 2004).

Budai, J. D.

G. E. Jellison, Jr., L. A. Boatner, J. D. Budai, B.-S. Jeong, and D. P. Norton, “Spectroscopic ellipsometry of thin film and bulk anatasee (TiO2),” J. Appl. Phys. 93, 9357-9541 (2003).
[CrossRef]

Felsteiner, J.

Yu. P. Bliokh, R. Vander, S. G. Lipson, and J. Felsteiner, “Visualization of the complex refractive index of a conductor by frustrated total internal reflection,” Appl. Phys. Lett. 89, 021908 (2006).
[CrossRef]

Herzinger, C. M.

C. M. Herzinger, B. Johs, W. A. McGahan, and J. A. Woolam, “Ellipsometric determination of optical constant for silicon and thermally grown silicon dioxide via a multi-stage, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Willey-VCH Verlag, 2004).

Ishida, H.

Iwata, T.

Jellison, G. E.

G. E. Jellison, Jr., L. A. Boatner, J. D. Budai, B.-S. Jeong, and D. P. Norton, “Spectroscopic ellipsometry of thin film and bulk anatasee (TiO2),” J. Appl. Phys. 93, 9357-9541 (2003).
[CrossRef]

Jeong, B.-S.

G. E. Jellison, Jr., L. A. Boatner, J. D. Budai, B.-S. Jeong, and D. P. Norton, “Spectroscopic ellipsometry of thin film and bulk anatasee (TiO2),” J. Appl. Phys. 93, 9357-9541 (2003).
[CrossRef]

Johs, B.

C. M. Herzinger, B. Johs, W. A. McGahan, and J. A. Woolam, “Ellipsometric determination of optical constant for silicon and thermally grown silicon dioxide via a multi-stage, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Kano, H.

H. Kano and W. Knoll, “A scanning microscope employing localized surface-plasmon-polaritons as a sensing probe,” Opt. Commun. 182, 11-15 (2000).
[CrossRef]

H. Kano and W. Knoll, “Locally excited surface-plasmom-polaritons for thickness measurement of LBK films,” Opt. Commun. 153, 235-239 (1998).
[CrossRef]

Knoll, W.

H. Kano and W. Knoll, “A scanning microscope employing localized surface-plasmon-polaritons as a sensing probe,” Opt. Commun. 182, 11-15 (2000).
[CrossRef]

H. Kano and W. Knoll, “Locally excited surface-plasmom-polaritons for thickness measurement of LBK films,” Opt. Commun. 153, 235-239 (1998).
[CrossRef]

Kretschmann, E. Z.

E. Z. Kretschmann, “Die Bestimmung Optischer Konstanten von Mettlen duch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313-324 (1971).
[CrossRef]

Lipson, S. G.

Yu. P. Bliokh, R. Vander, S. G. Lipson, and J. Felsteiner, “Visualization of the complex refractive index of a conductor by frustrated total internal reflection,” Appl. Phys. Lett. 89, 021908 (2006).
[CrossRef]

Lukosz, W.

Maeda, S.

Masui, A.

McGahan, W. A.

C. M. Herzinger, B. Johs, W. A. McGahan, and J. A. Woolam, “Ellipsometric determination of optical constant for silicon and thermally grown silicon dioxide via a multi-stage, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Norton, D. P.

G. E. Jellison, Jr., L. A. Boatner, J. D. Budai, B.-S. Jeong, and D. P. Norton, “Spectroscopic ellipsometry of thin film and bulk anatasee (TiO2),” J. Appl. Phys. 93, 9357-9541 (2003).
[CrossRef]

Otto, A.

A. Otto, “Excitation of nonradiative surface waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398-410 (1968).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, 1988).

Ruppin, R.

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter , 13, 1811 (2001).
[CrossRef]

Vander, R.

Yu. P. Bliokh, R. Vander, S. G. Lipson, and J. Felsteiner, “Visualization of the complex refractive index of a conductor by frustrated total internal reflection,” Appl. Phys. Lett. 89, 021908 (2006).
[CrossRef]

Wahlen, H.

Woolam, J. A.

C. M. Herzinger, B. Johs, W. A. McGahan, and J. A. Woolam, “Ellipsometric determination of optical constant for silicon and thermally grown silicon dioxide via a multi-stage, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Yamamoto, K.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Yu. P. Bliokh, R. Vander, S. G. Lipson, and J. Felsteiner, “Visualization of the complex refractive index of a conductor by frustrated total internal reflection,” Appl. Phys. Lett. 89, 021908 (2006).
[CrossRef]

J. Appl. Phys. (2)

C. M. Herzinger, B. Johs, W. A. McGahan, and J. A. Woolam, “Ellipsometric determination of optical constant for silicon and thermally grown silicon dioxide via a multi-stage, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

G. E. Jellison, Jr., L. A. Boatner, J. D. Budai, B.-S. Jeong, and D. P. Norton, “Spectroscopic ellipsometry of thin film and bulk anatasee (TiO2),” J. Appl. Phys. 93, 9357-9541 (2003).
[CrossRef]

J. Phys. Condens. Matter (1)

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter , 13, 1811 (2001).
[CrossRef]

Opt. Commun. (2)

H. Kano and W. Knoll, “Locally excited surface-plasmom-polaritons for thickness measurement of LBK films,” Opt. Commun. 153, 235-239 (1998).
[CrossRef]

H. Kano and W. Knoll, “A scanning microscope employing localized surface-plasmon-polaritons as a sensing probe,” Opt. Commun. 182, 11-15 (2000).
[CrossRef]

Opt. Lett. (1)

Z. Phys. (2)

A. Otto, “Excitation of nonradiative surface waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398-410 (1968).
[CrossRef]

E. Z. Kretschmann, “Die Bestimmung Optischer Konstanten von Mettlen duch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313-324 (1971).
[CrossRef]

Other (5)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Willey-VCH Verlag, 2004).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, 1988).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1989).

http//www.sigma-koki.com/index.html.

E. D. Patrik, ed., Handbook of Optical Constants of Solids, (Academic, 1985).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the optical setup using a modified Otto’s configuration.

Fig. 2
Fig. 2

Measurement results for an Au film with thickness 52 nm evaporated on a BK7-glass plate. (A) Elliptical fringe patterns obtained from a CCD camera for different wavelengths: (a)  λ = 532.0 nm , (b)  594.1 nm , (c)  632.8 nm , (d)  693.5 nm , and (e)  783.0 nm ; (B) reflectance profiles along YY lines on individual images. Solid curves show fitted curves with a four-layer model (prism, air, Au layer, and glass plate); and (C) numerically simulated reflectance intensity patterns as a function of the incident angle θ 1 and the wavelength λ for the corresponding estimated value of n ˜ m . A white point M in each pattern indicates the condition at which the measurement was carried out.

Fig. 3
Fig. 3

Refractive index n and extinction coefficient k of an Au layer as a function of wavelength λ, where white circles and triangles show estimated values of n and k, respectively, and black dots show literature ones. Two solid curves are polynomial fitted curves for the literature values.

Fig. 4
Fig. 4

Plots of n ( λ ) and k ( λ ) for a bulk state of Al (purity > 99.99 % ); white circles and triangles show estimated refractive indices and extinction coefficients, respectively, and black dots show literature values. Two solid curves are polynomial fitted curves for literature values.

Fig. 5
Fig. 5

Plots of n ( λ ) and k ( λ ) for Cu with a bulk state and that with two film states. The thicknesses of the films were 50 nm and 100 nm , each of which was evaporated on a 100 nm SiO 2 layer on a Si substrate. Black dots are literature values and two solid curves are polynomial fitted curves for the literature values.

Fig. 6
Fig. 6

(a) Fringe pattern measured at λ = 632.8 nm with θ 1 = 43.8 and that measured at λ = 693.5 nm with θ 1 = 43.4 for a structure of the sample shown in the same figure, (b) reflectance profile along a line XX shown in (a) for λ = 632.8 nm and that for 693.5 nm . A solid curve and a dashed curve show numerically calculated profiles for θ 1 = 43.8 and 43.1 , respectively, for λ = 632.8 nm (upper), and that for θ 1 = 43.4 and 42.8 , respectively, for λ = 693.5 nm (lower).

Equations (7)

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k x = k 0 ε m ε d ε m + ε d ,
ε r < ε d ( = 1.0 ) and Re { k x } > k 0 .
d = r 2 2 R ,
R p = | r p | 2 = | r 12 p + r 23 p exp ( i 2 β ) 1 + r 12 p r 23 p exp ( i 2 β ) | 2 ,
β = 2 π ( d λ ) ( n 2 2 n 1 2 sin 2 θ 1 ) 1 2 = 2 π d λ n 2 cos θ 2 .
r i j p = n j cos θ i n i cos θ j n j cos θ i + n i cos θ j ,
n i sin θ i = n j sin θ j .

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