Abstract

We have measured a propagation length L of TM0 and TE0 guided waves in a lossy Si film surrounded by identical dielectrics 632.8 nm in wavelength. The propagation length LATR(E) estimated from experimental attenuated total reflection (ATR) spectra deviated largely from the propagation length LATR(T) estimated from calculated ATR spectra in the range of small optical thickness of Si film hopt. This discrepancy may arise from an angular beam spread of incident light. We have proposed a method to measure L directly. This method gave us an L for TM0 guided waves of 1.6 mm at hopt = 6.1 nm. This value is in good agreement with LATR(T) when LATR(E)=0.2mm, under certain conditions.

© 1995 Optical Society of America

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  1. F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
    [Crossref]
  2. R. J. Crook, F. Yang, and J. R. Sambles, “An investigation of p- and s-polarized long-range optical modes supported by a strongly absorbing normal uniaxial thin organic film,” J. Mod. Opt. 40, 243–253 (1993).
    [Crossref]
  3. F. Yang, J. R. Sambles, and G. W. Bradberry, “Prism coupling to long-range coupled-surface modes,” J. Mod. Opt. 38, 707–717 (1991).
    [Crossref]
  4. G. P. Bryan-Brown, F. Yang, G. W. Bradberry, and J. R. Sambles, “Prism and grating coupling to long-range coupled-surface exciton-polaritons,” J. Opt. Soc. Am. B 8, 765–769 (1991).
    [Crossref]
  5. F. Yang, G. W. Bradberry, and J. R. Sambles, “Long-range surface mode supported by very thin silver films,” Phys. Rev. Lett. 66, 2030–2032 (1991).
    [Crossref] [PubMed]
  6. Z.-C. Wu, E. T. Arakawa, T. Inagaki, and T. Thundat, “Experimental observation of a long-range surface mode in metal island films,” Phys. Rev. B 49, 7782–7785 (1994).
    [Crossref]
  7. M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Studies on surface polaritons in ultrathin films sandwiched by identical dielectrics,” J. Phys. Soc. Jpn. 61, 2550–2556 (1992).
    [Crossref]
  8. M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Surface optic waves in ultrathin films bounded by identical slightly lossy materials,” J. Phys. Soc. Jpn. 62, 2719–2724 (1993).
    [Crossref]
  9. M. Fukui, S. Tago, and K. Oda, “Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam,” J. Phys. Soc. Jpn. 55, 973–980 (1986).
    [Crossref]
  10. R. W. Alexander, R. J. Bell, and C. A. Ward, “Two prism surface electromagnetic wave spectroscopy,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, Chichester, UK, 1982), p. 201.
  11. G. N. Zhizhin, M. A. Moskalova, E. V. Shomina, and V. A. Yakovlev, “Surface electromagnetic wave propagation on metal surfaces,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), p. 93.
  12. H. Shiba, M. Haraguchi, and M. Fukui, “Propagation length of surface plasmon polaritons propagating along air-metal interface,” J. Phys. Soc. Jpn. 63, 1400–1405 (1994).
    [Crossref]

1994 (2)

Z.-C. Wu, E. T. Arakawa, T. Inagaki, and T. Thundat, “Experimental observation of a long-range surface mode in metal island films,” Phys. Rev. B 49, 7782–7785 (1994).
[Crossref]

H. Shiba, M. Haraguchi, and M. Fukui, “Propagation length of surface plasmon polaritons propagating along air-metal interface,” J. Phys. Soc. Jpn. 63, 1400–1405 (1994).
[Crossref]

1993 (2)

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Surface optic waves in ultrathin films bounded by identical slightly lossy materials,” J. Phys. Soc. Jpn. 62, 2719–2724 (1993).
[Crossref]

R. J. Crook, F. Yang, and J. R. Sambles, “An investigation of p- and s-polarized long-range optical modes supported by a strongly absorbing normal uniaxial thin organic film,” J. Mod. Opt. 40, 243–253 (1993).
[Crossref]

1992 (1)

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Studies on surface polaritons in ultrathin films sandwiched by identical dielectrics,” J. Phys. Soc. Jpn. 61, 2550–2556 (1992).
[Crossref]

1991 (4)

F. Yang, J. R. Sambles, and G. W. Bradberry, “Prism coupling to long-range coupled-surface modes,” J. Mod. Opt. 38, 707–717 (1991).
[Crossref]

G. P. Bryan-Brown, F. Yang, G. W. Bradberry, and J. R. Sambles, “Prism and grating coupling to long-range coupled-surface exciton-polaritons,” J. Opt. Soc. Am. B 8, 765–769 (1991).
[Crossref]

F. Yang, G. W. Bradberry, and J. R. Sambles, “Long-range surface mode supported by very thin silver films,” Phys. Rev. Lett. 66, 2030–2032 (1991).
[Crossref] [PubMed]

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
[Crossref]

1986 (1)

M. Fukui, S. Tago, and K. Oda, “Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam,” J. Phys. Soc. Jpn. 55, 973–980 (1986).
[Crossref]

Alexander, R. W.

R. W. Alexander, R. J. Bell, and C. A. Ward, “Two prism surface electromagnetic wave spectroscopy,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, Chichester, UK, 1982), p. 201.

Arakawa, E. T.

Z.-C. Wu, E. T. Arakawa, T. Inagaki, and T. Thundat, “Experimental observation of a long-range surface mode in metal island films,” Phys. Rev. B 49, 7782–7785 (1994).
[Crossref]

Bell, R. J.

R. W. Alexander, R. J. Bell, and C. A. Ward, “Two prism surface electromagnetic wave spectroscopy,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, Chichester, UK, 1982), p. 201.

Bradberry, G. W.

F. Yang, G. W. Bradberry, and J. R. Sambles, “Long-range surface mode supported by very thin silver films,” Phys. Rev. Lett. 66, 2030–2032 (1991).
[Crossref] [PubMed]

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
[Crossref]

F. Yang, J. R. Sambles, and G. W. Bradberry, “Prism coupling to long-range coupled-surface modes,” J. Mod. Opt. 38, 707–717 (1991).
[Crossref]

G. P. Bryan-Brown, F. Yang, G. W. Bradberry, and J. R. Sambles, “Prism and grating coupling to long-range coupled-surface exciton-polaritons,” J. Opt. Soc. Am. B 8, 765–769 (1991).
[Crossref]

Bryan-Brown, G. P.

Crook, R. J.

R. J. Crook, F. Yang, and J. R. Sambles, “An investigation of p- and s-polarized long-range optical modes supported by a strongly absorbing normal uniaxial thin organic film,” J. Mod. Opt. 40, 243–253 (1993).
[Crossref]

Fukui, M.

H. Shiba, M. Haraguchi, and M. Fukui, “Propagation length of surface plasmon polaritons propagating along air-metal interface,” J. Phys. Soc. Jpn. 63, 1400–1405 (1994).
[Crossref]

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Surface optic waves in ultrathin films bounded by identical slightly lossy materials,” J. Phys. Soc. Jpn. 62, 2719–2724 (1993).
[Crossref]

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Studies on surface polaritons in ultrathin films sandwiched by identical dielectrics,” J. Phys. Soc. Jpn. 61, 2550–2556 (1992).
[Crossref]

M. Fukui, S. Tago, and K. Oda, “Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam,” J. Phys. Soc. Jpn. 55, 973–980 (1986).
[Crossref]

Haraguchi, M.

H. Shiba, M. Haraguchi, and M. Fukui, “Propagation length of surface plasmon polaritons propagating along air-metal interface,” J. Phys. Soc. Jpn. 63, 1400–1405 (1994).
[Crossref]

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Surface optic waves in ultrathin films bounded by identical slightly lossy materials,” J. Phys. Soc. Jpn. 62, 2719–2724 (1993).
[Crossref]

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Studies on surface polaritons in ultrathin films sandwiched by identical dielectrics,” J. Phys. Soc. Jpn. 61, 2550–2556 (1992).
[Crossref]

Inagaki, T.

Z.-C. Wu, E. T. Arakawa, T. Inagaki, and T. Thundat, “Experimental observation of a long-range surface mode in metal island films,” Phys. Rev. B 49, 7782–7785 (1994).
[Crossref]

Moskalova, M. A.

G. N. Zhizhin, M. A. Moskalova, E. V. Shomina, and V. A. Yakovlev, “Surface electromagnetic wave propagation on metal surfaces,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), p. 93.

Oda, K.

M. Fukui, S. Tago, and K. Oda, “Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam,” J. Phys. Soc. Jpn. 55, 973–980 (1986).
[Crossref]

Sambles, J. R.

R. J. Crook, F. Yang, and J. R. Sambles, “An investigation of p- and s-polarized long-range optical modes supported by a strongly absorbing normal uniaxial thin organic film,” J. Mod. Opt. 40, 243–253 (1993).
[Crossref]

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
[Crossref]

F. Yang, G. W. Bradberry, and J. R. Sambles, “Long-range surface mode supported by very thin silver films,” Phys. Rev. Lett. 66, 2030–2032 (1991).
[Crossref] [PubMed]

G. P. Bryan-Brown, F. Yang, G. W. Bradberry, and J. R. Sambles, “Prism and grating coupling to long-range coupled-surface exciton-polaritons,” J. Opt. Soc. Am. B 8, 765–769 (1991).
[Crossref]

F. Yang, J. R. Sambles, and G. W. Bradberry, “Prism coupling to long-range coupled-surface modes,” J. Mod. Opt. 38, 707–717 (1991).
[Crossref]

Shiba, H.

H. Shiba, M. Haraguchi, and M. Fukui, “Propagation length of surface plasmon polaritons propagating along air-metal interface,” J. Phys. Soc. Jpn. 63, 1400–1405 (1994).
[Crossref]

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Surface optic waves in ultrathin films bounded by identical slightly lossy materials,” J. Phys. Soc. Jpn. 62, 2719–2724 (1993).
[Crossref]

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Studies on surface polaritons in ultrathin films sandwiched by identical dielectrics,” J. Phys. Soc. Jpn. 61, 2550–2556 (1992).
[Crossref]

Shomina, E. V.

G. N. Zhizhin, M. A. Moskalova, E. V. Shomina, and V. A. Yakovlev, “Surface electromagnetic wave propagation on metal surfaces,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), p. 93.

Tago, S.

M. Fukui, S. Tago, and K. Oda, “Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam,” J. Phys. Soc. Jpn. 55, 973–980 (1986).
[Crossref]

Takabayashi, M.

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Surface optic waves in ultrathin films bounded by identical slightly lossy materials,” J. Phys. Soc. Jpn. 62, 2719–2724 (1993).
[Crossref]

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Studies on surface polaritons in ultrathin films sandwiched by identical dielectrics,” J. Phys. Soc. Jpn. 61, 2550–2556 (1992).
[Crossref]

Thundat, T.

Z.-C. Wu, E. T. Arakawa, T. Inagaki, and T. Thundat, “Experimental observation of a long-range surface mode in metal island films,” Phys. Rev. B 49, 7782–7785 (1994).
[Crossref]

Ward, C. A.

R. W. Alexander, R. J. Bell, and C. A. Ward, “Two prism surface electromagnetic wave spectroscopy,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, Chichester, UK, 1982), p. 201.

Wu, Z.-C.

Z.-C. Wu, E. T. Arakawa, T. Inagaki, and T. Thundat, “Experimental observation of a long-range surface mode in metal island films,” Phys. Rev. B 49, 7782–7785 (1994).
[Crossref]

Yakovlev, V. A.

G. N. Zhizhin, M. A. Moskalova, E. V. Shomina, and V. A. Yakovlev, “Surface electromagnetic wave propagation on metal surfaces,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), p. 93.

Yang, F.

R. J. Crook, F. Yang, and J. R. Sambles, “An investigation of p- and s-polarized long-range optical modes supported by a strongly absorbing normal uniaxial thin organic film,” J. Mod. Opt. 40, 243–253 (1993).
[Crossref]

F. Yang, J. R. Sambles, and G. W. Bradberry, “Prism coupling to long-range coupled-surface modes,” J. Mod. Opt. 38, 707–717 (1991).
[Crossref]

G. P. Bryan-Brown, F. Yang, G. W. Bradberry, and J. R. Sambles, “Prism and grating coupling to long-range coupled-surface exciton-polaritons,” J. Opt. Soc. Am. B 8, 765–769 (1991).
[Crossref]

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
[Crossref]

F. Yang, G. W. Bradberry, and J. R. Sambles, “Long-range surface mode supported by very thin silver films,” Phys. Rev. Lett. 66, 2030–2032 (1991).
[Crossref] [PubMed]

Zhizhin, G. N.

G. N. Zhizhin, M. A. Moskalova, E. V. Shomina, and V. A. Yakovlev, “Surface electromagnetic wave propagation on metal surfaces,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), p. 93.

J. Mod. Opt. (2)

R. J. Crook, F. Yang, and J. R. Sambles, “An investigation of p- and s-polarized long-range optical modes supported by a strongly absorbing normal uniaxial thin organic film,” J. Mod. Opt. 40, 243–253 (1993).
[Crossref]

F. Yang, J. R. Sambles, and G. W. Bradberry, “Prism coupling to long-range coupled-surface modes,” J. Mod. Opt. 38, 707–717 (1991).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. Soc. Jpn. (4)

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Studies on surface polaritons in ultrathin films sandwiched by identical dielectrics,” J. Phys. Soc. Jpn. 61, 2550–2556 (1992).
[Crossref]

M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Surface optic waves in ultrathin films bounded by identical slightly lossy materials,” J. Phys. Soc. Jpn. 62, 2719–2724 (1993).
[Crossref]

M. Fukui, S. Tago, and K. Oda, “Characteristics of long-range surface plasmon polaritons excited by fundamental Gaussian beam,” J. Phys. Soc. Jpn. 55, 973–980 (1986).
[Crossref]

H. Shiba, M. Haraguchi, and M. Fukui, “Propagation length of surface plasmon polaritons propagating along air-metal interface,” J. Phys. Soc. Jpn. 63, 1400–1405 (1994).
[Crossref]

Phys. Rev. B (2)

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
[Crossref]

Z.-C. Wu, E. T. Arakawa, T. Inagaki, and T. Thundat, “Experimental observation of a long-range surface mode in metal island films,” Phys. Rev. B 49, 7782–7785 (1994).
[Crossref]

Phys. Rev. Lett. (1)

F. Yang, G. W. Bradberry, and J. R. Sambles, “Long-range surface mode supported by very thin silver films,” Phys. Rev. Lett. 66, 2030–2032 (1991).
[Crossref] [PubMed]

Other (2)

R. W. Alexander, R. J. Bell, and C. A. Ward, “Two prism surface electromagnetic wave spectroscopy,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, Chichester, UK, 1982), p. 201.

G. N. Zhizhin, M. A. Moskalova, E. V. Shomina, and V. A. Yakovlev, “Surface electromagnetic wave propagation on metal surfaces,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), p. 93.

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Figures (14)

Fig. 1
Fig. 1

Sample geometry for ATR experiments.

Fig. 2
Fig. 2

Experimental angular scan ATR spectra with the TM0 GW resonances for three samples. The gap thickness was adjusted such that the intensity of the ATR dips was 0.2. (i) hopt = 6.3 nm, L ATR ( E ) ( 2 ) = 167.6 μ m. (ii) hopt = 18.6 nm, L ATR ( E ) ( 2 ) = 85.7 μ m. (iii) hopt = 26.0 nm, L ATR ( E ) ( 2 ) = 28.9 μ m.

Fig. 3
Fig. 3

Experimental angular scan ATR spectra with the TM0 GW resonances for two samples. The gap thickness was adjusted such that the intensity of the ATR dips was 0.8. (ii) hopt = 18.6 nm, L ATR ( E ) ( 8 ) = 64.5 μ m. (iii) hopt = 26.0 nm, L ATR ( E ) ( 8 ) = 25.5 μ m. The resonance for case (i) in Fig. 2 could not be observed for this coupling.

Fig. 4
Fig. 4

Propagation length against the optical thickness of Si film for the TM0 GW. Filled circles, L ATR ( E ) ( 2 ); concentric circles, L ATR ( E ) ( 8 ).

Fig. 5
Fig. 5

Experimental angular scan ATR spectra with the TE0 GW resonances for one sample. The gap thickness was adjusted such that the intensity of the ATR dips was 0.2 ( L ATR ( E ) ( 2 ) ) or 0.8 ( L ATR ( E ) ( 8 ) ). (i) L ATR ( E ) ( 2 ) = 122.9 μ m. (ii) L ATR ( E ) ( 8 ) = 101.6 μ m. hopt = 4.4 nm.

Fig. 6
Fig. 6

Propagation length L ATR ( E ) ( 2 ) versus the optical thickness of Si film for the TE0 GW.

Fig. 7
Fig. 7

Experimental setup for the ellipsometric measurements.

Fig. 8
Fig. 8

Optical thickness versus the mass thickness of Si film. The filled circles are the experimental points. The solid line was evaluated by the least-squares method and is expressed by hopt = 1.397hm − 2.352 in the thickness range hm > 3 nm. Note that the relationship between hopt and hm is no longer linear when hm approaches zero.

Fig. 9
Fig. 9

Dielectric constants f versus the optical thickness of a Si film. Filled circles, the real part of f; open circles, the imaginary part of f.

Fig. 10
Fig. 10

Propagation length versus optical thickness of a Si film for the TM0 GW. Filled circles, L ATR ( E ) ( 2 ); open circles, L ATR ( T ) ( 2 ); open triangles, L estimated from Eq. (1) of Ref. 7; filled triangles, L estimated from Eq. (12) of Ref. 7; filled squares, L measured experimentally by the method proposed in Section 4 of this paper.

Fig. 11
Fig. 11

Propagation lengths L ATR ( E ) ( 8 ) and L ATR ( T ) ( 8 ) versus the optical thickness of a Si film for the TM0 GW. Filled circles, L ATR ( E ) ( 8 ) open circles, L ATR ( T ) ( 8 ).

Fig. 12
Fig. 12

Sample geometry for a direct measurement of the propagation length: (a) Side view, (b) top view.

Fig. 13
Fig. 13

Angular scan ATR spectrum for (a) the TM-polarized light and (b) the radiative emission of TM0 GW energy at the sample edge as a function of the angle of incidence. hopt = 6.1 nm.

Fig. 14
Fig. 14

Emission intensity versus sample length for the TM0 GW. ln(Id) denotes the natural logarithm of Id. (i) hopt = 6.1 nm, L = 1.6 mm. (ii) hopt = 14.5 nm, L = 138.0 μm. (iii) hopt = 25.6 nm, L = 44.6 μm.

Equations (1)

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L ATR = λ 2 π p ( sin θ p 2 - sin θ p 1 ) ,

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