Abstract

In order to carry out precise measurements of the thickness of a dielectric layer deposited on a metal surface, we have introduced an ellipsometric measurement technique (EMT) to the modified Otto’s configuration (MOC) that is used for observing surface plasmon resonance (SPR). For that purpose, we have measured the thickness of the Au layer by the EMT at four different locations on an elliptic fringe pattern obtained from the MOC basing on a four-layer structure model: prism (BK7)-air-Au-substrate (BK7). Then, we have measured that of a TiO2 layer deposited on the Au layer by the EMT basing on a five-layer structure model: prism (BK7)-air-TiO2-Au-substrate (BK7). We have found experimentally that the combination of EMT and MOC is effective for measuring the thickness of the dielectric layer on the metal.

© 2010 Optical Society of America

1. Introduction

Recently, we have measured the wavelength dependency of the refractive index of a metal by using a modified Otto’s configuration[1] (MOC) for observing surface plasmon resonance (SPR), which was proposed by Bliokh and his coworkers[2]. The SPR is an electric excitation and also decays away exponentially from the metal-dielectric interface into both media, while propagates along the surface of the metal with a wave vector kx given by kx=k0εmεdεm+εd , where εm = εr + εi is the complex dielectric constant of the metal, εr and εi are its real and imaginary part, respectively, and εd(= 1.0) the dielectric constant of the dielectric medium (air)[2]. When the parallel component of the wave vector of the incident light to the interface becomes equal to kx, SPR is induced for εr < −εd (= −1.0) and Re{kx} > k 0[1, 2, 3].

In the MOC, a plane of a planoconvex singlet lens was optically contacted to the hypotenuse of a right-angled prism, and its convex sphere surface was made to contact to the plainer airmetal interface at one point. In this geometry, the thickness d of the air gap is automatically varied in a radial direction with using no mechanical moving parts for fixed values of the incident angle θ and the wavelength λ. When a condition for SPR is satisfied, the energy reflectance Rp of the p-polarized light is decreased largely and then the reflectance dip appears due to frustrated internal reflection occurred at a prism-air interface. This is explained by tunneling photons from the base of the prism to the metal through the dielectric barrier of the air:[3] Evanescent waves generated below the prism decay away exponentially from the interface and couple with surface plasmon-polaritons localized on the surface of the metal.

The SPR reflectance dip forms a two-dimensional circular fringe pattern in the MOC. When observing it, the circular pattern becomes an elliptical-fringe shape because of θ ≠ 0°. The radius r of the long axis of the ellipse gives the thickness d of the air gap by d = r 2/2R, where R is the radius of curvature of the planoconvex lens. Then we were able to estimate the complex dielectric index of the metal by comparing with the reference values calculated numerically. The optical configuration proposed by Otto[4] has an advantage over that by Kretschman[5] that is usually employed for a sensor purpose because it is applicable to measuring bulk samples as well as thin films. However, the thickness of the air gap d should be controlled precisely and accurately. One of the solutions for this technical difficulty was to use the simple imaging geometry proposed by Bliokh et.al.

Concerning the SPR, we have proposed an idea of introducing an ellipsometric measurement technique (EMT) to the Kretchmann’s configuration in the previous paper[6]. Through some numerical simulations, we demonstrated that the imaginary part of the refractive index of the absorptive sample deposited on the metal could be obtained with high sensitivity and precision. Therefore, by combining the EMT and the MOC, we can expect to construct a high-sensitive measurement system. This is a motivation and the purpose of the present study.

For that purpose, we have incorporated a rotating-analyzer-type ellipsometer to the MOC system for measuring the thickness of the dielectric layer. First, we have measured the thickness of the Au layer at four different locations on the elliptic fringe pattern basing on a four-layer model: prism (BK7)/air/Au/substrate (BK7). Next, we have measured the thickness of a TiO2 layer deposited on the Au layer basing on a five-layer model: prism (BK7)/air/TiO2/Au/substrate (BK7). In the present article, we describe the measurement system and demonstrate the effectiveness of the proposed technique through experimental results.

2. Experimental setup

Figure 1 shows a schematic diagram of the optical system. We used a 632.8nm-He-Ne laser (type 05-LHP-141, 5.0 mW, Melles Griot) as a light source. Through a beam expander (LBE-10; × 10, Sigma Koki) and a Glam-Thomson polarizer (GTPC-08-20AN, Sigma Koki), the p-polarized light was incident on a hypotenuse of a right-angled glass prism (BK7) with an angle of θ. Under the prism, a plane of a planoconvex singlet lens (SLB-30-500P; f = 500 mm; BK7, Sigma Koki) was optically contacted to it using an index matching oil (150CST, Nikon), and its convex sphere surface was made to contact to the plainer air-metal interface at one point. Then the thickness d of the air gap was automatically varied spatially. For the energy-reflectance Rp-measurements, the fringe pattern due to SPR was focused on a CCD detector (type CS5207B; 720 × 480 pixels with a pixel size 8.4µm × 9.8µm, Tokyo Denshi Kogyo) by a camera lens (f = 35 mm, Nikon). For the ellipsometric measurements at four locations on the fringe pattern, a combination of a pinhole (ϕ = 0.1mm) that works as a spatial filter and a silicon photodiode detector (type 818-UV/CM, Newport) was used. Then we varied the direction of the transmission axis of a Glam-Thomson analyzer (GTPC-08–20AN, Sigma Koki) with a stepwise manner. The stepping angle of the rotation of the analyzer was fixed at 5:0° and 100 signal accumulations were carried out for individual data acquisition.

 

Fig. 1. Schematic diagram of the optical setup of the rotating-analyzer ellipsometer (RAE) using a modified Otto’s configuration (MOC).

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3. Optical models for numerical simulation

Figure 2 shows two optical models used for numerical simulations and actual measurements: (a) a four-layer structure: prism (BK7)-air-Au-substrate (BK7) and (b) a five-layer structure: prism (BK7)-air-TiO2-Au-substrate (BK7). For the four-layer structure, an Au layer of a thickness d 1 was deposited on the BK7-glass substrate. For the five-layer structure, a TiO2 layer of thickness d 2 was deposited on the Au layer. A complex refractive index of Au at λ = 632.8nm is n1˜=0.172+3.440i and refractive indices of BK7 and TiO2 at λ = 632.8nm are np˜=1.515 and n2˜=2.490 , respectively. When preparing the two samples, we could not obtain accurate values of their thicknesses but approximate ones: d 1 ≅ 50nm and d 2 ≅ 150nm. These values will be determined accurately through the following experiments.

4. Experimental results and discussions

4.1. Measurement results for the four-layer model

Figure 3(a) shows the fringe pattern actually obtained from the sample with the four-layer structure, where θ = 43.7°±0.05°. Figures 3(b) and 3(c) shows cross-sectional Rp-profiles along lines X-X’ and Y-Y’ in Fig. 3(a), respectively. From four minima of the two Rp-profiles, we obtained the thickness d of the air layer at four different locations on the fringe pattern: d = 449∓40nm. A solid line shows a numerically-fitted curve for the measured Rp-profile. Then, we estimated the thickness d 1 of the Au layer at the four locations: d 1 = 54.0∓3.0nm.

 

Fig. 2. Two optical models used for numerical simulations and actual measurements: (a) a four-layer model (prism (BK7)-air-Au-substrate (BK7)) and (b) a five-layer model (prism (BK7)-air-TiO2-Au-substrate (BK7)).

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Fig. 3. (a) A measurement result of the fringe pattern obtained from a sample with the fourlayer structure, where θ = 43.7°±0.05°, (b) a cross-sectional Rp-profile along a line X-X’ in (a), and (c) that along a line Y-Y’ in (a). A solid line shows a theoretically fitted curve for each Rp-profile shown by a dotted line.

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Figures 4(a)–4(d) are plots of intensities as a function of the angle of the transmission axis of the analyzer of the rotating-analyzer type ellipsometer (RAE) at the four locations (A, B, C, and D) on the fringe pattern shown in Fig. 3(a) and individual fitted curves. Dotted and solid lines in Figs. 4(e)–4(h) show corresponding states of polarization ellipses of the reflected light and numerically-fitted ones, respectively, where (Δ,Ψ) = (63.66°±6.0°, 16.61°±3.2°) for the point A, (62.85°±5.8°, 16.31°±3.2°) for B, (63.34°±4.0°, 16.49°±3.2°) for C, and (62.86°±6.0°, 16.25° ±3.2°) for D. The thickness d 1 of the Au layer estimated from the EMT for the four locations were d 1 = 54.0∓1.0 nm for the point A, 53.8∓1.0 nm for B, 54.1∓1.0 nm for C, and 53.7∓1.0 nm for D. An averaged value of d 1fs is 54.0 nm. From these measurement results, we found that the EMT gave the same d 1-values as the conventional Rp-method within the error 0.3 nm at the four different locations.

 

Fig. 4. (a)-(d) Measurement results at locations (A)-(D) on the fringe pattern shown in Fig. 3(a) by using the RAE: plots of intensities as a function of the angle of the transmission axis of the analyzer. (e)-(h) Corresponding states of polarization ellipses of the reflected light (dotted lines) and numerically fitted ones (solid line).

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In order to demonstrate that the EMT is superior to the conventional Rp-measurement technique in sensitivity, we show one of the calculation results. Figure 5 shows two plots of squared sum of residuals between the experimentally obtained and the numerically fitted data as a function of the thickness of the Au layer, which were used in Fig. 3(c) and Fig. 4(d) for determining the thickness of the Au layer as 54.0 nm and 53.7 nm, respectively. Before making the plot, we set the number of sampled points to be equal for both and normalized the ordinate scales of the two experimentally obtained data. The steepness of the slope of the plot around the minimum point for the EMT, in comparison with that for he Rp-technique, indicates the superiority of the EMT in sensitivity for measuring the thickness of the Au layer.

 

Fig. 5. Two plots of squared sum of residuals between the experimentally obtained data and the numerically fitted ones as a function of the thickness of the Au layer, which were used in the conventional Rp-measurement in Fig. 3(c) and in the EMT in Fig. 4(d) for determining the thickness of the Au layer 54.0 nm and 53.7 nm, respectively.

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4.2. Measurement results for the five-layer model

Figure 6(a) shows the fringe pattern obtained from the sample with the five-layer structure, where θ = 46.45°±0.05°. Figures 6(b) and 6(c) shows cross-sectional Rp-profiles along lines X-X’ and Y-Y’ in Fig. 6(a), respectively. From four minima of the two Rp-profiles, we obtained the thickness d of the air layer at four different locations on the fringe: d = 306∓10 nm for a point A, 220∓11 nm for B, 304∓12 nm for C, and 306∓12 nm for D. A solid line shows a numerically fitted curve for the measured Rp-profile, where we put the thickness of the Au layer d1¯=54.0nm that was obtained in the previous section. Then, we estimated the thickness d 2 of the TiO2 layer at the four locations: d 2 = 149.5±1.1 nm for the point A, 148.7±1.2 nm for B, 149.4±1:2 nm for C, and 149.5±1.0 nm for D. We found that the thickness d 2 of the TiO2 layer varied slightly along the fringe pattern.

Figures 7(a)–7(d) are plots of intensities as a function of the angle of the transmission axis of the analyzer of the RAE at the four locations A-D on the fringe pattern shown in Fig. 6(a), respectively. Dotted and solid lines in Figs. 7(e)–7(h) show corresponding states of polarization ellipses of the reflected light and numerically-fitted ones, respectively, where (Δ,Ψ) = (−1.85°∓0.05°, 0.274°∓0.01°) for the point A, (−1.81°∓0.02°, 0.526°∓0.01°) for B, (−1.38°∓0.01°, 0.238°∓0.02°) for C, and (−1.40°∓0.01°, 0.218°∓0.02°) for D. The thickness d 2 of the TiO2 layer and that d of the air layer of estimated from the EMT for the four locations were d = 238±1 nm and d 2 = 149.6±0.2 nm for the point A, d = 210± nm and d 2 = 147.9±0.3 nm for B, d =305±1 nm and d 2 =149.4±0.2 nm for C, and d =308±2 nm and d 2 =149.5±1.0 nm for D. From these results, we found that the shape and direction of each ellipse were clearly distinguished with respect to each other. The distorted fringe pattern shown in Fig. 6(a) might be due to the spatial variation of the thickness of the TiO2 layer and which is sensitively dependent on the value of d 2. The EMT enables us to measure the thicknesses of TiO2 layer d 2 at the four different locations, which is somewhat difficult to obtain by the conventional Rp-measurement technique.

 

Fig. 6. (a) A measurement result of the fringe pattern obtained from a sample with the five-layer structure, where θ = 46.45°±0.05°, (b) a cross-sectional Rp-profile along a line X-X’ in (a), and (c) that along a line Y-Y’ in (a). A solid line shows a theoretically fitted curve for each Rp-profile shown by a dotted line, where we put the thickness of the Au layer d1¯=54.0nm .

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Because the absolute value of the real part of the refractive index of the TiO2 layer at the wavelength 632.8 nm is larger than that of the Au layer, a sort of an optical-waveguide mode might be generated in the TiO2 layer in the MOC. For the case of the conventional Kretchmann configuration, such a mode is known as a leaky mode[7, 8, 9]. For the case of the MOC, the same mode might be generated. In order to make it clear, we are going to calculate electric field strength of each layer by solving the Maxwellfs electromagnetic equations under the given boundary condition[10, 11, 12].

5. Conclusions

We have proposed a combined use of the EMT and the MOC for observing SPR for precise measurement of a thickness of a dielectric layer deposited on a metal surface. Because it is well-known that SPR is sensitive to various parameters such as the wavelength, incident angle, complex dielectric constants of individual layers, and other geometric parameters, enhancement in sensitivity and precision brought about by EMT is quite reasonable. This is because information on polarization of light is newly added to them. In EMT, we can obtain both phase and amplitude information on the reflected light by a common-optical-path polarization-sensitive interferometer. The amount of information obtainable from the EMT is larger than that from the conventional intensity-measurement technique. In addition, precision in phase measurements itself is usually higher than that of the conventional one. These are the reasons why the ellipsometric measurements are more precise than usual ones based on a measurement of reflected wave intensity. We have demonstrated actually that the thickness of a TiO2 layer on the Au layer can be obtained with precision. The proposed scheme should be applicable to a general-purpose SPR sensor for measuring complex refractive indexes of dielectric layers deposited on the metal surface.

 

Fig. 7. (a)-(d) Measurement results at points (A)-(D) on the fringe dip shown in Fig. 5(a) by using the RAE: plots of intensities as a function of the angle of the transmission axis of the analyzer. (e)-(h) Corresponding states of polarization ellipses of the reflected light (dotted lines) and numerically fitted ones (solid line).

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Acknowledgements

This work was supported in part by a Grant-in-Aid for Scientific Research (B) No. 21300167 from Japan Society for the Promotion of Science (JSPS).We wish to acknowledge Mr. Y.Wada, Mr. T. Wada, and Mr. K. Nishigaki for their experimental works.

References and links

1. T. Iwata and G. Komoda,“Measurements of complex refractive indices of metals at several wavelengths by frustrated total internal reflection due to surface plasmon resonance,” Appl. Opt. 47, 2386–2391 (2008). [CrossRef]   [PubMed]  

2. Y. 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]  

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. 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]  

7. M. Osterfeld and H. Franke, “Optical gas detection using metal film enhanced leaky mode spectroscopy,” Appl. Phys. Lett. 62, 2310–2312 (1993). [CrossRef]  

8. L. Levesque, B. E. Paton, and S. H. Payne, “Precise thickness and refractive index determination of polymide films using attenuated total reflection,” Appl. Opt. 33, 8036–8040 (1994). [CrossRef]   [PubMed]  

9. L. Levesque and B. E. Paton, “Detection of defects in multiple-layer structures by using surface plasmon resonance,” Appl. Opt. 36, 7199–75203 (1997). [CrossRef]  

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

11. M. Fukui and K. Matsugi, “Attenuated total reflection mode of surface polaritons in semi-infinite and finitesuperlattices,” J. Phys. Soc. Jpn. 56, 2964–2976 (1987). [CrossRef]  

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

References

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  1. T. Iwata and G. Komoda,“Measurements of complex refractive indices of metals at several wavelengths by frustrated total internal reflection due to surface plasmon resonance,” Appl. Opt. 47, 2386-2391 (2008).
    [CrossRef] [PubMed]
  2. Y. 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]
  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 Oberfl¨achenplasmaschwingungen, Z. Phys. 241, 313-324 (1971).
    [CrossRef]
  6. 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]
  7. M. Osterfeld and H. Franke, “Optical gas detection using metal film enhanced leaky mode spectroscopy, Appl. Phys. Lett. 62, 2310-2312 (1993).
    [CrossRef]
  8. L. Levesque, B. E. Paton, and S. H. Payne, “Precise thickness and refractive index determination of polymide films using attenuated total reflection, Appl. Opt. 33, 8036-8040 (1994).
    [CrossRef] [PubMed]
  9. L. Levesque and B. E. Paton, “Detection of defects in multiple-layer structures by using surface plasmon resonance, Appl. Opt. 36, 7199-75203 (1997).
    [CrossRef]
  10. F. Yang, J. R. Sambeles, and G. W. Bradberry, “Long-range surface modes supported by thin films, Phys. Rev. B 44, 5855-5872 (1991).
    [CrossRef]
  11. M. Fukui and K. Matsugi, “Attenuated total reflection mode of surface polaritons in semi-infinite and finite superlattices, J. Phys. Soc. Jpn. 56, 2964-2976 (1987).
    [CrossRef]
  12. M. Takabayashi, H. Shiba, M. Haraguchi, and M. Fukui, “Studies on surface polaritons in ultrathin films sandwitched by identical dielectrics, J. Phys. Soc. Jpn. 61, 2550-2556 (1992).
    [CrossRef]

2008 (1)

2007 (1)

2006 (1)

Y. 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]

1997 (1)

1994 (1)

1993 (1)

M. Osterfeld and H. Franke, “Optical gas detection using metal film enhanced leaky mode spectroscopy, Appl. Phys. Lett. 62, 2310-2312 (1993).
[CrossRef]

1992 (1)

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

1991 (1)

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

1987 (1)

M. Fukui and K. Matsugi, “Attenuated total reflection mode of surface polaritons in semi-infinite and finite superlattices, J. Phys. Soc. Jpn. 56, 2964-2976 (1987).
[CrossRef]

1971 (1)

E. Z. Kretschmann, “Die Bestimmung Optischer Konstanten von Mettlen duch Anregung von Oberfl¨achenplasmaschwingungen, 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]

Bliokh, Y. P.

Y. 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]

Bradberry, G. W.

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

Felsteiner, J.

Y. 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]

Franke, H.

M. Osterfeld and H. Franke, “Optical gas detection using metal film enhanced leaky mode spectroscopy, Appl. Phys. Lett. 62, 2310-2312 (1993).
[CrossRef]

Fukui, M.

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

M. Fukui and K. Matsugi, “Attenuated total reflection mode of surface polaritons in semi-infinite and finite superlattices, J. Phys. Soc. Jpn. 56, 2964-2976 (1987).
[CrossRef]

Haraguchi, M.

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

Iwata, T.

Komoda, G.

Kretschmann, E. Z.

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

Levesque, L.

Lipson, S. G.

Y. 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]

Maeda, S.

Matsugi, K.

M. Fukui and K. Matsugi, “Attenuated total reflection mode of surface polaritons in semi-infinite and finite superlattices, J. Phys. Soc. Jpn. 56, 2964-2976 (1987).
[CrossRef]

Osterfeld, M.

M. Osterfeld and H. Franke, “Optical gas detection using metal film enhanced leaky mode spectroscopy, Appl. Phys. Lett. 62, 2310-2312 (1993).
[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]

Paton, B. E.

Payne, S. H.

Sambeles, J. R.

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

Shiba, H.

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

Takabayashi, M.

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

Vander, R.

Y. 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]

Yang, F.

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

Appl. Opt. (4)

Appl. Phys. Lett. (2)

Y. 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]

M. Osterfeld and H. Franke, “Optical gas detection using metal film enhanced leaky mode spectroscopy, Appl. Phys. Lett. 62, 2310-2312 (1993).
[CrossRef]

J. Phys. Soc. Jpn. (2)

M. Fukui and K. Matsugi, “Attenuated total reflection mode of surface polaritons in semi-infinite and finite superlattices, J. Phys. Soc. Jpn. 56, 2964-2976 (1987).
[CrossRef]

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

Phys. Rev. B (1)

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

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 Oberfl¨achenplasmaschwingungen, Z. Phys. 241, 313-324 (1971).
[CrossRef]

Other (1)

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

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagram of the optical setup of the rotating-analyzer ellipsometer (RAE) using a modified Otto’s configuration (MOC).

Fig. 2.
Fig. 2.

Two optical models used for numerical simulations and actual measurements: (a) a four-layer model (prism (BK7)-air-Au-substrate (BK7)) and (b) a five-layer model (prism (BK7)-air-TiO2-Au-substrate (BK7)).

Fig. 3.
Fig. 3.

(a) A measurement result of the fringe pattern obtained from a sample with the fourlayer structure, where θ = 43.7°±0.05°, (b) a cross-sectional Rp -profile along a line X-X’ in (a), and (c) that along a line Y-Y’ in (a). A solid line shows a theoretically fitted curve for each Rp -profile shown by a dotted line.

Fig. 4.
Fig. 4.

(a)-(d) Measurement results at locations (A)-(D) on the fringe pattern shown in Fig. 3(a) by using the RAE: plots of intensities as a function of the angle of the transmission axis of the analyzer. (e)-(h) Corresponding states of polarization ellipses of the reflected light (dotted lines) and numerically fitted ones (solid line).

Fig. 5.
Fig. 5.

Two plots of squared sum of residuals between the experimentally obtained data and the numerically fitted ones as a function of the thickness of the Au layer, which were used in the conventional Rp -measurement in Fig. 3(c) and in the EMT in Fig. 4(d) for determining the thickness of the Au layer 54.0 nm and 53.7 nm, respectively.

Fig. 6.
Fig. 6.

(a) A measurement result of the fringe pattern obtained from a sample with the five-layer structure, where θ = 46.45°±0.05°, (b) a cross-sectional Rp -profile along a line X-X’ in (a), and (c) that along a line Y-Y’ in (a). A solid line shows a theoretically fitted curve for each Rp -profile shown by a dotted line, where we put the thickness of the Au layer d 1 ¯ = 54.0 nm .

Fig. 7.
Fig. 7.

(a)-(d) Measurement results at points (A)-(D) on the fringe dip shown in Fig. 5(a) by using the RAE: plots of intensities as a function of the angle of the transmission axis of the analyzer. (e)-(h) Corresponding states of polarization ellipses of the reflected light (dotted lines) and numerically fitted ones (solid line).

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