The broadband surface plasmon wave excitation using dispersion engineering

High sensitivity of surface-plasmon-based sensors stems from the fact that the surface plasmon is a resonance phenomenon. The resonance results from the phase-matching condition when the phase velocity of the surface plasmon wave and of the lateral component of the incident light become equal. We show that this condition can be satisfied simultaneously for many wavelengths. We demonstrate numerically and experimentally that this allows a surface plasmon resonance that extends over a broad wavelength range. We consider two methods of excitation of such broadband surface plasmon resonance: (i) patterning the interface where the surface plasmon propagates and (ii) broadband coupling through dispersion compensation. We demonstrate extremely broadband surface plasmon excitation at the Au-water or Au-air interface that extends through the whole near-infrared range from λ = 1 μm to 3 μm. We show how this broadband surface plasmon can be used for sensitive spectroscopic sensing, in particular for monitoring wetting/dewetting processes such as thin liquid film growth. © 2015 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (250.5403) Plasmonics; (300.6340) Spectroscopy, infrared; (230.2035) Dispersion compensation devices References and links 1. J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 462–493 (2008). 2. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008). 3. K. Johansen, H. Arwin, I. Lundström, and B. Liedberg, “Imaging surface plasmon resonance sensor based on multiple wavelengths: Sensitivity considerations,” Rev. Sci. Instrum. 71, 3530–3538 (2000). 4. S. Boussaad, J. Pean, and N. J. 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Introduction
A surface plasmon polariton is an electromagnetic wave propagating along a metal-dielectric interface.It is very sensitive to the optical properties of the dielectric medium in the close vicinity of the interface.This high sensitivity prompted development of chemical and bio-sensors based on surface plasmons [1,2].Conventional surface plasmon sensors measure optical reflectivity from the dielectric medium (analyte) in contact with the metal-coated prism under the condition of attenuated total reflection.When the incident angle or wavelength are varied, the optical reflectivity exhibits a minimum associated with the surface plasmon excitation.The position and the depth of this minimum are directly related to the optical properties of the analyte [3].It is widely believed that to achieve high sensitivity, the reflectivity minimum should be as narrow as possible [4][5][6].This belief is based on the vast experience of the sensing community with geometric resonances whose width is determined by absorption and scattering losses.However, surface plasmon resonance is not a geometric resonance, but results from a phase matching condition.The width of this resonance in the frequency domain is determined by the dispersion of the dielectric permittivity of the analyte rather than by losses.In this work we explore such unconventional broadband surface plasmon resonance and analyze the possibilities it offers for chemical and bio-sensing.
The broadband surface plasmon has been also discussed in the context of plasmonic circuitry elements such as modulators and antennas [7,8].Several excitation schemes have been suggested including aperiodic gratings etched on the metal [9], subwavelength slits [10], waveguides [11] or semiconductors at the frequencies above plasma edge [12].These coupling structures were designed using extensive numerical simulations and optimization [13][14][15], they are mostly aimed for the visible range and the maximum bandwidth achieved is 30-40%.In this work we aim at the infrared and near-infrared range and spectroscopic applications.We demonstrate here numerically and experimentally an extremely broad surface plasmon resonance that covers more than one octave frequency band.We achieve this using dispersion engineering.We also develop an intuitive approach that can be helpful for designing broadband surface plasmon couplers.

Broadband surface plasmon excitation
Consider a surface plasmon wave excited at the interface between a metal-coated highrefractive index prism and a lower refractive index analyte (the Kretschmann configuration).The surface plasmon wavevector is where ε d and ε m are dielectric permittivities of the analyte and of the metal, respectively.The excitation occurs when the projection of the incident light wavevector, k 0 = ω c n p sin θ , matches the surface plasmon wavevector, k 0 = k SP .Here, θ is the incident angle and n p = √ ε p is the refractive index of the prism.Equation 1 yields This relation defines θ , the incident angle for the surface plasmon excitation.The frequency dependence of θ results only from the dispersion of the dielectric permittivities, ε d (ω), ε m (ω), and ε p (ω).Since frequency does not appear explicitly in Eq. ( 2), this equation can be approximately satisfied in a broad frequency range, provided dispersions of ε d (ω), ε m (ω), and ε p (ω) compensate one another.Indeed, Fig. 1 shows that the resonance condition given by Eq. (2) corresponds to the intersection between the light line and the surface plasmon dispersion curve.The latter is convex; the light line can be also convex, its curvature arising from the prism dispersion.If the curvatures of these two lines match at the intersection point, the surface plasmon resonance can be excited in a broad frequency range.Alternatively, since the surface plasmon dispersion line is smeared due to absorption, effectively, it has some thickness.The whole spectral region, where the distance between the surface plasmon dispersion line and the light line is less than this thickness, corresponds to the broadband surface plasmon.
Figure 1 shows two ways to obtain broadband surface plasmon excitation: (1) anomalous dispersion achieved by the patterning of the metal or dielectric layer (dispersion compensation); and (2) clever use of the dispersion of the dielectric permittivity of the prism (broadband coupling).In what follows we analyse these two ways in detail.

Modifying light line curvature
Narrow SP Broadband SP k ω Fig. 1.Excitation frequency of the surface plasmon wave corresponds to the intersection of the surface plasmon dispersion line (green curve) with the light line (black curve).When these two curves significantly overlap, the broadband surface plasmon is excited.This can be achieved by engineering the surface plasmon dispersion (left panel) or light line curvature (right panel).

Broadband surface plasmon excitation by anomalous dispersion
To get intuition of the frequency dependence of the dielectric permittivity of the analyte ε d that allows the broadband surface plasmon excitation, we recast Eq. ( 2) assuming that the dielectric permittivity of metal is described by the Drude-Lorentz model [3], where ω p is the plasma frequency, τ is the relaxation time, and ε b + iε b is the bound electrons' contribution.Since in the optical and infrared range ωτ >> 1, the dominant term in Eq. ( 3) is the real part of the permittivity, We substitute this expression into Eq.( 2) and find Temporarily, we neglect frequency dependence of ε p .If the frequency dependence of ε d (ω) matches the frequency dependence of the right-hand side of Eq. ( 4), then the surface plasmon resonance is very broad.Since θ , the incident angle of the surface plasmon excitation, is close to the critical angle, Since ω < ω p , the denominator in Eq. ( 4) is negative, the right-hand side of Eq. ( 4) decreases with ω.To match this frequency dependence, ε d (ω) shall exhibit anomalous dispersion.
Figure 2 shows how frequency dependence of ε d (ω) affects the surface plasmon dispersion curve.In the absence of dispersion of ε d (Fig. 2(a)) the surface plasmon dispersion curve is bent to the right and crosses the light line in one point.This corresponds to the narrow-band surface plasmon.If ε d (ω) exhibits normal dispersion (Fig. 2(b)), the surface plasmon dispersion curve strongly bends to the right and the resulting surface plasmon is narrower.Anomalous dispersion of ε d (Fig. 2(c)) bends the surface plasmon dispersion curve to the left and allows it to overlap with the light line over a large spectral range.This corresponds to the broadband surface plasmon.To the right of the broadband surface plasmon (for larger incident angles), the surface plasmon dispersion curve crosses the light line in two points.This corresponds to two narrow band surface plasmons [16].

A broadband surface plasmon via patterning of the metal-dielectric interface
We have shown that in order to achieve broadband surface plasmon, the material covering the metal shall have anomalous dispersion.The natural materials with anomalous dispersion are lossy, hence we looked for the structural dispersion.It is well-known that the effective anomalous dispersion in the composite structures can be achieved by patterning the conducting layer [17][18][19].In particular, Refs.[20,21] demonstrated broadband absorbers based on plasmonic resonance and patterned conducting overlayer.Ref. [22] showed that anomalous dispersion can be achieved at the edge of the bandgap which naturally appears in the periodic array of conducting strips.Anomalous dispersion is especially pronounced for wide bandgap.Ref. [22] showed that the band gap in such structure can be widened due to the interaction with the bulk modes of the gratings.We used these considerations as guidelines for our design.
We considered metal-metal or dielectric-metal structure where the top layer is patterned and explored this configuration numerically using COMSOL software.Figure 3 sign: an Au-coated ZnS prism on top of which lies a grating of elliptical cross-section.The whole assembly is immersed in water.Figure 3(b) shows reflectivity from this setup for an Au grating.Note two bandgaps at 6000-6200 cm −1 and at 8000-8500 cm −1 .These bandgaps deform the surface plasmon dispersion curve in such a way that it approaches the light line (vertical direction).Due to the very low refractive index of Au, the bulk modes inside the grating are shifted to low frequencies and interact with the plasmonic modes.This results in the red shift of the second bandgap [22], in such a way that the surface plasmon dispersion line there is almost vertical.Therefore, by resorting to patterned conducting layers one can achieve surface plasmon excitation in the extended wavelength range around the bandgaps.Figure 3(c) shows simulated optical reflectivity from the similar configuration, where the grating is made of a high-refractive index dielectric.As expected, the location of the first bandgap is the same as in Fig. 3(b) because the periods of both gratings are identical.However, the deformation of the surface plasmon dispersion curve is insignificant making this configuration less favorable for broadband surface plasmon excitation.

A broadband surface plasmon using a low refractive index dielectric overlayer
Thin dielectric overlayers are frequently used to enhance sensitivity of the surface plasmon sensors and to protect the metal-coated sensor surface [23,24].In what follows we show that the dielectric overlayer can strongly modify the surface plasmon dispersion.Consider a layered analyte whose dielectric permittivity varies in the direction perpendicular to the layers.The effective refractive index sensed by the surface plasmon wave is a weighted average of the refractive indices of the layers, where Fig. 4. Surface plasmon propagation in a dielectric bilayer.The surface plasmon wave propagates along the conducting surface coated with a thin dielectric layer with refractive index n 1 which is immersed in another dielectric (analyte) with the refractive index n 2 .At short wavelengths (blue curve) the surface plasmon wave is confined within the dielectric coating and the effective refractive index corresponds to n 1 .At long wavelengths (red curve) the surface plasmon penetrates deep into the analyte and the effective refractive index corresponds to n 2 .For n 1 < n 2 the effective refractive index, as sensed by the surface plasmon wave, exhibits anomalous dispersion.
bly is immersed in the analyte with refractive index n 2 .Since the surface plasmon penetration depth δ is frequency-dependent (see Eq. ( 5)) then n e f f also depends on frequency, even in the absence of material dispersion.Indeed, at high frequency the penetration depth is small, δ < d.Therefore, the surface plasmon is confined within dielectric coating.Then n e f f ∼ n 1 .On the other hand, the penetration depth at low frequencies is big, δ > d.The surface plasmon is confined mostly in the analyte, in such a way that n e f f ∼ n 2 .When one goes from high to low frequencies, n e f f varies from n 1 to n 2 .This structural dispersion is not accompanied by losses.The case n 1 < n 2 corresponds to anomalous dispersion and the case n 1 > n 2 corresponds to normal dispersion.Figure 5 demonstrates the effect of dielectric coating of different thickness on the surface plasmon dispersion curve.In the absence of coating this curve is bent to the right.Figure 5(a) shows that for a low refractive index coating i.e., n 1 < n 2 , the surface plasmon dispersion curve becomes progressively bent to the left and this curvature increases with increasing thickness of the coating.This means that at certain thickness the inherent right curvature of the surface plasmon dispersion curve is compensated by the effect of coating.At coating thickness of 150 -200nm the surface plasmon dispersion line becomes almost vertical and overlaps significantly with the light line.This results in the broadband surface plasmon.Figure 5(b) shows that for a high refractive index coating i.e., n 1 > n 2 , the surface plasmon dispersion curve becomes progressively bent to the right and this curvature increases with increasing thickness of the coating.This curve crosses the light line only in one point and this corresponds to the narrow band surface plasmon.
We infer from this that a simple bilayer consisting of two non-dispersive dielectrics exhibits dispersion when it is probed by the surface plasmon wave.This consideration provides an intuitive explanation for the enhanced sensitivity of surface plasmon sensors with a dielectric overlayer [23,24].

Broadband coupling to the surface plasmon wave
We analyze now the broadband surface plasmon excitation in the standard Kretschmann configuration based on a metal-coated prism.Equation 2 indicates that the prism dispersion, ε p (ω), partially compensates for dispersion of the dielectric permittivities of the metal and of the analyte, ε m (ω) and ε d (ω).Prism dispersion has been used in the past for dispersion compensation in the context of lasers [25,26], for excitation of several narrow-band surface plasmons at the same incident angle [16], and for the measurement of the plasma edge in semiconductors [12].Assume for simplicity that the analyte is air, ε d ≈ 1. Figure 6 shows that if ε p has negligible dispersion, the surface plasmon dispersion curve is bent to the right due to the Drude term in the dielectric permittivity of metal (Eq.( 3)).On the other hand, if the dispersion of ε p is high enough, the surface plasmon curve is bent to the left.This bending allows a reasonably wide range for the broadband plasmon excitation.Moreover, prism dispersion affects also the angle of incidence.While for a hemispherical prism, the incident angle at the prism/metal/dielectric interface is the same for all frequencies, for a triangular prism it depends on frequency due to refraction at the front surface of the prism.Figure 6(c) shows that this is also favorable for the broadband surface plasmon excitation.

The broadband surface plasmon in air
We demonstrate here broadband surface plasmon excitation in air using Kretschmann configuration and a dispersive prism (Fig. 6(c)).Figure 7 shows our experimental setup.The Bruker FTIR spectrometer serves as a broadband light source.The collimated p-polarized infrared beam passes through the Au-coated right-angle sapphire prism attached to the chamber with a liquid or gaseous analyte.The intensity of the reflected beam, I(ν), is measured by the liquidnitrogen cooled MCT detector.To take into account that the detector sensitivity and the intensity of the incoming beam both depend on wavenumber, we measured I 0 (ν), the intensity of the reflected beam from a known analyte (background measurement).The reflectivity of the analyte under study was found from the following expression: R analyte (ν) = I analyte (ν) I 0 (ν) R 0 (ν), where I analyte (ν) is the intensity of the reflected beam and R 0 is the numerically calculated reflectivity of the analyte that was used as a background.I 0 (ν) and I analyte were both measured at the same incident angle and for the same polarization.The analyte for the background measurement was    We measured reflectivity from the water-filled chamber (background) then from the dry empty chamber for different incident angles and found the angle corresponding to the broadest reflectivity minimum, as shown in Fig. 8.The peak at 3000 cm −1 corresponds to the total internal reflection, while the reflectivity minimum, corresponding to the surface plasmon resonance, extends from 3600 cm −1 to at least 10000 cm −1 .In other words, it covers the whole near-infrared range and extends into the visible range.In comparison to Ref. [28] who achieved very precise dispersion compensation in the narrow wavelength range from 664 to 676 nm us-ing diffraction gratings, we achieved less precise but more broadband dispersion compensation, from 1 to 3 µm.The minimal reflectivity is 0.04 and it can be made even lower by fine-tuning the Au film thickness.In the context of broadband absorber applications, the minimal reflectivity is related to absorber efficiency.
Numerical calculations based on Fresnel formulae and Eq.(3) fit our measurements fairly well.To model optical properties of our ultrathin gold film used a Drude-Lorentz model with adjustable parameters rather than a more accurate model [29] for bulk gold since it is wellknown that optical properties of ultrathin gold films can considerably differ from the bulk values due to structural imperfections.

Broadband surface plasmon spectroscopy for monitoring thin film growth
The importance of thin liquid film wetting and adhesion behavior for technology can hardly be overestimated [31].The initial stages of condensation on substrate include nanometer and tens of nanometer-thick liquid films.Such thin films can hardly be seen in conventional microscopes, therefore they were studied by other tools such as by scanning tunneling microscopy (STM) [32,33], ellipsometry [34], and infrared spectroscopy [35].While STM is perfect for static measurements, it is not well suited for monitoring fast dynamics.On the other hand, the optical techniques can monitor fast dynamics but can not easily distinguish between continuous and discontinuous films, or smooth films and film with drops.Recently, Ref. [36] used surface plasmon resonance in the visible range and showed that measurements at more than one wavelength can distinguish between discontinuous and continuous films.We develop this approach further and claim that the broadband surface plasmon is beneficial for monitoring the dynamics of thin liquid films, continuous and discontinuous.This is related to the fact that the probe depth of the surface plasmon wave strongly depends on frequency [3].For the broadband surface plasmon resonance shown in Fig. 8, the probe depth in air increases from 0.25 µm at λ = 1 µm to 2.5 µm at λ = 3 µm.This means that the high-frequency wing of the surface plasmon resonance is more sensitive to thin films, while its low-frequency wing is more sensitive to bulk analyte.Figure 9 shows calculated reflectivity spectra for two analytes: a hypothetical dispersionless analyte whose refractive index is close to unity, and for a thin water film.The reflectivity at low frequencies is more sensitive to the bulk refractive index while the reflectivity at high frequencies is more sensitive to thin film formation, the difference in reflectivity being directly related to the refractive index and thickness of the film.In principle, by observing reflectivity changes in a broad frequency range one can distinguish between thin film formation and bulk refractive index changes.Such discrimination is a common problem in surface plasmon biosensing applications [1,37].is increased and the peak corresponding to the total internal reflection shifts from 3132 cm −1 to 3320 cm −1 .The blue line shows reflectivity from a 5 nm thick water film on Au.
The reflectivity above 7000 cm −1 is increased but the total internal reflection peak does not shift.
The most obvious practical implementation of the broadband surface plasmon spectroscopy is to use the broadband source and to scan the incident angle, as it was done, for example, in Ref. [38].However, this sequential approach is less suitable for the measurement of dynamic processes, such as thin film condensation/evaporation.In what follows we demonstrate how broadband surface plasmon excitation shown in Fig. 8 can be used to monitor kinetics of the water and ethanol condensation on the Au-coated sapphire in real time.To this end we tuned the incident angle of the infrared radiation in our setup (Fig. 7) to achieve a broad surface plasmon resonance in air.Then we introduced a small amount of liquid to the bottom of the flow chamber and closed all ducts.While the liquid evaporates, the vapor pressure in the closed chamber increases and a thin liquid film condenses on the vertical surface of the Au-coated sapphire prism [32,33].This film affects the conditions of the surface plasmon propagation that is translated into changes in the reflectivity spectrum.We measured the reflectivity spectrum continuously every 20 sec.The reflectivity reaches saturation after 20-30 minutes, although occasionally, it undergoes big spontaneous fluctuations.We attribute these fluctuations to liquid drops that form spontaneously on the vertical surface of the prism and then flow down.When the reflectivity reached saturation we evacuated the liquid, flushed the chamber with air, and repeated the experiment.Usually, the results of the first run differed from subsequent runs, as if the Au surface were passivated by the first exposure to the liquid [39].
Figures 10(a) and 10(b) show evolution of the reflectivity spectrum for water and for ethanol, respectively.The spectra change dramatically due to thin film condensation on Au.We tried to simulate the spectra assuming a liquid film with uniform thickness.Figure 11 shows a simulation for water, the calculated spectra for ethanol are very similar.Although the measured (Fig. 10) and simulated (Fig. 11) spectra look similar, they do differ.This difference may indicate that the liquid film is inhomogeneous and coexists with drops [34].In principle, surface plasmon scattering in such inhomogeneous film with drops can be calculated following the guidelines of Refs.[40], but this is beyond the scope of our present study.Here, we limited ourselves to fitting only the high-frequency wing of each measured curve, assuming a continuous liquid film with uniform thickness d(t).The insets to the Figs.10(a) and 10(b) show how this effective thickness grows with time.We find a saturation thickness of 13.7 nm at maximum humidity at ambient temperature.Thin water films on Au with similar thickness were observed previously using scanning tunneling microscopy [32,33].

Discussion and Conclusions
We demonstrate broadband surface plasmon excitation in air across the near-infrared wavelength range from 1 to 3 µm.Following the set of approaches discussed above, we believe that the broadband surface plasmon can extend to the visible range and to the mid-infrared range as well.This can be useful for the construction of broadband absorbers of infrared radiation [20,21].The broadband surface plasmon in air presents an interesting possibility of exciting a short surface plasmon pulse [41].Field enhancement associated with such surface plasmon pulse could be beneficial for lasing.Another possible application can be surface plasmon spectroscopy in solvent.
In summary, we have considered the broadband surface plasmon excitation in the Kretschmann configuration and demonstrated the following.
• Anomalous dispersion is beneficial for the broadband surface plasmon excitation.This can be achieved by fabrication of a photonic structure on top of metal or by introducing a thin dielectric film with a low dielectric constant.
• The broadband surface plasmon can be achieved by the dispersive prism coupler.We demonstrate a surface plasmon in air across the wavelength range 1-3 µm.
• The broadband surface plasmon spectroscopy is useful for the study of thin film growth, in particular, for distinguishing between continuous and discontinuous films.

Fig. 2 .
Fig. 2. Numerical simulation of the reflectivity from the ZnS/Au/dielectric trilayer as a function of wavenumber and incident angle.The Au film thickness is 18 nm.The deep blue regions indicate reflectivity minimum corresponding to the surface plasmon resonance.(a) Dielectric with negligible dispersion.Due to dispersion of dielectric permittivity of metal, ε m , the surface plasmon dispersion curve is slightly bent to the right with respect to the vertical direction (light line).(b) Dielectric with normal dispersion.The surface plasmon dispersion line is strongly bent to the right.(c) Dielectric with anomalous dispersion.The surface plasmon dispersion curve is bent to the left.The blue region between 5700 cm −1 and 7500 cm −1 is almost vertical i.e., strongly overlaps with the light line.This corresponds to the broadband surface plasmon.

Fig. 3 .
Fig. 3. (a) Numerical simulation of the surface plasmon excitation in the Kretschmann's configuration with the patterned metal-dielectric interface.We consider a ZnS/Au/ grating/water multilayer where on top of a 20 nm thick Au film lies a 40 nm thick grating of the elliptic cross-section, 0.6 µm period, and 0.3 duty cycle.(b) Au grating.(c) Dielectric grating, n = 3.The first band gap appears at the same wavenumber ν =6300 cm −1 for both grating, while the second bandgap for the Au grating shifted down to 8500 cm −1 with respect to its dielectric counterpart.

Fig. 5 .
Fig. 5. Thin dielectric overlayer strongly affects the surface plasmon dispersion.(a) Optical reflectivity as a function of incident angle and of the wavenumber for a ZnS/Au/dielectric trilayer immersed in water.The refractive index of the dielectric overlayer is low, n 1 = 1.2 < n water .Upon increasing layer thickness d the surface plasmon dispersion curve (blue) progressively bends to the left and for d =300-400 nm it is almost vertical.This is the optimal layer thickness for the broadband surface plasmon excitation.(b) Optical reflectivity as a function of incident angle and the wavenumber for a ZnS/Au/dielectric overlayer/water.The refractive index of the dielectric overlayer is high, n 1 = 1.6 > n water .Upon increasing layer thickness the surface plasmon dispersion curve (blue) progressively bends to the right, as if it were probing the analyte with strong normal dispersion.

Fig. 6 .
Fig. 6.A broadband surface plasmon in the Kretschmann configuration.Numerical calculation of the optical reflectivity.(a) Spherical Au-coated non-dispersive prism with n p = 1.7.The blue region, corresponding to the surface plasmon resonance, is bent to the right due to frequency-dependent Drude term in the dielectric permittivity of Au.(b) Hemispherical dispersive Au-coated sapphire prism.The blue region is bent to the left since prism dispersion partially compensates for Au dispersion.(c) Right-angle sapphire prism with the same Au coating.The broadband light beam enters the prism and diverges upon refraction at the flat prism surface, in such a way that the incident angle θ (ω) at the metal/analyte interface is frequency-dependent.The blue region is strongly bent to the left.The region with the vertical slope (4000 cm −1 -7000 cm −1 ) corresponds to the broadband surface plasmon and appears at α = 16.8 − 17 0 .The parameters of the simulation are taken from Ref. [27], namely, δ θ = 0.8 o , d Au =18 nm, ω p = 1.32 × 10 16 rad/sec.,τ = 6.23 × 10 −15 sec., ε b = 9.57, ε b = 2.51.

Fig. 7 .
Fig.7.Experimental setup.The collimated and polarized broadband infrared beam from the FTIR spectrometer impinges on the right-angle Au-coated sapphire prism.The reflectivity spectrum is measured by the liquid nitrogen-cooled MCT detector.A flow-chamber is tightly attached to the prism and can be evacuated or filled with desired analyte liquid using fine ducts.The background measurements were performed with chamber filled with distilled water.

Fig. 9 .
Fig.9.Calculated optical reflectivity from two analytes under condition of the broadband surface plasmon resonance.The red line indicates reflectivity of the Au-coated sapphire prism exposed to air (ε d = 1.00056).The green line shows reflectivity from the hypothetical dispersionless analyte with ε d = 1.008.In comparison to air, reflectivity above 7000 cm −1 is increased and the peak corresponding to the total internal reflection shifts from 3132 cm −1 to 3320 cm −1 .The blue line shows reflectivity from a 5 nm thick water film on Au.The reflectivity above 7000 cm −1 is increased but the total internal reflection peak does not shift.

Fig. 10 .
Fig. 10.Evolution of the reflectivity spectra after inserting liquid to the closed flow chamber.(a) Water.(b) Ethanol.The reflectivity grows with time, especially at high frequencies, indicating thin film formation on the Au-coated sapphire prism.The inset shows film thickness versus time.The solid lines stay for the exponential fit, d = d 0 (1 − e − t τ ), where d 0 =13.8 nm, τ = 4.3 min for water and d 0 =37 nm, τ = 1.5 min for ethanol.

Fig. 11 .
Fig. 11.Numerical calculation of the reflectivity from the Au-coated sapphire prism covered with a thin water film, under conditions of the broadband surface plasmon resonance.Film thickness is indicated at each curve.