Broadband surface plasmon wave excitation using dispersion engineering

Michael Chasnitsky; Michael Golosovsky; Dan Davidov

doi:10.1364/OE.23.030570

1. 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 [4–6]. 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 [13–15], 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.

2. Broadband surface plasmon excitation

Consider a surface plasmon wave excited at the interface between a metal-coated high-refractive index prism and a lower refractive index analyte (the Kretschmann configuration). The surface plasmon wavevector is

k_{S P} = \frac{ω}{c} \sqrt{\frac{ε_{d} ε_{m}}{ε_{d} + ε_{m}}}

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} = \frac{ω}{c} n_{p} \sin θ

, matches the surface plasmon wavevector, k₀ = k_SP. Here, θ is the incident angle and

n_{p} = \sqrt{ε_{p}}

is the refractive index of the prism. Equation 1 yields

\sin θ = \sqrt{\frac{ε_{d} ε_{m}}{ε_{p} (ε_{d} + ε_{m})}}

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.

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).

Download Full Size | PDF

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.

2.1. 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],

ε_{m} = 1 - \frac{ω_{p}^{2} τ^{2}}{1 + ω^{2} τ^{2}} + i \frac{ω_{p}^{2} τ}{ω (1 + ω^{2} τ^{2})} + ε_{b}^{'} + i ε_{b}^{″}

where ω_p is the plasma frequency, τ is the relaxation time, and

ε_{b}^{'} + i ε_{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,

ε_{m} \approx 1 - \frac{ω_{p}^{2}}{ω^{2}}

. We substitute this expression into Eq. (2) and find

ε_{d} \approx ε_{p} \sin^{2} θ [1 + \frac{ε_{p} \sin^{2} θ}{1 - \frac{ω_{p}^{2}}{ω^{2}} - ε_{p} \sin^{2} θ}]

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, $θ ~ θ_{c r} = \sin^{- 1} \sqrt{ε_{d} / ε_{p}}$ , then ε_p sin² θ ≈ ε_d > 1. 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].

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.

Download Full Size | PDF

2.1.1. 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 [17–19]. 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(a) shows our design: 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.

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 is shifted down to 8500 cm⁻¹ with respect to its dielectric counterpart.

Download Full Size | PDF

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.

2.1.2. 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,

n_{e f f} = \frac{1}{δ} \int_{0}^{\infty} n (z) e^{- \frac{z}{δ}} d z

where

δ = {[k_{s p}^{2} - {(\frac{ω}{c} n_{e f f})}^{2}]}^{- 1 / 2}

is the surface plasmon penetration depth. Equation 5 indicates that the dielectric layer closest to the interface has the strongest effect on n_eff.

Consider the Kretschmann configuration (Fig. 4) consisting of the metal-covered prism coated by a thin dielectric layer with thickness d and refractive index n₁. The whole assembly is immersed in the analyte with refractive index n₂. Since the surface plasmon penetration depth δ is frequency-dependent (see Eq. (5)) then n_eff 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_eff ~ n₁. 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_eff ~ n₂. When one goes from high to low frequencies, n_eff varies from n₁ to n₂. This structural dispersion is not accompanied by losses. The case n₁ < n₂ corresponds to anomalous dispersion and the case n₁ > n₂ corresponds to normal dispersion.

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 n₁ which is immersed in another dielectric (analyte) with the refractive index n₂. At short wavelengths (blue curve) the surface plasmon wave is confined within the dielectric coating and the effective refractive index corresponds to n₁. At long wavelengths (red curve) the surface plasmon penetrates deep into the analyte and the effective refractive index corresponds to n₂. For n₁ < n₂ the effective refractive index, as sensed by the surface plasmon wave, exhibits anomalous dispersion.

Download Full Size | PDF

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., n₁ < n₂, 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., n₁ > n₂, 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.

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, n₁ = 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, n₁ = 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.

Download Full Size | PDF

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].

2.2. 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.

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°. The parameters of the simulation are taken from Ref. [27], namely, δθ = 0.8°, d_Au =18 nm, ω_p = 1.32 × 10¹⁶ rad/sec., τ = 6.23 × 10⁻¹⁵ sec., $ε_{b}^{'} = 9.57, ε_{b}^{″} = 2.51$ .

Download Full Size | PDF

3. Experimental

3.1. 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 liquid-nitrogen cooled MCT detector. To take into account that the detector sensitivity and the intensity of the incoming beam both depend on wavenumber, we measured I₀(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: $R_{a n a l y t e} (v) = \frac{I_{a n a l y t e} (v)}{I_{0} (v)} R_{0} (v)$ , where I_analyte(ν) is the intensity of the reflected beam and R₀ is the numerically calculated reflectivity of the analyte that was used as a background. I₀(ν) and I_analyte were both measured at the same incident angle and for the same polarization. The analyte for the background measurement was bulk distilled water whose reflectivity spectrum is smooth.

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 the chamber filled with distilled water.

Download Full Size | PDF

We measured reflectivity from the water-filled chamber (background) and 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 using 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.

Fig. 8 A broadband surface plasmon in air. The red curve shows our measurements of the reflectivity from the sapphire/Au/air, while the black curve shows numerical simulation based on Fresnel formulae and Eq. (3). The fitting parameters are d_Au =16.5 nm, ω_p = 1.19×10¹⁶ rad/sec., τ = 2.1×10⁻¹⁵ sec., $ε_{b}^{'} = 11, ε_{b}^{″} = 16$ . The incident angle is α = 15.7° and the beam divergence is δα = 0.36°. Dielectric permittivity of sapphire was taken from Ref. [30].

Download Full Size | PDF

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 well-known that optical properties of ultrathin gold films can considerably differ from the bulk values due to structural imperfections.

3.2. 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].

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.

Download Full Size | PDF

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].

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, $d = d_{0} (1 - e^{- \frac{t}{τ}})$ , where d₀ =13.8 nm, τ = 4.3 min for water and d₀ =37 nm, τ = 1.5 min for ethanol.

Download Full Size | PDF

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.

Download Full Size | PDF

4. 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.

Acknowledgments

We are grateful to Alexander Zilbershtein for the help in experimentation and to Uriel Levy for helpful discussions. M.C. acknowledges support from the Harvey M. Krueger Family Center for Nanoscience and Nanotechnology, the Hebrew University of Jerusalem.

References and links

1. J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 462–493 (2008). [CrossRef] [PubMed]

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). [CrossRef] [PubMed]

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). [CrossRef]

4. S. Boussaad, J. Pean, and N. J. Tao, “High-resolution multiwavelength surface plasmon resonance spectroscopy for probing conformational and electronic changes in redox proteins,” Anal. Chem. 72, 222–226 (2000). [CrossRef] [PubMed]

5. K. Kurihara and K. Suzuki, “Theoretical understanding of an absorption-based surface plasmon resonance sensor based on kretchmann’s theory,” Anal. Chem. 74, 696–701 (2002). [CrossRef] [PubMed]

6. J. Hu, X. Sun, A. Agarwal, and L. C. Kimerling, “Design guidelines for optical resonator biochemical sensors,” JOSA B 26, 1032–1041 (2009). [CrossRef]

7. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]

8. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006). [CrossRef] [PubMed]

9. J.-S. Bouillard, S. Vilain, W. Dickson, G. A. Wurtz, and A. V. Zayats, “Broadband and broadangle spp antennas based on plasmonic crystals with linear chirp,” Scientific Reports 2, 829 (2012). [CrossRef] [PubMed]

10. G. Li and J. Zhang, “Ultra-broadband and efficient surface plasmon polariton launching through metallic nanoslits of subwavelength period,” Sci. Rep. 4, 5914 (2014). [PubMed]

11. J. Tian, S. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009). [CrossRef]

12. M. Cada, D. Blazek, J. Pistora, K. Postava, and P. Siroky, “Theoretical and experimental study of plasmonic effects in heavily doped gallium arsenide and indium phosphide,” Opt. Mater. Express 5, 340–352 (2015). [CrossRef]

13. F. Lopez-Tejeira, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007). [CrossRef]

14. A. Baron, E. Devaux, J.-C. Rodier, J.-P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11, 4207–4212 (2011). [CrossRef] [PubMed]

15. H. Liao, Z. Li, J. Chen, X. Zhang, S. Yue, and Q. Gong, “A submicron broadband surface-plasmon-polariton unidirectional coupler,” Sci. Rep. 3, 1918 (2013). [CrossRef] [PubMed]

16. A. Shalabney and I. Abdulhalim, “Prism dispersion effects in near-guided-wave surface plasmon resonance sensors,” Annalen der Physik 524, 680–686 (2012). [CrossRef]

17. J. B. Khurgin, “Slow light in various media: a tutorial,” Adv. Opt. Photon. 2, 287–318 (2010). [CrossRef]

18. J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

19. R. W. Boyd, “Material slow light and structural slow light: similarities and differences for nonlinear optics,” J. Opt. Soc. Am. B 28, A38–A44 (2011). [CrossRef]

20. R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009). [CrossRef]

21. K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011). [CrossRef] [PubMed]

22. F. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002). [CrossRef]

23. A. Shalabney and I. Abdulhalim, “Sensitivity-enhancement methods for surface plasmon sensors,” Laser & Photon. Rev. 5, 571–606 (2011). [CrossRef]

24. P. Bhatia and B. D. Gupta, “Surface-plasmon-resonance-based fiber-optic refractive index sensor: sensitivity enhancement,” Appl. Opt. 50, 2032–2036 (2011). [CrossRef] [PubMed]

25. F. Salin and A. Brun, “Dispersion compensation for femtosecond pulses using highindex prisms,” J. Appl. Phys. 61, 4736–4739 (1987). [CrossRef]

26. D. Kopf, G. J. Spuhler, K. J. Weingarten, and U. Keller, “Mode-locked laser cavities with a single prism for dispersion compensation,” Appl. Opt. 35, 912–915 (1996). [CrossRef] [PubMed]

27. A. Zilbershtein, M. Golosovsky, V. Lirtsman, B. Aroeti, and D. Davidov, “Quantitative surface plasmon spectroscopy: Determination of the infrared optical constants of living cells,” Vib. Spectrosc. 61, 43–49 (2012). [CrossRef]

28. W. Zong, C. Thirstrup, M. H. Sorensen, and H. C. Pedersen, “Optical biosensor with dispersion compensation,” Opt. Lett. 30, 1138–1140 (2005). [CrossRef] [PubMed]

29. P. G. Etchegoin, E. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006). [CrossRef] [PubMed]

30. I. Malitson, “Refraction and dispersion of synthetic sapphire,” J. Opt. Soc. Am. 52, 1377–1379 (1962). [CrossRef]

31. P. de Gennes, F. Brochard-Wyart, and D. Quere, Capillarity and Wetting Phenomena (Springer, 2004). [CrossRef]

32. A. Gil, J. Colchero, M. Luna, J. Gomez-Herrero, and A. M. Baro, “Adsorption of water on solid surfaces studied by scanning force microscopy,” Langmuir 16, 5086–5092 (2000). [CrossRef]

33. J. Freund, J. Halbritter, and J. Horber, “How dry are dried samples? water adsorption measured by stm,” Microsc. Res. Tech. 44, 327–338 (1999). [CrossRef] [PubMed]

34. S. Lipson, “A thickness transition in evaporating water films,” Phase Transitions 77, 677–688 (2004). [CrossRef]

35. P. Innocenzi, L. Malfatti, M. Piccinini, A. Marcelli, and D. Grosso, “Water evaporation studied by in situ time-resolved infrared spectroscopy,” J. Phys. Chem. A 113, 2745–2749 (2009). [CrossRef] [PubMed]

36. X. Li, X. Li, and C. Wang, “A new method for measuring wetness of flowing steam based on surface plasmon resonance,” Nanoscale research letters 9, 18 (2014). [CrossRef] [PubMed]

37. P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008). [CrossRef]

38. Z.-m. Qi, M. Wei, H. Matsuda, I. Honma, and H. Zhou, “Broadband surface plasmon resonance spectroscopy for determination of refractive-index dispersion of dielectric thin films,” Appl. Phys. Lett. 90, 181112 (2007). [CrossRef]

39. J. Canning, N. Tzoumis, J. K. Beattie, B. C. Gibson, and E. Ilagan, “Water on au sputtered films,” Chem. Commun. 50, 9172–9175 (2014). [CrossRef]

40. R. E. Arias and A. A. Maradudin, “Scattering of a surface plasmon polariton by a localized dielectric surface defect,” Opt. Express 21, 9734–9756 (2013). [CrossRef] [PubMed]

41. Z. L. Samson, P. Horak, K. F. MacDonald, and N. I. Zheludev, “Femtosecond surface plasmon pulse propagation,” Opt. Lett. 36, 250–252 (2011). [CrossRef] [PubMed]

Broadband surface plasmon wave excitation using dispersion engineering

Abstract

1. Introduction

2. Broadband surface plasmon excitation

2.1. Broadband surface plasmon excitation by anomalous dispersion

2.1.1. A broadband surface plasmon via patterning of the metal-dielectric interface

2.1.2. A broadband surface plasmon using a low refractive index dielectric overlayer

2.2. Broadband coupling to the surface plasmon wave

3. Experimental

3.1. The broadband surface plasmon in air

3.2. Broadband surface plasmon spectroscopy for monitoring thin film growth

4. Discussion and conclusions

Acknowledgments

References and links

Cited By

Figures (11)

Equations (5)

Optics Express