A spectroscopic refractometer based on plasmonic interferometry

The optical dielectric function $ϵ(λ)$ of a material is typically determined by measuring changes in the propagation direction (prism-based refractometers), or in the polarization or complex amplitude (ellipsometry and interferometry) of the incident light upon interaction (i.e., refraction or reflection) with the material.

For instance, prism-based refractometers (such as Abbe^1–3 or Pulfrich^4–6) use Snell's law to extract the index of refraction by finding the critical angle, or directly measuring the direction of the incident beam propagating through a prism, which is made of, in direct contact with or filled with the material of interest. Higher precision can be achieved using optical interferometers (such as Mach-Zehnder or Michelson) that determine the material refractive index by measuring shifts in the observed interference patterns.^7–13 Spectroscopic ellipsometry has also been widely used to determine the optical constants of thin films over a broad wavelength range by analyzing the polarization changes induced by specular reflection and adopting an appropriate model to describe the optical properties of the material.^14–22 

Due to the required bulky optical elements and typically large sample volumes, current methods are not easily scalable to small dimensions without sacrificing precision, wavelength span, or refractive index range.

Here, we propose and implement an alternative approach to optical refractometry that employs plasmonic interferometry^23,24—optical interferometry with surface plasmon polaritons (SPPs)—to characterize the optical properties of dielectric materials using ultra-small sample volumes.

SPPs are electromagnetic waves coupled to plasma oscillations supported by free electrons in metal films and characterized by an evanescent field amplitude that decreases exponentially away from the metal surface.^25–28 Since SPPs are highly confined at the metal surface, they can be used to “sense” the presence of adsorbed or deposited dielectric materials. This property has led to the development of surface plasmon resonance (SPR) biosensors^29–31 with unparalleled sensitivity.²⁹ However, SPR-based sensors typically rely on prisms,^32–34 metallic gratings,^35–37 or hole arrays³⁸ to resonantly couple the incident light into SPPs, using a wavelength-specific angle of incidence, which prevents broadband spectroscopic characterization of the dielectric medium. In contrast, diffractive scattering by a subwavelength-width groove etched in a metal film can generate SPPs at multiple wavelengths simultaneously and independently of the angle of incidence, thus adding spectroscopic capabilities to plasmonic interferometry.^{23,24,39–41}

In this work, we investigate plasmonic interferometry as a tool to precisely determine the optical constants of dielectric materials in a broad wavelength range. By employing an array of nanoscale slit-groove (SG) plasmonic interferometers,^42–47 we determine the relative permittivity of several dielectric materials in contact with the device surface. Plasmonic interferograms are measured by detecting SPP-mediated modulation of light transmission through the slit of several SG plasmonic interferometers, as a function of incident wavelength and slit-groove distance. At each wavelength, the measured oscillation period of the interferogram allows extraction of the SPP refractive index, from which the dielectric constant can be derived. Since the nano-groove in each plasmonic interferometer can excite SPPs at multiple frequencies simultaneously, the plasmonic refractometer allows simultaneous extraction of the material dielectric function at all wavelengths using the same, simple illumination setup, without requiring a priori knowledge of the functional dependence of the refractive index vs. incident wavelength. The proposed plasmonic refractometer offers a higher degree of system integration, while retaining the spectroscopic capability, high resolution, and wide applicability range of more conventional methods.

Figure 1(a) shows a schematic cross section of the proposed device, consisting of (i) an 80 μm-deep polydimethylsiloxane (PDMS) microfluidic channel to control the flow of dielectric materials in liquid phase, (ii) a metal film with integrated plasmonic interferometers, and (iii) a fused-silica substrate to serve as the transparent supporting layer. Figure 1(b) depicts a slit-groove plasmonic interferometer etched in a metal film with complex dielectric function $ϵm(λ)$ in direct contact with a material characterized by a dielectric function $ϵd(λ)$⁠. Upon illumination with a spatially coherent optical beam at normal incidence, the groove generates SPPs by diffractive scattering of the incident light. Following propagation toward the slit, the SPPs accrue a wavelength and material-dependent phase that can be measured by direct interference with a reference beam at the slit location. Light transmission through the slit carries information about the specific optical functions of the metal film and dielectric material supporting the SPP waves. A picture of the real device including a custom-made aluminum sample holder, as well as inlet and outlet tubing and microfluidic channel, is reported in Figure 1(c), where the active device area is made visible by white light illumination. A more detailed description of sample fabrication and experimental setup is reported in the  Appendix.

The interference between the SPP and the incident beam at the slit location can be modeled by defining a normalized transmitted intensity, $In(λ,p)$⁠, that can be obtained experimentally by normalizing the measured light intensity transmitted through the slit of an SG plasmonic interferometer (⁠$ISG$⁠) by the transmitted intensity through an individual reference slit (⁠$IS$⁠), and analytically expressed as

where β and $ϕG$ are the effective SPP scattering amplitude and phase, and $ñSPP$ is the SPP complex refractive index, given by²⁶ 

where n_SPP and κ_SPP are the real and imaginary parts of $ñSPP$⁠, and ϵ_m and ϵ_d are the complex dielectric functions of the metal and of the material in direct contact with it, respectively. Finally, $α=4πκSPP/λ$ represents the SPP absorption coefficient, which accounts for the SPP amplitude attenuation induced by propagation losses along the metal/dielectric interface. Aim of this work is to show that the wavelength-dependent dispersion of all of the parameters in Equations (1) and (2) can be extracted using plasmonic interferometry.

Figures 1(f)–1(g) show the averaged raw transmission spectra through an individual reference slit (Figure 1(d)) and through the slit of an SG plasmonic interferometer with p = 8.16 μm (Figure 1(e)), for a silver/air interface. The transmission spectrum in Figure 1(g) shows significant spectral modulation compared with the single slit case, as a result of SPP interference. Figure 2(a) presents the experimental normalized transmission spectra (⁠$In=ISG/IS$⁠) for an SG plasmonic interferometer with p = 8.16 μm for different, representative metal/dielectric interfaces, such as gold/air, silver/air, and silver/water. The normalized transmission spectra show enhancement and suppression as a function of wavelength, due to the constructive or destructive interference at the slit position between the incident beam and the SPP waves.

The solid orange curve in Figure 2(a) reports data for the gold/air interface case. For wavelengths longer than 650 nm, the normalized spectrum is similar to that obtained for silver/air, both in magnitude and peak positions. However, for wavelengths shorter than 540 nm, the normalized transmission spectrum for the gold/air interface case is constant and equal to 1. This value represents the normalized transmission of an isolated reference slit, suggesting that although the groove is able to excite SPPs, their propagation length is strongly reduced due to increased losses induced by interband transitions, occurring below 2.3 eV (i.e., ∼539 nm) for gold.⁴⁸ Therefore, the SG plasmonic interferometer behaves as an isolated slit for $λ<$ 540 nm, thus explaining the observed value of $In=1$⁠.

Since the interband transition for silver occurs at higher energies, i.e., 3.9 eV (∼318 nm),⁴⁸ the intensity oscillations are still visible down to 400 nm when silver instead of gold is used to support SPPs (black solid line, Figure 2(a)). The dashed black line in Figure 2(a) shows the normalized spectrum for the same interferometer etched in silver with p = 8.16 μm, when water is delivered on top of the device surface using the microfluidic channel. Compared with the silver/air case, a significant shift is observed in the peak positions as a result of the refractive index increase (black dashed line in Figure 2(a)). In addition, the intensity modulation becomes visible at longer wavelengths, since the SPP absorption coefficient is increased as a result of the larger dielectric function of water compared with air, which causes a stronger attenuation of the SPP amplitude for $λ<450 nm$⁠.

Figure 2(b) shows the normalized transmission spectra for an SG plasmonic interferometer with shorter arm length (p = 1.62 μm) for the three different metal/dielectric interfaces. As expected, fewer oscillations are observed as a result of the shorter interferometer arm length. Moreover, SPPs generated at the groove location can now reach the slit with reduced amplitude attenuation due to the shorter propagation distance.

Transmission spectra similar to those reported in Figure 2 were acquired for all of the interferometers fabricated on the same chip, which allows us to generate spectrally resolved interferograms, displayed in the form of color maps of normalized transmission intensity, $In(λ,p)$⁠, as a function of incident wavelength and arm length and reported in Figures 3(a)–3(c) for three different interfaces, i.e., gold/air, silver/air, and silver/water, respectively. A vertical cut in each color map corresponds to the normalized transmission spectrum for a plasmonic interferometer with a specific arm length, whereas a horizontal cut reveals the plasmonic interferogram, i.e., the normalized transmitted intensity as a function of arm length for a given incident wavelength. Alternating, oblique red and blue bands in the color maps correspond to constructive and destructive interference, respectively, whereas white color indicates $In=1$⁠, i.e., null interference between the SPP wave and the incident beam at the slit position. Figures 3(d)–3(f) show reconstructed color-mapped interferograms using Equation (1) together with the physical parameters as extracted from the fitting procedure described in the following. The reconstructed color maps were flipped vertically, thus forming mirror images of the experimental maps for easier comparison and visual inspection.

Figure 4 displays three representative plasmonic interferograms for the silver/air interface at λ = 750, 650, and 550 nm, respectively, with the symbols representing averaged intensity data from each SG plasmonic interferometer, corresponding to three different horizontal cuts in Figure 3(b). Each intensity profile at a given wavelength can be fitted using Equation (1) to determine the spatial period, i.e., $λSPP=λ/nSPP$⁠, from which $nSPP(λ)$ can be determined. The three solid curves in Figure 4 represent the nonlinear least squares fits at these three representative wavelengths. The same fitting procedure can be extended to all wavelengths, thus allowing extraction of the wavelength dependence of $nSPP$⁠, and all relevant parameters, for all metal/dielectric interfaces, with a spectral resolution of ∼0.4 nm, as determined by our experimental setup (see the  Appendix).

The best-fit values of $nSPP(λ)$ are presented in Figure 5(a) for various metal/dielectric interfaces. The lighter band around each curve indicates the 95% confidence interval as determined by propagation and statistical analysis of the experimental and fit errors. Error bars representing standard deviations are also included, generally well within the symbol size. The open symbols reported on the same graph represent reference data, calculated using the dielectric functions determined with conventional methods.^1,49–51 The results obtained with plasmonic refractometry agree well with the reference values.

By using Equation (2), together with the best-fit values of $ñSPP(λ)$ for silver/air and the tabulated $ϵair(λ)$⁠,⁵¹ we can determine the complex dielectric function of silver (i.e., $ϵsilver=ϵsilver,r+iϵsilver,i$⁠), which describes the optical properties of the specific silver film we deposited, including any possible contamination originating from film preparation and processing. $ϵsilver,r(λ)$ is shown as the black scatter plot in Figure 5(b), shadowed by a light-gray band representing the 95% confidence interval. The same procedure can be applied to the experimental results for a gold/air interface to extract the dielectric function of gold $ϵgold,r(λ)$⁠, reported in Figure 5(b) as the orange scatter plot. The open triangles represent reference data displayed on the same graph for comparison.⁴⁹ 

From the best-fit values of $nSPP(λ)$ for the various metal/liquid interfaces, reported as blue, green, and red scatter plots in Figure 5(a), and using the previously determined dielectric functions of the respective metal film $ϵm(λ)$⁠, the dielectric functions $ϵd(λ)$ of the liquids can then be extracted, as shown in Figure 5(b) for water (green), methanol (red), and ethanol (blue).

Figure 5(b) reports a summary of the extracted relative permittivity of various dielectric materials, demonstrating the potential of plasmonic interferometry as an alternative optical refractometer.

It is worth noting that although water and methanol in Figure 5(b) seem to have the same ε_r value at $λ∼$ 700 nm, closer inspection reveals that instead the two functions differ by a measurable $Δϵ=3×10−3$⁠, corresponding to a refractive index change of $Δn=1×10−3$⁠, a difference that the plasmonic refractometer can easily resolve.

The sensitivity of the proposed plasmonic refractometer can be affected by several factors. For example, at longer wavelengths, where the magnitude of $ϵm(λ)$ dominates the expression in Equation (2), the SPP refractive index becomes less sensitive to the presence of the dielectric material at the surface. However, the sensitivity of the interferometer can be improved by using longer arms, such that the product $pnSPP$ is proportionally increased, thus leading to measurable shifts in the plasmonic interferogram. From a theoretical standpoint, the detection limit of the proposed plasmonic refractometer is on par compared with SPR and other SPP-based sensing schemes.^24,41

Although we have only reported results for the real part of the dielectric function of the material in contact with the metal over a broad range of wavelengths and dielectric constant values, plasmonic interferometry is also capable of determining the imaginary part of $ϵd$⁠. Indeed, the imaginary part of the refractive index of lossy dielectrics can be extracted by fitting the exponential decay of the plasmonic interferograms envelope amplitude using Equation (1) to estimate α, i.e., the SPP absorption coefficient (provided sufficiently long interferometers are employed in order to observe a significant decrease in the interferogram envelope amplitude). From α (related to the interferogram amplitude decay) and $nSPP$ (governing the oscillation period), both the real and the imaginary parts of the material dielectric function can be calculated.

From the fitting procedure, other relevant parameters can also be determined, namely, the SPP excitation efficiency $β(λ)$ and scattering phase $ϕG(λ)$⁠, as reported in Figure 6 for different metal/dielectric interfaces. β decreases as the wavelength increases and is also affected by the materials at the interface. $ϕG$ is relatively insensitive to the presence of different materials at the metal interface, and it has a value close to π/2 over the entire spectral range. β and $ϕG$ are fundamental parameters that describe the light scattering process at the groove responsible for the SPP excitation. β and $ϕG$ can be used together with $ñSPP$ and Equation (1) to reconstruct the plasmonic interferograms at each wavelength, as well as the two-dimensional color maps, as already reported in Figures 3(d)–3(f), showing excellent agreement with the experimental color maps.

The geometry of the proposed refractometer is intrinsically planar and is amenable to integration into a relatively compact device, as shown in Figures 1(a)–1(c). The proposed system does not require prisms or other bulky optical means to couple incident light into SPPs, since the subwavelength groove acts as a broadband and localized source of SPPs in a wide wavelength range. Detection of the refractive index dispersion can be achieved by performing a simple measurement of light transmission through the slit of each interferometer, which could be also be accomplished by integrating the sensor chip onto a complementary metal-oxide-semiconductor (CMOS) photodiode array. Since the slits are identical, the transmission does not need to be corrected for the collection efficiency of the optical set-up or detector, thus greatly simplifying the data acquisition process. Another advantage of the proposed method in comparison with existing technologies is that much smaller sample volumes can be used to determine the optical properties of the material. Considering the skin depth of the excited SPPs—which for a silver/water interface varies between ∼0.1 and 0.4 μm in the 400–800 nm range—the estimated sampled volume is ∼6 nL. The sampled volume can be further reduced by employing a denser, spatially optimized array of circular (rather than linear) plasmonic interferometers.⁴⁰ 

In conclusion, we have designed, fabricated, and tested an optical refractometer consisting of a planar array of slit-groove plasmonic interferometers etched in a metal film (silver or gold) with device densities $>104/cm2$⁠. This alternative approach enables detection of the refractive index of dielectric materials over a broad wavelength range, without a-priori knowledge of the dispersion model for the dielectric function of the material. Compared with ellipsometry and other refractometric techniques, plasmonic interferometry can prove useful when ultra-small sample volumes and detection areas are required. This platform could help to generate tabulated functions for chemical analytes, biological markers, and other materials that are difficult to characterize with more conventional methods. Moreover, thanks to the intrinsic planarity of the fabrication process, and lack of bulky in-coupling optical elements to excite SPPs at multiple wavelengths simultaneously, the proposed plasmonic refractometer can be further developed into a portable spectroscopic tool.

This material was based upon work supported by the National Science Foundation under Grant No. CBET–1159255. The authors thank R. Beresford, T. Gregorkiewicz, D. Li, P. Liu, A. Zaslavsky, and R. Zia for useful discussions and suggestions.

The plasmonic refractometer was fabricated by depositing a 4 nm-thick Ti film onto a previously cleaned 1 mm-thick fused-silica slide, to serve as an adhesion layer, followed by e-beam deposition of a 300 nm-thick film of metal, gold or silver—two well-characterized noble metals that can effectively support the excitation and propagation of SPPs in the visible and near infrared range. Plasmonic interferometers were then fabricated by focused ion beam (FIB) milling, using a Ga liquid metal ion source with beam current of ∼100 pA and an accelerating voltage of 30 kV. More than 1500 plasmonic interferometers were milled consisting of slits and grooves with identical width, length, and depth (within 1% fabrication error), over an area of ∼15 mm², achieved by running a script to automatically move the FIB stage, adjusting beam focus and stigmatism at each sample location. The scanning electron microscope (SEM) and FIB systems were calibrated using a silicon test specimen with specific lengths of 1.9 μm and 10 μm from Electron Microscopy Science, and the reported interferometer arm length values were corrected accordingly. This calibration step is critical for accurate measurements of dielectric function values. Indeed, fits of the plasmonic interferograms using Equation (1) at any given wavelength λ can only determine $pnSPP$⁠. An error in p would therefore determine errors in the extracted $nSPP$⁠, affecting $ϵm$ and $ϵd$ as well.

The SG plasmonic interferometers in the array consist of a nanoslit flanked by a nanogroove with varying separation distance, as schematically shown in Figure 1(b). In addition, individual slits (Figure 1(d)) identical to that in the SG plasmonic interferometer were etched for normalization purposes. Figure 1(e) shows the SEM image of a representative SG plasmonic interferometer consisting of a 100 nm-wide, 15μm-long through slit, flanked by a 200 nm-wide, 15μm-long, and ∼20 nm-deep groove. The center-to-center distance p between the slit and the groove is defined as the arm length of the SG plasmonic interferometer, which is 8.16 μm for the specific interferometer shown in Figure 1(e). A total of five columns of 311 structures each was milled; specifically, three identical columns of SG plasmonic interferometers with p varying from 0.26 μm to 8.16 μm in steps of ∼25 nm and two columns of single slits placed on the left and right sides of the former three columns, respectively, serving as the reference for normalization of the raw transmitted intensity spectra through the slit of SG plasmonic interferometers.

To minimize the effects caused by uneven sample delivery, we designed, fabricated, and integrated a microfluidic channel made of PDMS. To improve uniformity of sample delivery and detection, we chose a channel depth (i.e., 80 μm) that is several orders of magnitude larger than the SPP skin depth in the dielectric. Moreover, thanks to the very short arm lengths (<8 μm), the sampled volume of each interferometer is relatively small (<50 μm³), thus ensuring uniform distribution of the liquid above each interferometer area.

A xenon arc lamp coupled to a microscope condenser was used to illuminate the surface of the plasmonic refractometer with a spatially coherent, normally incident light beam. The transmitted light intensity through the slit of each plasmonic interferometer was collected by a 0.6 NA, 40× objective lens, dispersed using a single-grating monochromator and then detected by a CCD camera. Finally, a customized script was used to automatically translate the optical microscope stage and acquire light transmission spectra for all the plasmonic interferometers in the array.

In order to improve the statistical significance of the experimental results and validate the proposed method, at any given value of the interferometer arm length p, the spectra of three nominally identical SG plasmonic interferometers were used to calculate a mean value at each wavelength and arm length, and the spectra of two single slits were averaged to obtain the mean reference transmission spectrum. Statistical analysis and propagation of errors were performed to extract all relevant quantities and calculate their mean values and standard deviations, leading to the 95% confidence bands reported in Figures 5 and 6.

Each color map originally consisted of 311 (number of devices) × 1340 (total number of recorded wavelengths) $≃417 000$ data points, resulting from an averaging process over five total columns of devices, for a total of more than 2 000 000 data points acquired per color map. The reported spectrally resolved interferograms show a reduced wavelength range, for a total of 170 000 points, and contain all the information needed to extract the relevant physical parameters, such as the dielectric functions of the materials under investigation.