1. Introduction

Optical biosensors are integrated devices capable of providing analytic information about a biological sample by the measurement of photons in the form of reflected or transmitted light [1–5]. Among them, surface plasmon resonance (SPR) biosensors have attracted increasing attention for label-free detection of small traces of biological and chemical markers. This approach is based on the use of surface plasmons polaritons (SPPs), which are p-polarized electromagnetic waves that can exist at the interface between a metal and a dielectric. SPR biosensors exploit the high sensitivity of SPPs to variations in the refractive index of the medium near the metal film, caused by adsorption of analyte molecules at the metal/dielectric interface [6–8].

Numerous plasmonic biosensor architectures have been proposed throughout the years, including those based on prism- and fiber-optic-based SPR configurations [9–12], long-range surface plasmon polariton (LRSPP) waveguides [13–15], localized surface plasmon resonance (LSPR) in metallic nanostructures [16,17], and extraordinary optical transmission (EOT) through subwavelength appertures [18,19], to name a few. In particular, sensor designs based on the EOT phenomenon [20–24] allow the development of biosensing platforms with collinear geometry using a standard illumination setup at normal incidence, which in turn facilitates its alignment and integration with additional optical elements [18,19]. There are several approaches that exploit the EOT phenomenon for biosensing. These include nanohole and nanoslits arrays [25–31] and interferometric architectures with a single slit [32–36] or hole [37,38] surrounded by a grating; or structures based on Mach-Zehnder interferometry [39,40]. Although these alternatives are excellent candidates as optical transducers in lab-on-a-chip systems, it is still necessary to improve their sensing performance so that they are viable for the sensing of biological samples with ultra-low analyte concentration.

In this work, we propose a novel nanoplasmonic biosensor scheme based on the interferometric excitation of multipolar plasmonic modes supported by a plasmonic nanoslit. Here, two counter-propagating SPP waves interfere at the location of the nanoslit, selectively exciting the dipolar and quadrupolar resonances of the structure depending on the phase relationship between the SPP waves. The large difference in the angular distribution radiated by the dipolar and quadrupole modes results in a large sensitivity to small phase shifts induced by analyte affecting one of the SPP waves. After evaluating the sensing performance through a finite-difference time-domain (FDTD) analysis, we estimate that the resolution can be up to one order of magnitude better than similar interferometric-based nanoplasmonic platforms, which makes it a promising candidate for the development of highly-sensitive biosensors.

2. Principle of operation

The schematic shown in Fig. 1(a) illustrates the proposed biosensor architecture. It consists of a 200 nm thick gold film on a SiO$_2$ substrate and partially covered by CYTOP, a polymer with refractive index that closely matches that of water [41]. A slit of width $w$ is milled in the gold film along the $z$-direction and a pair of gratings are designed on the top gold surface parallel to the slit at a distance $L$. The function of these gratings is to couple light incident from the top into SPP waves at the gold/CYTOP interface, and henceforth we will refer to them as in-coupling gratings. The analyte, assumed to be in an aqueous solution, is contained in the region between the slit and one of the in-coupling gratings as shown in Fig. 1(a). This region containing the analyte is referred to as the sensing arm, while that on the opposite side of the slit is referred to as the reference arm. A second pair of gratings are designed along the bottom gold surface on both sides of the slit. The function of these gratings is to tailor the angular spectrum of the light transmitted into the SiO$_2$ medium [21,42], and henceforth we will refer to them as out-coupling gratings. These gratings are of particular importance to obtain an optimum sensing performance, as the sensor operates under angular detection of light transmitted through the slit. The depth and period of the in-coupling (out-coupling) gratings are $d_1$ and $p_1$ ($d_2$ and $p_2$), respectively.

 

Fig. 1. (a) Schematic illustration of the proposed architecture: a 200 nm gold layer with a central slit of width $w$ on a SiO$_2$ substrate and bounded on the top by CYTOP and the analyte. Two SPPs coupled by gratings propagate towards the slit on the top interface. The presence of analyte on the sensing arm produces a phase difference $\Delta \phi$ between the SPPs at the aperture, resulting in a change in the transmitted light. (b) Near-field distribution of $\lvert$E$\rvert$ in the $x$-$y$ plane for a phase difference between the counter-propagating SPPs of (left) $\Delta \phi = 0$ and (right) and $\Delta \phi = \pi$. The insets show the real part of $E_x$ in the slit region. (c) Far-field angular distribution of the transmitted light without and with the out-coupling grating: $d_2=0$ (left) and $d_2= 50$ nm, $p_2= 560$ nm (right); in both cases, the top panels correspond to $\Delta \phi = 0$, and the bottom panel to $\Delta \phi = \pi$. (d) Far-field angular distribution of the transmitted light as a function of the bulk refractive index difference $\Delta n = n_\textrm {S}- n_\textrm {R}$, where $n_\textrm {S}$ and $n_\textrm {R}$ are the refractive index in the sensing and reference arms, respectively, for the case where an out-coupling grating is used. The parameters used for (b)-(d) are $\lambda = 900$ nm and $w = 360$ nm.

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As the excitation source, we consider an $x$-polarized spatially-coherent monochromatic light field propagating in the negative $y$ direction impinging onto the two in-coupling gratings. Furthermore, we assume that the slit is not directly illuminated. This could be achieved, for instance, by focusing individual beams onto each in-coupling grating. The incoming field thus excites SPP waves at the gold/CYTOP interface that propagate towards the slit along the two arms of the biosensor and interfere at the location of the slit with a phase difference, $\Delta \phi$, produced by the presence of the analyte on the sensing arm. The slit is designed to support localized surface plasmon (LSP) modes with dipolar and quadrupolar field symmetries. Such LSP modes can be preferentially excited by the SPP waves interfering at the slit if their near-field symmetry closely matches that of the slit’s LSP mode. Thus, by controlling the near-field SPP interference pattern through the phase difference, $\Delta \phi$, we can control the coupling of the incident field to each of the LSP modes of the slit. As will be shown below, this selective excitation of the LSP modes can drastically affect the angular radiation pattern of the field transmitted through the slit. Moreover, since the phase change $\Delta \phi$ is proportional to the analyte’s refractive index change, this mechanism can be exploited to achieve high sensitivity in an angular detection scheme.

To illustrate in more detail the principle of operation, we consider the case of a 360 nm wide slit and illumination at a wavelength of $\lambda$=900 nm. Figure 1(b) shows FDTD calculations of the magnitude of the near-field distribution near the slit for two phase differences, $\Delta \phi = 0$ on the left panel and $\Delta \phi = \pi$ on the right panel. The insets in each panel illustrate the real part of $E_x$ in the slit region, which is the dominant electric field component in the transmitted light. Clearly, when the two SPP waves arrive to the slit location in phase ($\Delta \phi = 0$), the produced near-field symmetry can efficiently excite the dipolar LSP mode of the slit, while the near-field symmetry produced when they arrive out of phase ($\Delta \phi = \pi$) efficiently excites the quadrupole LSP mode. The symmetry difference between the two LSP modes translates into a dramatically different far-field angular radiation pattern in transmission that can be controlled by $\Delta \phi$. This is observed in the left panel in Fig. 1(c), which shows the characteristic single-lobe and double-lobe far-field angular distributions of the dipolar and quadrupolar modes of Fig. 1(b) for $d_2 = 0$ (i.e. no out-coupling grating). To obtain optimum sensing performance and to reduce the measurement error under angular detection, it is necessary to tailor the angular distribution of the transmitted light such that the peak’s full-width at half-maximum (FWHM) is as narrow as possible [43]. This can be accomplished by optimizing the out-coupling grating parameters, $d_2$ and $p_2$. For instance, setting $d_2$ = 50 nm and $p_2$ = 560 nm with a duty cycle of 0.5, one achieves the narrowest angular width corresponding to FWHM = 4.06$^{\circ }$, as illustrated in the right panel in Fig. 1(c).

In the present case, the angular detection scheme involves relating the analyte’s refractive index change $\Delta n$ to the change in the angle of the peak far-field transmission, $\theta _p$. Throughout the text, we use $\Delta n = n_\textrm {S}- n_\textrm {R}$, where $n_\textrm {S}$ and $n_\textrm {R}$ are the refractive indices of the sensing and reference (CYTOP) arms, respectively. Furthermore, we set the arm length such that the SPPs reach the central slit with 10% of their intensities,

Figure 1(d) shows the calculated far-field transmitted through the slit as a function of $\Delta n$. One can observe the evolution of the far-field distribution from a dipolar pattern for $\Delta n =0$ (reference) to a quadrupolar pattern for $\Delta n =0.00625$. It is observed that the single peak in the far-field generated by the dipolar LSP evolves continuously into one of the far-field peaks generated by the quadrupolar LSP. This peak can therefore be tracked, and its angle labeled $\Theta _p$ taken as the measurand. For this particular design, the change of $\theta _p$ is almost linear with respect to $\Delta n$, going from $\theta _p=0^{\circ }$ to $\theta _p=-3.26^{\circ }$. However, given that the proposed architecture relies on the symmetry of the radiation pattern, it is important to study carefully the response of the structure for different slit widths and operating wavelengths to fully characterize the performance of the biosensor.

3. Sensing performance

To evaluate the performance of the proposed biosensor, we carry out FDTD simulations for various configurations of slit width ($w$), out-coupling grating parameters ($d_2$, $p_2$) and for various operating wavelengths, in order to assess well-established sensing metrics, such as the bulk and surface sensitivities and their respective figures of merit (FOM).

As illustrated in Fig. 1(d), the transmitted far-field radiation pattern evolves from a single-lobe (dipolar) to a double-lobe (quadrupolar) pattern as $\Delta n$ increases. Thus, the analyte concentration detection is performed by tracking the angular location of one of the lobe’s peaks, $\theta _p$ in the far field as a function of $\Delta n$. However, we note that such angular displacement is highly dependent on the slit’s width, $w$. This is because the transmitted far-field is highly correlated to the the near-field distribution of the dipole and quadrupole LSP modes and the efficiency with which they are excited by the interfering SPP waves. To assess the impact of the slit’s width on the biosensor performance we computed the values of $\theta _p$ as a function of $\Delta n$ for various $w$ values. The results are shown in Fig. 2(a) for $\lambda = 900$ nm, $d_2 = 50$ nm, and $p_2 = 560$ nm.

 

Fig. 2. Bulk sensing performance for $\lambda =900$ nm, $d_2 = 50$ nm, and $p_2 = 560$ nm. (a) Far-field peak angle $\theta _p$, as a function of the refractive index difference $\Delta n$ for different slit widths $w$. (b) Bulk sensitivity $S_B$ and (c) the respective figure of merit FOM$_B$ for each case. (d) Operational range and resolution for each $w$ value. The resolution is estimated as $R = m \sigma / S_B$, where $m=1,2,3$ and $\sigma = 0.0001^{\circ }$ is the noise in the setup, taken from [44].

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Consider for instance the case $w = 360$ nm in Fig. 2(a), which corresponds to the far-field evolution plotted in Fig. 1(d). For this slit width, both the dipolar and quadrupolar LSP modes are resonant at the excitation wavelength and can be excited with equal strengths provided that the interfering SPP waves at the slit have the correct symmetry. Thus, a linear transition is obtained from a dipolar to a quadrupolar far-field pattern (see Fig. 1(d)) as the symmetry of the interfering SPP waves evolve from having an even symmetry ($\Delta n=0$) to having an odd symmetry ($\Delta n = 0.00625$) at the slit. In turn, this results in a linear displacement of $\theta _p$ as a function of $\Delta n$. On the other hand, for $w = 200$ nm, only the dipolar LSP mode is resonant. Thus, the dipolar LSP mode is excited predominantly even for large values of $\Delta n$. Yet, an abrupt transition in the transmitted far field is produced for $\Delta n > 0.005$ because under those conditions the excitation of the quadrupolar LSP mode is sufficiently strong to dominate. As a results, a sudden change in $\theta _p$ is produced for $\Delta n > 0.005$.

The interesting dynamics of Fig. 2(a) are reflected in the bulk sensitivity, given by

In addition to the bulk sensitivity and its associated FOM, the sensing resolution and the operating range are also important parameters to characterize the performance of a sensing device. The operating range defines the range of values over which the analyte can be reliably measured, showing a linear dependence between the concentration and the measured parameter [45]. On the other hand, the resolution, $R$, is the minimum detectable change in the monitored parameter [46]. The latter can be calculated as

In our design, both the resolution and the operating range can be adjusted by varying the slit’s width, $w$, as shown in Fig. 2(d). Here, we have defined the operating range as the range where the sensitivity variation is smaller than 1%. We note that there is a trade-off between the resolution and the operational range. The best resolution is obtained for $w = 200$ nm, reaching values between $6.95 \times 10^{-9} \textrm { RIU}$ to $2.08 \times 10^{-8} \textrm { RIU}$ over an operating range of $2.06 \times 10^{-5}$ RIU. On the other hand, a maximum operating range of $1.04 \times 10^{-3}$ RIU is obtained for $w = 360$ nm, with a resolution ranging from $2.02 \times 10^{-7} \textrm { RIU}$ to $6.07 \times 10^{-7} \textrm { RIU}$.

A similar behavior is observed for other wavelengths. In each case, the out-coupling grating parameters $p_2$ and $d_2$ that resulted in the smallest FWHM were chosen, and they are listed in Table 1. Regarding the slit’s width, two extreme cases can be distinguished. On the one hand, the value $w$ that produces the highest sensitivity but the smallest operating range; and on the other hand, the $w$ parameter that produces the largest operating range but the least sensitivity. These cases are illustrated in Figs. 3(a) and 3(c) for bulk and in Figs. 3(b) and 3(d) for surface sensing. For the latter case, the surface sensitivity is estimated using the relation [7]

Here, we assumed the parameters $h_0 = 2.1$ nm and $h = 1.2$ nm, which are the thicknesses of a monolayer of bovine serum albumin (BSA) and anti-BSA, respectively, commonly used in experimental studies of surface sensitivity [47,48]. We note that the best performance is achieved for $\lambda = 1050$ nm. The highest sensitivities are $S_B = 1.12 \times 10^{5}$ deg/RIU and $S_S = 302$ deg/RIU, with their respective figures of merit FOM$_B = 2.51 \times 10^{4}\textrm { RIU}^{-1}$ and FOM$_S = 67.52\textrm { RIU}^{-1}$.

 

Fig. 3. Sensing performance as a function of wavelength $\lambda$ for the case of maximum sensitivity (top row) and maximum operating range (bottom row). (a) and (c) show the bulk sensitivity $S_B$ and figure of merit FOM$_B$, respectively, at each wavelength; (b) and (d) show the surface sensitivity $S_S$ and surface figure of merit FOM$_S$. $S_S$ was estimated using Eq. (1) considering an adlayer of $h_0=2.1$ nm and an analyte thickness of $h= 1.2$ nm, as shown in the inset in (b).

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Table 1. List of optimized structure parameters used in Fig. 3. In all cases, the duty cycle of the out-coupling grating is set to 0.5.

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4. Discussion

The performance results obtained above show that the proposed structure is promising for the implementation of an ultra-sensitive biosensor. Our analysis predicts that the bulk-sensing resolution could be up to an order of magnitude better than previously reported plasmonic interferometric-based biosensors [32,33,37,39,40]. The bulk sensitivity and FOM of the proposed design surpasses those achieved by approaches based on the Kretschmann configuration under angular interrogation [49–51]. An outstanding performance is predicted also for surface sensing, with a FOM$_S$ that could be up to one order of magnitude higher than previously reported results, both for localized plasmons and propagating SPPs [52,53]. The projected resolution is comparable to the performance obtained with approaches based on phase interrogation [54,55], without the need for complex optical detection systems. Additionally, our design has a smaller footprint and higher miniaturization potential than prism-based devices.

The proposed structure can be implemented using standard micro- and nanofabrication techniques. For instance, the in-coupling and out-coupling gratings can be fabricated via electron-beam lithography and etching, while focused ion-beam milling can be used to define the central slit in the gold film. The gold film can be deposited via evaporation or sputtering, and planarized via chemical-mechanical polishing [56]. The CYTOP layer can be spin-coated and cured, and optical lithography followed by a CYTOP-etching process can be used to expose the gold surface on the sensing arm [13] in order to define the sensing region. The fluidic channels that would be required to transport the analyte to the sensing region can be defined in a similar fashion, and a lid can be wafer-bonded to the structure to seal the channels [57]. In practice, however, it would be preferable to define the sensing region a few microns away from the central slit to avoid unnecessary alignment problems. Such a variation in the design is not expected to impact the results because the refractive indices of CYTOP and water are well matched, thus minimzing the effects of the CYTOP-fluid interface.

5. Conclusions

In conclusion, we proposed a novel high-sensitivity nanoplasmonic biosensor based on interferometric excitation of multipolar plasmonic modes, whereby two counter-propagating SPP waves interfering at the location of a plasmonic nanoslit, are capable of exciting selectively the dipolar and quadrupolar resonances of the structure based on the phase-shift between the SPP waves. The large difference in the angular distribution radiated by the multipolar modes results in a large angular sensitivity to small phase shift caused by analyte affecting one of the SPP waves. The bulk and surface sensing performance of the proposed structure was characterized through FDTD simulations and compared with previously reported works. We investigated the trade-off between the operating range and the resolution, which can be controlled by changing the slit’s width. In the configuration with high resolution but low operating range, the calculated sensitivities and FOM significantly outperform similar structures, with values as high as FOM$_B = 2.51 \times 10^{4}\textrm { RIU}^{-1}$ and FOM$_S = 67.52\textrm { RIU}^{-1}$. Moreover, the resolution is projected to be up to an order of magnitude better than the best plasmonic interferometric approaches and at the same level than architectures with phase detection techniques. On the other hand, the setting with large operating range exhibits a linear dependence between $\Delta n$ and the sensitivity, achieving an operating range of $10^{-3}$ RIU with a projected resolution of the order of $10^{-7}$ RIU. Our work suggest that this approach represents a promising alternative for sensing of biological samples with ultra-low concentrations, and is suitable for the development of lab-on-a-chip biosensing systems due to its miniaturization potential.