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Abstract
The presence of species other than the target biomolecules in the fluidic analyte used in the refractive index biosensor based on the surface plasmon resonances (SPRs) can lead to measurement ambiguity. Using graphene-based acousto-plasmonic biosensors, we propose two methods to eliminate any possible ambiguity in interpreting the measured results. First, we take advantage of the dynamic tunability of graphene SPRs in the acousto-plasmonic biosensor with a surface acoustic wave (SAW) induced uniform grating, performing measurements at different applied voltages. Second, a single measurement employing a similar biosensor but with SAW-induced dual-segment gratings. The numerical results show the capability of both methods in decoupling the effect of the target analyte from the other species in the fluid, enabling interpreting the measurement results with no ambiguity. We also report the results of our numerical investigation on the effect of measuring parameters like the target layer effective refractive index and thickness, and the fluid effective refractive index, in addition to the controlling parameters of the proposed acousto-plasmonic biosensor, including graphene Fermi energy and electrical signaling on the sensing characteristics. Both types of proposed biosensors show promising features for developing the next generation lab-on-a-chip biosensors with minimal cross-sensitivities to non-target biomolecules.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Surface plasmons (SPs) are highly confined electromagnetic waves that can exist at a metal/dielectric interface and hence are highly sensitive to the refractive index variations of the adjacent medium. For this reason, SPs became an attractive candidate for various sensing applications [1]. For instance, in plasmonic biosensors, a minute change in the target biomolecule concentration at the vicinity of the metal/dielectric interface modulates the effective refractive index of the sensing medium. This effect alters the SPs wavevector, which in turn can be detected by the resulting shift in the peak of the plasmonic absorption spectrum [2].
Sensors based on metallic surface plasmon resonances (SPRs) are widely used in visible and near-infrared wavelengths [3]. However, in mid- and far-infrared frequencies, SPs are weakly confined at the metallic/dielectric interfaces, limiting the resulting sensitivities [4]. In contrast, graphene with a lower loss [5,6], higher thermal conductivity [7], and dynamically tunable optical conductivity [8–10], has the capability of sustaining plasmonic fields highly confined to its interface with dielectric materials [11], in a wide range of wavelengths from mid-infrared to THz [12,13], and with longer lifetimes [5]. These promising properties have made graphene plasmonic an excellent tool for designing tunable lab-on-a-chip systems [9,14].
Several configurations exist by which one can successfully excite SPs in graphene and compensate for the inherent mismatch between the wavenumbers of SPs in graphene and those of light in free space in the mid-IR and THz frequencies. Some of these approaches are Otto-Kretschmann configurations [15], the graphene nano/micro-ribbons [16], and periodic diffraction gratings on a graphene sheet [17], [18]. As far as the use of grating is concerned, some research groups have shown that the dynamic surface gratings originated from the flexural waves [5] or the surface acoustic waves (SAW) on a substrate [19] can be exploited for excitation of single-mode SPs on a sheet of graphene. Moreover, we have recently demonstrated that the integration of appropriate interdigitated transducers (IDTs) with suitable signaling schemes in a graphene-based SAW platform can lead to a dual-segment SAW-induced grating, suitable for designing multi-mode acousto-plasmonic devices [20].
In this line of research, we have investigated the bio-sensing behavior of this platform, assuming that the delay line serves as the sensing region, is functionalized by appropriate bio-receptors, and is exposed to bio-fluidic samples. Our results demonstrate while benefiting from the tunable multimode plasmonic behavior, we can successfully eliminate the interference effect due to concentration variations of non-target particles in the surrounding fluid [21] and achieve efficient plasmonic sensing. Our proposed acousto-plasmonic biosensor decouples its output characteristics from those non-target interfering effects, leading to a new generation of plasmonic measurement tools with higher precision and accuracy.
2. Biosensor structure and operating principles
Figure 1 illustrates a 3D scheme of the proposed acousto-plasmonic refractive index sensor, designed for biological applications. The applied acousto-plasmonic platform in this study is the same as that we proposed earlier [20]. The substrate we considered for this study is a 128°-YX-cut LiNbO3 — i.e., a well-known piezoelectric crystal with a high electromechanical coupling coefficient of Κ2 = 5.4% [22]. The metallic IDT electrodes that partly cover the substrate surface on the left can serve as the source of induced Rayleigh-type surface acoustic waves (SAW) that propagate across the LiNbO3 surface. In other words, an appropriate electrical signal applied to the IDTs pursues the surface atoms to move in both longitudinal and transverse directions inducing a grating pattern as propagating across the surface. The grating period, Λ, depends on the IDTs pitch size in the signaling configuration.
Fig. 1. A 3D scheme of the acousto-plasmonic refractive index biosensor, including metallic IDT electrodes, adjacent to a delay line covered by a graphene layer, all deposited and patterned on top of a LiNbO3 piezoelectric substrate to generate SAW-induced gratings (by applying Vin). On the backside of the device, there is a back gate that allows tuning of the Fermi level of graphene via Vg. A microfluidic container on top of the graphene layer has an inlet (left) and an outlet (right) and is isolated from the IDTs. A fluid containing the target biomolecules is injected into the container via the inlet. An incident light beam illuminates the graphene to excite plasmonic waves at its interface with LiNbO3 for refractive index sensing due to the presence of the biomolecules.
On the right side of the IDTs, the substrate surface is covered by a sheet of graphene, serving as the delay line. Since it is highly probable that graphene sticks to the LiNbO3 surface, resulting in a small distance between each Carbon atom and the neighboring Nb atoms at the graphene/LiNbO3 interface (∼2.34 Å). Hence, the top graphene layer follows the SAW-induced grating pattern of the underlying LiNbO3 surface, confirmed both theoretically [23,24] and experimentally [25,26]. One can control the graphene Fermi level via an electrostatic gating scheme like placing a back gate on the back of the device [19]. Notably, one can implement the designed electrostatic gating structure by transferring graphene sheets onto the commercially available LiNbO3 thin film on the metal (Au) layer [27]. The graphene layer on the delay line serves as the sensing region, is assumed isolated from the IDTs, and functionalized by appropriate receptors to allow selective and efficient absorption of the introduced target bio-particles on the graphene surface. We have considered a microfluidic chamber on top of the graphene-coated delay line so that the analyte can be introduced to this sensing region through the left inlet and exit from the right-side outlet. Once the fluidic analyte is injected into the chamber, the target bio-particles are selectively absorbed on the graphene surface, forming a monolayer of the target layer. In our simulations, we assume the randomly absorbed target species on the graphene surface form an effective target layer with thickness t and an effective refractive index of nt. A fixed target layer thickness is assumed for a known target bio-particle type. So, nt varies proportional to the target concentration, and the consequent shift of plasmonic wavelength can reveal the corresponding change of the target concentration in the proposed sensing configuration. The effective index of the fluidic analyte above the target layer is defined as nf, which is correlated to the type and concentration of un-adsorbed non-target species in the fluid. Variations of nf can affect the effective index on the graphene layer, leading to a false shift in plasmonic wavelength. Eliminating this interference and decoupling the target variations from the fluid variation in the output plasmonic sensing has mostly remained challenging in conventional plasmonic biosensors.
Consider a normally incident p-polarized light beam is to excite and sustain SPs on the sinusoidally rippled graphene surface. In doing so, the equivalent wavevector of the SAW-assisted grating (|kGrating|=2$\pi$/Λ) must compensate for the strong mismatch between the SPs wavevector (kSP) and that of the incident light in free space (kLight). Figure 2(a) illustrates the SPs dispersion curve (solid red curve), the light line (green line), the grating-coupled line(black dashed line), and the corresponding wavevectors. As can be observed from this figure, kGrating = kSP−kLight, and also kLight ≈ 0 therefore kGrating ≈ kSP. So, when the wavevector matching occurs at the corresponding grating period, plasmons can be excited on the corrugated graphene by light illumination. Moreover, the grating period can be tuned by the pitch size in the electrical signaling. Effective index variations of the target layer on the graphene surface alter the SPs excitation condition, causing a shift in the resulting plasmonic absorption spectrum, which serves as a plasmonic biosensing quantity. Figure 2(b) shows the calculated dispersion curve and the lifetime of the excited SPs for dual-segment gratings (kSP1, kSP2, and kSP3). In contrast to uniform grating, this configuration leads to multimode plasmonic excitation. Figure 2(c) and 2(d) show a schematic cross-section of the generated uniform and dual-segment gratings, respectively. Here, we have displayed different penetration depths, corresponding to excited different plasmonic modes, concerning a fixed target layer thickness. The left and right IDT schemes in Fig. 2(e) display the signaling configurations corresponding to the uniform and dual-segment gratings.
Fig. 2. (a) The calculated dispersion (red solid curve) and lifetime (blue dashed curve) of graphene SPs versus wavenumber (kSP) for (a) the uniform, and (b) dual-segment gratings, wherein kLight, kGrating, and kSP represent the light, grating, and SPs wavevectors. A magnified view of direct light dispersion is shown on the left side of part (a). (c), (d) cross-views of the SAW-induced uniform and dual-segment gratings. (e) the signaling schemes applied to IDTs to generate the SAW-induced (left part) uniform and (right part) dual-segment gratings.
3. Simulation models and method
SAW propagation on a piezoelectric substrate is governed by Maxwell’s equations and the mechanical equations of motion. The electromechanically coupled equations are [28]:
and where T, D, S, and E represent the stress, electric displacement, strain, and electric field intensity vectors, and cE, εs, and e denote the matrices representing the elasticity for the electric field, permittivity for a constant strain, and the substrate piezoelectricity, while the superscript † is denoting the matrix is transposed. For simulation of the SAW propagation, we solved the electromechanically coupled equations, exploiting the 3D finite element method (FEM) using COMSOL Multiphysics 5.4 [29].For simulation of the SP modes excitation, we utilized the 2D FEM to solve Maxwell’s equations in a steady-state condition [17], while a normally incident p-polarized plane-wave optical beam is illuminating the sinusoidally rippled graphene surface (i.e., the SAW assisted gratings). Meanwhile, for the graphene photoconductivity, we employ semiclassical Drude model with a finite temperature correction [17]:
The wavelength of the incident light beam is considered to be in the range of 7-14 µm, for the electron-phonon interactions in graphene and LiNbO3 to be absent [13,31–34]. Note that in this frequency range, the photon energy is always less than 2EF. So, we can neglect the effect of interband transitions in our simulations [17].
4. Results and discussion
In our earlier work [20], we have shown that by applying an electric signal of amplitude A = 50 V and frequency of f = 16 GHz to 35 pairs of uniform IDTs with 250-nm pitch size, a uniform Rayleigh type SAW propagating across the 128°-YX-cut LiNbO3 substrate surface with the maximum achievable amplitude of h = 14.5 nm and period of Λ=250 nm can be induced. This uniform grating under an appropriate illumination can result in a single mode of plasmonic wave desired for biosensing applications. There, we have also demonstrated that applying suitable sequential signaling to the given uniform IDTs can result in a dual-segment grating that in turn can be used to excite multiple SP modes at the expense of reduced field intensities.
Note that the lifetime of SPs is about 100 fs, while SAW travels with a velocity of 4000 m/s [20]. In other words, SAW travels a distance of about 4 pm in the life cycle of SPs, which is negligible compared with our investigated SAW period of 250 nm. Therefore, for THz and IR plasmonic frequencies, the SAW-induced gratings can be approximated by static gratings [5].
4.1 Uniform grating sensor
Here, we assume that the SAW-induced grating is uniform, and span the wavelength of the p-polarized continuous incident wave over the range of 8-11.5 µm, while the rippled graphene surface is exposed to the water-based analyte fluid sample with suspended biological species (Fig. 1). We expect the plasmonic resonance conditions to be dependent upon the concentration and type of biological species present in the analyte and those absorbed by the graphene surface. Hence, any change in the species that can be manifested by a change in the fluid and target effective refractive indices — i.e., Δnf and Δnt — should result in a shift in the plasmonic spectrum. To achieve a realistic simulation of the sensing behavior, we used the experimental dispersion data for water from [35] to define nf, and assumed Δnf = 0, nt = 1.4, Δnt = 0.05, and t = 20 nm, we have calculated the average field intensity at the interface of graphene/LiNbO3 versus the incident wavelength.
Figure 3 compares the calculated spectra, showing the plasmonic peaks occurring at λ0 = 9.435 µm corresponding to nt = 1.4 (blue solid curve) and λ0 = 9.495 µm representing nt = 1.45 (red dots-dashes).
Fig. 3. Plasmonic field intensity spectra at the graphene/LiNbO3 interface for two cases of nt =1.4 and 1.45, where Δnf = 0, t = 50 nm.
The comparison reveals that the observed 60-nm redshift of the spectrum peak is resulted from the change of Δnt = 0.05 in the target refractive index, demonstrating the sensing capability of the biosensor.
To elaborate further on the capability of the plasmonic biosensor, we have investigated its response to variations of the parameters such as Δnt, Δnf, t, and EF. Considering variations 0≤Δnt≤0.06 and 0≤Δnf≤0.05 [35], together with 10 nm ≤ t≤100 nm [36,37], and 0.4 eV ≤ EF≤0.9 eV, we have calculated the profiles of Δλ0 versus t and EF for various conditions (Fig. 4). Concerning the choice of Fermi level range, we refer the readers to sections IV-A and IV-B of Ref. [20], wherein we have discussed this matter systematically. In Fig. 3(a) and 5(e) of that reference, we have shown for EF≤0.4 eV, due to low carrier concentration, the SPs’ field intensity becomes too weak for uniform and dual-segment gratings. Moreover, for EF≥ 1 eV, the operating wavelength approaches the lower limit of λ ≥ 7 µm below which the graphene optical phonons come into the picture, interacting with its free carriers [13,31,32]. Hence, o be on the safe side practically, we have chosen the given range for the Fermi level.
Fig. 4. Variations of Δλ0 as a function of a) t for EF = 0.6 eV, b) EF for t = 20 nm, and c) EF for t = 50 nm, while 0≤Δnt≤0.06 and 0≤Δnf≤0.05.
Fig. 5. Examples of Δλ0 related to the overlapping regions in Fig. 4, (a) t = 20 nm, Δnf = 0.03, Δnt = 0.02, at EF = 0.4 and 0.6 eV; (b) t = 30 nm, Δnf = 0.03, Δnt = 0.01, at EF = 0.4 and 09 eV; (c) t = 30 nm, Δnf = 0.06, Δnt = 0.02, and EF = 0.4 and 0.8 eV; and (d) t = 30 nm, Δnf = 0.05, Δnt = 0.01, and EF = 0.4 and 0.6 eV.
Figure 4(a) illustrates the color maps for Δλ0 versus t (the target layer thickness) for EF = 0.6 eV. The gradient red shade shows Δλ0 for Δnf = 0 and 0.01≤Δnt≤0.06, while the blue gradient shaded region represents a similar map for Δnt = 0 and 0.01≤Δnf≤0.05. To our anticipation, the blue area shows that the thicker the given target layer, the less sensitive the sensor is to a change in the fluid effective refractive index. That is because the electric field of the graphene SPs has to penetrate a longer distance to reach the biological species in the fluid. On the contrary, the red region demonstrates that the thicker the target layer, the more sensitive the sensor is to a change in nt for a given analyte. But the sensitivity starts to saturate as the target thickness approaches t≈ 45 nm. This observation corresponds to the maximum penetration depth of SPs in that layer, beyond which SPs can’t interact with the target layer. The penetration depth of field to the underlying layer is proportional to the SPs wavelength, which is about 45 nm in our simulation. It can be seen from these figures that the maximum Δλ0 is 120 nm for Δnt = 0.06. If we define sensitivity as S = Δλ0/Δnt, the maximum sensitivity of the uniform grating sensor is 2000nm/RIU.
Also seen from this figure is a zone over which the blue and red shades overlap. This zone, which is of special importance since most proteins are in this particular size range (i.e., 10-40 nm) [38], is where a given Δλ0 for any given t can either be due to a finite Δnt or Δnf, confusing the sensor operator in determining the origin of the wavelength shift. However, we propose that by performing multiple measurements at various EF values we can overcome this problem. Therefore, we must investigate the effect of EF on Δλ0. The results are shown in Fig. 4(b) and 5(c) for two values of t = 20 nm and 50 nm. Using these calculated data, we anticipate that splitting of Δλ0 results for Δnt or Δnf variations will be possible (As shown in points A and B in Fig. 4(b), which will be discussed shortly).
Figure 4(b) shows Δλ0 as a function of the Fermi energy of graphene for t = 20 nm. Again, the red and blue gradient regions correspond to changes of nt and nf respectively. A large overlapping zone is also present in this figure, which causes similar ambiguity in any individual measurements with different EF values. Similarly, Fig. 4(c) shows Δλ0 as a function of the Fermi energy of graphene for t = 50 nm, wherein no overlapping region remains between the red and blue gradient regions. This figure confirms that for large biomolecules (i.e. t≥42 nm according to Fig. 4(a), we can observe decoupled plasmonic output characteristics for the biosensor so that the measured Δλ0 can be assigned to a certain Δnt or Δnf.
We propose to overcome this precision shortcoming for smaller biomolecules in the graphene-based plasmonic sensor by performing multiple measurements at different EF values. Figure 5 presents four example cases with different target thicknesses, in which different Δnt or Δnf have resulted in similar outputs (Δλ0) at one EF, while can be distinguished and show different Δλ0 at another EF. For instance, the case of part (a) with EF = 0.4 eV and 0.6 eV are shown at point A in Fig. 4(b), where EF = 0.6 eV, and Δnt = 0.02 (dotted red curve) and Δnf = 0.03 (dashed blue curve) have led to equal Δλ0. However, by decreasing EF to 0.4 eV (at point B in Fig. 4(b)), distinguishable Δλ0 values have emerged. This capability to enhance the certainty of the sensing can be allowed by electrostatic gating configuration and benefiting from the tunable plasmonic behavior of graphene in this biosensor.
4.2 Dual-segment grating sensor
Next, we perform studies on SAW-induced dual-segment gratings configuration as a tool to enhance the accuracy of the sensor and overcome the mentioned ambiguity. We have shown that by employing a sequential signaling scheme (Fig. 2(e)), also discussed in [20], one can realize the dual-segment gratings pattern. This dual-segment gratings, in turn, leads to excitation of multiple SP modes (see Fig. 2(b)), whose wave vectors can be calculated by kSP≈2πm/(Λ1+Λ2), where m is an integer mode number. Introducing these new SP modes, we can obtain more data from the analyte medium by a single measurement, in contrast to the uniform grating. In other words, a single plasmonic wavelength in the uniform grating splits into three plasmonic wavelengths, including a shorter and a longer wavelength besides the original wavelength. Relating the shallower (deeper) penetration to the shorter (longer) plasmonic wavelength, this plasmonic mode mostly interacts with the target (fluid) layer, as shown in Fig. 2(d). Hence, benefiting from the dual-segment gratings, we can mostly get isolated information from the target and the fluid media, which can be used to eliminate the sensing ambiguity of the biosensor. Here, our dual-segment grating includes two segments with periods of Λ1 = 250 nm and Λ2 = 2×Λ1 = 500 nm with a maximum height of 6 nm. Figure 6 shows the resulting first three SP modes λi (where λ1> λ2> λ3) for two cases with different nt values of 1.4 and 1.45 (the same as Fig. 3), which shows different Δλi for each peak.
Fig. 6. Plasmonic field intensities at the graphene/LiNbO3 interface corresponding to the first three SP modes for nt = 1.4 and 1.45, where Δnf = 0.
Next, we have performed a complete study to elaborate the sensing functionality of the dual-segment gratings, to compare with the results of the uniform grating. Figure 7 displays the achieved Δλi (i = 0,1,2,3) profiles for the single-mode (Δλ0), as well as the first three SP modes (Δλ1, Δλ2, Δλ3), relating to the uniform and dual-segment gratings respectively, versus different EF and t, for different Δnt, Δnf values. In this figure, parts (a, e, i, and m) correspond to the uniform grating, and parts (b-d, f-h, j-l, and n-p) correspond to the first three modes of the dual-segment grating. Parts (a-h) reveal that the higher EF, the lower Δλi. This is because increasing EF changes the SPs excitation condition so that SPs with smaller wavelength is excited because the plasmonic dispersion curve of graphene is scaled by the factor of EF1/2 [38,39]. Smaller wavelength corresponds to smaller penetration depth into the sensing media and smaller overlapping region with the target layer, resulting in reduced sensitivity to nt and nf.
Fig. 7. The profiles of Δλi versus a-d) Δnt and EF (t = 20 nm), e-h) Δnf and EF (t = 20 nm), i-l) Δnt and t (EF = 0.6 eV), and m-p) Δnf and t (EF = 0.6 eV) for field intensity peaks of uniform (λ0) and dual-segment gratings (λ1, λ2, and λ3). The contours correspond to the equal Δλi, while the white numbers show Δλi values in nm.
Parts (i-l) show that Δλi increases by increasing the target layer thickness, because of the increased overlapping between the SP mode profile and the target layer. This increasing behavior continues until the target thickness reaches the penetration depth, after which Δλi variations saturates. This is more apparent for the shortest wavelength (λ3) with a shallower penetration depth. Finally, Fig. 7(m) to 7(p) exhibit that as the thickness of the target layer increases, the resulting Δλi does not change for different Δnf values or the output sensitivity of the sensor is diminished. This observation is in agreement with the lower penetration of the SP field to the fluid, for higher target thicknesses. Similarly, it is also evident in these figures that the non-sensitive regime to Δnf begins at lower t values for the shorter plasmonic wavelength of the multi-mode plasmonic modes. The contours correspond to the equal Δλi, while the white numbers show Δλi values in nm, and the Δλi steps of the contours are 10 nm. The maximum shift in the spectrum is 125 nm for 0.05 change in nt equivalent to the sensitivity of 2500 nm/RIU. Results shown in Fig. 7 reveal high contrast between Δλ1 and Δλ3 for different values of refractive indices and thickness of target layer.
Now, for evaluating the output efficiency of the acousto-plasmonic sensor, we define a figure of merit (FoMI = Δλi/FWHM) in both uniform and dual-segment operation modes, so that it reflects the detection accuracy of a plasmonic sensor. It is well established that higher Δλ and lower FWHM values result in higher sensitivity for the plasmonic biosensors. Thus, we display the calculated FoMI versus varying EF, t, Δnt, and Δnf in Fig. 8. It is observable that FoMI profiles have a trend similar to Δλ profiles in Fig. 7 because FWHM profiles do not depend on Δnt and Δnf, significantly and only varies by changes in EF. The white numbers in these graphs show steps of 0.05 for FoMI profiles. The maximum value for FoMI is 30 RIU−1.
Fig. 8. The profiles of FoMI versus (a-d) Δnt and EF (t = 20 nm), e-h) Δnf and EF (t = 20 nm), (i-l) Δnt and t (EF = 0.6 eV), and (m-p) Δnf and t (EF = 0.6 eV) for field intensity peaks of uniform (λ0) and dual-segment gratings (λ1, λ2, and λ3).
Furthermore, to complete the sensing efficiency evaluation, we define another figure of merit (FoMII= Δλ1-Δλ3), to demonstrate the capability of decoupling fluidic interference from the target variations in the dual-segment operation mode of the presented acousto-plasmonic biosensor. Thus, we display the calculated FoMII versus t, Δnt, and Δnf in Fig. 9. As depicted in Fig. 9(a), FoMII verses Δnf is always positive (0 to 42 for t = 20 nm), and the thicker the target layer, the smaller is FoMII. In contrast, FoMII versus Δnt has positive and negative values both (−15 to 30 for t = 20 nm). For thinner targets (t< 50 nm), FoMII < 0. The observed opposing behavior trend helps to distinguish variation in nt from nf in the proposed dual-segment configuration for small targets (t < 50 nm), which is not achievable in conventional plasmonic sensors. In other words, if the monitored FOMII is negative, we can conclude that the observed plasmonic shift (Δλ2) is mostly due to Δnt for target layers thinner than 50 nm. For instance, we plot FoMII versus different values of Δnf (solid-blue) and Δnt (dashed-red) for t = 20 nm in Fig. 9(c). We can see that if the target size (the target layer thickness) is known, we can decouple the fluid effect from the target effect and determine the exact value of the introduced Δnt or Δnf without ambiguity. The decoupling of sensing behavior from the interference of the surrounding medium originates from the previously discussed multi-mode plasmonic behavior in the dual-segment gratings. Figure 2(d) shows that exciting KSP1 and KSP3 expand the plasmonic field interaction to the fluid or confines it to the target layer. In other words, the plasmonic peak of λ1 is more sensitive to fluid tolerance (Δnf), while λ3 is mainly sensitive to target tolerance (Δnt). Thus, Δλ1 is larger (smaller) than Δλ3 versus increasing nf (nt), resulting in positive (negative) FoMII values for Δnf (Δnt).
Fig. 9. FoMII (=Δλ1-Δλ3) for the dual-segment gratings for various t, (a) Δnf, and (b) Δnt values (EF = 0.6 eV). (c) Comparison of FoMII variation versus different values of Δnf (solid-blue) and Δnt (dashed-red) for t = 20 nm (EF = 0.6 eV).
Table 1 compares the sensing characteristics (sensitivity, FoMI) for uniform and dual-segment gratings with those of other SPP Biosensors, wherever applicable. The dual-segment gratings generally have better performance than uniform gratings and both of them perform decently in comparison with other grating-based SPP sensors. Notably, FOMII, revealing the capability to decouple the fluid and target traces in the measured output signal in the proposed dual-segment biosensor, does not apply to uniform grating or the other conventional plasmonic sensors.
Afterward, we illustrate some selected cases to highlight further the efficiency of the multimode plasmonic sensor for distinguishing between the changes in the fluid and the target layer characteristics. Figure 10 displays the achieved Δλi data of the uniform grating (Δλ0), besides the dual-segment grating (Δλ1, Δλ2, Δλ3), for four different case studies. As we can see, all four different cases have shown roughly equal Δλ0 for the uniform grating, but the package of Δλj (j = 1, 2, 3) values for the dual-segment gratings are entirely distinguishable. It is observable that though Δλ2 values are similar to Δλ0 (due to having approximately the same wavelength), Δλ1 is sensitive to both Δnt and Δnf meanwhile, Δλ3 demonstrate more sensitivity to Δnt. In other words, the shorter wavelength is more sensitive to the target medium, while the longer wavelength interacts with both target and fluid media. To clarify the cross-sensitivity issue in the investigated single-mode plasmonic sensor, we can consider part (a) with t = 20 nm and EF = 0.6 eV, wherein data from Δλ0 is about 23 nm for both Δnt =0.02 and Δnf =0.03 so that one can’t distinguish target data from the fluid data. However, it is shown that Δλ1 and Δλ3 are 19 nm and 27 nm (Δλ1-Δλ3= -8 nm) for Δnt =0.02, while they are 37 nm and 16 nm (Δλ1-Δλ3= +21 nm) for Δnf =0.03, which can lead to overcoming the cross-sensitivity between the target and the fluid in the multi-mode plasmonic sensor; parts c to d follow this principle too.
Fig. 10. Cases which have the same Δλi for the uniform grating (λ0) but different values for the dual-segment gratings (λ1, λ2, and λ3) for various t values (EF = 0.6 eV).
Likewise, Fig. 11 shows the same principle, for example, cases of different EF values. Here, we see that for the same Δλ0 in the uniform grating, there is no need for multiple measurements at different EF values in the dual-segment grating, owing to additional data extracted from the different SP modes. For more clarification, we can observe that the presented cases have shown roughly equal Δλ0 and Δλ2 versus different Δnt and Δnf, in uniform and dual-segment gratings. However, the additional data relating to Δλ1 and Δλ3 in the dual-segment grating help to decouple the output trace of Δnt or Δnf.
Fig. 11. Cases with the same Δλi for the uniform grating (λ0) but different value for the dual-segment gratings (λ1, λ2, and λ3) for (a) Δnf = 0.03, Δnf = 0.02, and EF =0.7 eV, (b) Δnf = 0.06, Δnf = 0.04, and EF =0.7 eV, (c) Δnf = 0.03, Δnf = 0.02, and EF =0.8 eV, and (d) Δnf = 0.06, Δnf = 0.04, and EF =0.8 eV.
5. Conclusion
We have investigated a graphene-based SAW-assisted SPR refractive index biosensor and shown that undesired changes in the fluid refractive index can be a problem in determining the accurate result for the target measurement in plasmonic biosensors. In this study, we have proposed two approaches to overcome this shortcoming: (i) performing the measurement individually for each EF value; (ii) utilizing SAW-induced dual-segment gratings. The latter approach enables multi-mode plasmonic sensing and benefits from higher accuracy through one single measurement without the need for electrostatic gating of graphene. The maximum sensitivity of the dual-segment grating sensor is 2500 nm/RIU. Moreover, we defined two figures of merit (FoMI=Δλi/FWHM and FOMII=Δλ1−Δλ3) for the proposed acousto-plasmonic biosensor to demonstrate the sensing performance from the accuracy aspect and eliminate the interference of non-target bioparticles in the fluid. The excited multiple SP modes in the latter configuration respond differently to changes of the target or the fluid refractive indices and thus decouple the effect of fluid and target in the measured output, eliminating detection ambiguity and improving the accuracy. The proposed SAW-assisted plasmonic biosensor opens a new horizon for developing the next generation of highly sensitive and accurate reconfigurable biosensors.
Funding
Tarbiat Modares University (IG-39703); Iran National Science Foundation (96004575).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators, B 54(1-2), 3–15 (1999). [CrossRef]
2. Y. Chen and H. Ming, “Review of surface plasmon resonance and localized surface plasmon resonance sensor,” Photonic Sens. 2(1), 37–49 (2012). [CrossRef]
3. J. Zhu, J. J. Li, and J. W. Zhao, “Optimizing the plasmonic sensing of RNA folding based on local refractive index change of gold nanorod,” Appl. Surf. Sci. 275, 264–268 (2013). [CrossRef]
4. B. Vasić, G. Isić, and R. Gajić, “Localized surface plasmon resonances in graphene ribbon arrays for sensing of dielectric environment at infrared frequencies,” J. Appl. Phys. 113(1), 013110 (2013). [CrossRef]
5. M. Farhat, S. Guenneau, and H. Bağcı, “Exciting Graphene Surface Plasmon Polaritons through Light and Sound Interplay,” Phys. Rev. Lett. 111(23), 237404 (2013). [CrossRef]
6. M. Heidari and V. Ahmadi, “Graphene-based mid-infrared plasmonic isolator with multimode interferometer,” Opt. Lett. 45(20), 5764 (2020). [CrossRef]
7. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior Thermal Conductivity of Single-Layer Graphene,” Nano Lett. 8(3), 902–907 (2008). [CrossRef]
8. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]
9. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012). [CrossRef]
10. M. Heidari and V. Ahmadi, “Design and Analysis of a Graphene Magneto-Plasmon Waveguide for Plasmonic Mode Switch,” IEEE Access 7, 43406–43413 (2019). [CrossRef]
11. J. Wu, C. Zhou, J. Yu, H. Cao, S. Li, and W. Jia, “Design of infrared surface plasmon resonance sensors based on graphene ribbon arrays,” Opt. Laser Technol. 59, 99–103 (2014). [CrossRef]
12. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). [CrossRef]
13. H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013). [CrossRef]
14. D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015). [CrossRef]
15. Yu. V. Bludov, M. I. Vasilevskiy, and N. M. R. R. Peres, “Mechanism for graphene-based optoelectronic switches by tuning surface plasmon-polaritons in monolayer graphene,” EPL 92(6), 68001 (2010). [CrossRef]
16. J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García De Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012). [CrossRef]
17. W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012). [CrossRef]
18. T. M. Slipchenko, M. L. Nesterov, L. Martin-Moreno, and A. Y. Nikitin, “Analytical solution for the diffraction of an electromagnetic wave by a graphene grating,” J. Opt. 15(11), 114008 (2013). [CrossRef]
19. J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111(23), 237405 (2013). [CrossRef]
20. M. M. Mehrnegar, S. Darbari, H. Ramezani, and M. K. Moravvej-Farshi, “Designing Graphene-Based Multi-Mode Acousto-Plasmonic Devices,” J. Lightwave Technol. 37(9), 2126–2132 (2019). [CrossRef]
21. F. Bahrami, M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “Dual Polarization Measurements in the Hybrid Plasmonic Biosensors,” Plasmonics 8(2), 465–473 (2013). [CrossRef]
22. C. Fu, K. J. Lee, K. Lee, and S. S. Yang, “Low-intensity ultraviolet detection using a surface acoustic-wave sensor with a Ag-doped ZnO nanoparticle film,” Smart Mater. Struct. 24(1), 015010 (2015). [CrossRef]
23. J. Ding, L.-W. Wen, H.-D. Li, X.-B. Kang, and J.-M. Zhang, “First-principles investigation of graphene on the ferroelectric LiNbO3 (001) surface,” EPL 104(1), 17009 (2013). [CrossRef]
24. J. Ding, L. W. Wen, H. D. Li, and Y. Zhang, “Structure and electronic properties of graphene on ferroelectric LiNbO3 surface,” Physics Letters, Section A: General, Atomic and Solid State Physics 381(20), 1749–1752 (2017). [CrossRef]
25. Y. Fukaya, S. Entani, S. Sakai, I. Mochizuki, K. Wada, T. Hyodo, and S. I. Shamoto, “Spacing between graphene and metal substrates studied with total-reflection high-energy positron diffraction,” Carbon 103, 1–4 (2016). [CrossRef]
26. Z. Insepov, E. Emelin, O. Kononenko, D. V. Roshchupkin, K. B. Tnyshtykbayev, and K. A. Baigarin, “Surface acoustic wave amplification by direct current-voltage supplied to graphene film,” Appl. Phys. Lett. 106(2), 023505 (2015). [CrossRef]
27. NANOL: https://nanoln.com
28. R. Lerch, “Simulation of Piezoelectric Devices by Two- and Three-Dimensional Finite Elements,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 37(3), 233–247 (1990). [CrossRef]
29. S. Maouhoub, Y. Aoura, and A. Mir, “FEM simulation of Rayleigh waves for SAW devices based on ZnO/AlN/Si,” Microelectron. Eng. 136, 22–25 (2015). [CrossRef]
30. T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008). [CrossRef]
31. Q. Guo, F. Guinea, B. Deng, I. Sarpkaya, C. Li, C. Chen, X. Ling, J. Kong, and F. Xia, “Electrothermal Control of Graphene Plasmon–Phonon Polaritons,” Adv. Mater. 29(31), 1700566 (2017). [CrossRef]
32. Sh. Jalalvandi, S. Darbari, and M. K. Moravvej-Farshi, “Exact dispersion relations for the hybrid plasmon-phonon modes in graphene on dielectric substrates with polar optical phonons,” Opt. Express 29(17), 26925–26943 (2021). [CrossRef]
33. S. Kojima, K. Kanehara, T. Hoshina, and T. Tsurumi, “Optical phonons and polariton dispersions of congruent LiNbO 3 studied by far-infrared spectroscopic ellipsometry and Raman scattering,” Jpn. J. Appl. Phys. 55(10S), 10TC02 (2016). [CrossRef]
34. S. Kojima, “Composition Variation of Optical Phonon Damping in Lithium Niobate Crystals,” Jpn. J. Appl. Phys. 32(Part 1, No. 9B), 4373–4376 (1993). [CrossRef]
35. D. J. Rowe, D. Smith, and J. S. Wilkinson, “Complex refractive index spectra of whole blood and aqueous solutions of anticoagulants, analgesics and buffers in the mid-infrared,” Sci. Rep. 7(1), 7356 (2017). [CrossRef]
36. M. Wu, C. Chen, Z. Wang, H. Bachman, Y. Ouyang, P.-H. Huang, Y. Sadovsky, and T. J. Huang, “Separating extracellular vesicles and lipoproteins via acoustofluidics,” Lab Chip 19(7), 1174–1182 (2019). [CrossRef]
37. V. Schumaker, C. B. Anfinsen, J. Edsall, F. Richards, and D. Eisenberg, Lipoproteins, Apolipoproteins, and Lipases (Academic Press, 1994).
38. G. Si, Y. Zhao, E. Leong, and Y. Liu, “Liquid-Crystal-Enabled Active Plasmonics: A Review,” Materials 7(2), 1296–1317 (2014). [CrossRef]
39. A. J. Chaves, B. Amorim, Y. V. Bludov, P. A. D. Gonçalves, and N. M. R. Peres, “Scattering of graphene plasmons at abrupt interfaces: An analytic and numeric study,” Phys. Rev. B 97(3), 035434 (2018). [CrossRef]
40. J. P. Monteiro, J. Ferreira, R. G. Sabat, P. Rochon, M. J. L. Santos, and E. M. Girotto, “SPR based biosensor using surface relief grating in transmission mode,” Sens. Actuators, B 174, 270–273 (2012). [CrossRef]
41. P. Adam, J. Dostálek, and J. Homola, “Multiple surface plasmon spectroscopy for study of biomolecular systems,” Sens. Actuators, B 113(2), 774–781 (2006). [CrossRef]
42. B. Choi, X. Dou, Y. Fang, B. M. Phillips, and P. Jiang, “Outstanding surface plasmon resonance performance enabled by templated oxide gratings,” Phys. Chem. Chem. Phys. 18(37), 26078–26087 (2016). [CrossRef]
43. X. Dou, P.-Y. Chung, P. Jiang, and J. Dai, “Surface plasmon resonance and surface-enhanced Raman scattering sensing enabled by digital versatile discs,” Appl. Phys. Lett. 100(4), 041116 (2012). [CrossRef]
44. X. Dou, B. M. Phillips, P.-Y. Chung, and P. Jiang, “High surface plasmon resonance sensitivity enabled by optical disks,” Opt. Lett. 37(17), 3681 (2012). [CrossRef]
45. S. Nair, C. Escobedo, and R. G. Sabat, “Crossed Surface Relief Gratings as Nanoplasmonic Biosensors,” ACS Sens. 2(3), 379–385 (2017). [CrossRef]
46. H. Gao, J.-C. Yang, J. Y. Lin, A. D. Stuparu, M. H. Lee, M. Mrksich, and T. W. Odom, “Using the Angle-Dependent Resonances of Molded Plasmonic Crystals To Improve the Sensitivities of Biosensors,” Nano Lett. 10(7), 2549–2554 (2010). [CrossRef]
47. J. Guo, Z. Li, and H. Guo, “Near perfect light trapping in a 2D gold nanotrench grating at oblique angles of incidence and its application for sensing,” Opt. Express 24(15), 17259 (2016). [CrossRef]
