1. Introduction

Surface plasmons (SPs) propagate at a metal–dielectric interface, confining light in sub-wavelength dimensions [1]. During the past decade, SPs excited at a metal–dielectric interface have drawn significant interest for their applications in biosensing. However, metals are inherently lossy, and hence the propagation length of metal-based SPs is limited. In addition, the direct excitation of metal-based SPs is impossible due to the wave vector mismatch between the incident light and SPs and the difficulty in altering the dielectric properties to overcome such a mismatch [2]. On the other hand, plasmons excited at graphene–dielectric interface show controllable electromagnetic (EM) properties, comparatively low loss, and intense light absorption [3]. As a result, plasmons excited in graphene are promising alternatives for metal-based SPs in many areas of photonic and plasmonic devices, from mid-infrared (MIR) to terahertz (THz) wavelength region [4–7]. In addition, characteristics of graphene plasmons strongly depend on the substrate’s physical and geometrical parameters and can be tailored as per requirement [8].

Graphene shows an extraordinary property variation from dielectric to metallic responses at energies near $\hslash \omega \approx 2 E_f$, where $E_f$ is the Fermi energy, $\hslash$ is the reduced Planck’s constant, and $\omega$ is the angular frequency [9]. In graphene, $E_f$ can be efficiently controlled by doping [9,10]. Graphene conductivity ($\sigma _g$), especially the imaginary part, Im($\sigma _g$), changes sign from positive to negative when $\hslash \omega >2 E_f$, with the minimum at $\hslash \omega = 2 E_f$ [11,12]. The change of sign occurs since the electric field reverses the direction of induced current [13]. The negative sign of Im($\sigma _g$) confirms the presence of the transverse electric (TE) mode in graphene [12]. However, the TE mode’s dispersion relation is very close to the light line, and it cannot confine the incident light sufficiently [13]. On the other hand, when Im($\sigma _g)>0$, the transverse magnetic (TM) mode is supported in graphene [13]. Furthermore, graphene does not support TE and TM modes in the same wavelength region [2]. Graphene’s optical characteristics are changed by applying an electrical voltage, which modulates the plasmon resonance in the metal nanostructures [14,15]. Applying a suitable gate voltage ($V_g$) to the graphene and using an appropriate interfacing dielectric layer thickness allows the TM mode to be excited at a desired wavelength [16], allowing designing optoelectronic and plasmonic devices in optical frequency.

When $\hslash \omega < 1.667 E_f$, graphene shows metallic responses with a positive imaginary part of $\sigma _g$, supporting TM modes and ensuring strong light confinement with huge wave vectors [17]. However, graphene TM modes can reach the MIR range, whereas graphene TE modes up to the visible range [18]. In addition, TM modes show collective electron oscillations; therefore, the real part of $\varepsilon _g$ must be negative to excite them in graphene [19]. TM modes have been experimentally observed in graphene micro-ribbon arrays, infrared nano-imaging, nanoscopy, and sub-wavelength gratings from THz to infrared (IR) wavelength range [2,20,21]. Besides, when photon energies ($E_p$) are $> 2 E_f$, mono-layer graphene shows 2.3% light absorption, which limits the conversion from light to the electronic signals in a graphene layer [22].

The Kretschmann-based angular interrogation method is generally used to create SPs, showing a high signal-to-noise ratio. However, the resonance angle shifting must be significant for enhanced sensor performance. The sensitivity of a Kretschmann configuration sensor is usually low, $\sim$200 degrees/RIU (refractive index unit) [23]. It is possible to increase the sensitivity by decreasing the refractive index of the prism material, although this approach reduces the detection accuracy [23]. To overcome the low sensitivity problem, several research groups have proposed various modified structures [24–29], e.g., metal nano-grooves, graphene/hexagonal boron nitride (hBN) nanoribbons, metal/dielectric/metal-based plasmonic sensors to decrease the reflected light intensity. Furthermore, a silver (Ag)-gold (Au) grating SPR-based sensor has shown a maximum 346 degrees/RIU sensitivity [30]. However, these SPR sensors are not prism-based, which are extensively used commercially [31]. Besides, graphene nanostrips in Au-aluminium (Al)-based SPR sensors have shown a maximum 165 degrees/RIU sensitivity and 164.28 RIU$^{-1}$ figure-of-merit (FoM), respectively [32]. However, the effects of nanostrip geometry, such as thickness and length, on sensing performance have yet to be analyzed. Recently, an SPR sensor based on Au grating, where SPR and localized SPR (LSPR) coupling is proposed, achieved a maximum sensitivity of 397.3 degrees/RIU [33].

On the other hand, TM modes in doped monolayer graphene on a dielectric layer have been investigated through attenuated total reflectance (ATR) based technique in THz wavelength [34]. Likewise, graphene-based constructions using ATR have been proposed for polarizers and switches by adjusting $V_g$ [35,36]. In addition, graphene can be sandwiched between different dielectric materials, such as SiO$_{2}$ and Si layers, to control $E_f$ and the electron density ($n_g$) [8,37,38]. By applying a suitable $V_g$, $n_g$ can be increased. When $n_g\gtrsim 4\times$10$^{14}$ cm$^{-2}$, $E_f = 2.3$ eV [2,39]. Furthermore, the TM mode properties in graphene strongly depend on the relative permittivity ($\varepsilon _r$) and thickness ($d$) of SiO$_{2}$ [37]. However, it is observed that $\varepsilon _r$ of SiO$_{2}$ is comparatively small. The only parameter to increase the $E_f$ is the SiO$_{2}$ thickness. Alternatively, ZnO can be considered instead of SiO$_{2}$ due to its high $\varepsilon _r$ [40].

This work shows that TM modes can be excited in graphene using the ATR method in the visible spectrum without needing a noble metal. We show that graphene optical properties can be effectively tuned by changing the thickness of the interfacing dielectric layer ($d_{\text {ZnO}}$) and $V_g$. We use the Kubo analytical model to determine the graphene layer’s optical properties. The proposed sensor uses dual channels for refractive index sensing, where graphene nanostrips are placed in the first layer. These nanostrips scatter the incident light to a second graphene layer through several intermediate dielectric layers. Our proposed dual-channel sensor shows a maximum sensitivity of 2530 degrees/RIU when both sensing channels have the same refractive index.

This paper is organized as follows: Section 2 presents the proposed dual-channel sensor configuration. Section 3 describes the optical properties of different materials. We discuss the numerical method to solve Maxwell’s equations by the finite difference time domain (FDTD) technique in Sec. 4. We present the dynamics of incident light with the sensor structure in Sec. 5 and the sensing performances of the proposed dual-channel sensor in Sec. 6. Section 7 concludes the findings of this work.

2. Proposed dual-channel sensor

Figure 1 shows the proposed dual-channel graphene TM mode refractive index sensor. The proposed sensor structure is an effective substitute for the conventional Kretschmann configuration, allowing the sensor to excite TM modes in graphene using an oblique incidence of light. A semi-infinite BK7 prism is used as the glass substrate. Light is incident to the prism–graphene layer interface from the prism side using a collinear optical arrangement, which will help to reduce noise and miniaturize the sensor size [41]. The intensity of the reflected light is detected from the same side. The incident light has a wavelength of 633 nm.

 

Fig. 1. (a) Two-dimensional (2-D) schematic illustration of the proposed graphene nanostrips TM mode dual-channel refractive index sensor and (b) 3-D schematic view of a part of the proposed sensor that includes the BK7 prism layer, graphene nanostrips, and ZnO.

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Graphene nanostrip arrays are placed on the prism material with a separation distance between the strips $(L_a)$ of 100 nm, as shown in Fig. 1. The gaps between the strips are filled with air. Such a structure can be fabricated using the nanoimprint lithography technique as discussed in Ref. [42]. For the purpose of applying voltage, the strips are connected at one end by a conductive strip, as shown in Ref. [43] The air pockets between graphene strips help increase the resonance dip of the reflection profile [44]. The width ($W_g$) and thickness ($t_g$) of each graphene nanostrip are 500 nm and 50 nm, respectively. Graphene nanostrips have a periodicity ($K$) of $K=W_g+L_a=600$ nm. For numerical analysis, we have considered only one unit cell of the structure with periodic boundary conditions.

In the visible wavelength range, the graphene permittivity ($\varepsilon _g$) can be controlled using a suitable $V_g$ [38]. The ZnO layer used in the proposed sensor between the graphene and Si layers acts as an insulating layer, creating a parallel capacitor model [45]. Such an arrangement can change graphene’s optical properties [37]. We apply $V_g$ between Si and graphene to control $n_g$, $E_f$, and the electron mobility ($\mu _g$) of graphene [16,45]. The thicknesses of ZnO and Si are 5 nm and 50 nm, respectively. Graphene’s optical properties change with $V_g$, and it can behave like a noble metal in the visible wavelength range with a suitable $V_g$.

Two-dimensional (2-D) materials like graphene, tungsten diselenide (WSe$_2$), molybdenum disulfide (MoS$_2$), and tungsten disulfide (WS$_2$) can alter the surface characteristics to enhance the adsorption of bio-molecules [46]. We use single-layer WS$_2$ on top of the Si layer for bio-molecule adsorption. The proposed sensor uses two sensing channels. The first one is located on top of the WS$_2$ with a thickness $d_{S1}=100$ nm [47]. The second sensing layer is on top of the second graphene layer. The thickness of the second graphene layer is 50 nm. We also assume a thickness $d_{S2}=100$ nm for the second sensing channel. A 30-nm-thick BK7 glass layer separates the first sensing channel from the Si layer to decrease the reflected light intensity ($R$). This BK7 layer also acts as the substrate for the second sensing layer arrangement. The first graphene layer consists of nanostrips to help excite the TM modes in graphene. In addition, the periodic array of graphene nanostrips creates a scattering pattern, which illuminates the second graphene layer that acts like a metal [24] and produces TM modes at the second graphene–sensing layer interface.

The different layers of the proposed sensor are two-dimensional except for one of the graphene layers. These layers should be grown without much difficulty using the currently available fabrication techniques. In particular, the graphene layers can be deposited by evaporating atomic carbon in a vacuum using high temperatures [48]. Different dielectric materials can be grown on each other using evaporation or chemical vapor deposition techniques [49]. Nanoimprint lithography can create air gaps between the graphene strips [42]. The first sensing channel in the middle of the layers can be fabricated using a plano-convex singlet lens [50], and a glass flow cell can be used to inject the analyte [51].

3. Optical properties

The performance of the proposed dual-channel refractive index sensor depends on the constituent materials’ complex refractive indices. Therefore, the performance of the sensor also depends on the incident wavelength as materials show dispersive optical properties. The refractive index of BK7 prism is wavelength-dependent and can be determined by the method defined in Ref. [52]. The permittivity of the 2-D graphene monolayer is given by [53]

The optical properties of a few-layer graphene sheet are the same as the monolayer graphene [53]. Generally, $\sigma _g$ of a graphene sheet is calculated using the Kubo formula [17]

In this work, we use $v_f=1.49\times 10^6$ m/s [43] and determine the Fermi energy as $E_f=\sqrt {\hslash v_f (\pi n_g )}$ [55]. The graphene Fermi energy can be changed by applying $V_g$. The considered relation can be determined using a parallel-plate capacitor model. The $n_g$ of graphene is determined as $n_g=\varepsilon _r \varepsilon _{\text o} V_g/e d_{\text {ZnO}}$ [55]. Here, $\varepsilon _r$ is the permittivity of ZnO. We use $\varepsilon _r=8.5$ for ZnO [56]. Graphene $\mu _g$ is given by [57]

4. Simulation method

To determine $R$-profiles of the proposed dual-channel refractive index sensor, we solve 2-D vectorial Maxwell’s equations by the numerical FDTD method. We use the solutions for 2-D configurations as the proposed dual-channel structure is invariant in the $z$-direction. For 2-D simulations, we set 4000 nm $\times$ 600 nm simulation area, including the dual-channel sensing regions. The perfectly matched layer boundary condition is set in the $x$-direction, and the Bloch boundary condition is in the $y$-direction.

We have used non-uniform meshing in the simulation area, ensuring a high mesh accuracy and maximum mesh refinement. In our FDTD simulations, the mesh refinement approach obtains sub-cell precision and ensures accuracy for the metal layer and metal–dielectric interface [63]. We have used 1 ns simulation time to converge FDTD calculations. We have used a TM-polarized light source with a 633 nm wavelength. The incidence angle has been varied from 45$^\text {o}$ to 75$^\text {o}$ with step size 0.326$^\text {o}$ to determine the $R$-profile. The light source is placed in the bottom BK7 region at 1.90 $\mu$m from the BK7–graphene interface. We have also recorded the $R$-profiles using a monitor placed in the same bottom BK7 region at 1.95 $\mu$m from the same interface.

5. Dynamics of incident light

The traditional Kretschmann configuration-based sensors obey the following expression [23]

6. Results and discussion

Figure 2 shows the optical properties of graphene as functions of $V_g$ for three thicknesses of ZnO. Figure 2(a) shows that $n_g$ increases with $V_g$. $n_g$ also increases as $d_{\text {ZnO}}$ decreases. A similar trend in $E_f$ is observed in Fig. 2(b) with $V_g$ and $d_{\text {ZnO}}$. Alternatively, $\mu _g$ decreases when $V_g$ increases, as shown in Fig. 2(c), while $\mu _g$ increases as $d_{\text {ZnO}}$ increases.

 

Fig. 2. Optical properties (a) $n_{g}$, (b) $E_{f}$, and (c) $\mu _g$ of the graphene layer as functions of $V_{g}$ for different thicknesses of ZnO.

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Figure 3 shows $\varepsilon _g$ against the light wavelength for different values of $d_{\text {ZnO}}$ and $V_g$. First, we set $V_{g}=20$ V and change $d_{\text {ZnO}}$. Figure 3(a) shows the real part of $\varepsilon _g$ whereas Fig. 3(b) shows the imaginary part for different $d_{\text {ZnO}}$. The real part of $\varepsilon _g$ decreases as the wavelength increases. In addition, $d_{\text {ZnO}}$ significantly impacts the real part of $\varepsilon _g$. When $d_{\text {ZnO}}=5$ nm, the real part of $\varepsilon _g$ is negative. The negative real part of $\varepsilon _g$ confirms the existence of TM modes [12,19]. Furthermore, Im($\varepsilon _g$) of graphene is almost zero when $d_{\text {ZnO}}$ is 5 nm and 10 nm. The real part of $\varepsilon _g$ is positive and diverges logarithmically at 545 nm wavelength when $d_{\text {ZnO}}=15$ nm. The divergent behavior is due to the step-like change of the Im($\varepsilon _g$), indicating inter-band absorption of radiation at $\hslash \omega >2E_{f}$ [12].

 

Fig. 3. (a) Real and (b) imaginary parts of the graphene permittivity $(\varepsilon _g)$ as a function of the incident light wavelength for different thicknesses of ZnO. The applied gate voltage $(V_g)$ is 20 V in both cases. (c) Real and (d) imaginary parts of $(\varepsilon _g)$ as a function of the incident light wavelength for different $V_g$. The ZnO thickness $(d_{\textrm {ZnO}})$ is 5 nm in both cases.

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Figures 3(c) and 3(d) show $\varepsilon _g$ against wavelength for three different $V_{g}$, when $d_{\text {ZnO}}=5$ nm. It is noted that the real part of $\varepsilon _g$ becomes more negative as the wavelength increases, as shown in Fig. 3(c). The imaginary part of $\varepsilon _g$ has a small value when $V_{g}=20$ V, as shown in Fig. 3(d). However, when $V_{g}=60$ V, the imaginary part of $\varepsilon _g$ is also small. Therefore, it is clear that incident wavelength, $V_{g}$, and $d_{\text {ZnO}}$ have significant influences on $\varepsilon _g$. When $d_{\text {ZnO}}=5$ nm and $V_{g}=60$ V, $E_f\gg E_p$ in the visible wavelength range, as shown in Fig. 2(b). Therefore, $\sigma _g$ is dominated by intra-band interactions and can be estimated via the Drude model [64]. At 633 nm wavelength, the real part of $\varepsilon _g$ is negative, and the imaginary part has a nominal value. Hence, graphene acts like a noble metal.

Figure 4 shows the excitation of TM modes in graphene for different $V_g$. In Fig. 4(a), we show that two TM modes are excited when $V_g=20$ V. The first TM mode is excited at the BK7–graphene nanostrips–first sensing layer arrangement. The TM mode shows a symmetric behavior, i.e., one mode propagates at the graphene nanostrips–prism interface, and the other propagates between the graphene nanostrips and the first sensing layer arrangement. Scattering patterns are observed as air pockets are present in the graphene nanostrip layer. The scattered light reaches the second graphene layer and excites additional TM modes at the graphene–second sensing layer interface. Figures 4(b) and 4(c) show a similar tendency when $V_g=40$ V and 60 V, respectively. However, as the negative value of $\varepsilon _g$ (real) decreases with an increasing $V_g$, the excitation of TM modes in the second graphene layer increases with an increasing $V_g$. We have used $V_g=60$ V in the results presented in the following analysis. A recent study showed that a single layer of graphene sustained $V_g=60$ V [37]. As the proposed sensor has many graphene layers, it should be able to withstand the $V_g$ values applied in this work.

 

Fig. 4. Excitation of TM modes when $d_{\text {ZnO}}=5$ nm, $n_{S1}=n_{S2}=1.33$, $L_a=100$ nm, and $t_g=50$ nm with (a) $V_{g}=20$ V, (b) $V_{g}=40$ V, and (c) $V_{g}=60$ V.

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Figure 5 shows $R$-profiles as a function of the incident angle ($\theta _i$). As the proposed sensor has dual channels, the same or different sensing materials can be used for the channels. Figure 5(a) shows $R$-profiles when $n_{S1}=n_{S2}=1.33$ and $n_{S1}=n_{S2}=1.36$. In both cases, we observe two resonance dips. When $n_{S1}=n_{S2}=1.33$, we observe resonances at $49.80^\circ$ and $67.60^\circ$. We consider these two resonance angles as references, $\theta _{R1}$ and $\theta _{R2}$, for the first and the second sensing channels. On the other hand, when $n_{S1}=n_{S2}=1.36$, the first resonance occurs at $50.83^\circ$ and the second occurs at $70.20^\circ$. When $n_{S1}=n_{S2}=1.36$, the resonance angles shift and the $R$-profiles widen. At the same time, $R_{\text {min}}$ decreases slightly. We note that increasing $n_{S1}$ or $n_{S2}$ increases the light confinement, resulting in a decrease in $R_{\text {min}}$. In addition, increasing $n_{S1}$ or $n_{S2}$ increases the propagation loss of the excited TM modes [38]. Hence, the $R$-profiles widen.

 

Fig. 5. $R$-profiles of the proposed dual-channel refractive index sensor against the incidence angle for (a) different $n_{S1}=n_{S2}=n_{sc}$ values with $L_a=100$ nm and $t_g=50$ nm, (b) different $t_g$ values with $L_a=100$ nm and $n_{S1}=n_{S2}=1.33$, and (c) different $L_a$ values with $n_{S1}=n_{S2}=1.33$ and $t_g=50$ nm.

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Figure 5(b) shows the $R$-profile for different thicknesses of graphene nanostrips. $R$ value decreases when $t_g$ increases. However, when $t_g=50$ nm, the $R$ value is minimum. When $t_g>50$ nm, the $R$ value increases, indicating that the absorption of incident light decreases. A similar tendency is observed in Ref. [38]. In Fig. 5(c), we show the $R$-profile for three different values of $L_a$. We note that both TM resonances are minimum at $L_a=100$ nm, confirming the maximum absorption of incident light. Thus, in our proposed sensor, we set $L_a=100$ nm.

Figures 6(a) and 6(b) show the shifts of $\theta _{r1}$ and $\theta _{r2}$ for cases when $n_{S1}$ and $n_{S2}$ are the same or different. The shift in $\theta _{r1}$ and $\theta _{r2}$ increases as $n_{S1}$ or $n_{S2}$ increases. However, $\theta _{r1}$ shifts less than $\theta _{r2}$. When $n_{S1}=n_{S2}=1.45$, maximum value of $\theta _{r1}=53.88^ {\text o}$ and $\theta _{r2}=83.27^ {\text o}$ are observed. The angle shifting property is high when $n_{S1}=1.35$ to 1.45 and $n_{S2}=1.42$ to 1.45 for $\theta _{r1}$. Similar tendency is observed when $n_{S1}=1.37$ to 1.45 and $n_{S2}=1.41$ to 1.45 for $\theta _{r2}$. We note that the second sensing layer produces greater angle shifts and narrower spectral regions than the first. On the other hand, the proposed dual-channel refractive index sensor can sense two different sensing elements independently. For example, when $n_{S1}=1.36$ and $n_{S2}=1.40$, we get $\theta _{r1}=50.36^\circ$ and $\theta _{r2}=69.86^\circ$, as shown in Figs. 6(a) and 6(b), respectively.

 

Fig. 6. Resonance angles of the two channels of the proposed sensor (a) $\theta _{r1}$ and (b) $\theta _{r2}$ as functions of the sensing layers’ refractive indices.

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Figure 7(a) shows the resonance angle shifting when both channels have the same refractive index. When $n_{S1}=n_{S2}=1.33$, we find $\theta _{r1}=49.80^ {\text o}$ and $\theta _{r2}=67.60 ^ {\text o}$, respectively. Next, when $n_{S1}=n_{S2}=1.34$, we get $\theta _{r1}=49.99^ {\text o}$ and $\theta _{r2}=67.91 ^ {\text o}$. We calculate the sensitivities of the channels by $S_1=\Delta \theta _{r1}/ \Delta n_{S1}$ and $S_2=\Delta \theta _{r2}/ \Delta n_{S2}$. Figure 7(b) shows the combined sensitivity when both sensing channels have the same refractive index. The combined sensitivity $(S)$ of the proposed dual-channel sensor is calculated by multiplying the sensitivities of the individual channels as given by

Therefore, when $n_{S1}=n_{S2}=1.34$, $S=1645$ degrees/RIU. Increasing $n_{S1}$ and $n_{S2}$ with $n_{S1}=n_{S2}$ increases $S$ as well. When $n_{S1}=n_{S2}=1.45$, $S$ is the maximum with a value of 2530 degrees/RIU.

 

Fig. 7. (a) Resonance angles $\theta _{r1}$ and $\theta _{r2}$ against the same refractive index $(n_{S1}=n_{S2}=n_{sc})$ in both channels. (b) Sensitivity $(S)$ against the same refractive index $(n_{S1}=n_{S2}=n_{sc})$ in both channels.

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Figure 8 shows the sensitivity of the proposed sensor when $n_{S1}$ and $n_{S2}$ vary. Figure 8(a) shows the sensitivity of the first sensing channel, and Fig. 8(b) shows that of the second. We calculate the sensitivities of the first and second sensing channels using $S_1=(\theta _{r1}-\theta _{R1})/ (n_{S1}-1.33$) and $S_2=(\theta _{r2}-\theta _{R2})/(n_{S2}-1.33$), respectively. Both sensing channels’ sensitivity is the maximum when $n_{S1} =$ 1.340–1.355 and $n_{S2}=1.40$–1.45. We find $S_1=236$ degrees/RIU and $S_2=773$ degrees/RIU in a narrow refractive index region, which will help detect specific analytes with refractive index in this region with high sensitivity. Such high sensitivity in a narrow refractive index region has also been observed in Ref. [65]. In addition, the second sensing channel shows $\sim$3.25 times higher sensitivity than the first and significantly higher than the existing literature [52,66–69]. Recently, adjustable dual plasmons have been shown using single-layer graphene in the THz region, where the sensitivities are 0.92 THz/RIU and 1.08 THz/RIU for the first and the second transmission peaks, respectively [70]. We have compared our results with the existing literature in Table 1. For comparison, we have considered sensors that use 2-D graphene and operate at 633 nm incident wavelength.

 

Fig. 8. Sensitivities of the proposed sensor (a) $S_1$ and (b) $S_2$ against refractive index variations of the two channels.

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Table 1. Performance comparison of our proposed sensor with different recently reported sensors.

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We note that the 50-nm-thick graphene layer used in the proposed sensor will have many graphene monolayers. Researchers have recently demonstrated 100- and 200-nm-thick graphene layers [74,75]. Graphene’s optical properties are characterized by surface conductivity rather than volumetric permittivity. Bodepudi et al. showed that the conductivity of graphene could be modeled for a single layer and used to represent multiple layers by scaling the total conductivity by the number of layers [75]. Therefore, a $\sim$200-nm-thick graphene layer should behave similarly to monolayer or few-layer graphene. A 50-nm-thick graphene layer can be fabricated following the manufacturing process discussed in Ref. [74] or [75] and have monolayer-like optical properties. In addition, we have simulated the proposed structure using a graphene layer thickness of 3.4 nm, which is equivalent to only 10 graphene monolayers. The responses of the proposed sensor remain the same qualitatively, with a slight ($\lesssim 5$%) quantitative change. However, the sensor performance may significantly change if a 50-nm-thick graphite layer replaces the graphene layer.

7. Conclusion

We show that the unusual TM modes in graphene at visible wavelength can be excited using the proposed modified Kretschmann configuration without needing noble metal. Our proposed graphene nanostrips-based plasmonic sensor produces TM modes between graphene nanostrips and the first sensing layer. These nanostrips also scatter the incoming incidence light with a large propagating wave vector, producing another TM mode in the graphene–second sensing layer interface. The creation of TM modes depends on several factors, such as the gate voltage, incident wavelength, and thickness of ZnO. The proposed dual-channel refractive index sensor is highly sensitive when both channels have the same refractive index. In addition, it can detect refractive indices of the sensing channels separately using the two resonance dips. The structural and material properties used in the proposed sensor are conceivable and can easily be fabricated.