Introduction

The signatory characteristic of smaller wavelength of the SPs has brought forward widespread applications encompassing imaging [1, 2], sensing [3], nano-antenna [4], metamaterials [5,6,7], topological insulators [8], and recently ultra-fast processing [9, 10]. Direct light lacks momentum to excite these coherent charge density oscillations and therefore extra geometrical arrangements such as high refractive index prism, optical fiber/waveguide, grating, and rough surfaces are required to fetch the direct light the requisite momentum [3]. Conventionally, noble metals are used as SP exciting metallic layer. But these metals come with their own limitations such as thin film of gold (Au) agglomerates and forms island and therefore lacks uniformity; silver (Ag) and copper (Cu), on the other hand, are chemically unstable. To circumvent these issues of noble metals, conducting metal oxides (CMOs) are usually resorted on [11, 12]. These oxides not only show good conductivity as those of noble metals but can also form very thin uniform film [13]. An alternative route of taking advantage of remarkable properties of noble metals (Ag, Cu, etc.) bypassing their chemical unstableness is to cover the metal layers with thin protecting layer of some other almost non-permeable high permittivity materials such as graphene and silicon [14]. These covering materials not only protect the underlying metal from oxidation but also enhance the field within and therefore the device performance [13, 15, 16].

One of the ubiquitous applications of SPs is in refractive index sensing [17,18,19,20]. SPs excite at the interface of metal and dielectric and its field decay evanescently in transverse directions. The evanescently decaying tail of SPs in dielectric medium is very sensitive to the complex permittivity of the dielectric material, and therefore, the phenomenon has found enormous applications in the field of refractive index sensing. To realize SP-based sensors, two configurations have been proposed—the widely used Kretschmann configuration and the Otto configuration. Further, two methods of interrogation are practiced—wavelength interrogation and angular interrogation. Among numerous plasmonic sensing probes, optical fiber-based probes are found to demonstrate several advantageous features over other existing ones which include immunity to electromagnetic interferences, capability of remote sensing and online monitoring, miniaturization in size, ease of fabrication, and low cast.

In SP-based fiber-coupled bio-sensors, usually Au is used as SP exciting metallic layer. Au, in addition of being a chemically stable ideal (neglecting medium losses) plasmonic material, exhibits excellent bio-recognition properties. The hydrophobic surface of Au makes the immobilization of bio-entities such as proteins and antibody easy to achieve. Graphene, an sp2-hybridized, 2D, thinnest man-made material, has emerged as another competing plasmonic material endowed with virtues of bio-compatible materials [21]. Graphene has an extra edge on Au predominantly due to its large surface area. High charge carrier mobility incurred effective charge transfer, and the large wave vector inside the graphene results into the enhancement of the field and thereby the sensitivity of the graphene-based plasmonic sensors [22, 23]. In addition to its extensive applications in the field of sensing, it has found applications in numerous other fields such as in photo-detectors and transistors.

In the following, we propose a couple of SPR-based fiber-coupled refractive index sensors working in the IR region of the electromagnetic spectrum. As a surface exciting metallic layer, either Al or Cu has been utilized. On top of the metal layer, graphene and silicon are considered, respectively. These sensing probes are found to exhibit enormously high sensitivities with appreciable detection accuracies. Silicon being a high k-dielectric, a thin layer of it adds to the sensitivity of the device but with a limitation of formation of oxide layer on its surface which may lead to the deterioration the device performance. Furthermore, although, silicon has been reported to perform refractive index sensing, the applicability of such a probe is not promising in bio-sensing and therefore we have used graphene as an overlay which not only works as a bio-recognition layer but also protects the silicon from oxidation.

The Model

The schematic of the proposed sensing probe is shown in Fig. 1. To realize the fiber probe, cladding from the middle 1 cm section of the step-index multi-mode fiber is removed. On this bare core, a certain thickness of metal layer is deposited which is then followed by the deposition of the graphene and the silicon layers. Sensing liquid is kept in contact with the silicon layer. Transverse magnetically (TM) polarized light, from a polychromatic source, is launched in one end of the fiber and the transmitted light is detected from the other end. Light guiding in the fiber, on phase matching, gets coupled resonantly to the surface mode (SP). This phenomenon of resonant energy transfer is termed as surface plasmon resonance (SPR). The phase matching criteria for resonant transfer of energy is met at a particular wavelength, known as resonance wavelength λ res . The loss of the guided light due to the out-coupling appears at the output as a dip in the transmission/SPR spectrum.

Fig. 1
figure 1

Schematic of the fiber probe

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These sensors are usually characterized in terms of sensitivity and detection accuracy (DA) which are defined respectively as

$$ \mathrm{Sensitivity}=\frac{\varDelta {\lambda}_{res}}{\varDelta {n}_s}; $$
(1)

where numerator represents a change in resonance wavelength and the denominator the corresponding change in the refractive index of the sensing medium (n s );

$$ DA=\frac{1}{\varDelta {\lambda}_{fwhm}}; $$
(2)

where denominator represents the full width at half maximum of the resonance dip. DA predicts the accuracy with which minimum of the resonance dip can be located.

The position of the dip in the transmission spectrum varies with the sensing medium refractive index (RI). In the proposed study, we have chosen the RI of the sensing medium n s  = 1.330 RIU and the change in the RI introduced by the adsorption of bio-molecules Δn s  = 0.002 RIU. Choosing aqueous sensing medium RI equal to 1.330 RIU has wide open prospects in bio-sensing as the ambient RI environment of most of the bio-samples is around 1.330 RIU. For simulation, the diameter of the fiber is taken to be 600 μm and the numerical aperture 0.24.

Dispersion Relations

For dispersive modeling of the different materials involved, following dispersion relations have been used:

Dispersive behavior of the RI of the fiber core material is accounted for by Sellmeier relation given as [14]

$$ {n}_{core}\left(\lambda \right)=\sqrt{1+\frac{a_1{\lambda}^2}{\lambda^2-{b}_1^2}+\frac{a_2{\lambda}^2}{\lambda^2-{b}_2^2}+\frac{a_3{\lambda}^2}{\lambda^2-{b}_3^2}}; $$
(3)

where as and bs are the Sellmeier coefficients and for pure silica glass

$$ \begin{array}{lll}{a}_1=0.6961663,\hfill & {a}_2=0.4079426,\hfill & {a}_3=0.8974794,\hfill \\ {}{\mathrm{b}}_1=0.0684043,\hfill & {\mathrm{b}}_2=0.1162414,\hfill & {\mathrm{b}}_3=9.896161\hfill \end{array} $$

Drude relation is used to model the wavelength dispersion of metals [14]

$$ \upvarepsilon \left(\uplambda \right){=\upvarepsilon}_{\mathrm{r}}{+\mathrm{i}\upvarepsilon}_{\mathrm{i}}=1-\frac{\uplambda^2{\uplambda}_{\mathrm{c}}}{\uplambda_{\mathrm{p}}^2\left({\uplambda}_{\mathrm{c}}+\mathrm{i}\uplambda \right)}; $$
(4)

where λ p is the wavelength corresponding to the bulk plasma frequency and λ c denotes the collision wavelength and is related to the medium losses. The values of λ p and λ c for Cu and Al are listed in Table 1.

Table 1 Dispersion coefficients for metals
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The dispersion relation of the graphene reads as [24, 25]

$$ n\left(\lambda \right)=3.0+ i\frac{C}{3}\lambda; $$
(5)

where C = 5.446/μm is a constant. The single sheet thickness of graphene is ∼0.34 nm. Its total thickness depends on the total number of deposited layers (ℒ) and is given as 0.34 * ℒ nm.

Dispersive modeling of the silicon is accomplished using the following relation [26]

$$ n= A+{A}_1{e}^{-\lambda /{t}_1}+{A}_2{e}^{-\lambda /{t}_2}; $$
(6)

where A = 3.44904, A 1 = 2271.88813, A 2 = 3.39538, t 1 = 0.05304, and t 2 = 0.30384. The wavelength (λ) in all of the above relations is measured in micron.

Transmitted Power Calculation

Out of all the rays launched into the fiber input face, only those gets guided which are launched within a well-defined range of angle varying from θ 1 = sin−1(n cl /n core ) to θ 2 = π/2, where n core and n cl are, respectively, the refractive indices of the fiber core and the cladding. The angle θ is the angle between the ray and the normal to the core-cladding interface of the fiber. The total transmitted power delivered at the output end of the fiber, considering the guidance of all the launched rays, is given by [13]

$$ {P}_{trans}=\frac{\underset{\theta_1}{\overset{\theta_2}{\int }}{R}_p^{N_{ref}\left(\theta \right)}\frac{n_{core}^2 \sin \theta \cos \theta}{{\left(1-{n}_{core}^2{ \cos}^2\theta \right)}^2} d\theta}{\underset{\theta_1}{\overset{\theta_2}{\int }}\frac{n_{core}^2 \sin \theta \cos \theta}{{\left(1-{n}_{core}^2{ \cos}^2\theta \right)}^2} d\theta} $$
(7)

Where \( {N}_{ref}\left(\theta \right)=\frac{L}{D \tan \theta} \); N ref (θ) is the total number of reflections undergone by the ray in sensing probe of length L and core diameter D. R p is reflectance calculated using Fresnel’s formulae and well-developed multi-layer matrix method [27, 28].

Results and Discussion

In the following, we have studied the two SPR-based fiber-coupled sensors: the first using Cu as metal layer and the second using Al as metal layer. These two sensors are characterized in terms of sensitivity and DA. All the characterizations have been performed such that the transmission dips always be confined within the wavelength stretch of 1 to 3 μm which is well in the infrared region of the electromagnetic spectrum. Also, we have assumed that the abovementioned dispersion relations for the different layers are valid in the wavelength window of investigation. During optimization of the probe for sensitivity, it has been taken care of that DA always remains definable, i.e., arms of the transmission dips do not become shallower than the half of the maximum of the transmitted power (see ref. [14]). The details of the two probes are as follows.

Probe Using Cu as Metal Layer

To realize the probe, Cu is considered over the unclad portion of the fiber core which is followed by the graphene layers and then silicon as shown in Fig. 1. To start with, thickness of the Cu layer is fixed at 50 nm and only single sheet of graphene (single sheet thickness ℒ ∼0.34 nm) is considered. The thickness of the upper most layer of silicon is varied to maximize the sensitivity of the probe. Figure 2a shows the variation of sensitivity of this probe with thickness of silicon layer. The figure clearly depicts that with increasing thickness of silicon the sensitivity of the probe increases. We restricted the increasing thickness of silicon at 80 nm because beyond this thickness the transmission dip crosses the far edge (3 μm) of our wavelength window of investigation. Note that in Fig. 2a and in the figures thereafter, the layer thicknesses (on x-axis) are in the unit of micron. Next to optimize the no. of graphene layers, we fix the Cu layer thickness at 50 nm and silicon layer thickness at its optimized value of 80 nm. Figure 2b shows the variation of sensitivity with no. of graphene layers, and it can be observed that sensitivity becomes maximum for eight layers of graphene and therefore 8 * ℒ is the optimized thickness of the graphene layer. Note that with the addition of the graphene sheets, the sensitivity increases up to a certain limit and thereafter it starts to decrease. This behavior is attributed to the fact that at higher thickness of graphene, the losses of graphene sheets take over and therefore the electric field and hence the sensitivity enhancing characteristic of graphene deteriorate. Variation of sensitivity with Cu layer thickness is shown in Fig. 2c for probe with eight layers of graphene and 80 nm of silicon layer thickness. Maximum sensitivity of 23.50 μm/RIU is observed for probe with 40 nm thickness of Cu layer. Figure 2d–f reveals the corresponding cases of variation of DAs with different layers’ thicknesses as depicted in Fig. 2a–c, respectively. DA for the probe optimized for maximum sensitivity is found to be 1.879/μm. The SPR (transmission) spectra at the two values of the sensing medium RI for the optimized probe are presented in Fig. 2g which clearly shows that the SPR dips are well below the 3 μm wavelength limit.

Fig. 2
figure 2

a Variation of sensitivity with thickness (in μm) of silicon layer for probe with 50 nm of Cu layer and single layer of graphene. b Variation of sensitivity with number of graphene layers for probe with 50 nm of Cu layer and 80 nm of silicon layer. c Variation of sensitivity with thickness (in μm) of Cu layer for probe with eight layers of graphene and 80 nm of silicon layer. d Variation of DA with thickness (in μm) of silicon layer for probe with 50 nm of Cu layer and single layer of graphene. e Variation of DA with number of graphene layers for probe with 50 nm of Cu layer and 80 nm of silicon layer. f Variation of DA with thickness (in μm) of Cu layer for probe with eight layers of graphene and 80 nm of silicon layer. g SPR (transmission) curves for probe with 40 nm of Cu layer, eight layers of graphene, and 80 nm silicon layer. n s represents the refractive index of the sensing layer

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Further, to make the above probe compatible with the bio-sample sensing, either the silicon’s surface is to be activated with proper antigen, enzymes, etc. or a thin layer of bio-adsorbing material is to be coated on it. Owing to the excellent bio-adsorbing characteristics of graphene, we consider a few sheets of graphene on the previously optimized probe. As shown in Fig. 3a, with the deposition of graphene sheets, the sensitivity of the device decreases. As a trade-off, we choose only single sheet of graphene. This optimized probe results a maximum sensitivity of 20 μm/RIU with DA of 1.808/μm (Fig. 3b). Decrease in the DA with graphene layer thickness in Fig. 3b also reveals the lossy nature of the graphene sheet. Figure 3c shows the corresponding SPR spectra.

Fig. 3
figure 3

a Variation of sensitivity with number of outer graphene layers for probe with 40 nm of Cu layer, eight layers of inner graphene, and 80 nm of silicon layer. b Variation of DA with number of outer graphene layers for probe with 40 nm of Cu layer, eight layers of inner graphene, and 80 nm of silicon layer. c SPR (transmission) curves for probe with 40 nm of Cu layer, eight layers of inner graphene, 80 nm silicon layer, and single layer of outer graphene. n s represents the refractive index of the sensing layer

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Probe Using Al as Metal Layer

In this probe design, the Cu layer in the previous probe is replaced with Al leaving the rest of the layers the same. Initially, the thickness of Al is fixed at 50 nm, single layer of graphene is considered, and the thickness of silicon layer is varied to maximize the sensitivity of the probe as shown in Fig. 4a. As we increase the thickness of silicon layer, sensitivity increases but as soon as the thickness goes beyond to 85 nm, the DA becomes undefined (due to the shallowness of longer wavelength arm of the dip) and alongside the SPR dip crosses the 3 μm limit. Hence, we choose 85 nm as optimized thickness of the silicon layer.

Fig. 4
figure 4

a Variation of sensitivity with thickness (in μm) of silicon layer for probe with 50 nm of Al layer and single layer of graphene. b Variation of sensitivity with number of graphene layers for probe with 50 nm of Al layer and 85 nm of silicon layer. c Variation of sensitivity with thickness (in μm) of Al layer for probe with eight layers of graphene and 85 nm of silicon layer. d Variation of DA with thickness (in μm) of silicon layer for probe with 50 nm of Al layer and single layer of graphene. e Variation of DA with number of graphene layers for probe with 50 nm of Al layer and 85 nm of silicon layer. f Variation of DA with thickness (in μm) of Al layer for probe with eight layers of graphene and 85 nm of silicon layer. g SPR (transmission) curves for probe with 40 nm of Al layer, eight layers of graphene, and 85 nm silicon layer. n s represents the refractive index of the sensing layer

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In Fig. 4b, the no. of graphene sheets are optimized for maximum sensitivity of the probe with 50 nm of Al layer and optimized 85 nm thickness of silicon. The sensitivity is maximum for eight layers of graphene and beyond this no. of graphene layers the DA becomes undefined. In Fig. 4c, we have optimized the thickness of Al layer which comes out to be 40 nm with sensitivity of 24 μm/RIU. Figure 4d–f shows the corresponding DAs. DA for the optimized design is found to be 2.198/μm. The SPR plots for such a probe are shown in Fig. 4g.

Now, as discussed previously, for bio-sensing purposes, we consider a bio-recognition graphene layer on the top of the silicon layer. To optimize the no. of graphene layers, the sensitivity of this modified probe is observed with respect to the no. of graphene layers as depicted in Fig. 5a. The sensitivity is maximum (19.50 μm/RIU) when no. of graphene layers are either two or three. We choose two layers of graphene for our optimized design to have better DA which is 1.961/μm as shown in Fig. 5b. SPR plots for this probe showing SPR activity in the IR region are depicted in Fig. 5c.

Fig. 5
figure 5

a Variation of sensitivity with number of outer graphene layers for probe with 40 nm of Al layer, eight layers of inner graphene, and 85 nm of silicon layer. b Variation of DA with number of outer graphene layers for probe with 40 nm of Al layer, eight layers of inner graphene, and 85 nm of silicon layer. c SPR (transmission) curves for probe with 40 nm of Al layer, eight layers of inner graphene, 85 nm silicon layer, and two layers of outer graphene. n s represents the refractive index of the sensing layer

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As a concise summary, all the results of the present study are listed in Table 2. Note that the metals used in the study are highly chemically reactive and easily forms oxides. But, since they are protected with overlays of graphene and silicon, their chemical instability is no more an issue. Further, use of Cu and Al, being low-cost materials as compared to the Au and Ag, reduces the overall cost of the sensing probe considerably. The optimum value of sensitivity complying with the constraint of DA (i.e., definable fwhm width of transmission minima) resulted out of this study is 24 μm/RIU which, to the widest of our knowledge, is highest in the IR region around the given aqueous sensing medium RI range (see Table 3). Additionally, the sensitivity could further be increased by increasing the sensing medium refractive index until it becomes almost equal to that of the fiber core.

Table 2 Summary of results
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Table 3 Comparison with SPR-based IR sensors
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Table 3 presents a comprehensive comparative study of the proposed and the other exiting SPR-based sensing probes working in the IR domain of electromagnetic spectrum with sensing medium RI varying around that of water. The only comparable sensitivity is reported in ref. [32], but the SPR curves therein do not satisfy the constraint set by our definition of DA, i.e., DA is extremely poor and therefore proposed sensors stand far better.

Conclusion

A couple of SPR-based fiber-coupled IR sensors have been studied. Constituent layers of the probes are optimized, under the constraint set by DA, to exhibit giant sensitivities of 23.50 and 24 μm/RIU for probes using Cu and Al as metallic layer, respectively. The optimized design parameters of the probes are Cu (40 nm)/graphene (eight layers)/silicon (80 nm) and Al (40 nm)/graphene (eight layers)/silicon (85 nm). The corresponding bio-sensors having additional layers of graphene (single and two layers respectively) exhibit sensitivities of 20 and 19.50 μm/RIU with appreciably good DAs.

We hope that the present study will have high impact in bio- and chemical sensing.