1 Introduction

Recently, surface plasmon resonance (SPR) sensors have many advantages such as real-time and fast detection, low cost, simple structure, and high sensitivity. It has broad application prospects in biological sensors, biochemical sensors, gas sensing, diagnostics of medical issues [1, 2], optical switching, nonlinear optics, photodetection [3], and food safety detection [4]. SPR refers to the coherent charge density oscillations of the electrons at the metal–dielectric interface stimulated by p-polarized electromagnetic waves which are very sensitive to any changes in the refractive index (RI) of the surrounding [5, 6]. The propagating characteristics have been illustrated at the metal–dielectric interface by surface plasmon waves (SPW) with transverse directions decaying [7]. This decaying plays an important role in the sensing of any variations in the RI of the surrounding medium [8, 9]. The first observation of SPR phenomena began more than one hundred years ago by Wood [10]. Then, Liedberg initially used SPR for sensing purposes in 1983[11]. After that, the developments in the field of SPR sensors have drawn great attention and a lot of researches have been designed and configured [5, 12, 13].

There are two of the commonly used types of configurations for the SPR geometrics [14]; Kretschmann configuration [7], and Otto’s configuration [15]. The configurations of Kretschmann and Otto are based on the principle of attenuated total internal reflection (ATR) mechanism. Due to Otto’s configuration disadvantages, the configuration of Kretschmann has been used in a wide range [7, 16, 17].

There are a lot of techniques for SPR sensors excitation monitoring such as angle [18, 19], phase [20], intensity [21], and wavelength interrogation [4, 22]. For the configuration of Kretschmann, there are two types of interrogation: angle interrogation, and wavelength interrogation. For wavelength interrogation, the required light for the excitation is polychromatic [23] such as sunlight, a halogen lamp, LED, and OLED [24]. In this paper, we focus on SPR wavelength interrogated sensing technology [4].

The performance of SPR sensors depends on sensitivity, because it illustrates the ability of the sensor to detect the sensing medium or sample types and the concentration of these samples. High sensitivity is accomplished by the realization of a resonance angle large shift in angle interrogation or a resonance wavelength in a wavelength interrogation with the sensing mediums features small change, i.e., refractive index (RI)[25].

Kretschmann configuration remains the basic standard for commercial and conventional SPR systems but they have some disadvantages such as bulky, expensive, and not suitable for the remote sensing applications technology. So, waveguides and optical fiber-based SPR sensors have been developed in order to address these limitations [26]. Due to high sensitivity, compactness, remote sensing, the weight is light, flexible mechanics, and the ability of long-distance optical signal transmission; optical fiber SPR sensors have gained considerable attention in the last years. Such a sensor allows the sensing and the miniaturization in inaccessible locations [27].

Noble metals such as gold (Au) [28], silver (Ag) [29, 30], copper (Cu) [31], aluminum (Al) [32] have been used as a metal layer in the fabrication and the designing of SPR sensors. Silver (Ag) shows better detection accuracy, high resolution, and low cost. So, it has been used in a wide range of SPR sensors configurations [26]. Earlier, platinum (Pt) has been used as a metal layer in the high sensitivity optical fiber SPR sensors. Platinum metal is extremely transparent, has a high melting point, is considered inert, and has high chemical stability. Moreover, due to platinum (Pt) good efficiency and long stability, it is highly involved in various research areas [33].

A lot of researches have been developed to use indium tin oxide (ITO) as a metal layer in SPR sensors and experimentally investigated the SPR sensors of the silver interfaces protected by ITO thin film and these researches discuss the addition of the ITO layer on a silver layer. The addition of the ITO layer has been illustrated the improvements in the sensitivity and the stability of the SPR sensor [34, 35]. In a further experimental study, Szunerits et al. showed that the addition of the ITO layer on the silver layer protects against chemical degradation [36]. Conducting metal oxides (CMOs), like ITO, have recently been used as plasmonic material in SPR-sensing purposes, because they have a lot of advantages such as; a uniform thin layer, chemical stability, and band to band transitions absence [37].

There are many existing 2D nanomaterials such as transition metal dichalcogenides (TMDC), silicon (Si), germanium (Ge), and graphene (G) [38]. Graphene has been commonly used since it was discovered in 2004[39] as it has a special and unique electrical and optical characteristics [23] including; high carrier mobility, and optical transparency [40]. Graphene is considered an excellent material for highly sensitive sensors as it provides good assistance for the absorption of biomolecules due to its large surface area [16, 41] and the high real part of the dielectric constant can better help the metal energy of light absorption [42]. Graphene has drawn great attention in recent technologies and applications such as optical sensing, quantum effects [43], charge transfer plasmon (CTP) Metadevices [44], gated-controlled plasmonic metamaterials, light-harvesting, and nonlinear photonics [45].

In this study, a new fiber optic SPR sensor scheme has been developed for the enhancement of sensitivity (S) and figure of merit (FoM). The proposed SPR structure is based on a silver layer, a platinum layer, and an indium tin oxide (ITO) layer in addition to a graphene layer, which allows the biosensors to be suitable for highly sensitive chemical and biological applications. The resonance wavelengths, transmission curve, FWHM, FoM, and the sensitivity are theoretically analyzed using Fresnel equations and TMM. The contents of this paper are prearranged as; Sect. 2 is the modeling and the designing of the Sensor proposal. Section 3 includes SPR sensor metrics such as sensitivity, FWHM, and FoM. The simulations, discussions, and results are conferred in Sect. 4. Finally, Sect. 5 is the summary and the conclusion of our observations for this work.

2 Proposed sensor design and modeling

The plastic cladding around the core from the middle portion of a step-index multimode plastic-clad silica (PCS) fiber removed and coated with different materials (Ag, Pt, ITO, Graphene) and enclosed with the sensing medium as shown in Fig. 1. As mentioned above, the analysis of our configured SPR sensors has been done utilizing a wavelength interrogation method. A light source of polychromatic is launched with suitable parameters into the end of fiber optic and this launched light is received at the other end of the fiber. The resonance wavelengths depend on the sensing medium refractive index (RI).

Fig. 1
figure 1

Proposed optical fiber-based SPR sensor schematic diagram

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Fused silica optical fiber core is used with the diameter of (D = 600 μm). According to the Sellmeier dispersion relation, the fused silica refractive index \( \left( {n_{f} } \right) \) depends on the variation of the wavelengths as in Eq. (1) [46]:

$$ n_{f} \left( \lambda \right) = \sqrt { 1 + \frac{{k_{1 } \lambda^{2} }}{{\lambda^{2} - m_{1}^{2} }} + \frac{{k_{2 } \lambda^{2} }}{{\lambda^{2} - m_{2}^{2} }} + \frac{{k_{3} \lambda^{2} }}{{\lambda^{2} - m_{3}^{2} }}} $$
(1)

where (k1, k2, k3, m1, m2, m3) are Sellmeier coefficients which equal (0.6961663, 0.4079426, 0.8974794, 0.0684043 × 10−6, 0.1162414 × 10−6, 9.896161 × 10−6), respectively.

The second layer is Ag film and according to Drude formula as in Eq. (2) the complex RI of this metal film can be calculated as [46]:

$$ n_{m} = \sqrt {\varepsilon_{m} } = \sqrt {\varepsilon_{mr} + i\varepsilon_{mi} } = \left[ {1 - \frac{{\lambda^{2} \lambda_{c} }}{{\lambda_{p}^{2} \left( {\lambda_{c} + i \lambda } \right)}}} \right]^{{\frac{1}{2}}} $$
(2)

where collision wavelength is \( \lambda_{c} \) and the plasma wavelength is \( \lambda_{p} \), which \( \lambda_{c} \) and \( \lambda_{p} \) for Ag equal to 1.7614 × 10−5 m and 1.4541 × 10−7 m, respectively, and \( \varepsilon_{m} \) is the metal dielectric constant [47, 48]. The Imaginary part of the dielectric constant of the silver layer is not so high to own a good absorption of light for illustrating a great SPW excitation. To obtain a great SPW excitation, the deposition of graphene layers, Pt layers, and ITO layers on the silver metal layer surface has been used [19].

The following layer is platinum (Pt) and the complex RI and dielectric constant of Pt can be calculated from Drude model as in Eq. (2) with \( \lambda_{c} \) and \( \lambda_{p} \) values of 1.7614 × 10−5 m and 1.4541 × 10−7 m, respectively [49]. The fourth layer is indium tin oxide (ITO) and the RI and ITO dielectric constant can be derived from Drude model as in the following equation:

$$ n_{\text{ITO}} = \sqrt {\varepsilon_{\text{ITO}} } = \sqrt {\varepsilon_{\text{ITOr}} + i\varepsilon_{\text{ITOi}} } = \left[ {3.8 - \frac{{\lambda^{2} \lambda_{c} }}{{\lambda_{p}^{2} \left( {\lambda_{c} + i\lambda } \right)}}} \right]^{{\frac{1}{2}}} $$
(3)

where the values of \( \lambda_{c} \) and \( \lambda_{p} \) for ITO are 11.12 × 10−6 m and 5.649 × 10−7 m, respectively [31, 37, 50].

Graphene is the fifth layer of our design configuration with a complex RI that can be obtained from the following formula (4):

$$ n_{\text{Gr}} = 3 + i \times \frac{C}{3} \times \lambda $$
(4)

With the value of C = 5.446 × 10−6 m−1[52]. The graphene monolayer thickness is 0.34 nm. In the present study, this layer can be considered as d5 = G×0.34 nm. Where, G is graphene layers numbers [17, 51]. In our calculations, the mesh size is considered to be 5 nm. The sixth layer is the sensing medium with RI of ns = 1.33. Where (L) in Fig. 1 is the sensing medium length with the optimized value of L = 15 mm. The length of sensing medium (L) has a clear effect on the performance of the sensing.

Multilayer scheme sensors analysis using the transfer matrix method (TMM) and Fresnel equation coefficients for calculating reflectivity are more accurate, efficient, and take no approximation into account. For a model with L number of a layer as shown in Fig. 1 after applying boundary conditions tangential field can be as follow [52,53,54]:

$$ \left[ {\begin{array}{*{20}c} {\frac{{H_{1} }}{{E_{1} }}} \\ \end{array} } \right] = K_{2} K_{3} K_{4} K_{5} \ldots K_{L - 1} \left[ {\begin{array}{*{20}c} {\frac{{H_{L - 1} }}{{E_{L - 1} }}} \\ \end{array} } \right] $$
(5)

where \( H_{1} , H_{L - 1} \) and \( E_{1} ,E_{L - 1} \) are the magnetic and the electric fields tangential components of the first and Lth layer. For a propagating wave through medium K toward medium K + 1, it can be described by the transfer matrix as shown in the following Eq. (6):

$$ K_{L} = \left( {\begin{array}{*{20}l} {\text{Cos} \beta_{L} } \hfill & { - i \sin \beta_{L} /q_{L} } \hfill \\ { - iq_{L} \sin \beta_{L} } \hfill & {\text{Cos} \beta_{L} } \hfill \\ \end{array} } \right) $$
(6)

K is the combined multilayer structure’s overall characteristic matrix which can be obtained from the following equation:

$$ K = \mathop \prod \limits_{N = 2}^{L} K_{L} = \left( {\begin{array}{*{20}c} {K_{11} } & {K_{12} } \\ {K_{21} } & {K_{22} } \\ \end{array} } \right) $$
(7)

In order to calculate transfer matrix; phase shift qL and admittance βL should be computed using the following equations:

$$ q_{L} = \frac{{\left( {\varepsilon_{L} - n_{1}^{2} \sin^{2} \theta_{1} } \right)^{{\frac{1}{2}}} }}{{\varepsilon_{L} }} $$
(8)
$$ \beta_{L} = \frac{2\pi }{\lambda } d_{L} \left( {\varepsilon_{L} - n_{1}^{2} \sin^{2} \theta_{1} } \right)^{1/2} $$
(9)

where \( \lambda \) is the wavelength and \( \theta_{1} \) is the angle for the incident light. Also, \( d_{L} \) and \( \varepsilon_{L} \) are the thickness and the dielectric constant of Lth layer. Then, the calculation of the total reflection coefficient (rp) of the p-polarized(TM) incident light wave can be as follow:

$$ r_{p} = \frac{{\left( {K_{11} + K_{12} q_{L} } \right)q_{1} - \left( {K_{21} + K_{22} q_{L} } \right)}}{{\left( {\left( {K_{11} + K_{12} q_{L} } \right)q_{1} + \left( {K_{21} + K_{22} q_{L} } \right)} \right)}} $$
(10)

The reflectivity for defined multilayer configuration should be obtained and it can be given by the following equation:

$$ R_{p} = \left| {r_{p} } \right|^{2} $$
(11)

The generalized expression, for the normalized fiber optic SPR sensor power transmitted, can be given as follows:

$$ T_{P } = \frac{{\mathop \smallint \nolimits_{{\theta_{\text{cr}} }}^{{{\raise0.7ex\hbox{$\pi $} \!\mathord{\left/ {\vphantom {\pi 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} R_{P}^{{N_{\text{ref}} \left( \theta \right)}} \frac{{n_{\text{co}}^{2} \sin \theta \cos \theta }}{{(1 - n_{\text{co}}^{2} \cos^{2} \theta ) ^{2} }}{\text{d}}\theta }}{{\mathop \smallint \nolimits_{{\theta_{\text{cr}} }}^{{{\raise0.7ex\hbox{$\pi $} \!\mathord{\left/ {\vphantom {\pi 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} \frac{{n_{\text{co}}^{2} \sin \theta \cos \theta }}{{(1 - n_{\text{co}}^{2} \cos^{2} \theta ) ^{2} }}{\text{d}}\theta }} + 1 $$
(12)

where \( \theta_{\text{cr}} \) is critical angle of the fiber optic which can be obtained from \( \theta_{\text{cr}} = \sin^{ - 1} \left( {\frac{{n_{\text{clad}} }}{{n_{\text{co}} }}} \right) \), \( n_{\text{Co}} \) is the refractive index of the fiber core, and \( n_{\text{clad}} \) is the refractive index of the fiber cladding. \( N_{\text{ref}} \) is the number of ray reflections in the surface plasmon resonance fiber optic sensor which equal \( N_{\text{ref}} \left( \theta \right) = \frac{L}{D\tan \left( \theta \right)} \) where, D is diameter of fiber core and L is the length of sensing medium.

2.1 SPR sensors performance metrics

The sensitivity of SPR sensors can be obtained from the ratio between, the change in resonance wavelength,\( \Delta \lambda_{\text{res}} \) and, the change of refractive indices (RIs) for the sensing mediums,\( \Delta n \). The sensitivity of SPR sensors is obtained from Eq. (13) [54,55,56,57]:

$$ {\text{Sensitivity}}\left( {\text{S}} \right) = \frac{{\Delta \lambda_{\text{res}} }}{\Delta n}{\text{nm}}/{\text{RIU}} $$
(13)

The calculation of FWHM is determined as wavelength changes at the half of transmission curve [2, 58]. FWHM can be expressed as (14):

$$ {\text{FWHM}} = \Delta \lambda_{0.5} \;{\text{nm}} $$
(14)

FoM can be derived utilizing the following Eq. (15) [1, 59, 60]:

$$ {\mathrm{FoM}} = \frac{\mathrm{Sensitivity}}{\mathrm{FWHM}}{\mathrm{RIU}}^{ - 1} $$
(15)

Higher values of sensitivity and FoM are very important in order to obtain high-performance sensors [61].

3 Results and discussions

Firstly, Relation between the incidence of light modes and the performance of SPR sensors has been investigated. The Sensitivity and FoM are analyzed with the variations of the different light incidence mode or angles (θ). These modes are used for the excitation of SPR dips. The values of the incident angle are set to θ = 1.48, 1.49, 1.5, 1.51, and 1.52, respectively. In order to transmit the light in the multimode fiber, total internal reflection should be satisfied \( \left( {\theta > \theta_{\text{cr}} } \right) \). For our numerical studies, the values of following parameters are used, (fiber core diameter D = 600 μm, the length of sensing region L = 15 mm, the thickness of Ag layer = 30 nm, Pt layer thickness = 30 nm, ITO layer thickness = 4 nm, Graphene layer thickness = a monolayer = 0.34 nm and sensing medium with the RI of 1.33 RIU), in our design configuration. And these thickness values are the optimized values and it will be discussed in this section of the paper.

As it is obvious from Fig. 2, the SPR dips move to higher wavelength and the depth of SPR dips are increased with decreasing the value of θ. Also, this figure illustrates that the excitation mode of SPR cannot be observed at θ = 1.49 as the lowest point in the dip of SPR became flat and the resonance wavelength cannot be detected. The flat point of SPR dip is caused by the evanescent field penetration of higher-order incident modes “θ ≤ 1.49” through the layer of sensing leading to a leak of light instead of the absorption of resonance. For the angular control, there are a lot of methods for incident angle adjustments. First, the light is launched through a ring mask. Then by using a microscope objective, collimated beams are then focused at the center of the input of the fiber. Second, the fiber grinding or polishing method is also used to control the incident angle. The SPR coupling wavelength can be tuned selectively by the angle of incidence enhancement between the photon and the sensing area; with the fiber optic sensors, this can be achieved by the modification in the geometry of the tip of the probe.

Fig. 2
figure 2

Variation in transmission with the variation in the wavelength for different incidence angle

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In Fig. 3a, the relation between the resonance wavelength and the refractive index with respect to incidence angle (light modes) variations has been demonstrated. As shown in this figure, the resonance wavelength starts to change from 789 nm at RI = 1.33 and reached to 913 nm at RI = 1.36 RI for θ = 1.5. Then, with increasing the value of θ, the resonance wavelength decreasing gradually to range from 785 nm at RI = 1.33 to 907 nm at RI = 1.36 for θ = 1.51. After that, at θ = 1.52, the range of the resonance wavelengths is from 782 nm at RI = 1.33 to 904 nm at RI = 1.36.

Fig. 3
figure 3

a Resonance wavelengths versus refractive index for different incidence angle b Sensitivity versus incidence angle

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Figure 3b shows the relation between the sensitivity and the incidence angle, as it is obvious from this figure there is an increase in the sensitivity with decreasing the value of the incidence angle (θ) or in other meaning higher-order incident light mode. The value of sensitivity is 4150 nm/RIU at θ = 1.5 then it became 4060 nm/RIU and the lowest value of sensitivity has been achieved at θ = 1.52 to be 4002 nm/RIU.

After that, the figure of merit (FoM) is an important parameter for the optimization of the efficiency and the quality of the sensors and this has been illustrated in Fig. 4b. Due to the broadening happened to the transmission curve in Fig. 2, the FWHM increases with increasing the incidence angle with the values of 59 nm at θ = 1.5 and 86 nm at θ = 1.51. Then, the highest value is realized at θ = 1.52 to be 117 nm. As the figure of merit (FoM) is directly related to the sensitivity and inversely proportional to the FWHM so the figure of merit increases with decreasing the values of FWHM. From Fig. 4b, FoM value is 70 RIU−1 at θ = 1.5 then it decreased to be 34 RIU−1 at θ = 1.52.

Fig. 4
figure 4

a FWHM versus different incidence angle (Light Modes). b Figure of merit versus incidence angle

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Secondly, the optimization of the sensing medium layer length (L) has been taken into consideration for better SPR sensors design configuration. The optimized length of the sensing layer is shown in Fig. 5 that shows the relation between the transmission power and wavelengths regarding the variations of length for the sensing layer. As it is illustrated in Fig. 5, the optimized length of the sensing layer is 15 mm. While increasing the sensing medium length greater than 15 mm (20 mm and 25 mm) the dip of SPR becomes flat and there is no detection of the resonance wavelength. With decreasing the length of less than 15 mm (5 mm and 10 mm), the transmission decreased gradually.

Fig. 5
figure 5

Variation in transmission with variation in the wavelengths for different sensing layer length

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As it is demonstrated in Fig. 6a, the resonance wavelengths are increased with RI increasing for different sensing medium layer lengths. At sensing medium layer length of 5 mm, the resonance wavelength raises up gradually from 785 nm at RI = 1.33 to 907 nm at RI = 1.36. Then at L = 10, the resonance wavelength at RI = 1.33 is 787 nm and became 910 nm at RI = 1.36. Finally, the resonance wavelengths are maximized, for L = 15 mm, from 789 nm at RI = 1.33 to 913 nm at RI = 1.36.

Fig. 6
figure 6

a Resonance wavelengths versus refractive index for different sensing medium layer length b Sensitivity versus sensing medium layer length

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Form Fig. 6b, the sensitivity has been enhanced by increasing the sensing medium layer length (L). The minimum value of the sensitivity is 4000 nm/RIU and it has been achieved at the sensing medium layer length of L = 5 mm then the sensitivity became 4061 nm/RIU at L = 10 mm after that the maximum sensitivity occurred at L = 15 mm to be 4150 nm/RIU. As it is evident from Fig. 7, FWHM ascends with enlarging the sensing medium layer length. As there is a strong relationship between the sensitivity, FoM, and the FWHM, FWHM increases by increasing the sensing layer length to vary from 40 nm at L = 5 mm to 59 nm at L = 15 mm and this occurs due to the broadening in the power transmission curve as in Fig. 5. As a result, FoM decreases with sensing medium layer length increasing. As shown in Fig. 7b, the maximum value of the FoM is 100 RIU−1 at L = 5 mm. Then, at the sensing medium layer length of L = 10 mm, the FoM is 84 RIU−1. Finally, the minimum value of FoM has been detected at L = 15 mm with a value of 70 RIU−1.

Fig. 7
figure 7

a FWHM versus different sensing medium layer length b Figure of merit versus incidence angle

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The maximization for the thickness of the silver (Ag) layer is mandatory for the optimization of the performance of the SPR sensors. The relation between the transmission power and the wavelength, taking into consideration different thicknesses of the Ag layer, is shown in Fig. 8. As it is clear from this figure the transmission power increases with increasing Ag layer thickness and the resonance wavelength slowly increases. From this figure, the optimized layer of Ag layer thickness is 30 nm and lower than this value at 20 nm of Ag the dip of SPR became flat and the detection accuracy may be poor but there is a broad band of resonance which happens due to absorption loss rather than scattering loss inside a thin metal film. At the thickness of 40 nm, 50 nm, and 60 nm the transmission curve starts to move toward long wavelengths and FWHM seems to be narrow at a larger thickness of Ag layers.

Fig. 8
figure 8

Variation in transmission with variation in the wavelengths for different silver layer thickness

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It can be noticed form Fig. 9a that increases in resonance wavelengths with increasing Ag layer thickness with respect to the RI. At the thickness of 0 nm of the Ag layer or in another meaning the configuration of our proposed SPR sensors without silver layer, the resonance wavelengths range from 708 nm at RI = 1.33 to 797 nm at RI = 1.36. The thickness of 30 nm discloses the growth in the resonance wavelengths to be from 789 nm at RI = 1.33 and became 913 nm at RI = 1.36. Then, with increasing the Ag layer thickness to be 40 nm resonance wavelength ranges from 794 nm at RI = 1.33 to 916.5 nm at RI = 1.36. At Ag thickness of 50 nm, the resonance wavelengths extend from 797 nm at the RI = 1.33 to reach 919 nm at the RI = 1.36. Finally, at RI = 1.33, the resonance wavelengths begin to be 799 nm and extended at RI = 1.36 to be 920.6 nm with respect to Ag layer thickness of 60 nm. There is a reduction in the sensitivity as the Ag layer thickness increases due to resonance wavelength variation has been reduced. During our calculations, at the thickness of 0 nm of Ag, the sensitivity has been estimated at 2965 nm/RIU. The sensitivity is 4150 nm/RIU at the thickness of 30 nm of the silver layer then gets going to the minimized value 4000 nm/RIU at 60 nm thickness of the silver layer as illustrated in Fig. 9b.

Fig. 9
figure 9

a Resonance wavelengths versus refractive index at different silver layer thickness. b Sensitivity versus different silver layer thickness

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As shown in Fig. 8, the FWHM in the absence of a silver layer seems to be high with a value of 72 nm. As it is clear from Figs. 8 and 10a, the FWHM decreases gradually with increasing the Ag layer thickness. At the thickness of 30 nm of the Ag layer, the FWHM is 59 nm and then decreases to be 43.5 nm at a thickness of 60 nm of the Ag layer. From Fig. 10b, it is cleared that the FoM increases with increasing the thickness of the Ag layer. At 30 nm thickness of the Ag layer, the FoM corresponds to 70 RIU−1 and increased to 91 RIU−1 at the thickness of 60 nm of Ag layer passing through the FoM values of 76 RIU−1 at 40 nm of the Ag layer and the value of FoM is 86 RIU−1 at 50 nm of Ag layer thickness. During the analysis, the FoM in the absence of a silver layer decreased to be 41 RIU−1.

Fig. 10
figure 10

a FWHM versus different silver layer thickness b Figure of merit versus different silver layer

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Then, in order to have the maximum sensitivity, the maximum thickness of the Pt layer is required. It is noted from Fig. 11 that the resonance wavelength increases with increasing the thickness of the Pt layer and the minimum transmission has occurred at the thickness of 30 nm of the Pt layer. The resonance cannot be detected at the thickness of 20 nm of the Pt layer. Starting from the thickness of 30 nm of Pt layer, the transmission curve has increased and the incident light absorption starts to optimize in order to get the highest sensitivity.

Fig. 11
figure 11

Variation in transmission with variation in the wavelengths for different Pt layer thickness

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Figure 12a illustrates the relation between the resonance wavelength and RI for Pt layers with respect to different thicknesses of Pt layer. Firstly, at the thickness of 0 nm of the Pt layer, the resonance wavelengths vary from 591 nm at RI = 1.33 to 670 nm at RI = 1.36. Secondly, the resonance wavelengths of design configuration with 30 nm of Pt layer thickness are very wide as it starts from 789 nm at RI = 1.33 and great increasing happens at RI = 1.36 to be 913 nm and this illustrates the better sensitivity of our proposed sensor. The range of resonance wavelength increases at 40 nm Pt layer thickness is from 816.5 nm at the RI of 1.33 to 939 nm at 1.36 RI. At 50 nm, the wavelength of the resonance is 834 nm for the RI of 1.33 and became 954 nm at RI of 1.36. Finally, at the thickness of 60 nm, the range of resonance wavelengths starts from 842 nm at 1.33 RI to 960 at 1.36 RI.

Fig. 12
figure 12

a Resonance wavelengths versus refractive index at different Pt layer thickness. b Sensitivity versus different Pt layer thickness

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Due to the relation between the sensitivity and the change in the resonance wavelength, as shown in Figs. 11 and 12b, sensitivity(S) declines with increasing the thicknesses of the pt layer. The calculated sensitivity in the case of 0 nm of the Pt layer is estimated at 2630 nm/RIU. At a thickness of 30 nm of the pt layer, the sensitivity has been 4150 nm/RIU and reduced to be 3930 nm/RIU at the thickness of 60 nm of the Pt layer.

The relation between FWHM and the thickness of Pt layers, as in Fig. 13a, clears that the larger Pt layer thickness the lower FWHM can be obtained. Firstly, during our calculations, the estimated value of FWHM in the case of the Pt layer absence is 67 nm. Then, At 30 nm of the Pt layer, the FWHM has been 59 nm and decreased to be 39 nm at 60 nm of the Pt layer. Figure 13b indicates that there are increasing in FoM with increasing the thicknesses of the Pt layer. At 30 nm of Pt layer, the FoM has been 70 RIU−1 and at 40 nm thickness of Pt a gradual enhancement in the FoM has been achieved to be 81 RIU−1, and at 50 nm thickness of Pt the FoM is 95 RIU−1, and the maximum value is 99 at 60 nm thickness of the Pt layer. The value of FoM at the thickness of 0 nm of Pt layer is 39 RIU−1 which illustrates the great effect of the Pt layer on the FoM.

Fig. 13
figure 13

a FWHM versus different Pt layer thickness b Figure of merit versus different Pt layer thickness

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As ITO has good electrical and optical performance, it has been used in the optical fiber-based SPR sensors configurations. The optimized thickness of the ITO layer is very important in the designing and configuration of SPR sensors. At thicknesses of 0 nm, 1 nm, 4 nm, 8 nm, 12 nm, and 16 nm, the resonance wavelengths are taking into consideration for the calculation of the highest sensitivity. The resonance wavelength is 897 nm in the case of the absence of the ITO layer. At 1 nm the resonance wavelength cannot be noted. Then, with increasing the refractive index (RI) the resonance wavelength decreases as in Fig. 14. At the thickness of 4 nm of the ITO layer, the resonance wavelength was 862 nm then decreases to be 850 nm at 8 nm thickness of the ITO layer, and at 12 nm the resonance wavelength is 842 nm. Finally, at 16 nm thickness of the ITO layer, the resonance wavelength is 834 nm.

Fig. 14
figure 14

Variation in transmission with variation in the wavelengths for different ITO layer thickness

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As in Fig. 15a, the resonance wavelength increases with increasing the refractive index (RI). At the thickness of 0 nm of the ITO layer, the range of resonance wavelengths is from 767 nm at 1.33 RI to 855 nm at 1.36 RI. The range of resonance wavelengths is from 789 nm at 1.33 RI to 913 nm at 1.36 RI at the thickness of 4 nm of ITO. Then at the thickness of 8 nm of ITO, the resonance wavelengths are increased to be 791 nm at 1.33 RI and reached to be 887 nm at 1.36 RI but comparing to the thickness of 4 nm of ITO the resonance wavelength is reduced. Then, for 12 nm thickness of ITO, the range of the wavelength of the resonance is from 793 nm at RI of 1.33 to 871 nm at the RI of 1.36. Finally, the resonance wavelength, at the thickness of 16 nm of the ITO layer, ranges from 795 nm at 1.33 RI to 861 at 1.36 RI. Figure 15b illustrates the effect of the thickness of the ITO layer on the sensitivity which confirms that the sensitivity decreases with increasing the thickness of the ITO layer. Firstly, in the case of no ITO layer, the sensitivity is 2950 nm/RIU. The reduction in the sensitivity is remarked to be 4150 nm/RIU at 4 nm thicknesses, 3350.5 nm/RIU at the thickness of 8 nm, 2650 nm/RIU at 12 nm thicknesses, and 2330 nm/RIU at the thickness 16 nm of the ITO layer.

Fig. 15
figure 15

a Resonance wavelengths versus refractive index at different ITO layer thickness. b Sensitivity versus different ITO layer thickness

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The FWHM values have been decreased as ITO thickness increased as clarified in Fig. 16a. The calculated value of FWHM at 0 nm of the ITO layer is 61 nm. The value of FWHM at the thickness of 4 nm is estimated at 59 nm and declined to be 38 nm at 16 nm of the thickness of the ITO layer passing through the FWHM values of 48 nm, at the ITO thickness 8 nm, and 41 nm at the thickness of 12 nm of ITO which illustrates the effect of the ITO layer on the minimization of FWHM and optimization of the sensitivity. The optimized values of FoM have been detected at the thickness of 4 nm of ITO layer with the value of 70 RIU−1 then the FoM decreases gradually with increasing the thickness of the ITO layer and these values of FoM are 68 RIU−1 at 8 nm thickness of the ITO layer, 64 RIU−1 at 12 nm thickness of the ITO layer, and 61 RIU−1 at 16 nm thickness of the ITO layer, accordingly. The minimum value of FoM is 48 RIU−1 which detected at 0 nm thickness of the ITO layer. As shown in Figs. 8, 11, and 14, the transmission SPR dip seems flat and the detection accuracy may be poor but there is a broad band of resonance and it is not possible to detect the resonance point. The results related to the fact that at a very low thickness of the metal film, the electron density is not sufficient enough to the absorption of the incident laser energy due to which fewer transmission minima along with a flat transmission curve is observed. In other words, it happens due to absorption loss rather than scattering loss inside a thin metal film.

Fig. 16
figure 16

a FWHM versus different ITO layer thickness b Figure of merit versus different ITO layer thickness

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The last layer in our design configuration is graphene and the optimization of this layer is considered very effective in the design of the fiber-based SPR sensors because of good optical and electrical features of the graphene. The relation between the transmission and wavelength relevant to graphene layers numbers is clarified in Fig. 17. The resonance wavelength increases with increasing the graphene layers. In the case of the absence of the graphene layer, the resonance wavelength is 765 nm. Then, the resonance wavelengths are 793 nm for a monolayer of graphene, 872 nm for 2 layers of graphene, 943 nm for 3 layers of graphene, 992 nm for 4 layers of graphene, and 1022 nm for 5 layers of graphene.

Fig. 17
figure 17

Variation in transmission with variation in the wavelengths for different graphene layers

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The relation between the resonance wavelengths and refractive indices (RIs) with regard to the graphene layers numbers are introduced in Fig. 18a. For the 0 nm layer of graphene, the range of the resonance wavelength is from 765 nm at RI = 1.33 to 861 nm at RI = 1.36. For a monolayer of graphene, the range of the resonance wavelength is from 793 nm at RI = 1.33 to 917.5 nm at RI = 1.36. For a double layer of graphene, the resonance is estimated to be 872 nm at RI = 1.33 and 975 nm at RI = 1.36. With adding more layers of graphene, the range of resonance wavelength seems to be lower. For 3 layers of graphene, the resonance wavelength ranges from 943 nm at RI = 1.33 to 1020 nm at RI = 1.36. For 4 layers of graphene, the wavelength of the resonance at 1.33 RI is 992 nm and at 1.36 RI the resonance wavelength is 1050 nm. The last configuration is to add 5 layers of graphene, and the calculated range of resonance wavelengths is from 1015 nm at 1.33 RI to 1070 nm at 1.36 RI.

Fig. 18
figure 18

a Resonance wavelengths versus refractive index at different graphene layers thickness. b Sensitivity versus different graphene layers

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The sensitivity is calculated with changes in the number of the layers to get the best value of the sensitivity for the configured design. According to Fig. 18b, the optimized sensitivity is obtained at the monolayer of graphene which calculated to be 4150 nm/RIU, and the minimum value is received at 5 layers of graphene and estimated to be 1850 nm/RIU. The reduction in sensitivity has been remarked for increasing the number of graphene layers. The sensitivity (S) for a double layer of graphene is 3450 nm, for 3 layers is 2600 nm/RIU, and for 4 layers is 2000 nm/RIU. Also, this figure illustrates the effect of the graphene on the sensitivity of our proposed sensors as the sensitivity in the case of no graphene layer is minimized to be 3200 nm/RIU.

As shown in Fig. 19a, the value of FWHM is 55 in the case of no layers of graphene. Then, there are increasing in the values of FWHM with increasing the numbers of graphene layers and the FWHM minimum value is noted at the monolayer of Graphene with the value of 59 nm and increases to be 64 nm at a double layer of Graphene, 70 nm at three Graphene layers, 73 nm at four Graphene layers, and at five Graphene layers the FWHM is 75 nm. There is decreasing in the values of FoM with increasing the thickness of graphene. The calculated FoM at a monolayer of graphene is 70 RIU−1, at the double layer of graphene is 53 RIU−1, at 3 layers of graphene is 37 RIU−1, at 4 layers of graphene is 27 RIU−1, eventually, for the 5 layers of graphene, the FoM is estimated at 25 RIU−1. At no layers of graphene, the value of FoM is 58 RIU−1. Table 1 shows the influences between the layers and the optimized value of sensors parameters with different structures of the sensors.

Fig. 19
figure 19

a FWHM versus different graphene layer numbers b Figure of merit versus different graphene layers numbers

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Table 1 Optimization of the performance with different structure thicknesses
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Comparing to the configurations in Table 2, the proposed SPR fiber-based sensor`s sensitivity is considered high. Ag gives a better sensitivity than Au as well as adding graphene which providing the good absorption of the sensing materials molecule and protects Ag and Pt from oxidation. Some configurations show better sensitivity but the FoM is still low also these configurations have been used in a small range of RI change (1.33 to 1.335). The main performance parameter of the sensors is sensitivity (S) and reached in our proposed paper to be S = 4150 nm/RIU. Also, it observed that the FWHM is considered to be small related to other researches. The FWHM values are very important if using the structure as a sensor is required, specifically, to calculate nearby refractive index changes. The thinner the peak and the better signal to noise ratio you can achieve, allowing the detection of refractive indices small changes and the value of FWHM in our paper is optimized to be a minimum with a value of 59 nm. For obtaining a better SPR sensor, the last parameter is the FoM. FoM should be maximized and should be as high as it can in order to receive better sensitivity since it is proportional to the sensitivity as illustrated in the previous sections. Also from Table 2, the FoM is considered to be high in comparison with other researchers, and the best value for our SPR model reached to be 70 RIU−1. In addition to that, the enhancements in a lot of metrics of SPR sensors have been achieved which show the good performance and better reliability of our model in a lot of fields. The advantages of our model are low cost, high stability, high efficiency, which can be used in remote sensing applications and easy setup and configured in laboratories in addition to fast and remote detection SPR sensing features.

Table 2 The proposed and existing SPR fiber-based sensors performance comparisons
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4 Conclusion

In this research, theoretical and numerical analysis of SPR sensors based on optical fiber has been demonstrated. A highly sensitive sensor is achieved utilizing silver (Ag), platinum (Pt), and indium tin oxide (ITO), in addition to 2D nanomaterials (graphene). This scheme provides us with optimized results of maximum sensitivity and low FWHM in addition to high FoM. This proves that this sensor can be used in a lot of high sensitivity applications such as chemical, biomedical and industrial applications. In this search, 4150 nm/RIU is optimized sensitivity value and the FWHM is minimized to be 59 nm, and FoM was enhanced to be 70 RIU−1.