Introduction

Owing to the huge recent development of cities in countries worldwide, water is exposed to many pollutants including chemical and biological pollutants and hazardous heavy metal ions [1,2,3]. Numerous pollution sources, such as waste products of industry (e.g., acetone from silicon foundries) and agriculture (nitrates, pesticides, etc.), are disposed of in rivers leading to environmental pollution. The impact of excessive pollutants in drinking water can cause human morbidity and mortality, such as kidney failure, cardiovascular disease, nervous system failure, cancer, and brain damage [4, 5]. Additionally, polluted water has undesirable ecological effects on wildlife and marine life [6,7,8,9]. Therefore, the development of sensors for detecting, and monitoring, pollutants in water is a significant worldwide challenge. Among pollutant sensors, optical sensors [10] promise stability, sensitivity, a wide detection range, compactness, and short response time [11,12,13]. An important optical sensing mechanism is surface plasmon resonance (SPR) [14]. SPR refers to enhancement of the sensitivity of an optical sensor by a collective oscillation of free electrons, known as a surface plasmon wave, excited at a metal-dielectric interface. SPR is generated on coupling between the surface plasmon waves on a metal surface when irradiated with total internal reflection (TIR) evanescent waves from the dielectric, here a glass optical fiber, under certain conditions. When the wave vector of the fundamental fiber core mode (excited by an incident light wave) and the surface plasmon wave coincide, a distinct loss peak is obtained in the loss spectrum of the fundamental core mode. The resonance condition is satisfied at a particular wavelength known as the resonance wavelength, which is highly sensitive to the nature of the dielectric medium surrounding the metal film. Thus, if the optical properties of the dielectric medium should change, then the effective refractive index of the surface plasmon mode also changes. Accordingly, the resonance wavelength corresponding to the loss peak shifts its position towards longer or shorter wavelengths when analyte molecules bind over the plasmonic layer. Hence, the SPR optical sensing technique is sensitive to the presence of the analyte molecule through the change in RI. Such sensors offer potential for medical, biological, and chemical sensing, and for environmental monitoring [15,16,17].

Prisms and optical fibers are platforms to excite SPR because of their TIR phenomenon; but prisms are bulky [18] and fiber offers the more compact, possibly more economical, platform [19] as well as a remote sensing opportunity [20]. As the plasmonic optical fiber sensors depend on phase matching between the fiber core-guided mode and the surface plasmon polaritons (SPPs) [21], a convenient design format is the D-shaped (side-polished, then metal coated) optical fiber-based SPR sensor. Here, the incident light travelling in the fiber is coupled out into the thin metallic film [22]. Kadhim et al. [23] in 2020 proposed and simulated a SPR D-shaped, silica-glass, single-mode optical fiber sensor with silver grating; the D-shape exposed the fiber core. The sensor operated in the visible wavelength regime and when the RI of the theoretical analyte was varied between 1.33 and 1.39, the sensor showed RI sensitivity of 6400 nm /RIU [23]. Verma et al. [24] fabricated a silica-glass, single-mode optical fiber SPR sensor. The active surface was composed of a multi-layer of pyrrole/chitosan/ITO/Ag coated onto an optically unclad area of the fiber. Heavy metal ions, Cd2+, Pb2+, and Hg2+, were detected in contaminated water in the visible regime. The sensor detection limit for Cd2+ was 0.8 ppb and maximum sensitivity 0.418 nm per μg/l, up to a maximum of 70 μg/l beyond which the sensitivity became zero. Further, Villar et al. [25] simulated numerical NIR spectra and collected experimental NIR spectra with a D-shaped coated, single-mode, silica-glass fiber. Two different nano-coatings were analyzed: (i) a high RI continuous coating, 92 nm thick of indium tin oxide (ITO), and (ii) a layer-pair of poly(allylamine hydrochloride) (PAH) and poly(acrylic acid) (PAA), with 63 repeat layer-pairs deposited to achieve the desired thickness. Both operated in the NIR regime. The maximum sensitivity and figure of merit were 1566 nm/RIU and 1021/RIU, respectively, within a RI variation between 1.3 and 1.335. Pathak et al. [26] presented a SPR nominally D-shaped single-mode, silica-glass, optical fiber sensor with the concave hole above the exposed fiber core. The sensor was simulated for two types of sensing structures: coated with (i) gold (Au) film or (ii) Au nanowires, respectively. The 0.4 μm diameter, round-cross-section Au wires were designed, aligned, and touching along their length inside a concave “hole” in the fiber. The theoretical sensitivity reached 4471 nm/RIU using the Au nanowires, which compared favorably to a sensitivity of only 809 nm/RIU using the continuous Au coating, for RI, 1.33 to 1.38. Additionally, Dubey et al. [27] proposed two D-shaped optical fiber-based sensors in the NIR regime. The first design had Ag grating coated with titanium dioxide (TiO2), while the other had a tin dioxide (SnO2) layer on the core-cladding interface, with sensitivities of 15310 nm/RIU and 9810 nm/RIU, respectively [27].

All the aforementioned sensors [23,24,25,26,27] were designed to operate in the visible or NIR wavelength regimes. Yet, the fundamental vibrational absorption of, for instance, organic pollutant molecules is in the mid-infrared (MIR) regime [28], where extinction coefficients are ~105 times greater than those in the NIR overtone and combination vibrational absorption regime. Silica glass optical fibers are transmissive in the visible regime and also in the NIR (0.7–3 μm) [29] but are opaque in the MIR regimes (3–50 μm) [29]. To circumvent this limitation of silica glass fibers, other suitable materials are required to substitute silica. Chalcogenide glasses [30] or halide glasses [31] exhibit transparency in the MIR region. As a first step, indium fluoride (InF3)-based optical fibers were investigated here. InF3-based optical fibers have a transmission window from the ultraviolet (UV) to 5500 nm [32] (depending on length) and are available commercially (Le Verre Fluoré) with a loss of 0.05 dB/m at 3000 nm wavelength [33].

In this work, an InF3 glass-based D-shaped, single-mode optical fiber SPR sensor is proposed to operate in the MIR regime. The simulation addresses SPR sensing of various pollutants in water, viz. nitric acid (HNO3), hydrogen peroxide (H2O2), and polystyrene beads. A grating structure of gold (Au) nano-strips is arranged directly above the core region of the polished back D-shaped fiber to enhance the sensing performance with the aqueous analyte atop the Au grating.

The numerical analysis of the InF3-based glass, D-shaped, single-mode optical fiber SPR sensor with Au grating is performed using the full vectorial finite element method (FVFEM) [34,35,36]. The effect on sensor performance of the Au grating thickness, width and duty cycle, and the distance from the fiber center to the underneath of the deposited Au grating are presented. A tolerance study of the potential manufacturing route is performed, including grinding and polishing to make the D-shape fiber [32]. We demonstrate the highest sensitivity for analyte detection for the simulated MIR SPR fiber sensor than ever previously demonstrated before in the visible [23, 24], NIR [25,26,27, 37,38,39], and MIR [40] regions. Additionally, the reported sensor has the advantage of a simple design. On the other hand, the proposed sensor is limited to specific pollutants with specific concentrations (14% v/v HNO3, 15% v/v H2O2, 30% v/v H2O2, and 10% v/v polystyrene beads) in water. However, this study can be further extended to lower concentrations of the studied pollutants and/or investigating new pollutants such as heavy metals and chemical pollutants in water.

Design and Fabrication Considerations

Figure 1 depicts the proposed optical sensor setup for the simulation and the 2D cross-sectional view of the proposed SPR D-shaped InF3-based glass, single-mode optical fiber sensor. The fiber core diameter is 50 μm and the fiber outside diameter is equal to 250 µm, making the cladding thickness, 100 µm. The proposed fiber is side-polished to a height (h) of 5 μm from the center of the fiber core, to give a large plane sensing region (Fig. 1). The RIs of the core and cladding glasses are wavelength dependent and are taken from Salem et al. [41]; at λ = 3500 nm, the core refractive index is 1.488, while cladding RI is 1.466 [41] and so the calculated fiber numerical aperture (NA) is 0.24. The Au grating thickness (tg, correlates to thickness of Au deposited coating) is set to 50 nm; the width of each Au grating strip (wg) and the grating period (Λ) are taken 0.4 µm and Λ = wg/η, respectively, where η = 0.7 is the duty cycle defined as the ratio between the grating width and the period of Au strips.

Fig. 1
figure 1

Schematic of the proposed optical circuit of the simulated D-shaped InF3-based glass, optical fiber SPM sensor setup: a 3-dimensional view of D-shaped fiber and b 2-dimensional cross section of D-shaped fiber

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Gold (Au) is commonly employed in SPR-based sensors due to it being chemically inert and having exceptional plasmonic properties [42]. The dielectric constant of Au is calculated via the Drude–Lorentz model in Eq. (1) [43].

$${\varepsilon }_{\mathrm{m}}={\varepsilon }_{\infty }-\frac{{\omega }_{\mathrm{D}}^{2}}{\omega \left(\omega -j{\gamma }_{\mathrm{D}}\right)}-\frac{\Delta \varepsilon \cdot {\Omega }_{\mathrm{L}}^{2}}{\left({\omega }^{2}-{\Omega }_{\mathrm{L}}^{2}\right)-j{\Gamma }_{\mathrm{L}}\omega }$$
(1)

where \(\omega\) is the angular frequency of the guided wave, \({\gamma }_{\mathrm{D}}\) is the damping frequency, \({\omega }_{\mathrm{D}}\) is the plasma frequency, \({\varepsilon }_{\infty }=5.9673\) is the high frequency dielectric constant, \(\Delta \varepsilon =1.09\) is the weighted coefficient, and \({\Gamma }_{\mathrm{L}}\) and \({\Omega }_{\mathrm{L}}\) are the bandwidth and frequency of the Lorentz oscillator. Here, \({{\gamma }_{\mathrm{D}}/2\pi =15.92\mathrm{ THz},\omega }_{\mathrm{D}}/2\pi =2113.6\mathrm{ THz},{\Omega }_{\mathrm{D}}/2\pi =650.07\mathrm{ THz}\), and \({\Gamma }_{\mathrm{L}}/2\pi =104.86\mathrm{ THz}.\)

The same setup in Goya et al. [33] can readily be applied here, where the D-shaped side-polished fiber was fabricated using standard grinding and polishing. Also, as in Goya et al. [33], the InF3-based glass fiber was bonded in a V-grooved metal fiber holder using an UV-(ultraviolet)-curable epoxy resin to avoid fiber fracture, as fluoride glasses exhibit a low Young’s modulus and hardness compared to silica glass. To fabricate the Au grating, first, an Au layer can be deposited on the polished surface of the D-shaped InF3-based glass fiber via thermal evaporation, magnetron sputtering, or pulsed laser deposition [23] and then the grating patterned into the deposited Au coating using nanolithography [23].

The notional sensor optical circuit (Fig. 1) comprises a commercially available (Le Verre Fluoré) delivery fiber to couple broadband light from a MIR source into the core of the D-shaped InF3-based glass optical fiber. During the light propagation down the core of the D-shaped optical fiber, SPs are excited at the metallic/dielectric interface. Then, maximum loss is obtained at the resonance wavelength which can be detected using the optical spectrum analyzer (OSA) placed at the end of the D-shaped InF3-based glass optical fiber and PC analyzed.

Simulation Results

Initial Studies

The modal characteristics of the proposed D-shaped fiber are analyzed via COMSOL Multiphysics software package [44] based on FVFEM. A two-dimensional FEM is set up using an electromagnetic wave frequency domain (ewfd) solver where the maximum mesh element size is 1 µm. However, the thin plasmonic strips have a small mesh element size of 2 nm to maintain the simulation accuracy. A perfectly matched layer (PML) [45] boundary condition is applied to truncate the simulation region from all transverse directions. After performing an optimization study, a PML thickness of 1 µm is used to ensure numerical stability of the obtained results. The modes supported by the suggested structure are characterized by two main parameters: mode effective index (\({\mathrm{n}}_{\mathrm{eff}}\)) and confinement loss (L). Here, L is calculated from the imaginary part of the mode’s neff as in Eq. (2) [46].

$$\begin{aligned}\mathit{Confinement \;loss} \, \mathit{(L)}=&\;8.686\times \frac{2\pi }{\lambda (nm)}\times \left\{\mathit{imag}\left({n}_{eff}\right)\right\}\\&\times {10}^{7}dB/cm\end{aligned}$$
(2)

where λ is the wavelength and \({n}_{\mathrm{eff}}\) is the complex mode effective refractive index.

In order to prove the high accuracy of our numerical results, a comparison is performed with a D-shaped fiber that has been fabricated and simulated in [25]. Such a D-shaped fiber [25] has a solid core with a diameter of 8.2 µm, and a silica cladding region with a diameter of 125 µm. Moreover, a 92-nm coating of indium tin oxide (ITO) is deposited on the etched surface of the D-shaped fiber [25]. Figure 2 shows the measured (blue line) [25] and calculated theoretically (red line) transmissions through the D-shaped optical fiber reported in [25]. The dashed black line represents the calculated transmission based on our numerical model. It may be noted from this figure that a very good agreement between our simulated results and those reported experimentally and theoretically in [25] is obtained. This ensures the high accuracy of the reported numerical calculations.

Fig. 2
figure 2

The measured (blue line) [25] and calculated theoretically (red line) transmissions through D-shaped optical fiber [25] with 8.2 µm core diameter, 125 µm cladding diameter and 0.092 µm ITO thickness layer. The dashed black line represents the calculated transmission based on utilized model in our numerical simulations

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The function of the proposed and simulated SPR-based D-shaped optical fiber sensor is to detect different pollutants in water. Nitric acid (HNO3) is one of the water contaminants which may be dissolved in water with a concentration of 14%v/v [47]. The proposed device can sense the polluted water by detecting the shift in the resonance wavelength due to the RI change between pure and polluted water [47, 48]. It is worth mentioning that these data are taken at a temperature of 25°C (±1°C) [2]. In addition, in the studied wavelength range, water RI changes only slightly with temperature so the temperature dependence is not considered in this study. Figure 3a, b depicts the wavelength dependent real part and imaginary part of the refractive index of pure water and those of 14% v/v HNO3 in water (polluted water), respectively. As may be seen in Fig. 3a, the RIs for both pure water and 14% v/v HNO3 in water have two dips in the real parts at λ = 2802 nm (with n = 1.14) and at 2756 nm (with n = 1.13), respectively. Additionally, at λ = 3150 nm for pure water and λ = 3192 nm for 14% v/v HNO3 in water, the RIs reach their maximum values of 1.48 and 1.44, respectively. In addition, in Fig. 3b, the maximum values of the extinction coefficients for pure water and 14% v/v HNO3 in water occur at λ = 2950 nm (with κ = 0.298) and λ = 2936 nm (with κ = 0.262). Notably a distinct variation around λ = 3000 nm is observed in both the real and imaginary parts of water RI due to the 14%v/v addition of HNO3 dissolved in the water. Thus, a different optical behavior is expected due to the perturbation of the water RI by the dissolved HNO3. This behavior change is then exploited here to optimize the sensitivity of the proposed sensor.

Fig. 3
figure 3

a Real and b imaginary parts (i.e., the extinction coefficient), of the refractive index of pure water and 14%v/v HNO3 polluted water due to fundamental vibrations of O–H of water at ~ 3 μm wavelength [47, 48]

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The dispersion characteristics and optical loss spectrum of the fundamental core mode and SPM with pure water in contact with the Au grating are depicted in Fig. 4. The black curve refers to the confinement loss of the core mode, and the red (solid) and blue (dotted) curves represent the real parts of the effective refractive indices of the core mode and the SPM, respectively. From Fig. 4, the real (neff) of the core mode and the SPM both decrease with increasing wavelength. An intersection between the two effective indices of the two modes occurs at λ = 3663 nm (i.e., the resonance wavelength, λr) where the confinement loss of the core mode exhibits a distinct optical loss peak of about 67.8 dB/cm due to the strong coupling between the core mode and SPM. This coupling is induced thanks to the phase matching condition at which real (neff) of the fiber core mode is identical to that of the SPM. This strong coupling is confirmed by the coincidence of the optical loss peak and the intersection between the core mode and SPM effective indices.

Fig. 4
figure 4

Wavelength dependent confinement optical loss (black curve) and effective refractive indices of the x-polarized core mode (red curve) and SPM (blue curve) supported by the proposed D-shaped optical fiber structure, for dimensions (see Fig. 1b) of the Au grating selected to be: tg = 50 nm (thickness of Au coating), wg = 0.4 μm (width of patterned grating strip), η = 0.7 (duty cycle), and h = 5 μm (height of Au coating above the fiber core)

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Figure 5a, b shows the electric field distributions of the core mode at λ = 3450 nm and λ = 3950 nm away from λr (SPR wavelength) while Fig. 4c, d depicts the field profiles of the core mode and SPM at λr = 3663 nm. From Fig. 5, the coupling strength of the core mode at λr = 3663 nm (Fig. 4c) is higher than that at λ = 3450 nm (compared to Fig. 4a) and λ = 3950 nm (compare Fig. 4b). Additionally, at λr = 3663 nm, there is a strong coupling between the core mode and SPM, revealed by the strong overlap between the two modes as may be seen from Fig. 5c, d (i.e., the field profiles of these two modes are very similar as shown). It is evident from Fig. 5c, d that large power transfer will occur from the core-guided mode to the SPM due to the phase matching condition. Therefore, maximum optical loss of the core-guided mode occurs at λr, as revealed by the optical loss spectrum depicted in Fig. 4.

Fig. 5
figure 5

E(electric)-field distribution of the: a core mode at λ = 3450 nm; b core mode at λ = 3950 nm; c x-polarized core mode at λr = 3663 nm, and d SPM at λr = 3663 nm, for Au grating dimensions of tg = 50 nm, wg = 0.4 μm, η = 0.7, and h = 5 μm (see Fig. 1b)

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Note that only the fundamental x-polarized core mode is coupled with the SPM; in contrast, the fundamental y-polarized core mode remained well-confined in the core region with negligible coupling with the SPM. Therefore, only the fundamental x-polarized core mode is considered for all subsequent simulations.

It is well-known that the performance of SPR sensors is affected by the shift in the resonance wavelength (∆λr) for a particular change in the refractive index (∆n) of the analyte (here, the water sample). It is found here that a slight change in the RI of the water sample produces remarkable sensor sensitivity, as λr adapts to variations in the RI of the sensing medium, water. The SPR sensor sensitivity at a specific wavelength (S(λ)) is calculated using Eq. (3) [49]:

$$S(\lambda )=\frac{\Delta {\lambda }_{r}}{\Delta {n}_{ana}} (nm/RIU)$$
(3)

where Δλr and Δnana are the resonance wavelength shift and the variation of the RI of the analyte, respectively. Another important parameter is the full width at half maximum (FWHM) of the optical loss curve of the fundamental x-polarized core mode. The FWHM of the optical loss curve has a direct influence on the detection accuracy (DA) which is the inverse of FWHM (Eq. (4)) [23]. Therefore, a narrow FWHM produces optimal DA [23].

$$DA=\frac{1}{\mathit{ FWHM}}$$
(4)

Unfortunately, in some cases, the increase in sensitivity is accompanied by a decrease in DA leading to a trade-off between them [50]. Therefore, a figure of merit (FOM) is proposed here to help evaluate the sensor performance. We define the FOM as the ratio between the sensitivity (S(λ), see Eq. (3)) and the FWHM as depicted in Eq. (5). So, the larger the FOM, the better the sensitivity and the detection limit [51]:

$$\mathrm{FOM}=\frac{\mathrm{S}}{\mathrm{FWHM}}{\mathrm{RIU}}^{-1}$$
(5)

When pure water is polluted with 14%v/v nitric acid, a wavelength shift in the optical loss peak is expected to occur owing to the change in the RI of water. Figure 6 shows the wavelength-dependent confinement loss of the core mode for both pure and polluted (with 14% v/v HNO3) water. From Fig. 6, it may be seen that the resonance loss peak, which corresponds to the polluted water sample, is shifted to a shorter wavelength (λr = 3560 nm) with an increase in the confinement optical loss of the core mode. This means that a Δλ of 103 nm occurs due to the change in water purity when there is a dissolution in the water of 14% v/v HNO3. Accordingly, the calculated sensitivity for detecting HNO3 in water of this D-shaped InF3-based glass optical fiber SPR optical sensor (S, Eq. (3)) is equal to 25,470 nm/RIU with DA of 11.25 μm−1 and FOM = 286.69 RIU−1. It is worth noting that the sensor operation is limited by the available optical constants (n and k) of different concentrations of HNO3 in water and actually applied detection to 14% v/v. So, at present, we cannot test other concentrations with our proposed sensor. However, the high sensitivity obtained here reveals the efficiency of the detection process that may be extended to at least an order of magnitude lower.

Fig. 6
figure 6

Confinement optical loss spectra of the core mode for both pure water and 14% v/v HNO3 in water. The dimensions of the Au grating in the D-shaped InF3-based glass optical fiber SPR optical sensor are tg = 50 nm, wg = 0.4 μm, η = 0.7, and h = 5 μm (see Fig. 1b)

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Optimizing the Sensor for Detection of 14%v/v HNO3 Pollutant in Water

The sensor is optimized for detection of 14%v/v HNO3 pollutant in water. Thus, the geometrical parameters of the Au nano-grating in the proposed D-shaped InF3-based glass fiber SPR sensor are varied one at a time, while keeping the others constant. Each geometrical parameter is tested to investigate its effect on the sensor performance indicators including sensitivity (S, Eq. (1)), detection accuracy ((DA), Eq. (4)), and figure of merit (FOM Eq. (5)) exclusively for the detection of 14%v/v HNO3 pollutant in water; other pollutants are addressed later in the “Projected Fabrication Tolerance of Proposed Optimized Sensor” section. The following “Au Nano-grating Thickness (tg)” to “Summary of Optimized Au Nano-grating Parameters of the Sensor” sections report varying the Au nano-grating thickness (tg), duty cycle (η), width (wg), and distance from the side-polished surface of the fiber to the center of the fiber core (h), respectively.

Au Nano-grating Thickness (tg)

It is found that the surface plasmons are strongly influenced by the Au nano-grating thickness, tg. Figure 7a shows the wavelength-dependent optical loss spectra for tg varied from 30 to 50 nm, with a 5-nm step. By increasing tg, λr is shifted to shorter wavelengths from λr = 3710 nm (at tg = 30 nm) to 3665 nm (at tg = 50 nm) for pure water and from λr = 3610 nm (at tg = 30 nm) to 3560 nm (at tg = 50 nm) for water polluted with 14% v/v HNO3. Additionally, the maximum values of the optical loss curves change with the variation in tg.

Fig. 7
figure 7

a Wavelength-dependent optical loss curves of the fundamental core mode at different values of tg, and b the sensitivity (S) and FOM at different values of tg. The other dimensions were wg = 0.4 μm, η = 0.7, and h = 5 μm, respectively (as in Fig. 1b)

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From Fig. 7a, as tg is increased from 30 to 50 nm, the confinement loss of the fundamental x-polarized core mode became smaller in the case of a pure water analyte. This may be explained as follows. On increasing tg, the area of interaction between the light in the fiber core and the lossy by nature Au layer would tend to increase. Moreover, water exhibits a large extinction coefficient (ĸ) (Fig. 3b) at 2.7–3 μm. However, in the wavelength region from λ = 3600 to 4000 nm, the real part of the RI of pure water is quite small (< 1.4) making the RI contrast between the InF3-based glass fiber core (1.48–1.51 for commercially available InF3-based glass fiber) and the cladding (pure water) large. Thus, the mode is well confined in the InF3-based glass fiber core region and there is only weak interaction between the water analyte and Au grating nano-strips, leading to small loss values of the confined mode in the fiber core.

In contrast to the pure water analyte, for water polluted with 14%v/v HNO3 on increasing tg, the confinement loss is observed to increase; in addition, the optical loss curves became narrower. This may be explained by the now higher refractive index of the aqueous HNO3 analyte (> 1.4) in the wavelength range from 3400 to 3600 nm leading to large leakage from the fundamental confined core mode through the Au nano-grating to the polluted water analyte cladding.

Figure 7b shows the sensitivity (S, Eq. (3)) and FOM (Eq. (5)) as functions of tg for the detection of the HNO3 pollutant. A maximum sensitivity of 28,025 nm/RIU is achieved at tg = 35 nm and tg = 40 nm. However, the optical loss spectra in Fig. 7a show large FWHM of 127.77 nm and 110.97 nm for tg = 35 nm and tg = 40 nm, respectively. A large FWHM leads to uncertain pollutant detection due to the inherent spectral noise which affects the accuracy of the detection process [47]. Therefore, the FOM is investigated (Eq. (5)). From Fig. 7b, the highest FOM observed is 286.69 RIU−1 at tg = 50 nm, due to a small FWHM = 88.87 nm. Henceforward, tg is therefore fixed at 50 nm in the subsequent studies to ensure accurate detection.

Au Nano-grating Duty Cycle (η)

The gold nano-grating parameters, duty cycle (η) and grating width (wg), are next investigated to see if they could be optimized to further improve the performance of the proposed D-shaped InF3-based glass fiber SPR sensor; η and wg are expected to influence coupling between the D-shaped fiber core-guided mode and the SPM. The wg investigation is reported in the “Au Nano-grating Width (wg)” section. η is first investigated and varied from 0.6 to 0.8, in steps of 0.1, at constant tg = 50 nm (see “Au Nano-grating Thickness (tg)” section) and constant wg = 0.4 μm, h = 5 μm (as in Fig. 1b). From Fig. 8a, on increasing η from 0.6 to 0.8, the optical loss curves of the core fundamental mode for both pure and HNO3 14% v/v polluted water shift toward longer wavelengths. Thus, the resonance wavelengths (λr) are red shifted from 3380 to 4400 nm for pure water, and from 3360 to 4180 nm for polluted water. In comparing λr of pure water with that of water polluted with 14% v/v HNO3, λr is shifted to a shorter wavelength when water is polluted with 14% v/v HNO3 (Fig. 8a).

Fig. 8
figure 8

a Wavelength dependent optical loss of core mode at different values of η, and b the sensitivity (S) and FOM at different values of η. The initial dimensions of wg = 0.4 μm and h = 5 μm were used (see Fig. 1b). tg was fixed at its optimized value of 50 nm

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Figure 8b shows the sensitivity and FOM as a function of η. At η = 0.8, a high sensitivity of S = 56,049 nm/RIU is realized at (Fig. 8b) with high FOM of 743.3 RIU−1 due to a small FWHM of 75.4 nm. Although η = 0.8 gives the higher sensitivity and FOM, it has a low loss peak as shown from Fig. 8a. Accordingly, selecting η = 0.8 would reduce the amplitude sensitivity [52]. Instead, η = 0.7 is selected as the optimized value for high sensitivity, 25,476 nm/RIU and acceptable FOM, of 286.69 RIU−1, with a high optical loss peak of 67.9 dB/cm and 93.48 dB/cm for pure and polluted water analytes, respectively. Additionally, FWHM still has a small value of 88.9 nm and FOM reaches 286.7 RIU−1.

Au Nano-grating Width (wg)

To investigate the influence of the Au nano-grating width (wg) on sensor performance, wg is varied from 0.4 to 1.6 μm while tg, η, and h are fixed to 50 nm, 0.7, and 5 μm, respectively. Figure 9 shows the field distribution of the fundamental x-polarized core mode at different values of wg. By increasing wg from 0.4 to 1.2 μm, the field is pulled up (see Fig. 1b) from the InF3-based glass fiber core region to the metal/dielectric (Au/InF3-based glass) interface. In the simulation, this in turn enhances the SPM until a maximum coupling between the fundamental fiber core mode light and the SPM occurred at 1.2 μm (Fig. 9a–c). However, further increase in wg decreases the coupling strength between the core mode and the SPM (Fig. 9d). So, the optical loss of the core mode is found to increase gradually as wg is increased from 0.4 to 1.6 μm, reaching a sharp maximum peak at wg = 1.2 μm (Fig. 10a). By increasing wg beyond 1.2 μm, the core mode optical loss peak then reduces and broadens, i.e., FWHM increases. Moreover, increasing wg induces a slight blue shift in the resonance wavelength, λr.

Fig. 9
figure 9

E-field distributions at different values of wg: a 0.4 µm; b 0.8 µm; c 1.2 µm, and d 1.6 µm

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Fig. 10
figure 10

a Wavelength dependent optical loss of the core mode at different values of wg, and b the sensitivity (S, Eq. (3)) and FOM (Eq. (5)) at different values of wg. The utilized initial dimension of h = 5 μm (as in Fig. 1b). tg and η were fixed at their optimized values of 50 nm and 0.7, respectively

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The numerical calculations that describe Fig. 9 can be shown in Fig. 10a. Figure 10a depicts the wavelength dependent optical loss spectra of the fundamental x-polarized core mode when wg is varied from 0.4 to 1.6 μm, in 0.4 μm steps. By increasing wg, λr is shifted to shorter wavelengths for both pure water and water polluted with 14% v/v HNO3. It is worth mentioning that by increasing wg, the optical losses increase for both pure water and polluted water with 14% v/v HNO3 until it reaches its maximum peak at wg = 1.2 μm at resonance wavelength λr = 3600 nm (pure water) and 3530 nm (polluted water with 14% v/v HNO3). Then, increasing wg beyond 1.2 μm leads to a reduction in the optical losses for both pure water and polluted water with 14% v/v HNO3. Figure 10b depicts the S (λ) and FOM of the proposed optical sensor as functions of wg. It is revealed from this figure that a high sensitivity of 25,477 nm/RIU is obtained at wg = 0.4 μm. However, wg = 0.4 μm corresponds to a relatively large FWHM of ~ 88 nm with a low FOM of 288.5 RIU−1.

Accordingly, choosing wg = 0.4 μm would reduce the sensing accuracy of the D-shaped InF3-based glass fiber sensor to detect the HNO3 pollutant in water. Therefore, wg = 1.2 μm is selected as being optimal overall as the sharpest loss peak occurs here with the minimum FWHM of 36.5 nm; see Fig. 10a. Further, a maximum FOM of 488.8 RIU−1 and high sensitivity of 17,834 nm/RIU are also achieved at wg = 1.2 μm, as shown in Fig. 10b.

Distance from Side-Polished Surface of Fiber to Center of Fiber Core (h)

The effect on sensor performance of the distance from the side-polished surface to the fiber core center (h) is then investigated. It is worth noting that the fiber core diameter is 50 µm (see Fig. 1b) and h values of 3 µm, 4 µm, 5 µm, 6 µm, and 7 µm are studied (Fig. 10) for fixed values of tg, η, and wg of 50 nm, 0.7, and 1.2 μm, respectively (see Sections “Au Nano-grating Thickness (tg)”, “Au Nano-grating Duty Cycle (η)”, and “Au Nano-grating Width (wg)”, respectively). From Fig. 11a, increasing h causes the confinement optical loss of the fiber core mode to slightly decrease for both the pure water and polluted water. In addition, for h increases from 3 to 4 µm, λr of pure water is slightly shifted from 3610 down to 3600 nm (Fig. 11a). It is worth noting that h has a limited influence on λr as depicted in Fig. 11a. Figure 11b shows that by increasing h from 3 to 4 µm, the sensitivity (S, Eq. (1)) decreases from 20,381 to 17,834 nm/RIU, while the sensitivity is nearly constant on further increasing h beyond 4 µm. However, at h = 3 µm, a high sensitivity is achieved with small FOM. Therefore, the optimized value of h is chosen to be 4 µm since it gives the highest FOM of 487 RIU−1 with a relatively high sensitivity of 17,834 nm/RIU.

Fig. 11
figure 11

a Wavelength dependent optical loss of the core mode at different values of h, and b the sensitivity and FOM for different values of h. All other dimensions were fixed to their optimized values as tg = 50 nm, η = 0.7, wg = 1.2 μm, and h = 4 μm (cf. Fig. 1b starting values of these parameters)

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Summary of Optimized Au Nano-grating Parameters of the Sensor

The optimal structural parameters of the proposed D-shaped InF3-based glass optical fiber sensor are listed in Table 1 at which a high sensitivity of 17,834 nm/RIU and high FOM of 487 RIU−1 are attained. Note that the sensor is specifically optimized for a pollutant of 14%v/v HNO3 in water.

Table 1 The fabrication tolerance as expressed by sensor sensitivity (S (λ)) of the optimized D-shaped InF3-based glass optical fiber, for detecting the 14% v/v HNO3 in water. Each geometric parameter is varied consecutively within ± 5% of the optimized value, while keeping the other geometric parameters static at the optimized value
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Projected Fabrication Tolerance of Proposed Optimized Sensor

The fabrication tolerance of the proposed D-shaped SPR sensor design is investigated to look at its robustness to fabrication imperfections. Here, only one parameter is varied by ± 5% of its optimum value while the other geometrical parameters are kept at their optimum values as listed in Table 1. From the results in Table 1, it may be seen that the proposed water pollutant sensor exhibited sensitivity (S) better than 17,834 nm/RIU for all geometric parameters, which ensures stable performance when each parameter is varied between ± 5% of its optimized value.

Sensor Detection of Other Pollutants in Water

Using the proposed D-shaped InF3-based glass optical fiber SPR sensor to detect water pollutants other than HNO3 is explored, viz. hydrogen peroxide (H2O2), miscible with water, in v/v concentrations of 15% and 30%, and polystyrene beads, immiscible with water, in v/v concentration of 10%. The real and imaginary parts of the refractive indices of these pollutants in the MIR range are taken from [47] and are plotted with the pure water RI in Fig. 12a, b, respectively. As shown in Fig. 12a, the RIs curves of pure water and polluted water (with 15% v/v H2O2, 30% v/v H2O2, and 10% v/v polystyrene beads in water) have a dip around λ = 2770 nm. Additionally, around λ = 3150 nm, the RIs of pure water and polluted water (with 15% v/v H2O2, 30% v/v H2O2, and 10% v/v polystyrene beads in water) reach its maximum value. Additionally, the maximum value of the extinction coefficient for pure water and polluted water (with 15% v/v H2O2, 30% v/v H2O2, and 10% v/v polystyrene beads in water) occurs around λ = 2950 nm (Fig. 12b). It is worth noting that H2O2 is used for water disinfection purposes [53]. However, increasing the concentration of H2O2 beyond 5% in water causes skin irritation and possible burns, while eye contact may result in permanent eye damage. Also, it may cause severe digestive and respiratory tract irritation [54, 55]. Therefore, detection of 15% v/v H2O2 and 30% v/v H2O2 in water is investigated here. By adding the solublecontaminant, 15% v/v H2O2 and 30% v/v H2O2, to pure water, both the real and imaginary parts of the water refractive index change (Fig. 12a, b). Therefore, a shift in λr of the confinement loss peak which corresponds to the core mode is expected to occur by replacing the pure water sample with a polluted one.

Fig. 12
figure 12

a The real part and b imaginary part (extinction coefficient) of the refractive index of pure water and those of dissolved 15% v/v H2O2 in water, 30% v/v H2O2, and suspended 10%v/v polystyrene 0.1 μm diameter beads in water [44, 45]

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The sensitivity of the optimized sensor (see Table 1) towards various pollutants in water, viz. H2O2 (15% v/v and 30% v/v) and polystyrene 0.1 μm diameter beads (10% v/v). Figure 13a–c shows the wavelength-dependent confinement loss of the fundamental core mode in the D-shaped InF3-based glass optical fiber sensor of pure water and water with 15% v/v H2O2, 30% v/v H2O2, and 10% v/v polystyrene beads, respectively.

Fig. 13
figure 13

Confinement optical loss spectra of the core mode of the geometrically optimized (Table 1) D-shaped InF3-based glass optical fiber SPR sensor for pure water and a dissolved 15% v/v H2O2 in water, b dissolved 30% v/v H2O2 in water, c suspended10% v/v polystyrene 0.1 μm diameter beads in water

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From Fig. 13a for 15% v/v aq. H2O2, the resonance wavelength shifts from 3600 nm (in the case of pure water) to 3760 nm (corresponding to the maximum peak in the case of 15% v/v aq. H2O2). Thus, a Δλr of 160 nm is obtained, leading to a sensitivity of 12,308 nm/RIU and FOM of 160 RIU−1 as summarized in Table 2. As the concentration of H2O2 in water is further increased to 30% v/v, λr increases to 3840 nm (Fig. 13b). In this case, the calculated sensitivity and FOM are equal to 17,143 nm/RIU and 209 RIU−1, respectively. However, adding polystyrene 0.1 μm diameter beads to water with a concentration of 10% v/v induced a λr of 3760 nm (Fig. 13c). Hence, the sensitivity in this case is calculated to be 5333 nm/RIU while the FOM is 96 RIU−1.

Table 2 Performance analysis of the SPR sensor with different pollutants: H2O2 and polystyrene 0.1 μm diameter beads
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Table 3 depicts a comparison summary of the performance of the InF3-based glass optical fiber device proposed in this paper with that of previously reported optical fiber-based SPR sensors all of which were based on silica glass optical fibers; the comparison is made in terms of the sensor type, sensitivity, FOM, RI range, and operating wavelength range. The proposed design exhibits the highest sensitivity with comparable FOM when compared with those reported in [23, 25,26,27, 37, 38, 40, 56].

Table 3 Comparison of the sensing performance of the proposed device and those reported in the literature
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Conclusion

A MIR (mid-infrared) optical fiber sensor for water pollution detection is proposed and numerically analyzed for the first time to the Authors’ knowledge. The proposed sensor is based on a D-shaped InF3-based glass optical fiber with a gold grating structure deposited on the polished surface and depends on the SPR sensing mechanism. The geometrical dimensions of the Au grating are optimized. The proposed sensor can detect different pollutants in water such as 14%v/v (percent by volume) HNO3, 15%v/v and 30% v/v H2O2, and 10% v/v polystyrene 0.1 μm diameter beads. The sensing characteristics of the proposed sensor are analyzed using FVFEM (full vectorial finite element method) in the MIR fundamental vibrational absorption wavelength regime from 2900 to 4500 nm. In addition, the reported D-shaped optical fiber sensor is proven robust to fabrication errors in geometrical parameters by ± 5%. The obtained results reveal that a high sensitivity of 17,834 nm/RIU, 12,308 nm/RIU, 17,143 nm/RIU, and 5,333 nm/RIU was achieved for the detection of 14%v/v HNO3, 15% v/v H2O2, 30% v/v H2O2, and 10% v/v polystyrene beads in water sensing mechanism, respectively.

The geometrical dimensions of the Au grating are optimized. The proposed sensor has a FOM of 487 RIU−1, 160 RIU−1, 209 RIU−1, and 96 RIU−1 for 14% v/v HNO3, 15% v/v H2O2, 30% v/v H2O2, and 10% v/v polystyrene beads in water, respectively. Therefore, the reported sensor has the advantages of a simple design, yet higher sensitivity than similar sensors reported in the literature with a comparable FOM. The key to the higher sensor sensitivity found here is in applying SPM in the MIR wavelength regime using a MIR-transparent InF3-based glass optical fiber, D-shaped, as opposed to the work of others where SPM was applied in the visible or near-infrared regime using silica-glass fiber optics.