Analytical Design of a Portable Surface Plasmon Resonance Sensor by Using a Divergence Beam for Measuring Multiple Heavy Metals and Other Contamination Simultaneously

The study proposes a surface plasmon resonance (SPR) sensor for measuring water quality by detecting the presence of heavy metal ions and other contamination. The proposed SPR sensor operates in the Kretschmann configuration, which employs the divergence beam produced by the Powell lens. The beam is diverged to eliminate mechanical scanning, indicating that the sensor can measure water quality from deionized water (DIW) with refractive index (RI) of 1.3317, diluted DIW with multiple heavy metal ion such as Hg[II], Pb[II], Ni[II], Zn[II], Cu[II] at concentration of 100 μM and other pollutant with the RI of 1.34 without any mechanical movement. The proposed SPR sensor has a theoretical sensitivity of 399.45˚/RIU and resolution of 1.3456×10-8


INTRODUCTION
According to a water organization study, 16 million Tanzanians (28% of the population) lack access to safe water, and 44 million Tanzanians (73%) lack access to safely managed household sanitation facilities [1].The definition of safely managed water is a water source that is close to living premises, is available when needed, and is free of faecal and chemical contamination.
The consumed water is generated from water from surface sources such as rivers, streams, shallow and deep wells.These sources of water can be contaminated in various ways such as industrial activities like chemicals, metals, and organic substances into water bodies, which can cause severe water pollution.Furthermore, agricultural activities like farming, irrigation, livestock rearing, use of fertilizers, pesticides, and herbicides, can find their way into water sources through runoff and leaching.These chemicals can cause eutrophication, the growth of harmful algae, and contamination of drinking water.Besides that, improper disposal of sewage and wastewater can also lead to water pollution by introducing heavy metals.Untreated or partially treated wastewater contains high levels of nutrients, organic matter, and pathogens, which can harm aquatic life and human health.For example, a study conducted by Machiwa found that during the rainy season, all the waste material from industries and construction is directed to the sea through the Msimbazi River without any treatment which increases the contamination of the sea.Machiwa's works identified the presence of heavy metals in the coastal water.The findings observed that the water near the Dar es Salaam harbour is highly contaminated with cadmium (Cd) and chromium (Cr), while the areas of the harbour are highly contaminated with iron (Fe) and lead (Pb).Due to an increase in heavy metal pollution in Dar es Salaam's harbour, which can be carried by sea fish, which is directly consumed by people [2].The consumption of heavy metal ion water, an ineffective sanitation system and improper handling of non-piped water supply systems are the main causes of severe headaches, cancer, diarrhoea, cholera, dysentery, and typhoid [3,4] The government maintains a policy that ensures the company follows the regulation of pre-treating garbage before disposing it into the seas.Furthermore, the government emphasizes educating the public on basic hygiene principles such as the use of pit latrines and boiling drinking water.Boiling or chemically treating water can only kill microorganisms but cannot obviate heavy metals such as mercury ions, lead ions, and copper ions.
Due to budget constraints, the Tanzanian government has set a 2% target for water supply, sewerage, and waste management [5].Aside from budget constraints, the existing instruments for testing the quality of water supply are few and laboratory-based equipment.Poor sewage and waste pre-treatment management are among the contributing factors for contaminating the sea with heavy ion metal.
Conventional measurement instruments used by researchers to detect the quality of water by measuring the presence of heavy metals and other contamination are i) atomic absorption spectroscopy (AAS) [6] and ii) inductively coupled plasma mass spectroscopy (ICP-MS) [7].However, these instruments have the demerits of requiring sample pretreatment which makes them unsuitable for real-time water sample measurement and having complex detection mechanisms which require skilled personnel to interpret the results [8,9].Electrochemical impedance spectroscopy, voltammetry and polarography [10], and UV-visible spectrophotometer, also these devices has low detection accuracy in differentiating metal ions whose structure radii appear uniformly [11].Another common method of measuring metal ions in water is the chemiluminescence method which is not suitable for measuring low concentration [12].A common method is an electrochemical method, which uses chemical pretreatment of the sample to improve its ability to detect low concentrations of heavy metal ions in the wate r [13].The effect of adding chemicals to the sample is the possibility of causing the secondary contamination [13].In summary, the mentioned measurement instruments are too expensive for developing countries like Tanzania to purchase and operate.Furthermore, they are bulky and laboratory-based which is unsuitable for online heavy metal ion and other contamination monitoring in the drinking water.
An alternative approach of using the surface plasmon resonance (SPR) technique was proposed.Since the SPR sensors were discovered, the technique has been applied to the detection of bacteria [14,15] and coronavirus [16], the detection of adulteration of honey [17,18] and milky [19][20][21] and measuring the quality of food [22].In addition, SPR sensors were applied to measure heavy metal ions in the water [4,[23][24][25][26][27][28].Most of the proposed methods were able to detect one type of heavy metal ion at a time.Additionally were have very low sensitivity because they use convectional Kretschmann configuration, the prism with a high refractive index 1.7786 and it requires mechanical scanning to measure more than one heavy metal ion and other contaminant in water [23,27] Therefore, the goal of this research work is to perform an analytical analysis of the SPR-based optical instrument which was applied in measuring multiple heavy metal ions (Hg ) and other contamination simultaneously without mechanical scanning.The theoretical performance in measuring the minimum concentration of heavy metal ions and other contaminations present in the water solution was evaluated.Despite the commercial availability of some SPR-based biosensing instruments such as Biacore, Spreeta, Reichert, Bruker, Texas Instrument, Plasmetrix, and Biorad, which have high sensitivity and stability, making them ideal for biomolecule analysis and they can also be customized for quantifying heavy metal ion and other water contamination; however, they are very expensive and require a compatible accessory, which is also costly.They also require skilled personnel and have a high operational cost.
Since heavy metal ions cannot be eliminated by boiling water or well-cooking seafood thus, in such a scenario, there is a need to design a portable SPR sensor which is easy to use, low-cost, portable, and high-sensitivity instrument.

METHODOLOGY Theory and Mathematical Modelling of SPR Sensor
The wave vector of the generated evanescent wave along the horizontal axis can be expressed as (1) where np is the prism RI.

sin
When there is an oscillation of surface charges on the silver layer, the surface plasmon wave vector Ksp [29] can be expressed as , Here, , are the refractive indices of the silver and dielectric samples, respectively.Thus, Eq (2) demonstrates that changes in refractive index affect the horizontal wave vector of metal oscillating electron charges.
The perturbation in the presence of the prism gives [30] ( where is the thickness of the silver layer. Thus, the total wave vector is given as a summation of the surface plasmon wave vector and perturbed wave vector (4) The two wave vectors must match in order for the plasmons to resonate, yielding the resonance angle of (5)

SPR Sensor Model Design
Figure 2 illustrates a four-layer structure of the SPR when the p-polarized light with wavelength λ (632.8 nm) incident on the prism.To avoid mechanical translation or movement, the collimated source is passed through the Powell lens which diverges the laser beam to ensure that the beam incident on the prism-TiO2 interface covers the measurement range of the RI from 1.3317 to 1.34.The modified structure of the SPR sensor is proposed by stacking the layers of the dissimilar materials on the z-axis.These works choose the CaF2 prism has a refractive index of 1.4329 which is smaller than BK7 and FK51a with a refractive index of 1.5151 and 1.4853, respectively.It proven that the SPR sensor which uses the prism with low RI has higher sensitivity.The stacked layers consist of CaF2/TiO2/Silver/BaTiO3/sensing sample as shown in Figure 2. In which the prism, TiO2, silver BaTiO3, and sensing sample are the four layers that make up the proposed SPR sensor.While BaTiO3 is added to increase sensitivity and reduce the impact of oxidation, TiO2 is added to ensure that the silver is firmly connected to the prism and to increase figure of merit (FOM) [31].Table 1 shows optical and physical parameters used in the designing of the proposed SPR sensor.
The reflected beam from prism -TiO2 interface is reflected to other side of the prism.Therefore, the reflected intensity can be monitored by a charge couple device (CCD).

Detection of Heavy Metal Ion
The study uses the data published in the paper [32] for validating the performance the designed SPR sensor in detecting deionized water contaminated with the concentration of 100 μM the heavy metal ions.The study focuses not only on detecting contaminated water polluted by heavy metal ions and other pollutants which extends the RI of the diluted DIW to 1.34.

SPR Sensor Mathematical Modelling
The SPR reflectivity curve was calculated in this study using the matrix method [33] on MATLAB software.According to the boundary condition, the electric and magnetic fields, U1 and V1, at the first layer's boundary are related to those U4 and V4 at the last layer's interface, respectively, by (6) where M is the matrix representing the wave propagation response through different layers by .
Here, the factor qk is defined as ,

UU M VV
is the phase shift of k th layer with a thickness dk (9) As the result of the wave propagation through multilayer media, the total reflection coefficient for the transverse magnetic field is expressed by (10) with . (11) Finally, the reflectivity power can be calculated as .
The SPR Sensor Measurement Parameters The SPR sensor measurement parameters were extracted from the resonance curve, in which sensitivity, detection accuracy and quality factor.

Sensitivity
Sensitivity of the SPR biosensor is measured as change in resonance position in the reflectance curve (res) corresponding to the small change in the refractive index (ns) of the analyte.The sensitivity(S) is given by,

Detection Accuracy (DA)
DA is inversely proportional to the full width at half maximum (FWHM) of the reflectance curve and is given by, ( 14)

Quality Factor (Q) or Figure of Merits (FOM)
The quality factor of the SPR sensor depends on the sensitivity and FWHM [31].This implies that the higher the quality the better signal to noise ratio.Therefore, the quality factor (Q) is given the product of the detection accuracy (DA) and the sensitivity S, ( 15)

Resolution of the Proposed SPR Sensor
Resolution is the least change of RI that produced detectable output response, which can be expressed as below.( 16)

Optimization of Metal Thickness
The critical factor ensuring the photon energy is transformed into the surface plasmon wave is the thickness of the metal layer.The metal's optimum thickness ensures that at resonance, all the photon energies are converted to plasmon energy.With a sensing sample of 1.3317 for pure water and 1.34 for contaminated water samples, the thickness of the silver was opted from 44 and 56 nm (see Figure 3).Figure 1 demonstrates that the minimum dip occurred when the thickness of the silver was 44 nm, indicating an energy transfer efficiency of 80%.The energy transfer efficiency is decreased because of the strong evanescent field at silver/sample which fraction of it is coupled with few surface plasmons while excess photon energy will be reflected to the detector.Similarly, when the silver thickness is 56 nm the minimal dip increases to 0.02 and the energy transfer efficiency rises to 99.98%.Thus, the reduction of the minimum dip is a resulted of the weak evanescent field arriving at the silver/sample interface hence less evanescent energy can interact with surface plasmon.However, the minimum dip is almost zero and the energy k  ( ) transfer efficiency is close to 100% when the metal thickness is 54 nm.
The ideal thickness of the silver is beneficial in ensuring sufficient photon energy reaches the interface between the silver/sample.It also simplifies the algorithm of detecting the minimum dip using a straightforward technique.The silver film thickness was chosen to be 54 nm for the theoretical analysis study because it provides the best coupling between photon energy and plasmon energy at resonance.

Figure 3: SPR reflectivity curve for silver thickness optimization
The reflectance curve for a traditional SPR sensor is shown in Figure 4. Prism, silver, and the sensing sample are the only layers in a conventional SPR sensor.Pure water in the detecting sample has a RI of 1.3317, but contaminated water with other pollutants has a RI of 1.34.As can be observed in Figure 4, when the water's RI is increased to 1.34, the resonance position changes by 1.921˚ while the RI changes by 0.0038.The fullwidth at half maximum (FWHM) parameter controls the SPR sensor's accuracy, the higher the detection accuracy, the narrower the reflectivity.

Figure 4: SPR reflectivity curves for a conventional SPR sensor
The reflectance curve in Figure 5 indicates simulated results for the proposed SPR sensor.Also, Figure 5 shows that as RI of the sample increases because of the contamination of deionized water (DIW) being diluted with multiple heavy metal ions at the concentration of 100 μM, the resonance dip shifts toward a higher resonance position.It is anticipated that the proposed SPR sensor outperforms the convectional SPR sensors in terms of sensitivity.As seen in Figure 5, when the water's RI is increased to 1.34, the resonance position changes by 3.255 while the RI changes by 0.0083 while Figure 4 gives the resonance shift of 1.921 at the same change in RI, which implies noticeable improvement as the results of adding TiO2 and BaTiO3.The full width at half maximum (FWHM) and detection accuracy The full width at half maximum (FWHM) is the parameter that governs the SPR sensor's accuracy, the higher the detection accuracy, the narrower the reflectivity.Mathematical expressed as (17) Equation (17) signifies that the resonance angle increases the FWHM. Figure 7 shows as RI of the sample increases FWHM increases.This can be explained theoretically because FWHM is inversely proportional to the cosine of the resonance angle refer Eq (1) and Eq (17).The proposed SPR sensor has an average FWHM of 2.1710.Therefore, the detection accuracy (DA), and quality factor for the proposed SPR are each calculated as follows: 399.45/2.171= 183.9936/RIU, 1/ (2.171) = 0.4606, respectively.The proposed SPR sensor has improved sensitivity and quality factor over the convectional SPR sensor by 118 /RIU and 22.4936 /RIU, respectively, while the detection accuracy is decreased by 0.2394 which is caused by the broadening reflectivity curve due addition of BaTiO3 which causes backscattered photon field to increase hence radiation damping.In summary, the proposed SPR sensor outperformed the convectional SPR sensor in terms of sensitivity and quality factor or figure of merits by 50.98 % and 13.93 %, respectively.Meanwhile, the detection accuracy has lowered by 34.2 %.Even though the detection accuracy is an important parameter in the SPR sensor, for heavy metal ion detection in water, the important parameter is sensitivity.

Minimum Dip
The minimum dip is shallow as the level of contamination increases as shown in Figure 8.This implies the energy transfer efficiency is decreasing as RI of the samples is increasing.This happens because as the resonance angle increases because of water contamination, less photon energy is transferred to the silver/sample interface which resulting less photon energy is interacted with the plasmon energy.

Figure 5 :Figure 6 Figure 6 :
Figure 5: SPR reflectivity curves for a proposed SPR sensor

Figure 7 :
Figure 7: FWHM for a proposed SPR sensor

Figure 8 :
Figure 8: Minimum dip for a proposed SPR sensor

Table 3
compares the performance of proposed SPR sensors to previously published work.The results show that the proposed SPR sensor exceeds prior studies in terms of sensitivity and quality factor, both of which are crucial characteristics in detecting heavy metal ions in wate.