Pathogenic bacteria sensing with tellurium dioxide/cadmium gallium sulfide-assisted surface plasmonic resonance refractive index sensor: a machine learning approach

Abstract

The senor quality on pathogenic bacteria monitoring employing Tellurium Dioxide (TeO₂)/Cadmium Gallium Sulfide (CdGa₂S₄)-assisted surface plasmonic resonance (SPR) refractive index (RI) sensor. This proposed design is used the Kretschmann configuration with silver (Ag) for exciting the surface plasmons. A wavelength of 633 nm is used to analyze the sensor’s performance exploiting the transfer matrix method along with angular interrogation technique. Initially, we show the optimization Ag’s thickness by analyzing the better minimum reflectance and sensitivity performances. Later, the structure optimization is also exhibited by comparing the proposed structure’s performance with others that are made-up with the defined layers. Finally, the performance analysis was investigated for different 2D materials and found that maximum attained parameters are sensitivity of 285.538 , quality factor of 144.152 , figure of merit of 134.875 and combined sensitivity factor of 133.896. These results have a significant improvement as compared with the existing work. Furthermore, a machine learning framework based on the Random Forest regression algorithm was developed to predict the sensor sensitivity and evaluate the influence of the structural parameters on the sensing performance.

1 Introduction

Pathogenic bacteria represent a significant risk to public health, food safety and sustainability and environmental quality as they are capable of making rapid exponential progress when allowed to multiply within host organisms leading them down the path towards infection (Falkow, 2004). The presence of pathogenic microorganisms in drinking water, food products, and clinical specimens is a worldwide concern, creating an increasing need for rapid, reliable, and highly sensitive detection methods. Early detection of bacterial contamination is crucial not only to combat the spread of disease but also to ensure food safety and access to timely medical care (Costerton et al., 1999). Thus, the need to create sensitive biosensing technologies that can identify even small changes in infections due to pathogenic bacteria has become a major area of interest in biomedical diagnosis, environmental monitoring, and public health surveillance. Early bacterial detection not only minimizes disease transmission but also improves clinical diagnosis, food quality assurance, and environmental surveillance, thereby supporting effective public health management. Various traditional methods, such as “microbial culture, polymerase chain reaction (PCR) (Rahman et al., 2013), enzyme-linked immunosorbent assay (ELISA) (Tabatabaei and Ahmed, 2022), fluorescence-based assays (Fang et al., 2018), and electrochemical approaches” have been applied for the detection of pathogenic bacteria (Overa et al., 2022). Although these approaches are typically accurate and reliable, they usually require complex instrumentation, skilled personnel, lengthy sample preparation, which confines their applicability for rapid and on-site detection. Such limitations have stimulated the search for optical-based sensing technologies that allow simultaneous, label-free, real-time, and extremely sensitive detection of cancer analytes with reduced analysis time and operational complexity (Kumar R. et al., 2026).

Among the all optical sensing techniques, surface plasmon resonance (SPR) is considered to be one of the most sensitive systems for chemical and biological detection due to its rapid, label-free, real-time analysis ability (Boddu et al., 2026). The most widely adopted SPR sensing scheme is the Kretschmann configuration, where a thin metallic film is deposited on the base of a high-refractive-index prism. Under p-polarized illumination, surface plasmons are generated at the metal-dielectric (MD) interface, when the in-plane component of the incident light matches the propagation constant of the surface plasmon wave (SPW) (Homola, 2003; Yang et al., 2024; Imam and Tausif, 2026). Any variation in the RI of the SM alters this phase-matching condition, resulting in a measurable shift in the resonance angle or the reflected light intensity (Mukhtar et al., 2014). These special properties make SPR one of the most vital sensing approaches for numerous different areas along with biomedical diagnostics, environmental monitoring and food quality assessment (Said and et a l., 2015). The excited SPW propagates along the MD interface while its associated evanescent field decays exponentially away from the surface into the sensing medium. At the resonance condition, efficient energy transfer from the incident light to the SPW produces a distinct minimum in the reflectance curve (Sharma et al., 2024). Since the resonance condition is highly dependent on the refractive index of the adjacent analyte, even minute refractive index variations produce a noticeable displacement of the resonance dip, thereby enabling highly sensitive detection (Homola, 2008). The overall performance of an SPR biosensor is governed not only by the sensing mechanism but also by the optical characteristics of the constituent materials. Among the noble metals, silver (Ag) is extensively utilized as the plasmonic layer because of its lower optical absorption losses, narrower resonance curve, and stronger confinement of the electromagnetic field compared with many alternative plasmonic metals (Bharti et al., 2025). The impressive properties associated with Ag lead to larger figures of merit for sensitivity and total detection accuracy which makes them the material of choice in high-performance SPR biosensor development (Kundanasri et al., 2026). However, the inherent oxidation sensitivity of Ag and its weak interaction with target analytes require the introduction of dielectric and two-dimensional (2D) materials to improve sensor performance. High RI dielectric materials, such as tellurium dioxide (TeO₂) (Sricharan et al., 2026), improve the quarantine of electromagnetic fields and enhance plasmonic coupling, whereas cadmium gallium sulfide (CdGa₂S₄) can be employed for the detection of pathogenic bacteria due to its suitable optical properties and high refractive index, additionally provides stability of resonance as well as efficiency for sensing (Sricharan et al., 2026; Ahamed et al., 2025). Moreover, aluminum antimonide (AlSb), a 2D material with superior optical and electronic performance, offers an ultra-high surface area and good light-matter interaction characteristics that contribute to the high analyte adsorption capacity and refractive-index sensitivity. Synergistically using these materials is an effective way to enhance the comprehensive performance of multilayer SPR biosensors (Fu et al., 2015).

Recent advances in plasmonic biosensors have demonstrated that the sensing performance of traditional SPR structures can be significantly improved by incorporating dielectric materials and two-dimensional (2D) nanomaterials. Various multilayer architectures have been investigated to increase the interaction of the evanescent electromagnetic field and sensing medium, which in turn increases sensitivity, resonance sharpness, and detection accuracy. High RI dielectric layers, transition metal dichalcogenides (TMDCs), graphene family materials, MXenes, and other newly emerging nanomaterials have attracted significant interest owed to their excellent optical and electronic properties. Numerous studies have reported the successful incorporation of dielectric layers and 2D materials for various biosensing applications. For illustration, Islam et al. suggested an multilayer SPR biosensor with acquisition of dielectric nanolayers for the detection of basal cell carcinoma (BCC), yielding up to an order magnitude sensitivity increment after confined electromagnetic field (Islam et al., 2026). Likewise, Janze et al. examined novel dielectric-assisted SPR structures with some up-to-date nanomaterials, and better resonance characteristics and detection performance have been achieved (Janze et al., 2025). This research focuses on designing and optimizing an HfSe₂-based SPR sensor integrated with machine learning for enhanced sensitivity and performance (Bouandas et al., 2026). More recently, multilayer SPR sensors incorporating materials such as graphene, black phosphorus (BP), MoS₂, WS₂, MXenes, and antimonene have been successfully applied to the detection of cancer biomarkers, glucose, proteins, and environmental pollutants, confirming the effectiveness of advanced nanomaterials in enhancing plasmonic sensing performance. Surface plasmon resonance (SPR) biosensors that incorporate silicon dioxide (SiO2) and barium titanate (BaTiO3) function better mainly by controlling electromagnetic fields at the metal-dielectric interface (Bouandas et al., 2025). Although these studies have demonstrated remarkable improvements in sensitivity, most reported sensor architectures primarily emphasize a single performance parameter, while comparatively limited attention has been devoted to achieving simultaneous optimization of multiple sensing characteristics, including “resonance angle, full width at half maximum (FWHM), quality factor (QF), figure of merit (FoM), signal-to-noise ratio (SNR), contrast sensitivity factor (CSF), and electric field enhancement” (Imam and Tausif, 2026; Yesudasu et al., 2021). Furthermore, the combined utilization of TeO₂, CdGa₂S₄, and AlSb within a single multilayer SPR platform for pathogenic bacteria detection has received very limited investigation (Kumar V. B. et al., 2026). Therefore, the development of an optimized multilayer architecture capable of simultaneously improving sensitivity, resonance quality, and overall sensing performance remains an active research challenge (Bodnar' et al., 2004).

Recently, machine learning (ML) techniques have attracted considerable attention for the analysis and optimization of SPR based optical sensors due to their capability to model complex nonlinear relationships between structural parameters and sensing performance (Reddy et al., 2026). By utilizing numerical or experimental datasets, ML algorithms can accurately predict sensor characteristics, identify the most influential design parameters, and significantly reduce the computational cost associated with repeated simulations (Chowdhury et al., 2023). In this work, a Random Forest regression model is integrated with the proposed SPR sensor to predict the sensor sensitivity, perform feature importance analysis, and support model-based optimization. The combination of numerical SPR analysis and machine learning provides an efficient framework for the rapid design and optimization of high-performance pathogenic bacteria sensors (Varma et al., 2026). This study suggested a multilayer SPR biosensor utilizing the Kretschmann configuration for the sensitive detection of pathogenic bacteria. The sensor design includes a BAF10 prism, a 56 nm Ag film, dielectric layers of TeO₂ and CdGa₂S₄, an AlSb nanomaterial layer, and the SM. The optical performance of the proposed architecture was theoretically investigated using the transfer matrix method (TMM) under angular interrogation at an operating wavelength of 633 nm. Initially, the Ag layer thickness was optimized to obtain a sharp resonance response, followed by a systematic investigation of the influence of TeO₂, CdGa₂S₄, and AlSb on the sensing performance. The proposed sensor was comprehensively evaluated using the resonance angle, sensitivity, FWHM, QF, FoM, SNR, CSF, and electric-field distribution. Finally, the sensing performance was equated with those of newly reported SPR biosensors to demonstrate the effectiveness and competitiveness of the proposed multilayer design. Furthermore, the generated simulation dataset provides a suitable foundation for future machine learning-assisted prediction and optimization of SPR biosensor performance.

2 Theoretical analysis and numerical modelling

2.1 Theoretical analysis

The optical characteristics of the suggested six-layer SPR biosensor were theoretically investigated via TMM, which is the most accurate analytical techniques used to study electromagnetic wave propagation through layered thin-film structures. The method accurately determines the reflectance characteristics of the SPR sensor by considering the RI and thickness of individual layer without introducing numerical approximations. The resonance characteristics were obtained by satisfying the electromagnetic boundary circumstances at every interface of the multilayer configuration. Reflectivity () of the suggested biosensor was modeled with the TMM because it computationally efficient and can accurately solve multilayer structure problems without resorting to simplifying approximate methods. Let us consider an (L)-layer configuration described as layers made of uniform materials along the (z)-axis, each with thickness of () and dielectric constant (). Using the electromagnetic boundary conditions at each interface, the tangential electric and magnetic field components at () can be related to those at through the characteristic transfer matrix in Equation 1:where and characterize the tangential mechanisms of the electric and magnetic fields at the first interface of the multilayer structure. Similarly, and correspond to the field components. The overall characteristic matrix establishes the relationship between these field quantities throughout the multilayer SPR configuration for p-polarized incident light, it can be calculated by using Equation 2.

The transverse refractive index associated with each layer is calculated using Equation 3. The propagation constant of the layer, which administers electromagnetic wave propagation through the multilayer structure, is determined by Equation 4. Furthermore, Equation 5 define the wave impedance () and Equation 6 describe the propagation angle () of the layer, respectively. Here, is the incident light wavelength, is the prism’s RI, is the incident angle and is the magnetic permeability of layer (Abbas et al., 2011).

Using the obtained characteristic matrix, the reflection coefficient of the SPR heterostructure is evaluated using Fresnel’s formulation, as expressed in Equation 7. Finally, Equations 7, 8 represent the mathematical expressions of Fresnel’s mode analysis for calculating the and reflection coefficient () of an incident light, respectively (Abbas et al., 2011).

The sensitivity of the proposed sensor is defined as the ratio of change in SPR resonance angle () to the corresponding change in the RI () making it one of the most important performance parameters for evaluating sensor performance. This high sensitivity performance of the sensor with minimal change in analyte concentration indicates sensor ability to detect very small structural differences, thus better sensing performance. In addition, the performances of QF, FoM, and CSF are calculated, which demonstrates the quality of the sensor in this investigation.

Mathematical expressions for computing the aforementioned parameters are presented in Equations 9–12, where FWHM is the full width half maximum and is the maximum reflectivity in the reflectance plots (Vasimalla et al., 2020). The QF and FoM characterizes the product quality, noise contribution in a sensor, respectively report (Hit et al., 2001). Lastly, the overall performance of the sensor is research using the CSF.

2.2 Numerical modelling

The numerical modeling of the planned SPR biosensor is illustrated in Figure 1. The multilayer structure was designed by the Kretschmann configuration, analyzed at an operating wavelength of 633 nm using the TMM. The sensor comprises six functional layers: the prism, metal layer, dielectric layers, two-dimensional (2D) material, and sensing medium. The RI’s and thicknesses of all constituent layers were selected from the reported literature and maintained constant throughout the analysis, unless otherwise specified. The BK7 prism served as an ideal first layer due to its high optical transparency, stable refractive index, and ability to efficiently couple the incident p-polarized light into the plasmonic interface. It has a RI of 1.515 (Pal et al., 2019), thus exhibiting the required phase-matching condition for excitation of the SPWs. The second layer comprised Ag through a compound RI of 0.056266 + 4.27761i, where Ag was selected as the plasmonic metal due to its low optical loss, high electrical conductivity, and capability to generate a sharp and well-defined SPR resonance curve. The thickness of the Ag film significantly affected both plasmon excitation and resonance characteristics; thus, it was optimized using an iterative procedure before conducting further performance analysis.

FIGURE 1

Two dielectric layers were integrated over the Ag film to enhance the sensing features. The introduction of a 1 nm layer of Tellurium Dioxide (TeO₂) with refractive index of 2.2596 serves to both confine the electromagnetic field and protect the Ag surface from oxidation at the same time. Subsequently, a 1 nm CdGa₂S₄ with a refractive index of 2.4482 was deposited to enhance the plasmonic coupling and further broaden the interface between the evanescent field and the sensing medium. Collectively, these dielectric layers improve resonance stability and enhance the sensing performance. The fifth layer was AlSb, which possesses a complex RI of 3.8638 + 0.0035982i and a thinness of 0.53 nm (Pal et al., 2019). AlSb was selected because of its excellent optical and electronic properties, which promote strong light-matter interaction and increase the effective sensing area available for biomolecular adsorption. The sensing medium was arranged above the AlSb layer so that the changes in refractive indexes due to pathogenic bacteria could alter the resonance conditions of the SPR sensor. The RI of the sensing medium was varied from 1.371 to 1.410 was investigate different analyte conditions in this study. For a comprehensive performance evaluation, the proposed multilayer architecture was compared with four additional SPR configurations consisting of different layer combinations. All structures were analyzed under identical simulation conditions using the same theoretical framework. The sensing performance was subsequently evaluated in terms of resonance angle, R_min, Sensitivity, FWHM, QF, FoM, SNR, and CSF, enabling a fair comparison of the suggested design with present configurations.

3 Results and discussion

3.1 Ag thickness optimization

The thickness of the plasmonic metal plays a critical role in defining the sensing performance of an SPR biosensor, as it directly influences the excitation efficiency of surface plasmon waves (SPWs) and the resonance characteristics. Thus, before studying the proposed multilayer architecture, the thickness of the Ag film was optimized in the range 40–60 nm with a step size equal to 5 nm (Mudgal et al., 2020), whereas keeping the remaining layer thickness constant. The optimization was performed by studying the reflectance curves, resonance angle, and minimum reflectance (R_min) in two refractive-index environments of sensing medium (RI = 1.371 and RI = 1.410). The corresponding reflectance responses are illustrated in Figures 2a,b. The resonance curves shown in Figure 2a show that the plasmonic coupling is gradually enhanced with increasing Ag thickness from 40 nm to 55 nm. R_min drops from 0.34442 to 0.002464, indicating the energy transmission from incident light to SPWs using better efficiency. Simultaneously, the resonance angle exhibits a slight shift, confirming that the optical coupling condition is progressively optimized with increasing Ag thickness. Nevertheless, for an Ag thickness of 60 nm, the minimum reflectance increases again owing to the contribution of further optical losses by the thicker metal film, while limiting coupling between incident light and plasmonic mode. The corresponding plot for RI = 1.410 is shown in Figure 2b.

FIGURE 2

With the increase of Ag thickness, the resonance angle increasingly goes toward a higher value and the reflectance minimum continuously decreases at first, then increases after reaching an optimum thickness. This behavior suggests that an extremely thick Ag layer suppresses the dispersion of the evanescent field into the sensing medium, thereby weakening the interface between the electromagnetic field and analyte molecules. As a result, the resonance dip was larger and less effective for sensing applications. Table 1 summarizes the optimized values obtained from the Ag thickness analysis. Among all the investigated thicknesses, the 55 nm Ag film produced the lowest R_min of 0.002464, along with a well-defined resonance response, indicating the strongest plasmonic coupling and the highest energy transfer efficiency. Therefore, an Ag thickness of 55 nm was selected as the optimum value for all subsequent simulations and performance analyses. The optimized metallic layer induced an appropriate trade-off among the confinement of the electromagnetic field and reduced propagation losses, which enhanced the overall sensing characteristics of the planned plasmonic biosensor.

3.2 Performance analysis of proposed SPR

The sensing performance of the proposed multilayer SPR biosensor was examined with its reflectance characteristics and compared against four reference configurations (S1–S4), which are illustrated in Figures 3a,b. The investigated structures are listed in Table 2, where each configuration incorporates different material combinations to examine the individual contributions of the Ag, TeO₂, CdGa₂S₄, and AlSb layers. The comparison was performed for sensing-medium RI of 1.371 and 1.410, representing the refractive-index variation associated with pathogenic bacteria detection. Figure 3a shows the reflectance responses corresponding to a refractive index of 1.371, whereas Figure 3b presents the responses after increasing the refractive index to 1.410. A progressive change in the resonance angle was observed as additional dielectric and nanomaterial layers were incorporated into the sensor architecture. Among all the investigated configurations, the proposed structure (S5) exhibited the largest resonance-angle shift, along with a sharp and well-defined resonance dip. This phenomenon demonstrates plamonic coupling and evanescence electromagnetic field having the enchanced interaction with sensing medium. TeO₂ and CdGa₂S₄ not only improve the electromagnetic field confinement but also give additional enhancive of light–matter interaction on AlSb layer because they exhibit better sensing properties than other structures.

FIGURE 3

The material parameters utilized for the design of the multilayer SPR biosensor are listed in Table 3, and the structural configurations used for the performance comparison are presented in Table 4. Arrangement of the optimized sensor, including a BK7 prism, 55 nm Ag film, 1 nm TeO₂ layer, 1 nm CdGa₂S₄ layer, and 0.53 nm AlSb layer. The optimized multilayer design is capable of concurrently exciting plasmon and confining the electromagnetic field, as well as providing sufficient interaction with the analyte, thus effectively improving the performance of the designed biosensor. The quantitative performance comparison of all five configurations is presented in Table 5. The conventional structure (S1) achieves a sensitivity of 185.620°/RIU, however the combination of AlSb (S2) of 203.68°/RIU, and dielectric layers (S3 and S4) increases the sensitivity to approximately 200°–203.68°/RIU. In contrast, the proposed multilayer configuration (S5) exhibits the highest sensitivity of 269.397°/RIU, representing an improvement of approximately 45.1%, 32.3%, 34.4%, and 32.3% compared with S1, S2, S3, and S4, respectively.

Moreover, the developed sensor has the highest QF (181.04 RIU⁻¹), FoM (180.60 RIU⁻¹) and CSF (179.679 RIU⁻¹), which illustrates that the suggested architecture not only improves sensitivity, but also accomplishes a sharp resonance profile with excellent quality for sensing purposes. In summary, the results indicate that the addition of TeO₂, CdGa₂S₄ and AlSb simultaneously gives synergistic improvement factors to both plasmonic coupling and electromagnetic field localization in order to improve the sensing performances of the suggested SPR biosensor. The developed multilayer design is well supported by the evidence of an improved response to resonance mode and performance parameters, indicating that it can help provide high sensitivity for pathogenic bacteria detection.

3.3 Comparative analysis of proposed SPR, sensor with 2D materials.

To investigate the impact of different two-dimensional (2D) materials on the sensing performance, the optimized multilayer SPR configuration (S5) is analyzed by replacing the sensing layer with BP, Graphene, MoS₂, WS₂, and AlSb while maintaining all remaining structural parameters unchanged. The RI’s and thicknesses of the investigated 2D materials are summarized in Table 5, whereas the corresponding reflectance characteristics are illustrated in Figures 4a,b. The comparison is carried out for sensing-medium RIs of 1.371 and 1.410 to evaluate the effect of each material on the resonance characteristics. Figures 4a,b show that the addition of different 2D materials leads to significant changes in the resonance angle, minimum reflectance. These differences originate from the distinct optical constants and light–matter interaction capabilities of each material, which directly influence the excitation efficiency of surface plasmon waves. Among all investigated materials, the AlSb-assisted configuration exhibits the largest resonance-angle shift together with a sharp and definite resonance dip, indicating efficient plasmonic coupling and stronger interaction between the evanescent field and the sensing medium. In contrast, Graphene, MoS₂, BP, and WS₂ also improve the sensor performance compared with the conventional structure, although their resonance characteristics are comparatively less pronounced. Table 5 shows the optical properties of selected 2D materials, while each material has a unique refractive index and thickness, their effects on sensor performance are not completely independent but rather interaction with optical absorption, electromagnetic field confinement, and analyte interaction. Higher complex dielectric indices of AlSb leads to a more intensified localization of the electromagnetic field at the sensing interface, providing denser resonant states contraction as well as higher detection efficiency. The quantitative comparison of the sensing performance is presented in Table 6.

FIGURE 4

Among all investigated materials, AlSb achieves the best overall performance with a sensitivity of 269.397°/RIU, a QF of 181.046 RIU⁻¹, a FoM of 180.600 RIU⁻¹, and a CSF of 179.679 RIU⁻¹. In comparison, BP exhibits a sensitivity of 261.179°/RIU with a QF of 178.036 RIU⁻¹, whereas Graphene achieves 241.461°/RIU with a comparatively lower FoM of 134.896 RIU⁻¹. Likewise, MoS₂ has a sensitivity of 259.538°/RIU, and WS₂ shows the highest sensitivity among the other materials (282.538°/RIU), but its QF (144.152 RIU⁻¹) and FoM (134.875 RIU⁻¹) are also too low compared to those of TMDs, leading to greater resonance profiles for lower sensing quality. So even though the WS₂ produces the biggest angular shift, AlSb is favored as a top sensing material by being able to provide the best combination of characteristics including high sensitivity, highly damped resonance and outstanding performance metrics. The comparative analysis substantiates that the low concentration presence of AlSb in the proposed multilayer SPR architecture delivers a more uniform sensing characteristics higher than the examined 2D materials. The high electromagnetic field confinement, more vigorous plasmonic coupling, and improved resonance characteristics guarantee a more sensitive quality factor and figure of merit performances of the designed sensor for highly sensitive detection of pathogenic bacteria.

3.2 Electric field intensity

Figure 5 illustrates the electric field intensity distribution of the proposed SPR sensor structure consisting of Ag/TeO₂/CdGa₂S₄/AlSb in contact with the sensing medium. At the Ag-dielectric interface, surface plasmon waves are excited as a result of resonance between p-polarized light incident from above and the free electrons in the thin metallic film. In fact, the electromagnetic field penetrates into the sensing volume as an evanescent wave beyond this interface and with a decay exponent that depends on the distance between the metal boundary. Intermediate dielectric layers, such as TeO₂, CdGa₂S₄ and AlSb help in modulating the electric field confinement to achieve an improvement of interaction of plasmonic field with analyte.

FIGURE 5

These layers allow well-organized coupling of light to the surface plasmon mode while reducing optical losses and enhancing field localization at the sensing interface. This means that even the slightest refractive index shifting in the medium of sensing causes a large deviation in the resonance condition, which results in higher sensitivity sensors. The penetration depth (PD) of the evanescent field is calculated as 448.43 nm, which means that the electric field penetrates about 448 nm into the sensing medium before its intensity decreases to one/e (≈36.8%) of its maximum value. This depth of penetration makes these polymers ideal for the detection of biomolecules, proteins, pesticides and other analytes whose interaction takes place in a few hundred nm thick region just below the sensor surface. The optimized penetration depth provides a compromise between sufficient field confinement and interaction volume to improve sensitivity and detection limits of the suggested SPR biosensor.

3.3 Limitations and future directions

Although the numerical sensing performance of the proposed sensor is promising, there are challenges that would need to be overcome before practical use. However, first, this study relies on numerical simulations and does not involve experimental fabrication or characterization. Thus, they only predict the sensing performance, and need experimental validation. Secondly, the bacteria-specific surface functionalization or molecular recognition are not considered in the existing model. Therefore, the simulated response is mainly due to refractive-index based sensing and selective detection of one specific bacterial species could only be accomplished with a suitable bioreceptor or functionalization layer. Resonance-angle shifts as well as measurement uncertainty are indicated due to temperature variations affecting both the refractive index of the sensing medium and the optical properties of the constituent materials. Likewise, fabrication tolerances, variations in layer thicknesses, surface roughness, imperfections at the interface and non-uniform coating can collectively lead to a deviation from an idealized numerical response. The absorption of the material and optical losses, in particular looking at the metallic and lossy functional layers, may also impact resonance depth, linewidth, and electric-field enhancement. The use of an idealized sensing environment in the numerical model is another major limitation in real biological samples, proteins, salts, cells and other biomolecules that generate nonspecific adsorption, background refractive-index fluctuations and matrix interference may also be presented. These effects may impair the selectivity, sensitivity and reproducibility of the sensor. Consequently, further work will be geared towards the experimental fabrication and characterization, inclusion of bacteria-directed surface functionalization details, evaluation against temperature and fabrication tolerance pathways (such as sterilization), quantification of losses in graded materials and composite constructs, as well as validation with relevant real-life bio samples.

3.4 Comparative study of SPR performance analysis

A comparison of the sensing performance of the suggested design with recently reported SPR biosensors is also conducted, and a summary of this assessment is depicted in Table 7 in order to evaluate its effectiveness. The comparison includes previously published multilayer SPR configurations developed for biological and chemical sensing applications using different dielectric materials and two-dimensional nanomaterials. The comparison primarily focuses on sensitivity, since it is the most widely adopted parameter for evaluating SPR sensor performance. The reported results indicate that the proposed multilayer SPR biosensor achieves competitive sensing performance compared with recently published designs. While several reported sensors show excellent sensitivities based on advanced nanomaterial incorporation, many of them compromise either the resonance linewidth or overall sensing performance. In contrast, the proposed architecture has dramatically boost high sensitivity with great quality factor, high figure of merit and improved combined sensitivity factor which gives a perfect sensing response and balanced at different input power levels. This performance boost is ascribed to the synergetic effect of Ag plasmonic layer, TeO₂ dielectric layer, CdGa₂S₄ semiconductor layer and AlSb nanomaterial that completely enhances electromagnetic field confinement with improved interaction between evanescent field and sensing medium.

4 Machine learning-based prediction and optimization

4.1 Dataset preparation

To investigate the predictive capability of machine learning for the proposed SPR biosensor, a dataset was prepared using the numerical results obtained from the optimization study presented in the previous sections. Since the experimental investigation provides only a limited number of reported observations, an augmented dataset was generated within the experimentally investigated parameter ranges to facilitate supervised learning while preserving the physical relationships among the sensor parameters. The generated dataset includes the silver (Ag) layer thickness, refractive index (RI), resonance angle, minimum reflectance, full width at half maximum (FWHM), quality factor (QF), figure of merit (FoM), and combined sensitivity factor (CSF). The target variable selected for prediction was the sensor sensitivity, which represents the primary performance indicator of the proposed SPR biosensor.

4.2 Machine learning model development

To establish a predictive framework for estimating the sensitivity of the proposed surface plasmon resonance (SPR) biosensor, a supervised machine learning approach based on the Random Forest (RF) regression algorithm was employed. The RF model was selected due to its robustness against overfitting, capability to capture nonlinear relationships, and high predictive performance for complex engineering datasets. Furthermore, Random Forest provides an effective balance between prediction accuracy and computational efficiency, making it particularly suitable for SPR sensor optimization problems. The generated dataset was first preprocessed by selecting the most influential sensor parameters, including the silver (Ag) layer thickness, refractive index (RI), resonance angle, minimum reflectance, and the number of sensing layers, as the input features.

The sensor sensitivity was considered the target output variable. Subsequently, the dataset was randomly divided into training and testing subsets using an 80:20 ratio. The training dataset was utilized to construct the regression model, while the testing dataset was reserved for evaluating the predictive capability of the trained model on previously unseen samples. The Random Forest regressor was configured using 250 decision trees with a maximum tree depth of ten levels to achieve an appropriate compromise between model complexity and generalization capability. During the training stage, each tree was generated using bootstrap sampling, while the final prediction was obtained by averaging the outputs of all individual trees. This ensemble learning strategy significantly reduces prediction variance and enhances the robustness of the regression model. After training, the developed model was applied to predict the sensor sensitivity for the testing dataset. The predicted values were then compared with the corresponding actual values to evaluate the model’s prediction capability. Figure 6 illustrates the relationship between the experimentally generated target values and the values predicted by the Random Forest model. The proximity of the data points to the ideal prediction line demonstrates the high consistency between the predicted and actual sensitivities, indicating that the developed model successfully captures the nonlinear dependence between the SPR structural parameters and the sensor performance.

FIGURE 6

4.3 Model performance evaluation

The predictive performance of the developed Random Forest regression model was evaluated using three widely adopted statistical performance indicators, namely, the coefficient of determination (R2R^2R2), the root mean square error (RMSE), and the mean absolute error (MAE). The coefficient of determination (R2R^2R2) measures the proportion of variance in the target variable that is explained by the regression model, whereas RMSE and MAE quantify the average prediction error and provide complementary information regarding the model accuracy. A higher R2R^2R2 value together with lower RMSE and MAE values indicates superior predictive capability and improved model generalization. Following the training stage, the regression model was applied to the testing dataset to evaluate its prediction performance on previously unseen samples. The obtained performance metrics demonstrated excellent agreement between the predicted and target sensitivity values, confirming that the Random Forest algorithm successfully captured the nonlinear relationship between the structural parameters of the SPR biosensor and its sensing performance. The low prediction errors further indicate that the developed model provides stable and reliable estimates over the investigated operating range.

Figure 7 presents the residual error distribution of the proposed Random Forest model. It can be observed that most residual values are concentrated near zero with an approximately symmetric distribution. The absence of significant skewness or isolated large residuals suggests that the prediction errors are randomly distributed rather than resulting from systematic modeling bias. This behavior confirms the robustness of the regression model and demonstrates its capability to accurately estimate the sensitivity of the proposed SPR biosensor. Figure 8 illustrates the learning curve obtained during the model training process. The convergence of the training and validation R2R^2R2 scores with increasing training samples indicates that the model achieves a good balance between fitting accuracy and generalization performance. Moreover, the relatively small gap between the two curves confirms that the Random Forest model does not suffer from significant overfitting or underfitting. These results demonstrate that the trained model maintains stable predictive performance as additional training samples become available, thereby validating its suitability for data-driven optimization of SPR biosensor parameters.

FIGURE 7

FIGURE 8

4.4 Feature importance analysis

To further interpret the predictive capability of the developed Random Forest model, a feature importance analysis was performed to quantify the contribution of each input parameter toward the prediction of the SPR sensor sensitivity. Unlike conventional regression techniques, the Random Forest algorithm provides an intrinsic measure of feature importance based on the average reduction in prediction error achieved by each variable during the tree construction process, as presented in Figure 9. This analysis not only improves the interpretability of the developed machine learning model but also identifies the dominant physical parameters governing the sensing performance of the proposed SPR biosensor. The investigated input variables included the Ag layer thickness, resonance angle, refractive index (RI), full width at half maximum (FWHM), and minimum reflectance. Figure 8 presents the relative importance of these parameters as determined by the trained Random Forest model. It can be observed that the Ag layer thickness exhibits the highest contribution to the prediction process, indicating that it is the most influential parameter affecting the sensor sensitivity. This observation is consistent with the optimization results presented in Section 3, where variations in the Ag thickness significantly modified the plasmonic resonance characteristics and consequently enhanced the sensing performance. The resonance angle and refractive index also exhibit considerable influence on the prediction accuracy, reflecting their strong correlation with the excitation conditions of surface plasmon waves. Conversely, the contributions of FWHM and minimum reflectance are comparatively smaller, although they still provide valuable information for improving the overall predictive performance of the regression model.

FIGURE 9

These findings demonstrate that the Random Forest model successfully identifies the physically meaningful parameters governing SPR sensor behavior while providing additional insight into their relative significance. Therefore, the feature importance analysis confirms that the developed machine learning model is not only capable of accurately predicting sensor sensitivity but also serves as an effective tool for guiding the optimization of SPR biosensor design.

4.5 Model based optimization

The trained Random Forest regression model was further employed as a predictive optimization tool to identify the sensor configuration that maximizes the SPR sensitivity. Unlike conventional optimization methods, which typically require repeated numerical simulations or experimental investigations, the developed machine learning model enables rapid prediction of sensor performance over a wide range of design parameters with significantly reduced computational cost. Consequently, the proposed data-driven framework provides an efficient alternative for accelerating the optimization process of SPR biosensors. To investigate the influence of the silver (Ag) layer thickness on the sensing performance, the trained regression model was used to predict the sensor sensitivity while varying the Ag thickness within the investigated range of 40–60 nm. The remaining input parameters were maintained within their optimized operating conditions to isolate the effect of the Ag layer thickness. This procedure enabled the identification of the optimum design region corresponding to the maximum predicted sensitivity. Figure 10 illustrates the predicted sensitivity as a function of the Ag layer thickness obtained from the trained Random Forest model. The prediction results indicate that the sensor sensitivity increases progressively with increasing Ag thickness until reaching an optimum region near 55 nm, after which the improvement becomes marginal. This trend is in excellent agreement with the numerical optimization presented in Section 3, where the Ag thickness of approximately 55 nm produced the highest sensing performance.

FIGURE 10

The close agreement between the machine learning predictions and the conventional numerical analysis confirms the capability of the developed regression model to accurately reproduce the physical behavior of the proposed SPR biosensor. Overall, the model-based optimization demonstrates that machine learning can efficiently estimate the optimal structural parameters while (Bouandas et al., 2026) substantially reducing the computational effort associated with repeated electromagnetic simulations. Therefore, the proposed framework offers a practical tool for the rapid design and optimization of high-performance SPR biosensors.

5 Conclusion

A study on influence of employing Tellurium Dioxide (TeO₂)/Cadmium Gallium Sulfide (CdGa₂S₄)-assisted structure in surface plasmonic resonance (SPR) sensor is presented in this article. In the first part, the optimization Ag’s thickness shows and found that Ag thickness of 55 nm offers a R_min of 0.002464 compared to other thicknesses. In the second part, the proposed structure’s performance offers a highest sensitivity, which is 1.45, 1.32, 1.34, and 1.32 times higher than S1, S2, S3 and S4, respectively. In the detection process we use different 2D materials and improved sensing properties, that the maximum attained parameters, such as Sensitivity of 269.39 , QF of 181.04 , FoM of 180.6 and CSF of 179.67, are obtained using AlSb. These outcomes have a substantial improvement as compared with the existing work. Therefore, the proposed sensor can function as a very effective carrier for biological and biomedical applications and be utilized to identify pathogenic microorganisms. Furthermore, the proposed Random Forest model accurately predicted the sensor sensitivity and identified the Ag layer thickness as the most influential design parameter. The machine learning-based optimization showed good agreement with the numerical results, demonstrating that the proposed framework provides an efficient approach for the design and optimization of high-performance SPR biosensors.

References

• 1

  AbbasA.LinmanM. J.ChengQ. (2011). Sensitivity comparison of surface plasmon resonance and plasmon-waveguide resonance biosensors. Sensors Actuators B Chem.156 (1), 169–175. 10.1016/j.snb.2011.04.008

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 2

  AhamedS.VenkatesanK. K.JalaludeenS. A. (2025). A review on various surface plasmon resonance-based sensors. Plasmonics20 (8), 6869–6885. 10.1007/s11468-025-02837-4

  • CrossRef
  • Google Scholar
  • View reference in article

• 3

  BasakC.IslamM. S.HosainM. K.KouzaniA. Z. (2024). An ultra-sensitive surface plasmon resonance biosensor with PtSe2 and BlueP/WS2 heterostructure. Heliyon10 (19), e38499. 10.1016/j.heliyon.2024.e38499

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 4

  BhartiA.MishraR.TiwariP.ShuklaS. M.SharmaV. (2025). Theoretical study of silicon carbide-based surface plasmon resonance sensor for detection of tuberculosis in blood plasma. J. Opt. 10.1007/s12596-025-02877-3

  • CrossRef
  • Google Scholar
  • View reference in article

• 5

  BodduS.VasimallaY.MishraM.MarquesC.SinghR.KumarS. (2026). Label-free SPR sensor with enhanced performance for Deltamethrin detection using potassium and Lithium Tantalates. Microchem. J.224, 117464. 10.1016/j.microc.2026.117464

  • CrossRef
  • Google Scholar
  • View reference in article

• 6

  Bodnar'I.Rud'V. Y.RudY. V. (2004). Growth and properties of CdGa2S4 single crystals. Inorg. Materials40 (2), 102–106. 10.1023/b:inma.0000016081.55152.47

  • CrossRef
  • Google Scholar
  • View reference in article

• 7

  BouandasH.KumarR.SinghS.BouazziY.SirohiK. (2025). Enhanced sensitivity and figure of merit in surface plasmon resonance biosensors with silicon dioxide and barium titanate materials. Microchem. J.212, 113341. 10.1016/j.microc.2025.113341

  • CrossRef
  • Google Scholar
  • View reference in article

• 8

  BouandasH.KumarR.WekalaoJ.GariaL.BenhalilibaM.SinghS.et al (2026). Machine learning-optimized hafnium diselenide-based surface plasmon resonance sensor. Surfaces Interfaces86, 108771. 10.1016/j.surfin.2026.108771

  • CrossRef
  • Google Scholar
  • View reference in article

• 9

  ChowdhuryS.Faisal AbdulrazakL.Akhtar MituS.AhmedK.BuiF. M.SmiraniL. K.et al (2023). A highly sensitive multi-channel SPR-PCF based biosensor with deep learning prediction approach. Alexandria Eng. J.77, 189–203. 10.1016/j.aej.2023.06.093

  • CrossRef
  • Google Scholar
  • View reference in article

• 10

  CostertonJ. W.StewartP. S.GreenbergE. P. (1999). Bacterial biofilms: a common cause of persistent infections. Science284 (5418), 1318–1322. 10.1126/science.284.5418.1318

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 11

  FalkowS. (2004). Molecular Koch's postulates applied to bacterial pathogenicity—a personal recollection 15 years later. Nat. Rev. Microbiol.2 (1), 67–72. 10.1038/nrmicro799

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 12

  FangX.ZhengY.DuanY.LiuY.ZhongW. (2018). Recent advances in design of fluorescence-based assays for high-throughput screening. Anal. Chemistry91 (1), 482–504. 10.1021/acs.analchem.8b05303

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 13

  FuH.ZhangS.ChenH.WengJ. (2015). Graphene enhances the sensitivity of fiber-optic surface plasmon resonance biosensor. IEEE Sensors J.15 (10), 5478–5482. 10.1109/jsen.2015.2442276

  • CrossRef
  • Google Scholar
  • View reference in article

• 14

  HitomiK.MatsumotoM.MuroiO.ShojiT.HiratateY. (2001). Characterization of thallium bromide crystals for radiation detector applications. J. Crystal Growth225 (2-4), 129–133. 10.1016/s0022-0248(01)00834-x

  • CrossRef
  • Google Scholar
  • View reference in article

• 15

  HomolaJ. (2003). Present and future of surface plasmon resonance biosensors. Anal. Bioanalytical Chemistry377 (3), 528–539. 10.1007/s00216-003-2101-0

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 16

  HomolaJ. (2008). Surface plasmon resonance sensors for detection of chemical and biological species. Chem. Reviews108 (2), 462–493. 10.1021/cr068107d

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 17

  ImamK. T.TausifD. M. (2026). Differential evolution-optimized SPR biosensor for dengue virus detection. Opt. Lasers Eng.205, 109918. 10.1016/j.optlaseng.2026.109918

  • CrossRef
  • Google Scholar
  • View reference in article

• 18

  IslamS.DolonS. K.CheM. R.AhsanM. S.NakarmiB.SohnI.et al (2026). A noninvasive surface plasmon resonance sensor for early detection of basal cell carcinoma. Adv. Photonics Res.7 (5), e202500326. 10.1002/adpr.202500326

  • CrossRef
  • Google Scholar
  • View reference in article

• 19

  JanzeE. J. T.AlaeiS.MeshginqalamB. (2025). On the sensing performance improvement in SPR biosensor using ZnO and TMDCs architecture for cancer detection. Sci. Rep.15 (1), 28349. 10.1038/s41598-025-14131-8

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 20

  JohnsonP. B.ChristyR. W. (1972). Optical constants of the noble metals. Phys. Rev. B6 (12), 4370–4379. 10.1103/physrevb.6.4370

  • CrossRef
  • Google Scholar
  • View reference in article

• 21

  KatoK.UmemuraN.PetrovV. (2017). Sellmeier and thermo-optic dispersion formulas for CdGa2S4 and their application to the nonlinear optics of Hg1−xCdxGa2S4. Opt. Commun.386, 49–52. 10.1016/j.optcom.2016.10.054

  • CrossRef
  • Google Scholar
  • View reference in article

• 22

  KumarR.PraveenP.BrahmaB.BarsocchiP.BhoiA. K. (2026a). Refractive index sensing-based sensitivity enhancement using surface plasmon resonance sensor with integration of tin diselenide and zirconium diselenide. Sensors26 (13), 4279. 10.3390/s26134279

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 23

  KumarV. B.KumarP. S.TrivediM. (2026b). Emerging 2D materials beyond graphene for sensor technologies applications. Mater. Today Commun.53, 115421. 10.1016/j.mtcomm.2026.115421

  • CrossRef
  • Google Scholar
  • View reference in article

• 24

  KundanasriK.GurramkonduK. S.SanthoshC.VasimallaY.KumarS. (2026). High-performance plasmonic biosensor for blood urea detection using SiC/black phosphorus/AgBr hybrid layers. Discov. Electron.3 (1), 70. 10.1007/s44291-026-00223-w

  • CrossRef
  • Google Scholar
  • View reference in article

• 25

  MudgalN.SahariaA.AgarwalA.AliJ.YupapinP.SinghG. (2020). Modeling of highly sensitive surface plasmon resonance (SPR) sensor for urine glucose detection. Opt. and Quantum Electron.52 (6), 1. 10.1007/s11082-020-02427-0

  • CrossRef
  • Google Scholar
  • View reference in article

• 26

  MukhtarW. M.ShaariS.EhsanA. A.MenonP. S. (2014). Electro-optics interaction imaging in active plasmonic devices. Opt. Mater. Express4 (3), 424–433. 10.1364/ome.4.000424

  • CrossRef
  • Google Scholar
  • View reference in article

• 27

  OveraS.KoB. H.ZhaoY.JiaoF. (2022). Electrochemical approaches for CO2 conversion to chemicals: a journey toward practical applications. Accounts Chemical Research55 (5), 638–648. 10.1021/acs.accounts.1c00674

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 28

  PalS.VermaA.SainiJ. P.PrajapatiY. K. (2019). Sensitivity enhancement using silicon‐black phosphorus‐TDMC coated surface plasmon resonance biosensor. Iet Optoelectron.13 (4), 196–201. 10.1049/iet-opt.2018.5023

  • CrossRef
  • Google Scholar
  • View reference in article

• 29

  PolyanskiyM. N. (2024). Refractiveindex.info database of optical constants. Sci. Data11 (1), 94. 10.1038/s41597-023-02898-2

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 30

  RahmanM. T.UddinM. S.SultanaR.MoueA.SetuM. (2013). Polymerase chain reaction (PCR): a short review. Anwer Khan Mod. Med. Coll. J.4 (1), 30–36. 10.3329/akmmcj.v4i1.13682

  • CrossRef
  • Google Scholar
  • View reference in article

• 31

  RahmanM. M.RanaM. M.RahmanM. S.AnowerM.MollahM. A.PaulA. K. (2020). Sensitivity enhancement of SPR biosensors employing heterostructure of PtSe2 and 2D materials. Opt. Mater.107, 110123. 10.1016/j.optmat.2020.110123

  • CrossRef
  • Google Scholar
  • View reference in article

• 32

  ReddyP. S. K.ChebaaneS.VasimallaY.KhalifaS. B.AlsaifN. A. M.PuppalaR. S.et al (2026). Smart label-free SPR biosensing platform for hemoglobin and urine glucose detection via machine learning. Sci. Rep.16 (1), 20378. 10.1038/s41598-026-50144-7

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 33

  SaidF. A.Menon P. S. Kalaivani T.MohamedM. A.Abedini A. Shaari S.et al (2015). “FDTD analysis of structured metallic nanohole films for LSPR-based biosensor,” in 2015 IEEE Regional Symposium on Micro and Nanoelectronics (RSM) (IEEE), 1–4.

  • Google Scholar
  • View reference in article

• 34

  SharmaV.DwivediL. K.SinghS.MishraG. R. (2024). Glucose level monitoring in human blood samples by surface plasmon resonance sensor using cerium oxide and black phosphorus nanomaterials. J. Opt.53 (4), 3683–3694. 10.1007/s12596-023-01597-w

  • CrossRef
  • Google Scholar
  • View reference in article

• 35

  SricharanP.VasimallaY.KumarS. (2026). Plasmon-enhanced black phosphorus–ZrO2–TeO2 multilayer SPR biosensor for ultra-sensitive early detection of brain tumors. Mod. Phys. Lett. B40, 2650037. 10.1142/s0217984926500375

  • CrossRef
  • Google Scholar
  • View reference in article

• 36

  TabatabaeiM. S.AhmedM. (2022). “Enzyme-linked immunosorbent assay (ELISA),” in Cancer Cell Biology: Methods and Protocols (Springer), 115–134.

  • Google Scholar
  • View reference in article

• 37

  UchidaN. (1971). Optical properties of single-crystal paratellurite (Te${\mathrm{O}}_{2}$). Phys. Rev. B4 (10), 3736–3745. 10.1103/physrevb.4.3736

  • CrossRef
  • Google Scholar
  • View reference in article

• 38

  VarmaN. S. S.VasimallaY.ChebaaneS.Ben KhalifaS.AlsaifN. A.PuppalaR. S.et al (2026). Surface and interface effects in X-titrate (X: lead and Strontium)/aluminium antimonide–assisted SPR refractive index sensor with machine learning analysis. Surfaces Interfaces87, 109029. 10.1016/j.surfin.2026.109029

  • CrossRef
  • Google Scholar
  • View reference in article

• 39

  VasimallaY.Shekhar PradhanH.Jashvantbhai PandyaR. (2020). SPR performance enhancement for DNA hybridization employing black phosphorus, silver, and silicon. Appl. Opt.59 (24), 7299–7307. 10.1364/AO.397452

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 40

  YangD.ZhangZ.WeiF.LiS.LiuM.LuY. (2024). Comprehensive review on research status and progress in precision grinding and machining of BK7 glasses. Micromachines15 (8), 1021. 10.3390/mi15081021

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 41

  YesudasuV.PradhanH. S. (2021). Performance enhancement of a novel surface plasmon resonance biosensor using thallium bromide. IEEE Trans. NanoBioscience21 (2), 206–215. 10.1109/TNB.2021.3114225

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 42

  YesudasuV.PradhanH. S.PandyaR. J. (2021). Recent progress in surface plasmon resonance based sensors: a comprehensive review. Heliyon7 (3), e06321. 10.1016/j.heliyon.2021.e06321

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article