Dielectric interlayer-enhanced surface plasmon resonance biosensor with 1D convolutional neural network surrogate modelling for cancer biomarker, glucose, and low refractive index analyte detection

Abstract

Introduction:

Surface plasmon resonance (SPR) biosensors based on the Kretschmann configuration offer label-free, real-time detection of molecular interactions and are applicable to cancer-associated bioreceptors, glucose, and low refractive index (RI) analytes. Existing dielectric-enhanced SPR designs and machine learning optimization studies are typically conducted as separate research topics, with few frameworks combining both approaches within a single multianalyte platform.

Methods:

A multilayer SPR biosensor incorporating dielectric and two-dimensional nanomaterial interlayers was designed using a BK-7 prism, a copper plasmonic film, silicon nitride (Si₃N₄), zinc oxide (ZnO), molybdenum disulfide (MoS₂), and a bismuth trioxide (Bi₂O₃) overlayer. The optical response was evaluated using the Transfer Matrix Method (TMM) and finite element modelling (FEM) in COMSOL Multiphysics. Individual layer thicknesses were optimized through systematic parametric analysis. A one-dimensional convolutional neural network (1D CNN) surrogate model was trained on FEM-generated parametric sweep data to predict sensor spectral responses across varying structural parameters. Model performance was assessed using the coefficient of determination, relative absolute error, relative squared error, and symmetric mean absolute percentage error.

Results and discussion:

The sensor was evaluated over three refractive index ranges: cancer-associated bioreceptors (1.360–1.401 RIU), glucose solutions (1.335–1.347 RIU), and low-RI chemical analytes (1.29–1.38 RIU). The optimized design achieved a peak angular sensitivity of 1,100°/RIU for both cancer-associated bioreceptor and glucose detection, a highest figure of merit of 157.143 RIU⁻¹ for glucose sensing, and a maximum angular sensitivity of 550°/RIU for low-RI analytes. The 1D CNN surrogate model achieved coefficients of determination greater than 0.994 for MoS₂ thicknesses up to approximately 1.35 nm and greater than 0.961 for ZnO thicknesses between 1.5 and 6.0 nm, with performance degradation at higher thicknesses attributed to output dynamic range compression. The proposed design combines numerical electromagnetic modelling with machine learning to accelerate sensor optimization for SPR-based biosensing applications.

Introduction

Recent advances in photonic biosensing have led to the development of integrated lab-on-chip (LoC) platforms that combine optical transducers with microfluidic sample handling for rapid, label-free molecular detection [1, 2]. Photonic biosensors, including surface plasmon resonance (SPR), localized SPR, silicon photonic waveguides, photonic crystal fibers, interferometric sensors, and optical resonators, have been applied to the detection of nucleic acids, proteins, extracellular vesicles, circulating tumor cells, and other disease-related biomarkers [3, 4]. These technologies support liquid biopsy by enabling the analysis of blood, serum, plasma, saliva, and other body fluids for early cancer detection, disease monitoring, and treatment assessment without requiring tissue biopsy [5, 6]. Their compatibility with miniaturized optical platforms and their ability to perform label-free, real-time measurements have expanded their use in precision diagnostics and personalized medicine [7].

Advances in microfabrication and microfluidics have enabled SPR-based lab-on-chip biosensors that integrate sample preparation, analyte transport, biomolecular recognition, and optical measurement within a single platform [8, 9]. Microfluidic flow cells improve sample delivery by handling microliter-scale volumes, increasing mass transport, reducing reagent consumption, and maintaining controlled laminar flow during measurement [10, 11]. Current LoC platforms also incorporate multiplexed sensing, in which different capture probes are immobilized on the same sensing surface to detect multiple biomarkers from a single clinical sample.

Liquid biopsy is used in oncology to detect and monitor tumor-derived biomarkers circulating in blood, serum, plasma, urine, saliva, and cerebrospinal fluid [12–14]. Biomarkers commonly analysed include circulating tumor cells (CTCs), circulating tumor DNA (ctDNA), cell-free RNA species such as microRNAs and long non-coding RNAs, extracellular vesicles, exosomes, and soluble cancer biomarkers including carcinoembryonic antigen (CEA), prostate-specific antigen (PSA), cancer antigen CA-125, and alpha-fetoprotein (AFP) [15–17]. The refractive indices of cancer-associated bioreceptors and their binding complexes typically lie between 1.360 and 1.401 RIU, corresponding to the cancer detection range investigated in this study. Binding events within this refractive index range produce measurable changes at the sensor surface that can be detected using angular interrogation SPR systems [18–20].

Surface plasmon resonance biosensors are suitable for liquid biopsy because they monitor molecular interactions in real time without fluorescent, enzymatic, or radioactive labels [21, 22]. The evanescent field extends approximately 200 nm from the sensor surface, making the measurement sensitive to surface-bound binding events while reducing contributions from unbound molecules in the surrounding solution [23]. SPR platforms based on the Kretschmann configuration can also be integrated with microfluidic sample delivery systems that operate with microliter-scale clinical specimens [24]. The sensor developed in this study is designed to operate over three refractive index ranges: cancer-associated bioreceptors (1.360–1.401 RIU), glucose solutions (1.335–1.347 RIU), and low-refractive-index analytes (1.29–1.38 RIU).

As the number of structural design variables increases, electromagnetic simulation becomes computationally expensive. Machine learning methods, including random forest (RF), gradient boosting machine (GBM), and extreme gradient boosting (XGBoost), have been applied to simulation-generated datasets to predict sensor performance and identify suitable structural configurations with fewer numerical simulations [25, 26]. SHapley Additive exPlanations (SHAP) provide quantitative estimates of the contribution of each design variable to the predicted sensor response, allowing interpretation of machine learning models and supporting parameter optimization [27, 28].

Published studies commonly investigate dielectric-enhanced SPR structures or machine learning optimization as separate research topics. Many dielectric-enhanced SPR designs target a single analyte or use a fixed multilayer configuration. Machine learning studies often optimize a limited number of structural parameters or focus on one sensing application. Fewer studies combine dielectric interlayer engineering, systematic electromagnetic optimization, and validation across multiple analyte classes within a single framework.

This study presents a dielectric interlayer-enhanced SPR biosensor for detecting cancer-associated bioreceptors, glucose, and low-refractive-index analytes. The proposed multilayer Kretschmann configuration incorporates dielectric interlayers to increase evanescent field confinement and strengthen interaction between the optical field and the analyte. The optical response is analysed using the Transfer Matrix Method and finite element modelling to evaluate resonance angle, angular sensitivity, detection accuracy, and figure of merit. The sensor is assessed over three application-specific refractive index ranges representing cancer-associated bioreceptors, glucose solutions, and low-refractive-index analytes. A machine learning framework is developed to predict sensor performance from simulation data, identify optimized structural parameters, and quantify the influence of individual design variables on sensor behaviour. This approach combines electromagnetic modelling and data-driven prediction within a single optimization framework for SPR biosensor design.

Design and modelling

The proposed sensing architecture consists of a BK-7 prism, a copper plasmonic film, silicon nitride (Si₃N₄), zinc oxide (ZnO), a molybdenum disulfide (MoS₂) nanosheet, and a bismuth trioxide (Bi₂O₃) functional overlayer. Each layer is selected to modify the optical response of the multilayer structure and improve coupling between the surface plasmon mode and the sensing medium.

Figure 1I shows a conventional surface plasmon resonance (SPR) sensor based on the Kretschmann configuration. A BK-7 prism serves as the optical coupling element through which p-polarized light is incident on the multilayer structure. The sensing stack contains a metallic plasmonic film and dielectric layers beneath the sensing medium. When the phase-matching condition is satisfied, incident photons excite surface plasmon waves at the prism-metal interface, producing a resonance dip in the reflected light spectrum. A photodetector records the reflected intensity, and changes in the resonance angle are used to determine refractive index variations caused by molecular binding at the sensor surface.

FIGURE 1

Figure 1II illustrates the proposed multilayer SPR configuration. The sensing stack includes dielectric and two-dimensional material layers that modify the electromagnetic field distribution near the sensing interface. These layers increase the interaction between the evanescent field and the analyte by improving plasmonic field confinement. The reflected optical signal is monitored by the detector and computer system, allowing continuous measurement of resonance-angle shifts produced by biomolecular interactions.

Figure 1III compares the electric-field intensity distributions of the conventional and proposed sensor structures. The conventional configuration exhibits field confinement near the metal-dielectric interface with electromagnetic energy distributed over a wider region. The proposed multilayer structure produces a stronger electric field concentrated close to the sensing surface, indicating more efficient excitation of surface plasmons. The increased field confinement increases the interaction between the optical field and the analyte, resulting in greater sensitivity to refractive index changes.

The ZnO layer acts as a dielectric matching layer between the copper film and the sensing medium. Its relatively high refractive index and wide bandgap improve optical impedance matching, reduce radiation losses, increase the overlap between the evanescent field and the analyte, and produce a narrower resonance dip.

The Si₃N₄ layer is positioned adjacent to the copper film to modify the effective dielectric environment of the surface plasmon mode. Because Si₃N₄ exhibits low optical absorption over the operating wavelength range, it enables adjustment of the resonance condition while introducing minimal additional loss. This layer provides an additional degree of freedom for tuning the resonance independently of the MoS₂ and Bi₂O₃ layers.

The MoS₂ nanosheet increases light-matter interaction because of its large optical absorption coefficient and high carrier confinement. Its two-dimensional structure modifies the local electromagnetic field at the sensing interface and increases the interaction between the surface plasmon mode and molecules adsorbed on the sensor surface.

The Bi₂O₃ overlayer functions as a high-refractive-index capping layer positioned directly beneath the sensing medium. This layer concentrates the evanescent field near the outer sensing interface where bioreceptors are immobilized, increasing the overlap between the optical field and surface-bound analytes. The resulting field distribution improves the sensor response to refractive index variations generated during biomolecular binding.

The dielectric interlayers in the proposed sensor perform different optical functions within the multilayer structure. The ZnO layer serves as an impedance-matching layer between the copper plasmonic film and the sensing medium. Its relatively high refractive index and wide bandgap improve coupling between the plasmonic mode and the sensing region, resulting in a narrower resonance dip and greater overlap between the evanescent field and the analyte.

The Si₃N₄ layer is located adjacent to the copper film and modifies the effective dielectric environment of the surface plasmon mode. Because Si₃N₄ has low optical absorption at the operating wavelength, it allows the resonance condition to be adjusted with minimal additional optical loss. This layer provides independent control of the resonance characteristics without relying on the optical properties of the MoS₂ or Bi₂O₃ layers.

MoS₂ was selected as the two-dimensional sensing material because its semiconducting, layer-dependent dielectric properties provide strong interaction with the optical field and offer sulfur-terminated surface sites suitable for bioreceptor immobilization. Metallic MXenes such as Ti₃C₂T_x exhibit higher free-carrier optical losses at comparable thicknesses, reducing plasmonic field confinement. Black phosphorus is susceptible to oxidation under ambient conditions, which limits long-term stability. Graphene has high carrier mobility but no bandgap. At thicknesses required to produce measurable plasmonic interaction, its broadband optical absorption increases damping, broadens the resonance linewidth, and lowers the figure of merit.

The Bi₂O₃ overlayer acts as a high-refractive-index capping layer positioned directly beneath the sensing medium. This layer concentrates the evanescent field near the sensor surface where bioreceptors are immobilized, increasing the interaction between the optical field and surface-bound analytes.

The results presented in Results and discussion (Figures 2, 3) show that sensor performance depends on both material selection and layer thickness. Reflectance response, resonance depth, and amplitude sensitivity vary substantially with the thickness of individual layers while the material composition remains unchanged. For the MoS₂/ZnO parameter sweep, the minimum reflectance varies from approximately 0.15%–1.08% over less than a threefold change in layer thickness. Variation of the copper thickness changes the minimum reflectance by more than 67 percentage points over the investigated range.

FIGURE 2

FIGURE 3

The peak angular sensitivity of 1,100°/RIU is obtained through joint optimization of material composition and structural geometry. The optimization procedure considers the thickness of each layer together with the material stack rather than treating these parameters independently. The proposed design is evaluated for three analyte categories, cancer-associated bioreceptors, glucose solutions, and low-refractive-index analytes, using the same optimized multilayer architecture. This unified optimization framework distinguishes the present design from previous multilayer SPR sensors that employ fixed layer thicknesses or optimize only a subset of structural parameters.

The fabrication process begins with preparation of the BK-7 prism substrate, as shown in Figure 4a. A copper plasmonic film is deposited onto the prism surface using a thin-film deposition method such as DC magnetron sputtering or thermal evaporation to form the plasmon-supporting interface (Figure 4b). A ZnO dielectric layer is subsequently deposited on the copper film to modify optical coupling and the electromagnetic field distribution (Figure 4c). A MoS₂ nanosheet is then transferred or grown on the dielectric layer to form the multilayer heterostructure (Figure 4d). A Bi₂O₃ capping layer is deposited over the MoS₂ layer to complete the sensing stack (Figure 4e).

FIGURE 4

The sensor surface is functionalized by immobilizing capture antibodies that selectively bind the target analyte (Figure 4f). The immobilization procedure is intended to maintain stable attachment of the bioreceptors while preserving their binding activity. The functionalized sensor is then exposed to a sample containing the target antigens (Figure 4g). Antigen-antibody binding produces local refractive index changes at the sensing interface, resulting in a shift in the surface plasmon resonance condition. The completed sensor is integrated into an SPR measurement system consisting of a light source, a BK-7 prism coupling arrangement, and a photodetector (Figure 4h). Changes in the reflected optical signal are used to determine the resonance-angle shift associated with analyte binding.

Although this study is based on numerical modelling, the proposed multilayer structure is designed using materials and thickness ranges compatible with established thin-film fabrication methods. The copper layer can be deposited by DC magnetron sputtering or thermal evaporation under high-vacuum conditions. These techniques routinely provide angstrom-level thickness control, and in situ quartz crystal microbalance monitoring can be used to reproduce the optimized copper thickness range of 22–53.5 nm identified in this study.

The ZnO and Bi₂O₃ dielectric layers are compatible with atomic layer deposition (ALD) and RF magnetron sputtering. Both methods provide high thickness uniformity for nanometer-scale films. ALD is particularly suitable for depositing layers thinner than 5 nm because of its precise control of film thickness and conformal surface coverage.

The MoS₂ sensing layer can be fabricated by transferring mechanically or liquid-phase exfoliated flakes onto the dielectric stack or by direct chemical vapor deposition (CVD). Mechanical and liquid-phase exfoliation are suitable for laboratory-scale device fabrication, whereas CVD provides better thickness uniformity and is more suitable for large-area sensor arrays, although it requires additional process optimization.

The optimized layer thicknesses identified in this study include several films below 3 nm. Fabricating continuous and uniform films at these dimensions remains challenging. Surface roughness, thickness variations, and interface defects can broaden the resonance linewidth and reduce the sharpness of the reflectance minimum compared with the ideal planar interfaces assumed in the numerical model. Experimental assessment of these fabrication effects is outside the scope of the present work and is identified as a limitation requiring future investigation.

The outer MoS₂ and Bi₂O₃ surfaces provide suitable interfaces for bioreceptor immobilization. Covalent antibody attachment can be achieved using established carbodiimide (EDC/NHS) coupling chemistry, while streptavidin-biotin conjugation provides an alternative approach for oriented antibody immobilization. Both methods are compatible with MoS₂-based sensing surfaces.

For measurements involving biological fluids such as serum or plasma, nonspecific adsorption can be reduced by applying surface-blocking layers after antibody immobilization. Bovine serum albumin (BSA) and polyethylene glycol (PEG)-based passivation layers are commonly used for this purpose. Reusable sensor operation would also require periodic surface regeneration using procedures such as mild acidic solutions or high-ionic-strength buffer washes to remove bound analytes while preserving receptor activity.

These fabrication and surface functionalization procedures are compatible with the proposed sensor architecture but have not been experimentally evaluated in the present study. Experimental fabrication and characterization are required to verify the numerical predictions reported here.

Pathway to lab-on-chip integration

The proposed multilayer surface plasmon resonance (SPR) biosensor uses a planar multilayer structure and an optical interrogation scheme that are compatible with established thin-film microfabrication and microfluidic technologies. This study is limited to electromagnetic modelling, structural optimization, and machine learning-based performance prediction. Experimental integration into a lab-on-chip (LoC) device has not been performed. The optimized sensor design provides a basis for future development of an integrated platform that combines sample handling, optical sensing, and automated analysis.

Microfluidic integration

A possible route toward LoC implementation is the integration of the optimized SPR sensing surface with a microfluidic delivery system. Microfluidic channels can transport microliter- or nanoliter-scale liquid samples while reducing reagent consumption and sample volume. In one implementation, a microfluidic chamber fabricated from polydimethylsiloxane (PDMS), glass, or cyclic olefin copolymer (COC) could be bonded to the BK-7 prism using oxygen plasma treatment or adhesive bonding. The microchannel would be positioned above the Cu/Si₃N₄/ZnO/MoS₂/Bi₂O₃ multilayer stack so that samples flow across the functionalized sensing surface.

Fluid flow in microscale channels is typically laminar because of the low Reynolds number. Under these conditions, analyte transport is more predictable, reducing flow-induced measurement variation. Flow rate can also be adjusted to modify the residence time of analytes near the sensing surface and influence mass transport during binding. The same microfluidic network could be designed to deliver buffer solutions, washing solutions, blocking agents, and regeneration solutions through automated flow control.

Additional sample-processing modules could be incorporated upstream of the sensing chamber. These may include plasma separation units, particle filters, passive micromixers, dilution chambers, concentration modules, or cell-sorting structures. Integration of these components could allow biological samples such as whole blood, serum, saliva, urine, sweat, or cerebrospinal fluid to undergo preliminary processing within the same device. Experimental evaluation of these functions has not been carried out in the present study.

Surface functionalization and biomolecular recognition

Implementation of the proposed sensor requires immobilization of recognition molecules on the Bi₂O₃/MoS₂ sensing surface. Established surface chemistries such as EDC/NHS coupling, silane functionalization, thiol chemistry, and streptavidin-biotin conjugation are compatible with antibody, aptamer, peptide, enzyme, or molecularly imprinted polymer immobilization, depending on the intended sensing application.

After receptor immobilization, passivation layers such as bovine serum albumin (BSA), polyethylene glycol (PEG), or zwitterionic polymers may be applied to reduce nonspecific adsorption during measurements involving biological fluids. Surface regeneration using low-pH glycine solutions, high-ionic-strength buffers, or mild detergents may permit repeated sensing cycles by removing bound analytes while maintaining receptor activity. These procedures require experimental verification for the proposed multilayer structure.

Multiplexed detection capability

The planar geometry of the proposed SPR sensor allows the sensing surface to be divided into independently functionalized regions. Each region can be modified with a different capture molecule to detect multiple analytes within the same sample.

Potential targets include carcinoembryonic antigen (CEA), prostate-specific antigen (PSA), alpha-fetoprotein (AFP), cancer antigen CA-125, glucose, inflammatory cytokines, cardiac biomarkers, and infectious disease biomarkers. Selection of target panels depends on the intended clinical application and requires experimental validation.

Multiplexed sensing can be implemented using spatially separated sensing regions on a single chip or through independently addressable microfluidic channels that direct samples to different functionalized areas. The present study does not evaluate either multiplexing strategy experimentally but demonstrates a sensor architecture that is compatible with both approaches.

Multiplexing strategies

Spatial multiplexing can be implemented by patterning multiple sensing regions on the SPR substrate. Each region is functionalized with a different capture molecule and interrogated using imaging SPR or multichannel photodetectors. This approach allows several biomarkers to be measured from the same sample.

Temporal multiplexing uses independently addressable microfluidic channels to deliver different samples or reagents to the sensing region in sequence. Sequential operation reduces carryover between measurements and enables repeated use of the sensing platform following surface regeneration.

These multiplexing approaches are compatible with applications requiring measurement of multiple biomarkers, including cancer diagnostics, metabolic disease assessment, and infectious disease testing. Their implementation requires experimental validation.

Portable point-of-care implementation

The proposed SPR architecture is compatible with components commonly used in portable optical sensing systems. Compact semiconductor laser diodes or high-power light-emitting diodes (LEDs) can provide monochromatic illumination. Angular interrogation may be performed using microelectromechanical systems (MEMS) mirrors or miniature motorized rotation stages. Reflected optical signals can be measured using complementary metal-oxide-semiconductor (CMOS) photodetectors or photodiode arrays.

Embedded microcontrollers or field-programmable gate arrays (FPGAs) can be used for resonance-angle estimation, signal processing, temperature compensation, and calibration. Battery-powered operation is feasible using low-power electronic components, although power consumption depends on the optical source, electronics, and measurement frequency.

Wireless communication modules such as Bluetooth Low Energy (BLE), Wi-Fi, or 5G could be incorporated to transfer measurement data to smartphones, hospital information systems, or cloud-based data platforms. Integration of these components has not been investigated in the present study.

Machine learning integration

The one-dimensional convolutional neural network (1D-CNN) developed in this work provides a computational model for predicting sensor performance from structural parameters. Within the optimized parameter ranges, the trained model estimates sensor responses without repeated electromagnetic simulations.

In a future LoC implementation, the trained model could be incorporated into embedded software for resonance prediction, baseline correction, signal filtering, drift compensation, anomaly detection, and calibration. These functions require validation using experimentally acquired data because the present model was trained on numerical simulation results.

Future studies may evaluate alternative machine learning models, including transformer-based architectures or physics-informed neural networks (PINNs), for analysing experimental measurements and compensating for fabrication variability.

Manufacturing considerations

The proposed multilayer structure is compatible with established thin-film fabrication methods. The copper layer can be deposited using DC magnetron sputtering or thermal evaporation. ZnO and Bi₂O₃ films are compatible with atomic layer deposition (ALD) and RF magnetron sputtering. MoS₂ may be incorporated through chemical vapor deposition (CVD), liquid-phase exfoliation, or transfer of few-layer films.

These fabrication methods are widely used in thin-film and microelectronic manufacturing and can be adapted for wafer-level processing. Disposable polymer microfluidic cartridges fabricated by injection molding or hot embossing could be integrated with the SPR chip for single-use operation. Fabrication reproducibility, process control, and device calibration require experimental verification before clinical implementation.

Clinical translation pathway

The present work establishes a computationally optimized sensor architecture. Fabrication, integration with microfluidics, portable instrumentation, and clinical validation remain future stages of development.

Mathematical modelling and electromagnetic analysis

The optical response of the proposed multilayer SPR sensor is rigorously modeled using the Transfer Matrix Method (TMM), which characterizes wave propagation across the stratified medium consisting of the BK-7 prism, plasmonic metal film, ZnO dielectric layer, two-dimensional nanomaterial sheet, Bi₂O₃ layer, and the sensing medium. For a structure composed of N layers, each layer j is described by a characteristic matrix relating the tangential electric and magnetic field components at its boundaries [29, 30].where , , and denote the complex refractive index, thickness, and propagation angle within layer , and is the free-space wavelength. Since the excitation is p-polarized, is adopted throughout the stack.

The overall optical response of the full multilayer assembly is obtained by sequentially multiplying the individual layer matrices, yielding the total characteristic matrix of the system [25, 26].

This composite matrix encapsulates the cumulative phase accumulation and field continuity conditions across every interface, from the prism-metal boundary through to the sensing medium.

The reflectance of the structure, which forms the principal observable in SPR interrogation, is derived directly from the elements of together with the optical admittances of the incident (prism) and exit (sensing) media [27, 28]where and correspond to the admittance terms of the prism and sensing medium, respectively. The reflectance as a function of incidence angle, wavelength, and analyte refractive index produces the resonance dip from which sensor performance is evaluated.

Excitation of the surface plasmon mode occurs when the in-plane wavevector of the incident light matches the propagation constant of the surface plasmon polariton (SPP) supported at the metal-dielectric interface. This phase-matching requirement is expressed through the SPP dispersion relation:where and are the complex permittivities of the metallic film and adjacent dielectric/nanomaterial layer, is the prism refractive index, and is the resonance angle at which the reflectance minimum occurs. The presence of the ZnO, two-dimensional nanomaterial, and Bi₂O₃ layers modifies the effective seen by the plasmon mode, directly shifting relative to the conventional configuration.

Finally, the sensing performance of the device is quantified through angular sensitivity, full width at half maximum (FWHM), and the resulting figure of merit (FOM), which together capture both the responsiveness and resolution of the resonance signal [31, 32].where is the resonance-angle shift induced by a refractive-index change in the sensing medium, and FWHM is extracted from the reflectance curve at half the resonance dip depth. Equations 1–5 collectively form the closed-form electromagnetic framework used to compute the reflectance spectra, predict resonance positions, and benchmark the sensitivity enhancement achieved by the proposed nanomaterial-augmented multilayer design relative to the conventional SPR configuration. Equations 1–5 collectively form the closed-form electromagnetic framework used to compute the reflectance spectra, predict resonance positions, and benchmark the sensitivity enhancement achieved by the proposed nanomaterial-augmented multilayer design relative to the conventional SPR configuration.

Results and discussion

The proposed sensor structure was numerically investigated using COMSOL Multiphysics v6.3, and an extensive parametric optimization study was carried out to identify the most suitable layer dimensions capable of producing strong plasmonic resonance and superior optical characteristics. The optimization process focused on evaluating the influence of individual layer thicknesses on both the maximum and minimum reflectance values, thereby providing insight into resonance quality, optical confinement, and coupling efficiency. All parametric studies reported below were conducted using the layer-thickness ranges, fixed companion-layer values, and analyte refractive-index windows specified for each sweep ranges held fixed within each respective sensing-performance evaluation. All reflectance spectra were computed at the design wavelength used throughout this study, consistent with the Transfer Matrix Method formulation presented in Equations 1–5, ensuring that every reported sensitivity, FOM, and resolution value in Tables 1–3 was generated under a common and explicitly stated set of simulation conditions. It is important to distinguish between the reflectance-magnitude modulation discussed in the parametric layer-thickness studies, which reflects the depth and sharpness of the resonance dip and is primarily diagnostic of plasmonic coupling efficiency, and the resonance-angle shift discussed in the cancer, glucose, and low-refractive-index sensing analyses, which constitutes the sensor’s actual measurable sensing signal and is the quantity from which angular sensitivity () is directly calculated, as defined in Equation 5. While a deeper, sharper resonance dip generally improves the precision with which the resonance angle can be located—and therefore indirectly supports higher achievable sensitivity and figure of merit—the magnitude of reflectance change at a fixed angle is not itself the sensing observable; it is the angular position of the resonance minimum, and its shift with analyte refractive index, that is tracked in a practical angular-interrogation SPR measurement.

The thickness of the MoS₂ layer is varied systematically from 0.30 nm to 2.75 nm in increments of 0.35 nm, generating eight discrete thickness points (0.30, 0.65, 1.00, 1.35, 1.70, 2.05, 2.40, and 2.75 nm) across which the reflectance response is evaluated for three fixed ZnO thicknesses of 1.5 nm, 3.0 nm, and 4.5 nm, corresponding to Figures 2a–c.

For the ZnO = 1.5 nm configuration, the maximum reflectance increases monotonically from 98.095% to 98.362% across the eight MoS₂ thicknesses (98.095%, 98.171%, 98.227%, 98.269%, 98.301%, 98.327%, 98.346%, 98.362%), yielding a mean maximum reflectance of (standard deviation) and a total dynamic range of percentage points, confirming that the resonance peak remains tightly confined within a narrow optical band even as MoS₂ thickness increases nearly ninefold. The corresponding minimum reflectance values (0.666%, 0.325%, 1.055%, 0.170%, 0.807%, 0.157%, 0.186%, 0.769%) display a markedly different, non-monotonic oscillatory pattern, with a mean of and a coefficient of variation , indicating that while the upper reflectance envelope evolves smoothly, the resonance-dip depth itself is highly sensitive to small thickness perturbations, consistent with interference-driven mode competition between adjacent dielectric layers.

For the ZnO = 3.0 nm case, the maximum reflectance values (98.087%, 98.164%, 98.221%, 98.264%, 98.296%, 98.321%, 98.341%, 98.358%) yield a mean of and a comparable dynamic range of 0.271 percentage points, while the minimum reflectance values (0.692%, 0.348%, 1.024%, 0.183%, 0.781%, 0.168%, 0.201%, 0.743%) average , again reflecting strong dip-depth variability () despite the closely matched upper-envelope statistics relative to the 1.5 nm case. For the ZnO = 4.5 nm configuration, maximum reflectance values (98.102%, 98.179%, 98.234%, 98.275%, 98.308%, 98.334%, 98.353%, 98.369%) produce a mean of with a dynamic range of 0.267 percentage points, and the minimum reflectance values (0.641%, 0.312%, 1.079%, 0.159%, 0.835%, 0.148%, 0.177%, 0.792%) average (). Taken together, the three ZnO configurations exhibit essentially invariant maximum-reflectance statistics (means clustering within a 0.012-percentage-point band of one another), while minimum-reflectance variability remains consistently high across all cases, confirming that MoS₂ thickness governs resonance sharpness through a mechanism largely decoupled from the ZnO-layer thickness itself.

The ZnO layer thickness is subsequently varied from 1.5 nm to 12.0 nm in 1.5 nm increments (1.5, 3.0, 4.5, 6.0, 7.5, 9.0, 10.5, 12.0 nm), with the analysis repeated for three fixed MoS₂ thicknesses of 0.30 nm, 0.65 nm, and 1.00 nm.

For MoS₂ = 0.30 nm, the maximum reflectance values (99.959%, 99.958%, 99.956%, 99.954%, 99.950%, 99.944%, 99.933%, 99.906%) decline gradually and monotonically, with a mean of and a total drop of only percentage points across the full thickness range, indicating exceptional stability of the upper reflectance envelope (). The minimum reflectance values (2.196%, 0.884%, 0.933%, 1.152%, 1.452%, 2.219%, 2.772%, 3.814%) follow a distinctly parabolic trend, decreasing from 2.196% to a localized optimum of 0.884% at ZnO = 3.0 nm before rising steadily to 3.814% at ZnO = 12.0 nm; this yields a mean of () and identifies an optimal ZnO thickness near 3.0 nm at which resonance-dip depth is maximized for this MoS₂ thickness. For MoS₂ = 0.65 nm, the maximum reflectance values (99.958%, 99.957%, 99.955%, 99.953%, 99.949%, 99.943%, 99.931%, 99.904%) give a mean of , while the minimum reflectance values (2.168%, 0.862%, 0.912%, 1.124%, 1.421%, 2.185%, 2.735%, 3.779%) follow the same U-shaped dependence with a mean of and an optimum again located at ZnO = 3.0 nm. For MoS₂ = 1.00 nm, the maximum reflectance values (99.960%, 99.959%, 99.957%, 99.955%, 99.952%, 99.946%, 99.935%, 99.908%) average , and the minimum reflectance values (2.224%, 0.903%, 0.951%, 1.176%, 1.486%, 2.251%, 2.806%, 3.852%) average , preserving the same parabolic minimum-reflectance profile. Across all three MoS₂ thicknesses, the consistent location of the resonance-depth optimum at ZnO ≈3.0 nm, together with peak reflectance levels uniformly exceeding 99.90%, identifies this thickness as a robust design point largely independent of MoS₂ variation within the tested range.

The Si₃N₄ thickness is varied from 0.60 nm to 2.35 nm in 0.25 nm increments (0.60, 0.85, 1.10, 1.35, 1.60, 1.85, 2.10, 2.35 nm), evaluated against three fixed Cu thicknesses of 22 nm, 24 nm, and 30 nm.

For Cu = 22 nm, the maximum reflectance values (99.959%, 99.960%, 99.959%, 99.959%, 99.960%, 99.959%, 99.960%, 99.959%) are essentially invariant, with a mean of and a total spread of just 0.001 percentage points, confirming negligible sensitivity of the upper reflectance envelope to Si₃N₄ thickness at this Cu thickness. The corresponding minimum reflectance values (1.083%, 1.783%, 0.814%, 1.541%, 1.481%, 0.821%, 1.443%, 1.864%), by contrast, exhibit a pronounced zig-zag oscillation with a mean of () and a range of 1.050 percentage points, reflecting an alternating high-low interference pattern consistent with higher-order fringe contributions superimposed on the primary resonance. For Cu = 24 nm, the maximum reflectance values (99.958%, 99.959%, 99.958%, 99.958%, 99.959%, 99.958%, 99.959%, 99.958%) average , while the minimum reflectance values (1.114%, 1.742%, 0.846%, 1.503%, 1.447%, 0.852%, 1.401%, 1.827%) average (), preserving the same oscillatory dip pattern shifted only marginally from the 22 nm case. For Cu = 30 nm, the maximum reflectance values (99.960%, 99.961%, 99.960%, 99.960%, 99.961%, 99.960%, 99.961%, 99.960%) average , and the minimum reflectance values (1.051%, 1.816%, 0.789%, 1.578%, 1.519%, 0.798%, 1.474%, 1.896%) average (). The defining trend across all three Cu thicknesses is therefore a near-perfectly stable maximum-reflectance plateau exceeding 99.95% combined with a consistently volatile minimum-reflectance response, indicating that Si₃N₄ thickness primarily modulates resonance-dip depth through fine interference effects rather than altering overall optical confinement.

The Cu layer thickness is varied across the widest range examined, from 22.0 nm to 53.5 nm in 4.5 nm increments (22.0, 26.5, 31.0, 35.5, 40.0, 44.5, 49.0, 53.5 nm), evaluated for three fixed Si₃N₄ thicknesses of 0.60 nm, 1.30 nm, and 1.80 nm.

For Si₃N₄ = 0.60 nm, the maximum reflectance rises steadily from 95.374% to 98.037% (95.374%, 95.955%, 96.534%, 97.029%, 97.415%, 97.699%, 97.899%, 98.037%), with a mean of and a total increase of percentage points. Examining the successive increments, , reveals a progressively diminishing step size—0.581, 0.579, 0.495, 0.386, 0.284, 0.200, and 0.138 percentage points—characteristic of a saturating, asymptotic approach toward an upper reflectance limit as Cu thickness increases. The minimum reflectance, in sharp contrast, collapses from 75.430% to 8.164% (75.430%, 68.235%, 59.625%, 49.699%, 38.825%, 27.749%, 17.115%, 8.164%), yielding a mean of and an exceptionally large coefficient of variation of , with a total decline of 67.266 percentage points across the studied range—consistent with the originally noted reduction exceeding 67 percentage points. The decrement sequence (−7.195, −8.610, −9.926, −10.874, −11.076, −10.634, −8.951 percentage points) shows the decline accelerating through the middle of the range before decelerating near 53.5 nm, indicative of a sigmoidal sharpening of the resonance dip as the metallic film thickness approaches its optimal plasmon-supporting regime.

For Si₃N₄ = 1.30 nm, the maximum reflectance values (95.421%, 96.003%, 96.581%, 97.076%, 97.461%, 97.746%, 97.945%, 98.083%) average with a comparable total rise of 2.662 percentage points, while the minimum reflectance values (74.986%, 67.812%, 59.241%, 49.348%, 38.521%, 27.492%, 16.903%, 7.982%) average (), declining by 67.004 percentage points overall. For Si₃N₄ = 1.80 nm, the maximum reflectance values (95.328%, 95.910%, 96.488%, 96.982%, 97.368%, 97.652%, 97.853%, 97.990%) average with a 2.662-percentage-point rise, and the minimum reflectance values (75.861%, 68.645%, 60.002%, 50.036%, 39.116%, 27.994%, 17.332%, 8.337%) average (), declining by 67.524 percentage points. Across all three Si₃N₄ thicknesses, the near-identical mean increases in maximum reflectance ( percentage points) and the consistently large, comparable declines in minimum reflectance ( percentage points, ) demonstrate that Cu thickness is the dominant parameter governing resonance sharpness in the proposed structure, with the dip depth approximately following an effective average sensitivity of Equation 6

Over the 22.0–53.5 nm range, confirming that increasing Cu thickness substantially deepens the resonance dip and sharpens the overall reflectance response, while leaving the upper reflectance envelope only modestly affected and largely insensitive to Si₃N₄ thickness.

Following optimization of the layer geometry, the sensor’s diagnostic performance was assessed across twelve refractive-index (RI) values spanning 1.360 to 1.376, 1.380, 1.381, 1.385, 1.387, 1.390, 1.392, 1.395, 1.399, and 1.401, representative of the RI contrast associated with cancer-related biological samples. Ten distinct material configurations, corresponding to the optimized thicknesses derived from the preceding parametric study, were evaluated under identical RI conditions, with results presented in Figures 5a–j.

FIGURE 5

For the first configuration, the maximum reflectance progressively decreases from 99.941% to 97.765% as RI increases (99.941%, 99.931%, 99.912%, 99.894%, 99.887%, 99.849%, 99.816%, 99.729%, 99.615%, 99.185%, 97.742%, 97.765%), yielding a mean of and a total decline of 2.199 percentage points. The corresponding minimum reflectance rises sharply from 0.752% to 69.811% (0.752%, 0.798%, 1.592%, 1.996%, 2.030%, 3.405%, 4.582%, 7.239%, 10.217%, 17.508%, 43.286%, 69.811%), giving a mean of and a total modulation depth of percentage points across the 0.041-unit RI span, corresponding to an average amplitude sensitivity of .

For the second configuration, the maximum reflectance values (99.939%, 99.929%, 99.910%, 99.892%, 99.885%, 99.847%, 99.814%, 99.726%, 99.612%, 99.181%, 97.698%, 97.721%) average , while the minimum reflectance values (0.781%, 0.824%, 1.621%, 2.028%, 2.064%, 3.442%, 4.623%, 7.286%, 10.261%, 17.556%, 43.338%, 69.859%) average , with a modulation depth of 69.078 percentage points and .

The third configuration shows maximum reflectance values of 99.944%, 99.934%, 99.915%, 99.897%, 99.890%, 99.852%, 99.819%, 99.733%, 99.619%, 99.189%, 97.785%, and 97.808%, averaging , alongside minimum reflectance values of 0.728%, 0.773%, 1.566%, 1.972%, 2.006%, 3.378%, 4.548%, 7.198%, 10.174%, 17.462%, 43.221%, and 69.745%, averaging with a 69.017-percentage-point modulation depth and .

For the fourth configuration, maximum reflectance values of 99.938%, 99.927%, 99.908%, 99.890%, 99.883%, 99.845%, 99.811%, 99.723%, 99.608%, 99.177%, 97.664%, and 97.688% average , while minimum reflectance values of 0.806%, 0.851%, 1.648%, 2.056%, 2.093%, 3.473%, 4.656%, 7.325%, 10.302%, 17.603%, 43.387%, and 69.904% average , the largest mean among the ten cases, with a modulation depth of 69.098 percentage points and .

The fifth configuration yields maximum reflectance values of 99.946%, 99.936%, 99.917%, 99.899%, 99.892%, 99.855%, 99.822%, 99.736%, 99.622%, 99.193%, 97.821%, and 97.844%, the highest mean among all configurations at , together with minimum reflectance values of 0.703%, 0.749%, 1.541%, 1.943%, 1.978%, 3.351%, 4.519%, 7.167%, 10.138%, 17.416%, 43.165%, and 69.689%, the lowest mean at , with a 68.986-percentage-point modulation depth and —indicating this configuration provides the sharpest baseline resonance and the highest overall reflectance contrast, albeit with marginally lower amplitude sensitivity than the other nine cases.

The sixth configuration produces maximum reflectance values of 99.940%, 99.930%, 99.911%, 99.893%, 99.886%, 99.848%, 99.815%, 99.727%, 99.613%, 99.183%, 97.716%, and 97.739% (mean ), and minimum reflectance values of 0.769%, 0.815%, 1.608%, 2.014%, 2.048%, 3.423%, 4.601%, 7.258%, 10.239%, 17.531%, 43.314%, and 69.832% (mean ), with a modulation depth of 69.063 percentage points and .

For the seventh configuration, maximum reflectance values of 99.943%, 99.933%, 99.914%, 99.896%, 99.889%, 99.851%, 99.818%, 99.731%, 99.617%, 99.187%, 97.759%, and 97.782% average , while minimum reflectance values of 0.739%, 0.785%, 1.578%, 1.982%, 2.017%, 3.391%, 4.561%, 7.219%, 10.194%, 17.481%, 43.249%, and 69.773% average , yielding a 69.034-percentage-point modulation depth and .

The eighth configuration exhibits maximum reflectance values of 99.937%, 99.926%, 99.907%, 99.889%, 99.882%, 99.844%, 99.810%, 99.721%, 99.606%, 99.175%, 97.648%, and 97.671%, the lowest mean among all ten cases at , paired with minimum reflectance values of 0.817%, 0.863%, 1.659%, 2.068%, 2.104%, 3.486%, 4.669%, 7.341%, 10.319%, 17.621%, 43.405%, and 69.918%, giving and the largest modulation depth of any configuration at 69.101 percentage points, corresponding to the highest amplitude sensitivity, —identifying this case as the most RI-responsive of the ten, at the cost of the lowest baseline reflectance contrast.

The ninth configuration shows maximum reflectance values of 99.945%, 99.935%, 99.916%, 99.898%, 99.891%, 99.854%, 99.821%, 99.735%, 99.621%, 99.191%, 97.804%, and 97.827% (mean ), with minimum reflectance values of 0.716%, 0.761%, 1.554%, 1.958%, 1.992%, 3.365%, 4.534%, 7.184%, 10.156%, 17.439%, 43.194%, and 69.716% (mean ), a 69.000-percentage-point modulation depth, and .

The 10th configuration produces maximum reflectance values of 99.942%, 99.932%, 99.913%, 99.895%, 99.888%, 99.850%, 99.817%, 99.730%, 99.616%, 99.186%, 97.751%, and 97.774% (mean ), and minimum reflectance values of 0.747%, 0.792%, 1.586%, 1.990%, 2.024%, 3.399%, 4.575%, 7.233%, 10.211%, 17.501%, 43.279%, and 69.804% (mean ), with a 69.057-percentage-point modulation depth and .

Averaged across all ten configurations, the maximum reflectance converges to and the minimum reflectance to , while the amplitude sensitivity, expressed generally as Equation 7

Clusters tightly between 1,682.6% and 1,685.4 %/RIU (mean , ), demonstrating that the resonance-based detection mechanism is highly reproducible across material variants. Configuration five offers the sharpest baseline resonance and highest peak reflectance contrast, making it best suited for resolving subtle RI shifts near the lower end of the tested range, whereas configuration eight delivers the greatest overall modulation depth and amplitude sensitivity, favoring discrimination at the upper end of the RI spectrum associated with malignant tissue signatures. Across all configurations and RI values, the maximum reflectance never falls below 97.6%, while the minimum reflectance spans nearly two orders of magnitude, from sub-1% values at RI = 1.360 to almost 70% at RI = 1.401, confirming the sensor’s strong evanescent-field interaction with the analyte and its capacity to resolve the fine RI differences characteristic of cancer-related biological samples.

The sensing capability of the optimized design as depicted in Figures 6a–c was further evaluated for low-index analytes using ten RI values spanning 1.29 to 1.38 in increments of 0.01 (1.29, 1.30, 1.31, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38), with three optimized material configurations tested to assess robustness across this regime.

FIGURE 6

For the first configuration, the maximum reflectance values (99.901%, 99.881%, 99.849%, 99.790%, 99.667%, 99.371%, 98.923%, 99.317%, 99.713%, 99.855%) average and exhibit a distinctly non-monotonic profile, declining steadily from RI = 1.29 to a local minimum of 98.923% at RI = 1.35 before recovering to 99.855% by RI = 1.38. Quantifying this behavior, the decline phase proceeds at an average rate of , while the subsequent recovery phase occurs nearly twice as fast, at , indicating an asymmetric resonance response around the inflection point near RI = 1.35. The minimum reflectance values (29.856%, 30.789%, 33.122%, 35.878%, 38.618%, 45.367%, 61.953%, 81.721%, 91.376%, 91.185%) rise sharply across the same range, averaging (), with a total modulation depth of percentage points over , corresponding to an average amplitude sensitivity of .

The second configuration closely reproduces this behavior: the maximum reflectance values (99.898%, 99.878%, 99.846%, 99.787%, 99.663%, 99.366%, 98.917%, 99.311%, 99.708%, 99.851%) average with the same characteristic dip-and-recovery shape centered at RI = 1.35, while the minimum reflectance values (30.114%, 31.042%, 33.388%, 36.136%, 38.891%, 45.628%, 62.197%, 81.964%, 91.591%, 91.402%) average , producing a modulation depth of 61.477 percentage points and —within 0.5%/RIU of the first case, confirming strong reproducibility under minor variations in material distribution.

The third configuration yields maximum reflectance values of 99.904%, 99.884%, 99.852%, 99.793%, 99.671%, 99.377%, 98.930%, 99.324%, 99.719%, and 99.860% (mean ), alongside minimum reflectance values of 29.593%, 30.528%, 32.861%, 35.613%, 38.351%, 45.103%, 61.712%, 81.486%, 91.159%, and 90.971% (mean ), with a 61.566-percentage-point modulation depth and , again closely matching the other two cases.

Averaged across all three configurations, the maximum reflectance converges to and the minimum reflectance to , while the amplitude sensitivity clusters tightly between 683.1% and 684.1%/RIU (mean , ), confirming excellent repeatability across material variants. Although the absolute sensitivity in this low-index regime (∼684%/RIU) is markedly lower than that observed in the cancer-detection range (∼1,684%/RIU), the sensor still maintains maximum reflectance above 98.9% throughout and achieves a minimum-reflectance swing exceeding 61 percentage points, demonstrating that the proposed multilayer architecture retains strong electromagnetic interaction with the analyte and remains a viable platform for low refractive index biological and chemical sample detection.

Glucose-sensing capability was evaluated using six refractive-index values corresponding to physiologically relevant glucose concentrations: 1.335, 1.336, 1.337, 1.338, 1.341, and 1.347, spanning a narrow total range of RIU. Three optimized material configurations were tested to confirm reproducibility over this fine RI window as demonstrated in Figures 7a–c.

FIGURE 7

For the first configuration, the maximum reflectance values (99.776%, 99.771%, 99.767%, 99.762%, 99.746%, 99.704%) decline gradually, averaging with a total drop of only 0.072 percentage points, underscoring the extreme stability of the upper reflectance envelope across this narrow RI window. The minimum reflectance values (0.244%, 0.297%, 0.344%, 0.370%, 0.534%, 0.946%) average (), with a total modulation depth of percentage points, corresponding to an average amplitude sensitivity of . Examining the interval-by-interval response reveals a non-uniform, accelerating sensitivity: the rate rises from between 1.335 and 1.336, to between 1.336 and 1.337, dips to between 1.337 and 1.338, then climbs sharply to between 1.338 and 1.341, and reaches between 1.341 and 1.347—indicating that the sensor’s local sensitivity increases markedly toward the upper end of the glucose-relevant RI range.

The second configuration shows closely matching behavior, with maximum reflectance values of 99.773%, 99.768%, 99.764%, 99.759%, 99.743%, and 99.701% (mean , range 0.072 percentage points) and minimum reflectance values of 0.259%, 0.312%, 0.358%, 0.386%, 0.551%, and 0.968% (mean ), yielding a modulation depth of 0.709 percentage points and , consistent with the first case to within 1%/RIU.

The third configuration produces maximum reflectance values of 99.779%, 99.774%, 99.770%, 99.765%, 99.749%, and 99.707% (mean , range 0.072 percentage points) and minimum reflectance values of 0.229%, 0.281%, 0.329%, 0.354%, 0.518%, and 0.924% (mean ), giving a modulation depth of 0.695 percentage points and .

Averaged across the three configurations, the maximum reflectance converges to and the minimum reflectance to , while the amplitude sensitivity remains tightly clustered between 57.9% and 59.1%/RIU (mean , ), confirming excellent reproducibility despite minor variations in material arrangement. The combination of a maximum reflectance consistently above 99.70% with a nearly fourfold rise in minimum reflectance over a refractive-index change of just 0.012 RIU demonstrates that the optimized sensor resolves the subtle RI shifts characteristic of clinically relevant glucose concentration changes, supporting its suitability for high-precision, non-invasive glucose monitoring.

Figure 8 presents the spatial distribution of the electric field magnitude together with the corresponding quantitative field-strength profiles of the proposed plasmonic sensor, evaluated at three incidence angles: two off-resonance conditions ( and ) and the resonant excitation angle (). The upper row comprises two-dimensional color-contour maps depicting the near-field intensity distribution across the periodic ring-resonator architecture, normalized to a common color scale spanning to V/m. At the off-resonance angles of and , the electromagnetic field is distributed weakly and relatively uniformly along the ring structures, with negligible concentration at the resonator gaps that constitute the sensing hotspots. By comparison, the resonant condition exhibits pronounced field confinement tightly localized at the sensing gap of each ring, indicating efficient excitation of the surface plasmon mode and a substantial enhancement of the near-field intensity within the device’s active detection region.

FIGURE 8

Figures 8a–c quantify the electric field norm as a function of arc length along the resonator periphery for each incidence angle, corroborating the trends observed in the contour maps. Figure 8a, corresponding to the off-resonance condition at , shows a modest, gradually varying field magnitude that reaches a maximum of approximately V/m before declining slightly, with no pronounced resonant features across the measured arc-length interval of 2.4–3.3 μm. Figure 8b, corresponding to the resonant condition at , reveals a marked increase in field magnitude near an arc length of 3.0 μm, exceeding V/m and forming pronounced oscillatory peaks along the resonator; this enhancement reflects efficient coupling of the phase-matched incident light to the plasmonic mode, resulting in strong electromagnetic energy concentration at the sensing sites.

Figure 8c, corresponding to the second off-resonance condition at , demonstrates substantially weaker field interaction, consistent with the corresponding contour map. The electric field norm remains close to zero across most of the 0.5–4.5 μm arc-length range, with only a minor, low-amplitude feature, not exceeding V/m, observed near 3.0 μm. Taken together, the results in Figure 9 establish that only the resonant incidence angle of produces substantial near-field amplification and confinement at the sensor’s functional hotspots, whereas the off-resonance angles fail to excite appreciable localized plasmonic fields. This behavior is consistent with the sensing mechanism of the proposed device, in which resonant field confinement enhances light-analyte interaction and, consequently, detection sensitivity relative to non-resonant excitation conditions.

FIGURE 9

Cancer detection performance analysis

Table 1 presents the sensing performance of the proposed cancer detection platform over a refractive index range of 1.36–1.401 RIU. The sensitivity increases from 137.500°/RIU at n = 1.368 and remains 137.500°/RIU at n = 1.376, before rising to 275.000°/RIU at n = 1.380 and reaching a maximum value of 1,100.000°/RIU at n = 1.381. Subsequently, the sensitivity fluctuates between 275.000°/RIU, 550.000°/RIU, and 366.667°/RIU, attaining values of 275.000°/RIU at n = 1.385, 550.000°/RIU at n = 1.387, 366.667°/RIU at n = 1.390, 550.000°/RIU at n = 1.392, 366.667°/RIU at n = 1.395, 275.000°/RIU at n = 1.399, and 550.000°/RIU at n = 1.401.

The DR decreases steadily from 56.349 at n = 1.36 to 55.644, 55.013, 54.446, 53.936, 53.476, 53.060, 52.684, 52.343, 52.034, 51.753, and 51.499 at n = 1.401. Likewise, the DA decreases monotonically from 0.556 to 0.526, 0.500, 0.476, 0.455, 0.435, 0.417, 0.400, 0.385, 0.370, 0.357, and 0.345. In contrast, the SR increases continuously from 1.452 to 1.548, 1.646, 1.744, 1.844, 1.945, 2.046, 2.149, 2.253, 2.358, and 2.464, indicating progressive enhancement in sensor resolution.

The SNR decreases gradually from 0.579 to 0.550, 0.524, 0.500, 0.478, 0.458, 0.440, 0.423, 0.407, 0.393, and 0.379. Parameter X increases from 0.280 to 0.284, 0.287, 0.291, 0.294, 0.297, 0.300, 0.303, 0.306, 0.309, and 0.311. The Q-factor decreases consistently from 42.000 at n = 1.36 to 40.368, 38.900, 37.571, 36.364, 35.261, 34.250, 33.320, 32.462, 31.667, 30.929, and 30.241, demonstrating the gradual broadening of the resonance response as the refractive index increases.

Glucose detection performance analysis

Table 2 summarizes the glucose sensing characteristics for refractive indices ranging from 1.335 to 1.347 RIU. The sensitivity values are 400.000°/RIU at n = 1.336, 100.000°/RIU at n = 1.337, 300.000°/RIU at n = 1.338, 400.000°/RIU at n = 1.341, and 1,100.000°/RIU at n = 1.347, corresponding to the maximum sensor response. The FWHM broadens progressively from 3.500° at n = 1.335°–4.200°, 4.900°, 5.600°, 6.300°, and 7.000° at n = 1.347. Similarly, the FOM values vary from 95.238 RIU⁻¹ to 20.408 RIU⁻¹, 53.571 RIU⁻¹, 63.492 RIU⁻¹, and 157.143 RIU⁻¹, with the highest value achieved at n = 1.347.

The Q-factor decreases steadily from 21.171 to 17.738, 15.286, 13.446, 12.016, and 10.871, while the DL values are 0.013, 0.086, 0.026, 0.021, and 0.007, respectively. The DR decreases from 39.608 to 36.352, 33.836, 31.820, 30.160, and 28.763, whereas the DA declines from 0.286 to 0.238, 0.204, 0.179, 0.159, and 0.143.

The SR values are 5.040, 8.643, 7.760, 8.367, and 7.412, while the SNR values are 0.095, 0.020, 0.054, 0.063, and 0.157. Parameter X assumes values of 0.160, 0.059, 0.139, 0.177, and 0.388. The optimum glucose sensing condition occurs at n = 1.347, where the sensitivity reaches 1,100.000°/RIU, the FOM reaches 157.143 RIU⁻¹, and the DL decreases to 0.007.

Low refractive index analyte detection performance analysis

Table 3 presents the performance characteristics of the proposed sensor for low-refractive-index analytes over the range 1.29–1.38 RIU. The sensitivity increases almost linearly from 350.000°/RIU at n = 1.30°–375.000°/RIU, 400.000°/RIU, 425.000°/RIU, 450.000°/RIU, 475.000°/RIU, 500.000°/RIU, 525.000°/RIU, and 550.000°/RIU at n = 1.38. Correspondingly, the FOM increases from 63.636 RIU⁻¹ to 65.789 RIU⁻¹, 67.797 RIU⁻¹, 69.672 RIU⁻¹, 71.429 RIU⁻¹, 73.077 RIU⁻¹, 74.627 RIU⁻¹, 76.087 RIU⁻¹, and 77.465 RIU⁻¹, indicating progressively improved sensing efficiency.

The Q-factor exhibits relatively minor variations, decreasing from 13.302 to 13.091, 12.912, 12.746, 12.623, 12.540, 12.523, 12.552, 12.464, and 12.056. The DL values are 0.034, 0.033, 0.034, 0.031, 0.028, 0.023, 0.018, 0.033, and 0.243, while the DR values are 0.608, 0.640, 0.670, 0.659, 0.729, 0.797, 0.941, 1.159, 0.723, and 0.150. Similarly, the DA decreases gradually from 0.189 to 0.182, 0.175, 0.169, 0.164, 0.159, 0.154, 0.149, 0.145, and 0.141.

The SNR values are 0.273, 0.281, 0.271, 0.295, 0.317, 0.369, 0.448, 0.275, and 0.056, whereas the SR values are 11.839, 12.236, 13.626, 13.028, 12.590, 11.002, 9.101, 17.546, and 133.589. Parameter X increases from 0.461 to 0.488, 0.493, 0.543, 0.592, 0.684, 0.815, before decreasing to 0.583 and 0.182. The highest sensitivity (550.000°/RIU) and FOM (77.465 RIU⁻¹) are achieved at n = 1.38, while the maximum DR (1.159) occurs at n = 1.36, demonstrating the sensor’s effectiveness for low-refractive-index analyte detection.

Figure 9 compares the key performance metrics of the proposed SPR biosensor for cancer detection, glucose detection, and low-RI analyte sensing. The cancer and glucose sensing cases achieve the highest peak sensitivity of 1,100°/RIU, whereas the low-RI sensing case exhibits a gradual sensitivity increase from 350° to 550°/RIU. The FOM follows trends similar to sensitivity, with the cancer detection case attaining the highest value of 1100 RIU⁻¹. The Q-factor and DR generally decrease with increasing refractive index for cancer and glucose detection, while the low-RI case maintains relatively stable Q values. The SR increases with refractive index in the cancer detection case and reaches exceptionally high values for low-RI sensing. The DL decreases near the optimal sensing regions, indicating enhanced detection capability, while variations in SNR and parameter X further demonstrate the sensor’s ability to distinguish refractive-index changes under different sensing conditions. Overall, the results confirm the versatility of the proposed sensor for high-sensitivity detection of cancer biomarkers, glucose concentrations, and low-index analytes.

Performance evaluation of the 1D CNN model for behaviour prediction

In this study, a one-dimensional convolutional neural network (1D CNN) is employed as a surrogate model to predict the spectral behaviour of the proposed biosensor across varying structural parameters. CNNs belong to the class of deep learning architectures specifically designed to exploit local spatial or sequential correlations within input data through the application of learnable convolutional filters. Unlike fully connected feedforward networks, which treat all input features as independent, 1D CNNs apply a series of convolutional kernels that slide across the input feature vector, enabling the model to detect and encode local patterns, gradients, and dependencies—properties that are particularly well-suited to the quasi-continuous parametric sweep data generated from electromagnetic simulations.

The 1D CNN architecture adopted in this work consists of a structured sequence of functional layers. The input layer receives one-dimensional feature vectors derived from the COMSOL Multiphysics finite element simulation outputs, encoding the sensor’s spectral response (e.g., reflectance or transmission spectra) as a function of the structural layer thickness under investigation. This is followed by one or more convolutional layers, each comprising a bank of learnable filters of a specified kernel size that perform element-wise inner product operations over local windows of the input, producing feature maps that encode hierarchical representations of the input signal. A rectified linear unit (ReLU) activation function is applied after each convolutional operation to introduce nonlinearity into the model, enabling it to approximate complex, nonlinear input-output mappings characteristic of layered plasmonic and photonic sensor responses.

Batch normalisation layers are incorporated after activation to stabilise training dynamics by normalising the distribution of intermediate activations, thereby mitigating internal covariate shift and accelerating convergence. Max-pooling or average-pooling layers reduce the spatial dimensionality of the feature maps, retaining the most salient features while suppressing noise and reducing computational load. Following the convolutional feature extraction stages, the resulting feature maps are flattened and passed through one or more fully connected (dense) layers, which aggregate the extracted features and map them to the output prediction space. Dropout regularisation is applied within the dense layers to reduce overfitting by stochastically deactivating a fraction of neurons during training, thereby promoting generalisation to unseen parametric configurations. The final output layer produces a scalar prediction corresponding to the sensor’s resonance behaviour (e.g., resonance wavelength shift, sensitivity, or spectral peak position) for a given structural parameter value.

The model is trained using the Adam optimiser with a mean squared error (MSE) loss function, and performance is evaluated on a held-out test set using a comprehensive battery of statistical metrics: MSE, root mean squared error (RMSE), mean absolute error (MAE), coefficient of determination (R²), adjusted R², explained variance score (EVS), Pearson correlation coefficient (R), normalised RMSE (NRMSE), and mean absolute percentage error (MAPE). For the Si₃N₄ case, additional metrics including symmetric MAPE (SMAPE), relative absolute error (RAE), and relative squared error (RSE) are introduced to provide a more diagnostically complete picture of model behaviour in regimes where output dynamic range compression can render percentage-based metrics artificially favourable. Together, these metrics assess not only the magnitude of prediction errors but also the model’s capacity to capture the structural and functional form of the sensor’s parametric response—a critical distinction in regions where the output variance narrows while underlying nonlinearities intensify.

Performance under MoS₂ thickness variation

The first parametric study investigates the predictive performance of the 1D CNN as MoS₂ layer thickness is systematically varied from 0.30 nm to 2.40 nm in increments of 0.35 nm. The quantitative results are consolidated in Table 4, with visual corroboration provided through scatter plots in Figure 10 and heat map plots in Figure 11. These two visualisation modalities serve complementary diagnostic purposes: scatter plots directly compare predicted versus ground truth output values along the ideal diagonal, while heat maps reveal the spatial distribution of prediction error density across the parametric space.

FIGURE 10

FIGURE 11

At the lowest MoS₂ thickness of 0.30 nm, the 1D CNN delivers strong predictive performance. The MSE is recorded at 1.60 × 10⁻⁴ and the RMSE at 0.012662, reflecting low absolute prediction error across the test set. The MAE of 4.904 × 10⁻³ confirms that the average pointwise deviation between predicted and actual values is well below one percent of the output range. The R² value of 0.996130 and adjusted R² of 0.996101 together indicate that the model explains 99.61% of the total variance in the sensor output, with the adjusted R² accounting for the number of predictors and confirming that the model’s explanatory power is not inflated by parameter count. The EVS of 0.996145 is closely aligned with R², confirming the absence of systematic prediction bias. The Pearson correlation coefficient of 0.998063 reflects an exceptionally strong linear concordance between predicted and actual values. The NRMSE of 1.27% and MAPE of 0.49% further confirm near-ideal prediction accuracy, establishing that the model is well-calibrated to the sensor response at this baseline MoS₂ loading.

At 0.65 nm thickness, marginal improvements in error metrics are observed. The MSE decreases slightly to 1.47 × 10⁻⁴ and RMSE to 0.012105, while MAE reduces to 4.444 × 10⁻³. The R² improves to 0.996415 and adjusted R² to 0.996387, with EVS at 0.996429 — the highest R² recorded across the entire MoS₂ sweep—suggesting that the 1D CNN adapts most effectively to the spectral response at this intermediate thickness. The Pearson correlation of 0.998206 and MAPE of 0.44% with NRMSE of 1.21% collectively confirm the model’s peak predictive fidelity within this parametric case.

At 1.00 nm, the model maintains high reliability. MSE is 1.54 × 10⁻⁴, RMSE is 0.012421, and MAE is 4.871 × 10⁻³. The R² of 0.995120 and adjusted R² of 0.995083, supported by EVS = 0.995138 and R = 0.997557, confirm that over 99.5% of variance is explained with no meaningful divergence between observed and adjusted fit quality. The NRMSE of 1.24% and MAPE of 0.49% remain within acceptable bounds for surrogate modelling of photonic devices.

Continuing to 1.35 nm, performance remains strong with MSE = 1.43 × 10⁻⁴, RMSE = 0.011969, and MAE = 4.158 × 10⁻³ — the lowest MAE recorded within this parametric sweep. R² = 0.994389, adjusted R² = 0.994347, and EVS = 0.994401, with R = 0.997191, NRMSE = 1.20%, and MAPE = 0.42%. While a mild downward trend in R² relative to the 0.65 nm peak is apparent, the model retains high accuracy and its predictions continue to exhibit strong correlation with finite element simulation outputs.

At 1.70 nm, a more noticeable decline in R² becomes apparent. The R² drops to 0.988659 and adjusted R² to 0.988573, with EVS = 0.988681 and R = 0.994313. Despite this structural degradation in variance explanation, absolute errors remain controlled: MSE = 1.31 × 10⁻⁴, RMSE = 0.011455, MAE = 2.903 × 10⁻³, NRMSE = 1.15%, and MAPE = 0.29%. The substantial decrease in MAE at this thickness—from 4.158 × 10⁻³ at 1.35 nm to 2.903 × 10⁻³ at 1.70 nm—indicates that the output dynamic range is narrowing, meaning the distribution of sensor responses over the test set is more tightly clustered, which naturally suppresses absolute error while the model’s ability to track relative variance weakens.

This dynamic range compression effect becomes more pronounced at 2.05 nm, where R² falls to 0.948060 and adjusted R² to 0.947667, with EVS = 0.948121 and R = 0.973684. The MSE is 1.29 × 10⁻⁴, RMSE is 0.011369, and MAE has further decreased to 2.071 × 10⁻³, with NRMSE = 1.14% and MAPE = 0.21%. The R² value here indicates that approximately 5.2% of the output variance is no longer captured by the model, a meaningful decline relative to the sub-1% unexplained variance observed at lower thicknesses. This signals that the 1D CNN is beginning to lose its capacity to generalise to the spectral complexity introduced by thicker MoS₂ layers.

The most critical degradation occurs at the maximum MoS₂ thickness of 2.40 nm, where R² collapses to 0.744747 and adjusted R² to 0.742813, with EVS = 0.745025 and R = 0.863104. These values indicate that the model explains only 74.5% of the total output variance, representing a dramatic deterioration relative to the 99.6% achieved at 0.65 nm. Despite this, the absolute error metrics remain deceptively low: MSE = 1.30 × 10⁻⁴, RMSE = 0.011408, MAE = 1.709 × 10⁻³, NRMSE = 1.14%, and MAPE = 0.17%. The continued decline in absolute errors alongside falling R² is a direct consequence of the narrowing output distribution at extreme MoS₂ thicknesses, where the sensor response becomes increasingly insensitive to further parametric change, compressing the test set outputs toward a near-constant value and artificially suppressing magnitude-based error metrics. The reduced Pearson R of 0.8631 confirms that the predicted values are significantly less correlated with the simulation ground truth, and the scatter plots in Figure 10 at this thickness would be expected to show visible dispersion and clustering artefacts around the diagonal. Overall, the 1D CNN delivers highly reliable predictions for MoS₂ thicknesses up to approximately 1.35 nm, beyond which model performance progressively and measurably degrades as the spectral response transitions into a regime of increased electromagnetic confinement and reduced parametric sensitivity.

Performance under ZnO thickness variation

The second parametric study evaluates 1D CNN performance under ZnO layer thickness variation from 1.5 nm to 10.5 nm in increments of 1.5 nm. Scatter plots are presented in Figure 12, heat map representations in Figure 13, and quantitative performance metrics are consolidated in Table 5. This case spans a broader absolute thickness range than the MoS₂ sweep and reveals a more dramatic and physically interpretable degradation trajectory.

FIGURE 12

FIGURE 13

At 1.5 nm ZnO thickness, the model achieves excellent predictive performance: MSE = 1.51 × 10⁻⁴, RMSE = 0.012296, MAE = 4.808 × 10⁻³, R² = 0.995216, adjusted R² = 0.995180, EVS = 0.995233, R = 0.997605, NRMSE = 1.23%, and MAPE = 0.48%. These values mirror the high accuracy observed in the MoS₂ case at thin film regimes, confirming that the 1D CNN is well-configured to learn the sensor’s spectral response across both material systems when layer thicknesses are small and the electromagnetic response is smoothly varying.

At 3.0 nm, performance remains high with MSE = 1.43 × 10⁻⁴, RMSE = 0.011952, MAE = 4.199 × 10⁻³, R² = 0.994225, adjusted R² = 0.994181, EVS = 0.994241, R = 0.997108, NRMSE = 1.20%, and MAPE = 0.42%. The model continues to explain over 99.4% of variance with no evidence of systematic bias, as confirmed by the close agreement between R² and EVS.

At 4.5 nm, a gentle decline begins: MSE = 1.32 × 10⁻⁴, RMSE = 0.011491, MAE = 3.031 × 10⁻³, R² = 0.989399, adjusted R² = 0.989318, EVS = 0.989421, R = 0.994685, NRMSE = 1.15%, and MAPE = 0.30%. The model retains strong performance, explaining 98.9% of output variance, though the MAE has decreased notably from 4.199 × 10⁻³ at 3.0 nm to 3.031 × 10⁻³ at 4.5 nm, again reflecting the progressive compression of output dynamic range as ZnO thickness increases.

At 6.0 nm, performance degrades more noticeably: MSE = 1.29 × 10⁻⁴, RMSE = 0.011377, MAE = 2.217 × 10⁻³, R² = 0.961524, adjusted R² = 0.961232, EVS = 0.961587, R = 0.980573, NRMSE = 1.14%, and MAPE = 0.22%. While the correlation coefficient of 0.9806 remains strong and MAPE is low, the R² of 0.9615 reveals that approximately 3.9% of the output variance is no longer captured—a meaningful structural loss for high-fidelity surrogate modelling.

The degradation accelerates at 7.5 nm, where R² drops sharply to 0.840279 and adjusted R² to 0.839067, with EVS = 0.840418, R = 0.916668, MSE = 1.30 × 10⁻⁴, RMSE = 0.011403, MAE = 1.809 × 10⁻³, NRMSE = 1.14%, and MAPE = 0.18%. At this thickness, the 1D CNN explains only 84.0% of the output variance, indicating that the model can no longer reliably capture the full complexity of the ZnO-mediated spectral response. The decline in the Pearson correlation from 0.9806 at 6.0 nm to 0.9167 at 7.5 nm confirms that predictions are becoming progressively decoupled from the simulation ground truth.

At 9.0 nm, the model’s predictive power deteriorates severely: R² = 0.451870, adjusted R² = 0.447711, EVS = 0.452134, R = 0.672213, MSE = 1.31 × 10⁻⁴, RMSE = 0.011428, MAE = 1.621 × 10⁻³, NRMSE = 1.14%, and MAPE = 0.16%. With less than 45.2% of variance explained and a Pearson correlation of only 0.6722, the model is operating far outside its reliable prediction domain. The scatter plots in Figure 12 at this thickness would be expected to display substantial scatter and departure from the ideal diagonal, consistent with the weak EVS of 0.4521.

The most extreme outcome is observed at 10.5 nm, where R² becomes negative at −0.378175 and adjusted R² at −0.388629, with EVS = −0.377902. A negative R² value is a statistically critical indicator, signifying that the 1D CNN performs worse than a trivial mean-baseline predictor—that is, predicting the unconditional mean of the output distribution would yield lower squared error than the CNN’s actual predictions. The annotated Pearson correlation of 0.614960 (marked with an asterisk in Table 5, denoting diminished statistical reliability) confirms that prediction and ground truth are only weakly and unreliably correlated. Paradoxically, absolute error metrics remain low: MSE = 1.31 × 10⁻⁴, RMSE = 0.011442, MAE = 1.523 × 10⁻³, NRMSE = 1.14%, and MAPE = 0.15%. This decoupling between absolute error magnitude and R² is fully explained by the near-complete collapse of the output dynamic range at this extreme ZnO thickness, where the sensor’s spectral response converges toward an approximately constant value across all test samples, rendering percentage- and magnitude-based error metrics numerically trivial and structurally meaningless. These results collectively establish that the 1D CNN is well-suited for ZnO thicknesses up to approximately 4.5–6.0 nm, with 6.0 nm representing a practical upper bound for reliable deployment, beyond which a deeper architecture, an expanded and more diverse training dataset, or physics-informed regularisation would be necessary to restore predictive fidelity.

Performance under Si₃N₄ thickness variation

The third and final parametric case evaluates the 1D CNN’s behaviour prediction capability under systematic variation of the Si₃N₄ layer thickness from 0.60 nm to 2.35 nm in increments of 0.25 nm. Scatter plots and heat map representations are provided in Figures 14, 15 respectively, and the full set of performance metrics is tabulated in Table 6. This case employs an expanded metric suite relative to Tables 4, 5, incorporating SMAPE, RAE, and RSE alongside the standard metrics, thereby providing a more complete and diagnostically robust characterisation of model performance—particularly in regimes where the output range compression artefact renders MAPE and RMSE misleadingly optimistic.

FIGURE 14

FIGURE 15

At the baseline Si₃N₄ thickness of 0.60 nm, the 1D CNN achieves solid predictive performance: MSE = 1.32 × 10⁻⁴, RMSE = 0.011479, MAE = 2.977 × 10⁻³, R² = 0.987897, EVS = 0.987921, MAPE = 0.30%, SMAPE = 0.29%, RAE = 1.21%, and RSE = 0.0121. The R² of 0.9879 indicates that the model explains 98.8% of the output variance at this thickness, and the RAE of 1.21% and RSE of 0.0121 confirm that the prediction error is minimal in both absolute and relative structural terms. The close agreement between MAPE and SMAPE (0.30% vs. 0.29%) indicates no asymmetric prediction bias across the output range.

At 0.85 nm, model performance undergoes a noticeable degradation step. R² decreases to 0.961567, EVS to 0.961631, while MSE remains nearly constant at 1.30 × 10⁻⁴ and RMSE at 0.011388. However, the more diagnostic metrics reveal the true extent of the degradation: RAE increases from 1.21% to 3.84% and RSE from 0.0121 to 0.0384 — a more than threefold increase in both relative error measures. MAPE decreases slightly to 0.23% and SMAPE to 0.22%, but this is attributable to the shrinking output range rather than improved model accuracy. The R² value of 0.9616 indicates that approximately 3.8% of variance is no longer explained by the model, marking the onset of meaningful generalisation loss.

By 1.10 nm, the degradation becomes substantially more pronounced. R² falls to 0.865999, EVS to 0.866152, RAE climbs to 13.40%, and RSE to 0.1340. This represents an order-of-magnitude increase in the relative absolute error compared to the 0.60 nm baseline, confirming that the 1D CNN is losing its ability to track the functional form of the Si₃N₄-modulated sensor response. The absolute metrics remain artificially low—MSE = 1.30 × 10⁻⁴, RMSE = 0.011404, MAE = 1.870 × 10⁻³, MAPE = 0.19%, SMAPE = 0.18% — masking the true scale of predictive failure. The scatter plots in Figure 14 at this thickness would be expected to reveal visible lateral dispersion around the ideal diagonal, consistent with an EVS of 0.8662 reflecting only partial variance capture.

At 1.35 nm, the model’s explanatory power falls below the threshold of practical utility: R² = 0.596169, EVS = 0.596442, RAE = 40.38%, RSE = 0.4038. With barely 59.6% of variance explained and a relative absolute error exceeding 40%, the 1D CNN can no longer provide reliable predictions of the sensor’s Si₃N₄-dependent spectral behaviour at this thickness. The MSE and RMSE remain nearly stationary at 1.31 × 10⁻⁴ and 0.011426 respectively, and MAPE has declined to 0.17%, while SMAPE is 0.16% — values that would be misleadingly interpreted as indicators of good performance in the absence of the R²- and RAE-based diagnostics.

A near-complete collapse of predictive utility is observed at 1.60 nm: R² = 0.035094, EVS = 0.035412, RAE = 96.49%, RSE = 0.9649. An R² of only 0.035 means that the model explains a mere 3.5% of the total output variance, rendering it statistically equivalent to a mean-value predictor. The RAE of 96.49% indicates that the model’s cumulative absolute error is 96.5% as large as that of a naïve baseline predictor that always predicts the mean—confirming that virtually all predictive information has been lost. The MSE is 1.31 × 10⁻⁴, RMSE is 0.011439, MAE is 1.562 × 10⁻³, MAPE is 0.16%, and SMAPE is 0.15%. The continuing decline of MAE and MAPE alongside catastrophically deteriorating R² and RAE starkly illustrates the deceptive nature of absolute error metrics in this compressed output range regime.

Beyond 1.60 nm, R² turns negative and deteriorates progressively and severely. At 1.85 nm: R² = −0.737380, EVS = −0.736982, RAE = 173.74%, RSE = 1.7374, MSE = 1.31 × 10⁻⁴, RMSE = 0.011448, MAE = 1.495 × 10⁻³, MAPE = 0.15%, SMAPE = 0.15%. At 2.10 nm: R² = −1.393692, EVS = −1.392915, RAE = 239.37%, RSE = 2.3937, MSE = 1.31 × 10⁻⁴, RMSE = 0.011453, MAE = 1.454 × 10⁻³, MAPE = 0.15%, SMAPE = 0.14%. At the maximum thickness of 2.35 nm: R² = −1.748771, EVS = −1.747883, RAE = 274.88%, RSE = 2.7488, MSE = 1.31 × 10⁻⁴, RMSE = 0.011456, MAE = 1.428 × 10⁻³, MAPE = 0.14%, SMAPE = 0.14%.

These increasingly negative R² values—reaching −1.749 at 2.35 nm—combined with RSE values exceeding 2.74 and RAE approaching 275%, confirm unambiguously that the 1D CNN is producing predictions that diverge systematically and catastrophically from simulation ground truth in this high-thickness regime, performing more than 2.7 times worse than a simple mean-baseline predictor in terms of squared relative error. The stabilisation of MAPE and SMAPE in the range of 0.14%–0.15% across the 1.85–2.35 nm band is a direct artefact of the near-constant output distribution in this regime, where the Si₃N₄ layer has reached a thickness at which its contribution to the sensor’s spectral response saturates, causing the ground truth outputs to cluster near a fixed value and making percentage-based error norms trivially small regardless of prediction quality. In this context, the RAE and RSE serve as the only reliable diagnostic metrics, providing unambiguous evidence of total predictive failure.

The Si₃N₄ parametric study establishes that the 1D CNN delivers acceptable behaviour prediction only up to approximately 0.85 nm, with a moderate but increasingly unreliable performance window extending to 1.10 nm, and comprehensive failure of predictive generalisation beyond 1.35 nm. These findings underscore a critical boundary condition for the deployment of this surrogate model and highlight the necessity of either constraining the operationally relevant Si₃N₄ thickness range to the sub-nanometre domain, augmenting the training dataset with denser sampling in the high-thickness regime, or adopting a more expressive deep learning architecture—such as a residual CNN, a bidirectional LSTM, or a physics-informed neural network—to recover predictive fidelity across the full parametric space.

The training dataset for the 1D CNN surrogate model was generated directly from the COMSOL Multiphysics finite element simulations described in Results and discussion, comprising the full set of reflectance spectra obtained across the systematically swept layer thicknesses (Cu, ZnO, MoS₂, Si₃N₄) and the analyte refractive-index ranges corresponding to the cancer, glucose, and low-refractive-index sensing regimes. For each fixed structural configuration, the corresponding reflectance-versus-angle curve was treated as a one-dimensional input vector, with the simulated reflectance values serving as the ground-truth regression targets. The dataset was partitioned into training and held-out test subsets, with the test partition withheld entirely from the optimization process and used exclusively for the performance evaluation reported in Tables 4–6. The 1D CNN was selected over fully connected (dense) regressors and classical ensemble methods such as random forest or gradient boosting because its convolutional kernels exploit the local, sequential structure of the angle-resolved reflectance curves—adjacent angular samples in an SPR reflectance spectrum are physically correlated through the resonance lineshape, a structural prior that 1D convolution captures directly through its sliding-window operation, whereas feature-independent regressors must learn these correlations purely from data, typically requiring substantially larger training sets to achieve comparable accuracy. To mitigate overfitting, the network incorporates dropout regularization within its fully connected layers, stochastically deactivating a fraction of neurons during each training iteration to prevent the model from memorizing training-set-specific noise, together with batch normalization after each convolutional activation to stabilize the training dynamics and reduce sensitivity to weight initialization. Training was performed using the Adam optimization algorithm with a mean-squared-error loss function, selected for its adaptive per-parameter learning-rate behavior and its established robustness for regression tasks involving smoothly varying physical response curves. Rather than reporting a single aggregate accuracy figure, model performance was evaluated independently at each discrete structural thickness value within the parametric sweep, using a battery of nine complementary statistical metrics (MSE, RMSE, MAE, R², adjusted R², explained variance score, Pearson correlation coefficient, normalized RMSE, and MAPE), supplemented for the Si₃N₄ case by symmetric MAPE, relative absolute error, and relative squared error. This multi-metric, per-configuration evaluation strategy was adopted specifically to guard against the overfitting risk inherent in any single-pass accuracy metric: as demonstrated in Tables 4–6, R² and Pearson correlation can degrade sharply—in some cases becoming negative, indicating performance worse than a trivial mean-baseline predictor—even while absolute error metrics such as MAE and NRMSE remain numerically small, a decoupling that occurs when the underlying output dynamic range compresses at extreme layer thicknesses. By explicitly reporting this degradation rather than masking it behind a single favorable metric, we establish well-defined parametric validity boundaries (e.g., MoS₂ thickness up to ≈1.35 nm and ZnO thickness up to ≈6.0 nm for reliable R² > 0.96 performance) within which the surrogate model can be deployed with confidence, and beyond which full electromagnetic simulation or an expanded, more densely sampled training set would be required.

Contemporary advancements in machine learning (ML) and deep learning intelligence have driven innovative interdisciplinary research integrating electric vehicle (EV) battery systems and solid-state optoelectronic engineering, enabling intelligent, data-driven optimization of energy and photonic devices. A wealth of prevailing EV battery challenges, including accurate fault prognosis, reliable state-of-health evaluation, precise overdischarge detection, scientific retirement-state forecasting, and comprehensive failure diagnostics, have been effectively addressed via customized deep learning architectures and data-centric intelligent analytical frameworks [33–37]. Complementarily, ML/DL-driven predictive paradigms have revolutionized EV energy management research, supporting systematic modeling of energy consumption mechanisms, real-world residual driving range estimation, feature-based consumption characteristic analysis, and intelligent optimization of charging timing and operational energy behaviours for electric buses, all validated using large-scale field mobility datasets [38–42].

To further enhance the predictive accuracy, generalization capability, and operational robustness of battery and energy intelligent systems, recent studies have adopted cutting-edge machine learning and artificial intelligence technologies, including diffusion-based signal reconstruction algorithms, multi-label adaptive feature optimization strategies, cross-modal spatio-temporal fusion models, frequency-domain intelligent dehazing architectures, and low-latency edge computing offloading frameworks [43–47]. Beyond energy intelligence, ML-enabled optimization methodologies have also facilitated breakthrough progress in III-nitride optoelectronic devices. Advanced algorithm-assisted structural and parameter optimization approaches have significantly improved the light extraction efficiency of InGaN- and GaN-based light-emitting diodes, realizing performance enhancement through intelligent electrode parameter tuning, optimized nanoscale surface patterning, cooperative scattering structure design, and epitaxial buffer-layer configuration optimization [48–52].

For high-performance AlGaN-based deep-ultraviolet (DUV) optoelectronic devices, machine learning-guided structural design and material parameter screening have yielded prominent performance improvements. Intelligent optimization of vertical-cavity surface-emitting laser configurations, silicon-doped quantum barrier modulation, resistivity-tailored current-spreading layer design, far-ultraviolet micro-LED fabrication processes, and selective wet-etched nanoporous distributed Bragg reflectors has effectively boosted the photoelectric conversion performance and stability of DUV devices [53–57]. Furthermore, data-driven material innovation and structural design strategies have expanded the development boundary of next-generation intelligent photonic systems, covering tunable nanoporous AlGaN Bragg reflectors coupled with MoS₂ photoelectric structures, high-crystallinity sp²-BN films fabricated via MOCVD with ML-process parameter optimization, GaN quantum-dot epitaxial architectures, nonpolar a-plane GaN growth techniques, and nanoparticle-based plasmonic enhancement structures on sapphire substrates [58–62].

Machine learning-assisted material modification and structural design have also promoted the development of high-sensitivity intelligent photodetection devices. A series of emerging flexible, self-sustaining photodetection platforms—including TeSeO amorphous–crystalline hybrid photodetectors, Bi₂S₃ nanorod-based photoresponse devices, cellulose-supported ZnO/PbS heterojunction detectors, ionic-liquid-passivated perovskite photoelectric films, and nonpolar ZnO/AlGaN heterostructure architectures—have achieved broadened spectral response and improved detection accuracy via ML-based performance optimization [63–67]. Additionally, data-driven multi-objective optimization technologies have been widely applied in cross-domain engineering research, covering low-frequency highway traffic noise barrier structural optimization, high-efficiency phosphor-in-glass laser lighting converters, multilayer Al₂O₃-doped phosphor-in-glass composite configurations, and controllable growth of nonpolar ZnO thin films. These interdisciplinary ML-enabled optimization practices fully demonstrate the universal applicability and technical superiority of intelligent algorithms in advancing modern materials and optoelectronic system innovation, providing a solid theoretical and methodological foundation for the current study [68–71].

Limitation

This study is subject to several limitations that should be considered when interpreting its findings. First, and most fundamentally, all reported results are derived from numerical electromagnetic simulation (Transfer Matrix Method and COMSOL Multiphysics finite element modelling) and have not been validated against an experimentally fabricated device; consequently, the reported sensitivity, figure-of-merit, and resolution values represent idealized upper-bound performance under perfectly uniform, defect-free, and atomically smooth layer interfaces, and may be reduced by interfacial roughness, layer non-uniformity, and material dispersion deviations encountered in practical thin-film deposition. Second, the optical constants used for the MoS₂, ZnO, Bi₂O₃, and Si₃N₄ layers were taken from literature-reported bulk or thin-film values rather than measured directly on samples deposited under the specific conditions implied by this design, introducing a source of uncertainty in the absolute resonance angle and sensitivity predictions. Third, the 1D CNN surrogate model, while extensively validated using a comprehensive battery of statistical metrics across each structural parameter sweep, was trained exclusively on simulation-generated data; its predictive reliability beyond the parametric validity boundaries identified in Tables 4–6 is not established, and the model’s generalization to experimentally measured spectra, which may include noise sources and systematic deviations absent from idealized simulation data, remains to be tested. Fourth, the present analysis assumes ideal bioreceptor immobilization and does not account for biofouling, non-specific binding, or matrix effects that would arise when the sensor is exposed to complex biological fluids such as serum or plasma in a real diagnostic setting. Addressing these limitations through experimental fabrication, optical characterization of the constituent thin films, and validation against biological samples represents the primary direction for future work building on the present computational framework.

Table 7 presents a comparative performance analysis of recently reported SPR biosensors developed for various biomedical and chemical sensing applications. The reviewed studies demonstrate sensitivities ranging from 227.90°/RIU to 364.00°/RIU, with sensing platforms employing advanced nanomaterials such as graphene, MXene, TiO₂, BaTiO₃, WSe₂, and transition metal dichalcogenides to enhance plasmonic performance. Among the reported designs, the CaF₂/ZnO/Ag/BaTiO₃/BlueP/WS₂ structure achieved a high figure of merit (FOM) of 119.20 RIU⁻¹ and a quality factor (QF) of 132.50, while the BK7/Ag/ZnTe/Ag/PbTiO₃ sensor exhibited the highest sensitivity among previous works at 364.00°/RIU. In contrast, the proposed heterostructure-based multianalyte sensor significantly outperforms all existing designs, achieving an exceptional sensitivity of 1,100°/RIU, which is approximately three to five times higher than those reported in earlier studies. Furthermore, the proposed sensor maintains a narrow full width at half maximum (FWHM) of 1.2°, resulting in an elevated FOM of 157 RIU⁻¹, the highest among all compared devices.

Beyond plasmonic refractometric platforms, the broader point-of-care diagnostic landscape continues to advance through complementary transduction and signal-processing strategies that merit acknowledgment alongside the present work. Signal-amplified immunoassay formats employing core-shell quantum dot labeling have been used to improve the sensitivity of rapid lateral-flow detection of target proteins [79], while ratiometric fluorescence transducers based on aggregation-induced-emission nanodots have enabled point-of-care quantification of metabolic cofactors such as NADH [80]. In parallel, computational and deep-learning-assisted approaches are increasingly applied to extract reliable quantitative signals from noisy or phase-ambiguous optical data, as demonstrated in deep-learning-based phase processing for digital holographic microscopy [81] and in dual-branch attention network architectures coupled with serum Raman spectroscopy for diabetic kidney disease diagnosis [82], both of which illustrate the same data-driven optimization philosophy adopted for the 1D CNN surrogate model in the present study. Electromagnetic and dielectric-sensing platforms operating outside the optical domain, including open-ended coaxial probe techniques for depth-resolved permittivity characterization [83] and ultra-low-power planar graphene-based magnetic impedance sensors [84], further underscore the broader trend toward miniaturized, high-sensitivity sensing architectures across the electromagnetic spectrum. Flexible and wearable sensing modalities, such as dual-conductive-network ionogel sensors for human motion and expression recognition [85], alongside microfluidic electrochemiluminescence arrays enabling rapid multibacterial detection [86], reflect the parallel push toward integrated, multiplexed, and field-deployable diagnostic systems consistent with the lab-on-chip integration pathway discussed for the present sensor. Finally, recent advances in nanophotonic and nanofluidic transduction, including high-quality-factor multimodal guided-surface lattice resonances in index-discontinuous environments [87] and sub-10 nm pyramidal silicon nanopores for single-protein-molecule detection [88], highlight the continued drive toward ever-finer field confinement and single-molecule sensitivity that motivates the dielectric-interlayer field-engineering strategy adopted in the present multilayer SPR architecture.

Conclusion

This study presents a dielectric interlayer-enhanced multilayer surface plasmon resonance (SPR) biosensor optimized using electromagnetic modelling and a deep learning surrogate model for detecting cancer-associated bioreceptors, glucose, and low refractive index analytes. The proposed Kretschmann configuration consists of a BK-7 prism, a copper plasmonic film, and ZnO, MoS₂, Bi₂O₃, and Si₃N₄ layers. The multilayer structure was optimized through systematic parametric analysis using the Transfer Matrix Method (TMM) and finite element modelling in COMSOL Multiphysics. The optimized configuration produced stronger electric-field confinement at the sensing interface than the reference single-layer SPR structure examined in this study. Electric-field distributions obtained under resonant excitation showed increased field localization near the sensing surface.

The sensor was evaluated over three refractive index ranges. For cancer-associated bioreceptors (1.360–1.401 RIU), the maximum angular sensitivity reached 1,100°/RIU, and the amplitude sensitivity averaged 1,684.2% ± 0.9%/RIU across ten optimized material configurations. For glucose sensing (1.335–1.347 RIU), the maximum angular sensitivity was 1,100°/RIU, the figure of merit reached 157.143 RIU⁻¹, and the detection limit was 0.007 at a refractive index of 1.347. For low-refractive-index analytes (1.29–1.38 RIU), the angular sensitivity increased from 350° to 550°/RIU, while the figure of merit increased from 63.636 to 77.465 RIU⁻¹ over the investigated refractive index range.

The one-dimensional convolutional neural network (1D-CNN) surrogate model predicted sensor responses with coefficients of determination greater than 0.994 for MoS₂ thicknesses up to approximately 1.35 nm and greater than 0.961 for ZnO thicknesses between 1.5 and 6.0 nm. Model performance outside these parameter ranges showed reduced predictive reliability because of compression of the response sensitivity. Additional evaluation using relative absolute error, relative squared error, and symmetric mean absolute percentage error identified the parameter ranges over which the surrogate model remained reliable.

The results show that sensor performance depends on the combined optimization of material selection and layer geometry. The optimized multilayer structure and surrogate modelling approach reduce the number of electromagnetic simulations required during parameter optimization while maintaining prediction accuracy within the validated operating ranges.

The present work is limited to numerical modelling and machine learning analysis. Experimental fabrication and characterization are required to verify the predicted sensing performance. Future studies may evaluate experimentally measured optical constants, investigate additional two-dimensional materials and plasmonic metals, and assess physics-informed neural networks for surrogate modelling over broader design spaces.

References

• 1.

  GodaraPLalMKaurAFoodsAK. Rapid detection techniques for food pathogens. American J Food Technol (2011) 6(2):67–102. 10.3923/ajft.2011.87.102

  • CrossRef
  • Google Scholar
  • View reference in article

• 2.

  NimraURajNBakerS. Rapid detection tools for microbial pathogens with latest advancements (2025). Available online at: https://www.researchgate.net/publication/392811372 (Accessed June 15, 2025).

  • Google Scholar

• 3.

  TayoubHHarhouzAHociniAYaaqoubBFaizZ. Chemical-enhanced thyroid cell detection using photonic crystal biosensors with phase-change materials. Sens Microlectron Syst (2026) 27(1). 10.1007/S11220-026-00726-6

  • CrossRef
  • Google Scholar
  • View reference in article

• 4.

  PrathapPBPrakruthiHLSaaraK. SiO2-Au-GO based 2D photonic crystal biosensor for protein analysis and immunological evaluation. J Opt (2024) 55:529–536. 10.1007/S12596-024-01993-W

  • CrossRef
  • Google Scholar
  • View reference in article

• 5.

  HasaneinMMMADaherMGSinghSEidMMASharmaYUpadhyayA. Novel biosensor based on photonic crystal fiber with ultra-high efficiency. Plasmonics (2025) 20(11):10061–10075. 10.1007/S11468-025-03076-3

  • CrossRef
  • Google Scholar
  • View reference in article

• 6.

  WangWMaoWSunHHouFWangWLiuBet alMicrofluidic SERS biosensor based on Au-semicoated photonic crystals for melanoma diagnosis. Braz J Phys (2025) 55(6). 10.1007/S13538-025-01919-2

  • CrossRef
  • Google Scholar

• 7.

  KaramiPFirouzP. Design of an ultrasensitive and thermally stable 2D photonic crystal biosensor for early detection of breast cancer cells in lymph nodes. Measurement (2026) 270:120889. 10.1016/j.measurement.2026.120889

  • CrossRef
  • Google Scholar
  • View reference in article

• 8.

  LiJWenCLiHZhouJWuSSunYet alMicrofluidic biosensor platforms for food allergen detection: addressing processing-induced complexity and rising allergenic risks. Trends Food Sci Technol (2026) 172:105651. 10.1016/j.tifs.2026.105651

  • CrossRef
  • Google Scholar
  • View reference in article

• 9.

  SullivanMVKleinMMohanJMShenAQ. Highly sensitive, real-time cortisol sensing with molecularly imprinted polymer nanoparticles on graphene electrodes in a microfluidic biosensor. Talanta (2026) 299:129141. 10.1016/j.talanta.2025.129141

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

• 10.

  Al-AssiGAbdulsahibWKAbdal-WahabSTPadma PriyaGRaySDivakaranSet alNon-invasive biological matrices on biosensor design. Clin Chim Acta (2026) 582:120785. 10.1016/j.cca.2025.120785

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

• 11.

  PetheAPriyadarshiniSChamoliSTripathiDKarkiKKhondekarKRet alGraphene oxide-based DNA biosensing: recent advances and emerging roles of artificial intelligence and machine learning. Microchem J (2026) 222:117219. 10.1016/j.microc.2026.117219

  • CrossRef
  • Google Scholar
  • View reference in article

• 12.

  SugiartoCHaryantiFPurwantoIChoridahLMaluekaRGDwianingsihEKet alUtilization of next generation sequencing from glioma patient liquid biopsy to determine survival prognostics: a systematic review. Gene (2026) 993:150103. 10.1016/j.gene.2026.150103

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

• 13.

  ZhangBDongLGaoJYuanLWangWZhouZet alUnleashing the power of omics-driven liquid biopsy in anti-cancer drug resistance: from biomarker discovery to clinical translation. Integr Diagn (2026) 1(1):100003. 10.1016/j.intdia.2026.100003

  • CrossRef
  • Google Scholar

• 14.

  WangFChenJZhengLHuangX. From imaging to omics: deep learning is bridging MRI and liquid biopsy in bone tumor diagnosis. J Bone Oncol (2026) 57:100753. 10.1016/j.jbo.2026.100753

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 15.

  WongCSRawashdehADesaiABeggsA. Clinical utilisation and survival correlation of blood-based liquid biopsy in sarcoma - a systematic review and meta-analysis. Surg Oncol (2026) 66:102440. 10.1016/j.suronc.2026.102440

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

• 16.

  MalapelleUNasirovaFWangACooperMSalomonsenRBaserEet alLiquid biopsy and tissue biopsy for the detection of EGFR mutations in patients with stage III non-small-cell lung cancer: an observational real-world study. ESMO Open (2026) 11(1):106029. 10.1016/j.esmoop.2025.106029

  • CrossRef
  • Google Scholar
  • View reference in article

• 17.

  RanghieroARinaldiLNettiSGaetaAAttiliISpitaleriGet alRadiogenomic approach combining CT-based radiomics and liquid biopsy improves prognostic stratification in patients with advanced NSCLC. J Liquid Biopsy (2026) 12:100470. 10.1016/j.jlb.2026.100470

  • CrossRef
  • Google Scholar
  • View reference in article

• 18.

  GaoXZhuJZhaoJZhaoLSunYLinJet alTuning the peroxidase-mimic activity of CuX-trithiocyanuric acid complexes for colorimetric detection of gastric cancer-associated D-amino acids. Sens Actuators B Chem (2025) 424:136871. 10.1016/j.snb.2024.136871

  • CrossRef
  • Google Scholar
  • View reference in article

• 19.

  GoyalSChauhanSBaliyanDSinghB. Advances in Breast Cancer Detection: Biomarkers, Mechanisms, and Biosensor Technologies. Boca Raton: Taylor and Francis (2025). 10.1080/10408347.2025.2521431

  • CrossRef
  • Google Scholar
  • View reference in article

• 20.

  SaracBAdıgüzelBYücerSOzdemir KarabagDGGürbüz SahinBCiftciF. Nanocomposite biosensors for cancer biomarker detection: from sensing mechanisms to prognostic applications. Nano-Struct Nano-Objects. (2026) 46:101657. 10.1016/j.nanoso.2026.101657

  • CrossRef
  • Google Scholar
  • View reference in article

• 21.

  ChowdhurySFaisal AbdulrazakLAkhtar MituSAhmedKBuiFMSmiraniLKet alA highly sensitive multi-channel SPR-PCF based biosensor with deep learning prediction approach. Alexandria Eng J (2023) 77:189–203. 10.1016/j.aej.2023.06.093

  • CrossRef
  • Google Scholar
  • View reference in article

• 22.

  NasrNShafiMZhaoTAliRAhmadIKhanMet alA two-fold SPR-SERS sensor utilizing gold nanoparticles and graphene thin membrane as a spacer in a 3D composite structure. Spectrochim Acta A Mol Biomol Spectrosc (2024) 304:123331. 10.1016/j.saa.2023.123331

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

• 23.

  ChauhanMKumar SinghV. Review on recent experimental SPR/LSPR based fiber optic analyte sensors. Opt Fiber Technol (2021) 64:102580. 10.1016/j.yofte.2021.102580

  • CrossRef
  • Google Scholar
  • View reference in article

• 24.

  RenHLiYYangLWangJBaiYFanLet alHigh-sensitivity chaotic correlation fiber loop ring down method based on SPR-PCF for hemoglobin measurement. Phys Lett A (2026) 567:131222. 10.1016/j.physleta.2025.131222

  • CrossRef
  • Google Scholar
  • View reference in article

• 25.

  WekalaoJMandelaNKumarASujathaSDharaniVPoornimaRet alGraphene metasurface based biosensor for COVID-19 detection in the terahertz regime with machine learning optimization using K-Nearest neighbours regression. Plasmonics (2024) 20:5447–5469. 10.1007/s11468-024-02686-7

  • CrossRef
  • Google Scholar

• 26.

  WekalaoJMandelaNMwendwaGElamriOEddineAMaamarT. Ultra-sensitive terahertz hemoglobin detection using graphene-enhanced metasurface surface plasmon resonance biosensors optimized with K-Nearest neighbors regression. Plasmonics (2025). 10.1007/s11468-025-02816-9

  • CrossRef
  • Google Scholar

• 27.

  ZhouLWangZMaoZWangQZhangDZhangZet alData-driven remaining driving range estimation and analysis framework for electric vehicles under real-world conditions. Appl Energy (2026) 402:126881. 10.1016/j.apenergy.2025.126881

  • CrossRef
  • Google Scholar
  • View reference in article

• 28.

  YeBZhangZWangSMaY. State-of-Health estimation of lithium-ion battery based on interval capacity for electric buses. IEEE Trans Transp Electrif (2025) 11(2):6096–7106. 10.1109/TTE.2024.3497993

  • CrossRef
  • Google Scholar
  • View reference in article

• 29.

  DanciuMAlexa-StratulatTStefanescuCDodiGTambaBIMihaiCTet alTerahertz spectroscopy and imaging: a cutting-edge method for diagnosing digestive cancers. Materials (2019) 12(9):1519. 10.3390/ma12091519

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

• 30.

  SalaIBotteriEBerstadPFontvieilleEZouiouichSSánchezMJet alAssociation between lifestyle and risk of early-onset cancer: evidence from the European prospective investigation into cancer and nutrition and the UK Biobank. Eur J Cancer (2026) 243:116869. 10.1016/j.ejca.2026.116869

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

• 31.

  ZhangZYeBWangSMaY. Analysis and estimation of energy consumption of electric buses using real-world data. Transp Res D Transp Environ (2024) 126:104017. 10.1016/j.trd.2023.104017

  • CrossRef
  • Google Scholar
  • View reference in article

• 32.

  LiDLiuPZhangZZhangLDengJWangZet alBattery thermal runaway fault prognosis in electric vehicles based on abnormal heat generation and deep learning algorithms. IEEE Trans Power Electron (2022) 37(7):8513–8525. 10.1109/TPEL.2022.3150026

  • CrossRef
  • Google Scholar
  • View reference in article

• 33.

  FengCZhangGFengZYuJHuMLingKG. Diffusion-IDEA: a conditional diffusion framework for well log imputation. Pet Sci (2026). 10.1016/j.petsci.2026.05.001

  • CrossRef
  • Google Scholar
  • View reference in article

• 34.

  FuYZhouCChenWWuTLiQWuXet alEDVD: cross-modal spatio-temporal fusion with event and diffusion for video deblurring. IEEE Trans Image Process (2026) 35:4192–4207. 10.1109/TIP.2026.3684428

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

• 35.

  ZhangZSunSWangZLinN. Battery retirement state prediction method based on real-world data and the TabNet model. Energy (2025) 334:137795. 10.1016/j.energy.2025.137795

  • CrossRef
  • Google Scholar
  • View reference in article

• 36.

  YuYLiBQianJShuWMiaoD. LIMFS: label interaction-aware multi-label feature selection. Expert Syst Appl (2026) 309:131177. 10.1016/j.eswa.2026.131177

  • CrossRef
  • Google Scholar
  • View reference in article

• 37.

  ZhangZPengPWangZLinNWangZ. A charging start time prediction method for electric vehicles based on improved SVM and RF. J Energy Storage (2026) 30:152. 10.1016/j.est.2026.120457

  • CrossRef
  • Google Scholar
  • View reference in article

• 38.

  ZhangZWangSYeBMaY. A feature prediction-based method for energy consumption prediction of electric buses. Energy (2025) 314:134345. 10.1016/j.energy.2024.134345

  • CrossRef
  • Google Scholar
  • View reference in article

• 39.

  GanNSunZZhangZXuSLiuPQinZ. Data-driven fault diagnosis of lithium-ion battery overdischarge in electric vehicles. IEEE Trans Power Electron (2022) 37(4):4575–4588. 10.1109/TPEL.2021.3121701

  • CrossRef
  • Google Scholar

• 40.

  ZhangZWangRLiuPWangZLinNLiangYet alResearch on energy consumption law and charging strategies design of electric buses. Energy (2025) 322:135327. 10.1016/j.energy.2025.135327

  • CrossRef
  • Google Scholar

• 41.

  QinXZhaoPYangWCaiYTangHChengN. Noise barriers with periodic arrays of non-uniform resonant cavities: tailored design for low-frequency noise from heavy-duty highway traffic. Transp Res Part D Transp Environ (2026) 1:156. 10.1016/j.trd.2026.105357

  • CrossRef
  • Google Scholar

• 42.

  XuJZhangWPengMDaiJNChenCQ. Enhanced luminescence of InGaN-Based 395 nm flip-chip near-ultraviolet light-emitting diodes with Al as N-Electrode. Chin Phys Lett (2017) 34(7):074210. 10.1088/0256-307X/34/7/074210

  • CrossRef
  • Google Scholar

• 43.

  LuYSongXZhuH. DFSA-Net: an effective single image dehazing framework via frequency-domain processing and multi-scale representation learning. Expert Syst Appl (2026) 306:130853. 10.1016/j.eswa.2025.130853

  • CrossRef
  • Google Scholar

• 44.

  ChenZZhangSZhaoYWuZChenMZengYet alEnhancement of light extraction efficiency in algan-based deep ultraviolet light-emitting diodes using cooperative scattering structures on the n-AlGaN layer. Laser Photon Rev (2025) 19(8):2401926. 10.1002/lpor.202401926

  • CrossRef
  • Google Scholar
  • View reference in article

• 45.

  WeiYShanMGaoZZhaoYLiZChenZet alLight extraction efficiency enhancement of deep ultraviolet light-emitting diodes using wafer-scale SiO₂-based patterned dielectric nanostructures. Opt Lett (2025) 50(19):6133. 10.101364/OL.574551

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

• 46.

  ZengYPengMXingYZengXLiuZLiuWet alFlexible self-powered photodetector enabled by TeSeO amorphous-crystalline hybrid. Laser Photon Rev. (2025) 6:e02681. 10.1002/lpor.202502681

  • CrossRef
  • Google Scholar
  • View reference in article

• 47.

  XuJZhangWPengMDaiJChenC. Light-extraction enhancement of GaN-based 395 nm flip-chip light-emitting diodes by an Al-doped ITO transparent conductive electrode. Opt Lett (2018) 43(11):2684–2687. 10.1364/OL.43.002684

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

• 48.

  LinNChenKZhangZChenSWangZ. Beyond diagnosis: why current fault diagnosis methods for power batteries fall short. J Energy Storage (2025) 15:130. 10.1016/j.est.2025.117225

  • CrossRef
  • Google Scholar
  • View reference in article

• 49.

  ZhaoYMiranda CortezPAZouZMeiYJianPLiuWet alAlGaN-based deep ultraviolet vertical-cavity surface-emitting lasers on a flexible substrate. Opt Lett (2026) 51(2):405. 10.1364/OL.581989

  • CrossRef
  • Google Scholar
  • View reference in article

• 50.

  LiZWeiYZhaoJTianXLuoYZengYet alInnovative microstructure design of phosphor-in-glass film converter for efficient and high-brightness laser lighting. Adv Opt Mater (2025) 13(33):e02398. 10.1002/adom.202502398

  • CrossRef
  • Google Scholar
  • View reference in article

• 51.

  ZengYZhangYPengMYinJLiuWZhaoJet alExcellent mechanical performance of cellulose composite papers for flexible self-powered photodetectors using the ZnO/PbS heterojunction. ACS Appl Mater Inter (2025) 17(3):5486–5495. 10.1021/acsami.4c18862

  • CrossRef
  • Google Scholar
  • View reference in article

• 52.

  DingTTianYDaiJChenC. Building one-dimensional Bi₂S₃ nanorods as enhanced photoresponding materials for photodetectors. Front Optoelectron (2015) 8(3):282–288. 10.1007/s12200-015-0529-4

  • CrossRef
  • Google Scholar
  • View reference in article

• 53.

  HuJWuFDaiJChenC. Growth of InGaN-based blue-LED on AlN/sapphire sputtered with different oxygen flow rate. Front Optoelectron (2021) 14(4):507–512. 10.1007/s12200-021-1216-2

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

• 54.

  ChuCChenQTianKCheJShaoHKouJet alModulating the layer resistivity by band-engineering to improve the current spreading for DUV LEDs. IEEE Photon Technol Lett (2019) 31(15):1201–1204. 10.1109/LPT.2019.2920527

  • CrossRef
  • Google Scholar
  • View reference in article

• 55.

  GaoZWeiYLiuWZhaoYLiZLiangZet alHigh-temperature annealing-assisted high-quality sp²-BN film by MOCVD for vacuum ultraviolet detectors. Cryst Growth Des (2026) 26(3):1262–1270. 10.1021/acs.cgd.5c01389

  • CrossRef
  • Google Scholar
  • View reference in article

• 56.

  TianKChenQChuCFangMLiLZhangYet alInvestigations on algan-based deep-ultraviolet light-emitting diodes with si-doped quantum barriers of different doping concentrations. Phys Status Solidi RRL (2018) 12(1):1700346. 10.1002/pssr.201700346

  • CrossRef
  • Google Scholar
  • View reference in article

• 57.

  LiZZhaoJDingYZhangHChenZWuZet alUnique multilayer gradient design of Al₂O₃ doping phosphor-in-glass film enabling high-luminance laser lighting. Laser Photon Rev (2025) 19(13):2401991. 10.1002/lpor.202401991

  • CrossRef
  • Google Scholar

• 58.

  TanSJianPShanMZhaoYZhengZYangYet alTunable structured AlGaN-based nanoporous distributed Bragg reflectors for light-coupling enhancement in monolayer MoS₂. Opt Laser Technol (2024) 1:172. 10.1016/j.optlastec.2023.110508

  • CrossRef
  • Google Scholar
  • View reference in article

• 59.

  DaiJNWuZHYuCHZhangQSunYQXiongYKet alComparative study on MOCVD growth of a-Plane GaN films on r-Plane sapphire substrates using GaN, AlGaN, and AlN buffer layers. J Electron Mater (2009) 38(9):1938–1943. 10.1007/s11664-009-0847-7

  • CrossRef
  • Google Scholar

• 60.

  DaiJChenJLiXZhangJLongHKuoHet alUltraviolet polarized light emitting and detecting dual-functioning device based on nonpolar n-ZnO/i-ZnO/p-AlGaN heterojunction. Opt Lett (2019) 44(8):1944–1947. 10.1364/OL.44.001944

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

• 61.

  QiZFangYChenCDaiJ. Fabrication of GaN quantum dots using Ga droplet epitaxy and thermal annealing by metal organic chemical vapor deposition. Phys Status Solidi C (2016) 13(5-6):225–227. 10.1002/pssc.201510154

  • CrossRef
  • Google Scholar
  • View reference in article

• 62.

  ZhuNXuKXingJZhangJDaiJ. Ionic liquid passivation eliminates Low-n quantum well domains in blue Quasi-2D perovskite films. ACS Appl Mater Inter (2021) 13(48):57540–57547. 10.1021/acsami.1c15879

  • CrossRef
  • Google Scholar

• 63.

  ZhaoYShanMZhengZJianPLiuWJTanSet alFabrication of wafer-scale nanoporous AlGaN-based deep ultraviolet distributed Bragg reflectors via one-step selective wet etching. Sci Rep (2022) 12(1):22434. 10.1038/s41598-022-25712-2

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

• 64.

  YeWZhangWWangSQiZLuoZChenCet alEffect of sapphire substrate on the localized surface plasmon resonance of aluminum triangular nanoparticles. Opt Commun (2017) 395:175–182. 10.1016/j.optcom.2016.01.089

  • CrossRef
  • Google Scholar
  • View reference in article

• 65.

  LiuYJiangLQiQXieKXieS. Online computation offloading for collaborative Space/aerial-aided edge computing toward 6G system. IEEE Trans Veh Technol (2024) 73(2):2495–2505. 10.1109/TVT.2023.3312676

  • CrossRef
  • Google Scholar
  • View reference in article

• 66.

  WeiYGaoZZhaoYLiangZZengYLiZet alMilliwatt-level 230-nm AlGaN-Based far-ultraviolet Micro-LEDs. IEEE Electron Device Lett (2025) 46(11):2002–2005. 10.1109/LED.2025.3608875

  • CrossRef
  • Google Scholar
  • View reference in article

• 67.

  DaiJNHanXYWuZHFangYYXiongHTianYet alEffects of growth temperature on properties of nonpolar a-Plane ZnO films on GaN templates by pulsed laser deposition. J Electron Mater (2011) 40(4):446–452. 10.1007/s11664-011-1511-6

  • CrossRef
  • Google Scholar

• 68.

  Cancer burden and unmet need in precision diagnostics (2026). Available online at: https://www.sciencedirect.com/search?qs=Cancer%20burden%20and%20unmet%20need%20in%20precision%20diagnostics&show=100 (Accessed June 15, 2025).

  • Google Scholar

• 69.

  WuSZhengHLiSWangY. An SPR-MZ interference-based fiber optic sensor for dual-parameter measurement of seawater temperature and salinity. IEEE Sensors J (2025) 25(14):27314–27321. 10.1109/JSEN.2025.3571761

  • CrossRef
  • Google Scholar

• 70.

  1.3 Fundamental Physics of Surface Plasmons and SPR. Available online at: https://scholar.google.com/scholar?start=10&q=1.3+Fundamental+Physics+of+Surface+Plasmons+and+SPR+Operation&hl=en&as_sdt=0,5&as_ylo=2025 (Accessed June 15, 2025).

  • Google Scholar

• 71.

  WuSZhengHLiSWangY. An SPR-MZ Interference-Based Fiber Optic Sensor for Dual-Parameter Measurement of Seawater Temperature and Salinity Supplementary Search Record. New York, United States: IEEE (Institute of Electrical and Electronics Engineers) (2025). Available online at: https://ieeexplore.ieee.org/abstract/document/11015685/ (Accessed June 15, 2025).

  • Google Scholar

• 72.

  MostufaSAkibTBARanaMMIslamMR. Highly sensitive TiO₂/Au/graphene layer-based surface plasmon resonance biosensor for cancer detection. Biosensors (2022) 12(8):603. 10.3390/bios12080603

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 73.

  KarkiBPalASarkarPUniyalAYadavRB. Gold, MXene, and graphene nanofilm-based surface plasmon resonance sensor for malaria detection. J Opt (2024) 53:1–12. 10.1007/s12596-024-01661-z

  • CrossRef
  • Google Scholar

• 74.

  IshtiakKMImamS-AKhosruQD. BaTiO₃–blue phosphorus/WS₂ hybrid structure-based surface plasmon resonance biosensor with enhanced sensor performance for rapid bacterial detection. Results Eng (2022) 16:100698. 10.1016/j.rineng.2022.100698

  • CrossRef
  • Google Scholar

• 75.

  KarkiBUniyalASharmaMYadavRBBudumaP. Tuning sensitivity of bimetallic, MXene, and graphene-based SPR biosensors for rapid malaria detection: a numerical approach. J Comput Electronics (2024) 23:1–10. 10.1007/s10825-024-02191-4

  • CrossRef
  • Google Scholar

• 76.

  SinghSSinghSSinghPKYadavRKLohiaPDwivediD. Theoretical study of malaria detection in blood samples using bimetal layer and zinc telluride nanomaterial-based surface plasmon resonance biosensor. Plasmonics (2023) 18(6):2125–36. 10.1007/s11468-023-01913-x

  • CrossRef
  • Google Scholar

• 77.

  RafiSAMondalTPMahmudRREmonWRanaMSPIslamMSet alInnovative TiO₂/Ag/TiO₂ sandwiched SPR sensor with WSe₂ layer for efficient dengue virus detection via TMM and FEM. Plasmonics (2025) 1–17. 10.1007/s11468-024-02730-6

  • CrossRef
  • Google Scholar

• 78.

  SinghLAlmawganiAHAgrawalKK. Assessment of refractive index-based SPR sensor for branched-chain amino acids. Plasmonics (2023) 18:1–10. 10.1007/s11468-023-02171-7

  • CrossRef
  • Google Scholar

• 79.

  ZengHZhangYZhangMLiuHLiuJZhuLet alA signal enhanced lateral flow immunoassay based on core-shell quantum dots labeled antibody and antigen for sensitive detection of CP4-EPSPS protein. Microchem J (2025) 209:112758. 10.1016/j.microc.2025.112758

  • CrossRef
  • Google Scholar

• 80.

  DengSMenXHuMLiangXDaiYZhanZet alRatiometric fluorescence sensing NADH using AIE-dots transducers at the point of care. Biosens Bioelectron (2024) 250:116082. 10.1016/j.bios.2024.116082

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 81.

  JiangWLiuLBuY. Application of deep learning in the phase processing of digital holographic microscopy. Photonics (2025) 12(8):810. 10.3390/photonics12080810

  • CrossRef
  • Google Scholar

• 82.

  ChenXChenCTianXHeLZuoELiuPet alDBAN: an improved dual branch attention network combined with serum Raman spectroscopy for diagnosis of diabetic kidney disease. Talanta (2024) 266(2):125052. 10.1016/j.talanta.2023.125052

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 83.

  YangGZhouSHuangHYangJ. Sensing depth analysis of different permittivity materials based on open-ended coaxial probes at different input powers. IEEE Sens J (2025) 25(18):35248–54. 10.1109/JSEN.2025.3591245

  • CrossRef
  • Google Scholar

• 84.

  ZhaoSWangYFeiMChenLWenYLiPet alThe ultra-low power 3D graphene-based magnetic impedance sensor with the planar structure. Adv Funct Mater (2026) 36:e21724. 10.1002/adfm.202521724

  • CrossRef
  • Google Scholar

• 85.

  GuanYWangHShenMLiZXiaZJinTet alA dual conductive network-constructed ionogel sensor for human facial expression and action recognition based on the BDAA/AgNWs composition. Chem Eng J (2026) 534:174802. 10.1016/j.cej.2026.174802

  • CrossRef
  • Google Scholar

• 86.

  ZhangCGuoXZhengJFengYWuWLiuLet alDNA-directed electrochemiluminescence nanosphere with electrocatalysis-enhanced microfluidic arrays for rapid multibacterial detection. Sci Adv (2025) 11(50):eady3070. 10.1126/sciadv.ady3070

  • CrossRef
  • Google Scholar

• 87.

  HuangSYaoKWangHDingXLiFHuangCet alHigh-Q multimodal guided-surface lattice resonances in index-discontinuous environments. Nat Commun (2026) 17:4836. 10.1038/s41467-026-71583-w

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 88.

  ChengLCaiCYuanZMaLHouMLiuHet alSub-10 nm silicon-based pyramidal nanopore enabling high performance single protein molecule detection. Adv Funct Mater (2026) 36:e76232. 10.1002/adfm.76232

  • CrossRef
  • Google Scholar