In recent years, metamaterial absorbers (MMAs) artificially engineered structures typically comprising three or more material layers have attracted significant interest in the scientific community. Their unique electromagnetic properties, such as negative refractive index, cloaking capability, superlensing, and enhanced absorption, have enabled a wide range of applications, including infrared and radar systems, antennas, compact wireless components, and advanced sensing platform [1],[2]. The rapid growth of the global population, coupled with the continuous release of chemical pollutants[3] from industrial processes, vehicular emissions, and the incineration of waste, has significantly contributed to the accumulation of toxic gases in the atmosphere. Consequently, the development of highly sensitive gas sensors is essential for real-time monitoring and detection of these hazardous gases. For that, a metamaterial-based sensor operating in the terahertz frequency range is proposed for the efficient detection of toxic gases present in polluted atmospheres [4],[5]. In [6], aflatoxin was classified as a Class I carcinogen by the International Agency for Research on Cancer (IARC), and this highly toxic carcinogen mainly contaminates agricultural products such as peanuts, corn, and grains, thus causing mold and spoilage of these foods. Accurate and sensitive detection of such contaminants has therefore become crucial to ensure food safety. In this context, perfect metamaterial absorbers (PMAs) with unique EM properties have gained interest. Due to their ability to achieve near-unity absorption at specific resonant frequencies, PMAs enable strong analyte field interactions, thereby enhancing sensitivity. These characteristics render them highly suitable for applications in sensing, absorption-based technologies, biomedical diagnostics, industrial component recognition, and imaging applications [7],[8], [9]. Numerous sensor configurations based on metamaterial absorbers have been extensively explored for the characterization of both solid and liquid analytes[10]. In particular, the designs presented in [2], [11] employed sample placement directly on the resonator surface, facilitating efficient detection of solid materials. The control of electromagnetic wave modes in metamaterials is enabled through the precise design of their unit cell structures. By incorporating terahertz (THz) technology into metamaterial platforms, it becomes feasible to develop spatial optical sensing systems with potential applications in industrial deterioration monitoring and environmental permeability analysis. Their unique properties can effectively improve the performance of the THz absorber and even make it possible to design revolutionary devices[12], [13]. However, natural materials generally exhibit weak electromagnetic responses in the terahertz (THz) regime, limiting their applicability in THz technologies. To overcome this constraint, metamaterials structures have been introduced. Through careful control of unit cell geometry, scale, and arrangement, these artificial materials enable electromagnetic behaviors absent in nature[14]. Despite significant advancements, the practical deployment of such structures remains limited due to fabrication complexities, angular sensitivity, and insufficient experimental validation in numerous proposed designs. In paper [10], Metamaterial absorber-based sensors have advanced in sensitivity, yet monolithic designs with dual-phase detection and experimental verification in the S-band remain underexplored. Mia et al. proposed [15] a highly efficient terahertz metamaterial absorber that achieves near-perfect absorption above 99.9% at three distinct resonance frequencies, with sensitivities reaching 479.5 GHz per refractive index unit, demonstrating a strong capability for the accurate detection of nonlinear optical liquids and organic substances. The paper [16] designed a gear-shaped triple-band THz metamaterial absorber achieving near-unity absorption and high sensitivity of 56.67 THz/RIU for ethanol detection, showing strong structural tunability and polarization insensitivity. However, performance may degrade under angular incidence and physical bending, affecting real-world reliability. Moreover, a terahertz metasurface-based microfluidic sensor was introduced in [17], featuring a self-aligned cap and pedestal configuration to position the fluidic channel within the region of intensified electromagnetic fields, thereby strengthening the interaction between light and analyte for improved sensing efficiency. In addition, a polarization-insensitive metamaterial sensor developed for chemical sensing and EMI shielding demonstrates stable resonance at 10 GHz, offering a sensitivity of 18.87, a high Q-factor of 475, and a Figure of Merit of 4411.80, confirming its potential for real-time liquid chemical detection in industrial applications[18]; however, its performance under high-temperature and broadband operating conditions remains limited, requiring further optimization for robust deployment. Metamaterial (MTM) sensors have demonstrated versatility in detecting various chemical substances across a wide range of frequency. Another work [19] introduced a portable, efficient sensor for fuel identification, where the resonance frequency shifted by 72 MHz, accompanied by a − 4 dB change in reflection magnitude when differentiating between branded and unbranded diesel. For gasoline, the shift was 12 MHz with a − 6 dB reflection change. Later, in [20] a plasmonic sensor achieved 2527.6 nm/RIU sensitivity and detected honey quality and lactose concentration, showing significant potential for biomedical sensing. Bakir et al. show an oil-detecting MTM sensor[21].A triple-band THz metamaterial absorber with snowflake resonators achieved peak absorptions of 97.43%, 79.22%, and 99.02%, offering sensitivities up to 473.86 GHz/RIU for liquid detection [22]. In addition, A triple-band THz metamaterial absorber with symmetrical split-ring geometry achieved high absorption (~ 99%) at 9.42, 9.86, and 10.03 THz, showing strong sensitivity (up to 2.56 THz/RIU) and high Q-factors for precise gas detection [23] it’s polarization independence and high FOM values highlight its potential for environmental and chemical sensing. In recent work, studies have explored MTM absorber-based sensors using SRR structures, showing high absorption rates (> 98%) across S and C bands and stable performance under varying conditions [24]. Moreover, higher sensitivity (0.93) and a Q-factor exceeding 150 have also been reported, confirming their potential in oil quality detection and microfluidic applications. This paper [25] presented studies about that compact metamaterial-based sensors operating in the X-band (8–12 GHz) can achieve high sensitivity (0.91) and Q-factors up to 350 for distinguishing liquid types based on permittivity differences. Furthermore, a transmission line-based MTM sensor was demonstrated in [26] to detect fuel adulteration, exhibiting a 50 MHz resonance shift between pure and adulterated diesel. Similarly, Banerjee et al. [27] designed a swastika-shaped µ-negative THz absorber with 99.65% absorption and 2.12 THz/RIU sensitivity, enabling RI and gas sensing. Together, these studies demonstrate the broad applicability of metamaterial sensors for detecting diverse materials such as solids, liquids, gases, and biomolecules, as supported by additional findings in related research[28],[29] ,[30]. Abdul karim et al. designed[31] Split ring resonator-based metamaterial sensors have demonstrated effective detection of fuel adulteration by monitoring resonance frequency changes. However, many existing designs are limited by narrow operating bandwidths and reduced sensitivity outside specific frequency ranges, restricting their practical applications. A multi-resonant THz metamaterial absorber showcased almost unity absorption at 1.7, 2.8, 3.2, and 3.5 THz for detecting fungi, yeast, and pesticides [32]. Its strong dielectric sensitivity, structural tunability, and angle stability support applications in food safety and label-free sensing.

This work proposes a novel, high-efficiency terahertz (THz) metamaterial absorber tailored for advanced industrial sensing applications, exhibiting near-unity absorption and superior sensitivity through a carefully engineered multilayer structure. The sensor architecture is based on a periodic arrangement of patterned copper resonators deposited on an FR-4 dielectric substrate, featuring an innovative unit cell composed of interconnected circular geometries with a centrally embedded ring. This configuration facilitates enhanced electromagnetic field confinement and resonance hybridization, resulting in sharp and distinct absorption peaks at 0.96 THz, 2.112 THz, and 3.94 THz, with absorption efficiencies of 99.918%, 99.996%, and 99.853%, respectively. The sensor exhibits maximum refractive index sensitivities of 771.3 GHz/RIU across the resonant modes, alongside elevated good quality factors enabling precise detection of minor dielectric perturbations. Additionally, the proposed design is inherently polarization-insensitive and maintains angular stability over a broad range of incidence angles, thereby ensuring operational robustness under varying field conditions. The multifunctional sensing capability of the proposed platform enables effective detection and differentiation of a wide spectrum of analytes relevant to industrial and chemical domains, including glucose, food-grade oils, chemical solvents, petroleum-based fuels, pesticides, gaseous species, solid materials, and adulterants. These attributes render the proposed sensor a highly suitable candidate for integration into compact, real-time THz spectroscopy platforms, facilitating label-free and non-destructive analysis for practical industrial applications.

The proposed terahertz (THz) sensing platform utilizes a triple-band metamaterial absorber designed to achieve near-unity absorption at distinct resonant frequencies of 0.96 THz, 2.112 THz, and 3.94 THz. These resonances correspond to well-defined electromagnetic modes that facilitate strong field confinement within the engineered metasurface, thereby significantly enhancing sensor sensitivity and detection reliability. The metasurface structure comprises concentric copper ring resonators developed on an FR-4 dielectric substrate underpinned by a continuous copper ground plane. This configuration in Fig. 1 promotes pronounced electric field localization within the nanoscale gaps of the unit cell, enabling robust interaction between the incident THz radiation and the analyte material. The absorber’s geometry and material composition are optimized to maximize absorption efficiency, attaining approximately 99.99% at each resonance frequency, which is critical for high-precision sensing applications. Sample preparation involves extracting target analytes from industrial or environmental sources, followed by their deposition onto the metasurface using a controlled process. These techniques ensure uniform and reproducible analyte coverage, facilitating consistent sensor response. Upon illumination with broadband THz radiation, the resonant modes exhibit distinct absorption peaks sensitive to local changes in the dielectric environment induced by the presence of analytes. The sensing mechanism exploits the dependence of resonance frequency shifts on variations in the refractive index of the surrounding medium. The resulting perturbations in the absorption spectra enable label-free identification and quantification of diverse substances, including food contaminants, biochemical agents, fuels, gases, pesticide residues, and solid-state materials. Real-time monitoring is achievable due to the rapid electromagnetic response of the system, while the design’s compatibility with standard photolithographic fabrication processes supports scalable production and integration.This methodology establishes a robust, scalable, and versatile THz sensing framework with broad applicability in industrial, environmental, and biochemical domains, offering a pathway toward advanced label-free detection technologies with high sensitivity and specificity.

(a) (b) (c)

Figure 2. Schematic representation of the proposed metamaterial sensor (a) periodic unit cell array and geometric configuration, (b) enlarged view of concentric ring resonator structure, and (c) cross-sectional layer composition of the sensor.

The schematic illustration and simulation environment of the proposed sensor are presented in Fig. 2. The design is based on a metamaterial-inspired unit cell architecture with lateral dimensions of 55 × 55 µm² and an overall thickness of 6.79 µm. Periodic boundary conditions were applied along the x- and y-axes to represent an array, while a boundary condition was set along the z-axis to prevent reflections. This setup allowed accurate evaluation of absorption characteristics and resonance behavior for sensing applications. The sensor adopts a tri-layer structure composed of a continuous copper ground plane, an FR-4 dielectric spacer, and a patterned copper metasurface acting as the resonator. FR-4, selected for its favorable dielectric stability, thermal robustness, and widespread use in microwave circuitry, serves as the intermediate layer, supporting the guided propagation of surface-confined modes essential for resonant operation [33]. On the top layer, a concentric ring resonator is etched into the copper surface. Copper provides low resistive losses, enabling strong electromagnetic resonance and near-perfect absorption at multiple THz frequencies (0.96, 2.112, 3.94 THz). This high conductivity is crucial for achieving high quality factors (Q-factors) and Figure of Merit (FoM) in sensing applications[34], configured to s upport localized electromagnetic field enhancement within the sensing region. This arrangement maximizes interaction between the structure’s near fields and the sample under test, allowing subtle variations in permittivity to induce observable shifts in the resonant frequency. The symmetry and alignment of the rings promote a uniform response, while the thin copper metallization ensures minimal resistive losses. Together, these features yield a compact, planar sensor highly responsive to dielectric perturbations, demonstrating promise for non-destructive analysis and real-time monitoring. Figure 2 illustrates the geometric configuration of the proposed metamaterial absorber, which consists of periodically arranged unit cells in both the Px and Py directions, each with a length of 55 µm. The unit cell features three concentric circular resonators with center radii R₁ = 8.5 µm, R₂ = 13 µm, and R₃ = 25 µm. The widths of the first and second rings are W₁ = 2.4 µm and W₂ = 2.05 µm, respectively. The structure is composed of three layers: a metallic ground layer with a thickness of t₁ = 0.2 µm, a dielectric substrate of thickness t₂ = 6.35 µm, and metallic patches on top with a thickness of t₃ = 0.24 µm. The design enables tailored electromagnetic response by carefully adjusting these geometric parameters, ensuring strong absorption performance at the target frequencies.

The optical characteristics of the proposed structure are quantified by two fundamental parameters: transmittance T(ω) and reflectance R(ω). Transmittance represents the fraction of incident electromagnetic energy transmitted through the device, while reflectance denotes the portion reflected. These parameters are extracted from the scattering parameters S21​ and S11​, respectively, which are obtained via full-wave electromagnetic simulations conducted using CST Microwave Studio. The absorption spectrum A(ω) is subsequently determined based on the conservation of energy, as given by:

A(ω) = 1 − T(ω) − R(ω)…………………………………….(1)

where T(ω)=∣S₂₁∣² and R(ω)=∣S₁₁∣². This formulation ensures a comprehensive account of the incident energy by attributing it solely to transmission, reflection, and absorption processes, consistent with established electromagnetic theory [35]. To achieve optimal absorption performance, the metamaterial absorber's structural and electromagnetic parameters were systematically tuned in this study. Key geometric variables, such as resonator dimensions, spacing, and layer thicknesses, were varied to maximize absorption. Material properties such as the conductivity of the metallic layers and the dielectric constant of the substrate were also adjusted to fine-tune impedance matching and minimize reflection losses. Additionally, parametric tuning has been done for the absorber in order to maintain high absorption across a wide range of incidence and polarization angles.

The Fig. 3(a-c) illustrates the impact of individual layer thicknesses on the absorption performance of the proposed triple-band metamaterial absorber. Variation in the bottom layer thickness (t₁) slightly shifts the resonance frequencies, with an optimal value of 0.20 µm enhancing wave confinement and minimizing transmission for strong absorption. Changes in the substrate thickness (t₂​) notably affect resonance behavior due to optical path length and phase variation, with t₂ = 6.35 µm yielding well-defined absorption peaks via constructive interference. The top layer thickness (t₃) has the most pronounced effect, significantly altering the position and intensity of absorption peaks; at t₃ = 0.24 µm, near-unity absorption across all three bands is achieved. The sensitivity of the absorber’s spectral response to variations in resonator widths was further examined using two concentric resonator rings, W1 and W2. As shown in Fig. 3(d), modifying W₁​ within the range of 2.1 µm to 2.8 µm leads to clear shifts in the resonance frequencies, emphasizing its critical role in dictating the lower and mid-frequency absorption bands. The optimal performance, marked by distinct and high-intensity peaks, is observed at W₁​=2.4 µm, indicating efficient excitation of resonant modes. Figure 3(e) illustrates the effect of adjusting W_2​ from 2.0 µm to 2.6 µm, with notable changes in the absorption profile, particularly influencing the higher frequency band. A peak response is achieved at W₂​=2.05 µm, where the structure supports strong field confinement and energy dissipation. The Fig. 3(f) – 3(h) shows the variation in absorption intensity as a function of frequency (0.5–4.5 THz) and three key geometric parameters: the outer radius of the center circle (R₀), the center radius of the first ring (R₁), and the center radius of the second ring (R₂). In Fig. 3(f), tuning R₀ (6.5–10.5 µm) demonstrates a strong influence on the lower frequency band (0.96 THz), where R₀ = 8.5 µm yields an optimized triple-band response. Figure 3(g) shows the variation in R₁ (11–15 µm), significantly affecting the mid-frequency resonance (2.11 THz), with R₁ = 13 µm providing a distinct peak and Fig. 3(h) highlights the impact of R₂ (22–26 µm) on the higher frequency band (3.94 THz), where R₂ = 25 µm exhibits a prominent absorption peak.

The substrate material and radiating material plays an important role in determining the electromagnetic response of a metamaterial absorber that reflects in Fig. 4. For the proposed triple-band absorber, three substrates fused silica, FR-4, and MgF₂ were evaluated based on their reflectance characteristics at the resonance frequencies. FR-4 demonstrated superior absorption performance, achieving minimal reflectance values of approximately 0.0008 at 0.96 THz, 4.028×10^− 5 at 2.112 THz, and 0.0015 at 3.94 THz, indicating excellent impedance matching and strong resonance behavior in Fig. 4(a). In comparison, fused silica exhibited reflectance of 0.13 at 1.012 THz, 0.1693 at 2.224 THz, and 0.2637 at 4.204 THz, respectively, reflecting its reduced effectiveness, especially at higher frequencies due to increased dielectric loss. MgF₂ showed intermediate performance, with reflectance values of 0.1431 at 0.868 THz, 0.098 at 1.904 THz, and 0.245 at 3.564 THz. These results identify FR-4 as the optimal substrate for achieving high absorption (because of low reflectance) across the target THz bands, data are given in Table I. Respectively. For materials selection, the variations in the material properties, as summarized in Table II, result in noticeable shifts in the resonant behavior of the proposed structure, demonstrating the sensitivity of its electromagnetic response to constituent materials. The choice of radiating material significantly affects the reflecting resonance depth and efficiency that depicts in Fig. 4(b). Copper demonstrates the best performance, achieving very low reflectance (~ 0.001–0.005) at all three resonance frequencies, confirming its strong resonance behavior and near-perfect absorption. Silver and Gold also exhibit good performance with slightly higher reflectance, making them viable alternatives depending on cost and fabrication constraints. Aluminum, however, shows substantially higher reflectance (~ 0.091–0.320), indicating reduced absorption efficiency.

The generation of electric and magnetic fields results from the circulation of current within the metallic component located on the surface of the MTM absorber. When a metallic element traverses a surface current, it gives rise to the generation of a magnetic field. The magnetic field changes, leading to the generation of an electric field. The interrelationship between the E-field, H-field, and surface current can be elucidated through Maxwell’s equations [37], as outlined in Eq. (2). Figure 5 illustrates the E-field, H-field, and surface current distribution, respectively at resonance frequencies.

The E-field is related to surface current density by the following equation in (3).

Upon these terms, the electric field (E-field) distributions of the proposed triple-band metamaterial absorber are shown in Fig. 5(a). Each panel shows the spatial localization of the E-field, with the intensity increasing from blue (low) to red (high). The field is concentrated near the inner region at 0.96 THz, indicating resonance due to the central structure. At 2.116 THz, the field shifts outward to the middle ring, while at 3.94 THz, it is strongest around the outer ring, signifying excitation of different resonant modes. The H-field distributions of the proposed metamaterial absorber shown in Fig. 5(b) harness distinct magnetic resonance modes across its triple-band spectrum. At the lowest frequency, magnetic energy is tightly confined to the core, signaling a fundamental resonance. As the frequency increases to 2.11 THz, the field disperses into the mid-region, indicating a transition to a more complex mode. At the highest frequency, 3.94 THz, the magnetic field shifts outward, wrapping around the structure’s periphery. The surface current distributions reveal distinct resonant behaviors crucial for strong absorption. At 0.96 THz, anti-parallel currents between the top and bottom surfaces indicate a fundamental magnetic dipole resonance (Fig. 5c, 5d). The current paths become more distributed and complex at 2.11 THz, suggesting the excitation of a higher-order resonance mode. Particularly on the top layer in Fig. 5(c) at 3.94 THz surface currents concentrate along the outer ring edges, indicating an edge-coupled high-frequency resonance.

The first Fig. 6(a) explores the impact of structural bending on the absorption performance. When the unit cell is bent with radii of 60 µm and 100 µm, compared to the flat case (0 µm bending), a noticeable blueshift and distortion occur in the higher-frequency resonances (2.112 THz and 3.94 THz), while the lowest band (0.96 THz) remains relatively stable. This shift in peak positions indicates the design’s sensitivity to geometric deformation, especially at shorter wavelengths, which can influence the device’s efficiency under mechanical stress. The second Fig. 6(b) compares four internal resonator configurations: single-band absorbers using only the center, top, or bottom strip, and a full triple-band circular structure. The circular design is the only one that supports all three targeted resonances 0.96 THz, 2.112 THz, and 3.94 THz with high absorption (close to unity). The single-strip configurations exhibit selective absorption: the center strip primarily contributes to the 0.96 THz mode, while the top and bottom strips support resonances at 2.11 THz and 3.94 THz, respectively. These findings confirm that achieving broadband, multi-resonant absorption requires a complete circular geometry, with each segment contributing to different resonance modes.

The plot in Fig. 7(a) illustrates the absorber’s response to varying polarization angles from 0° to 90° across the frequency range of 0.5 to 4.5 THz. The absorption remains consistently high at all three resonance peaks 0.96 THz, 2.112 THz, and 3.94 THz with near-unity values, regardless of the polarization orientation. This strong polarization insensitivity highlights the structure's rotationally symmetric design, which ensures stable electromagnetic interaction for any linear polarization angle, making it ideal for environments where the incident wave polarization cannot be controlled. Figure 7(b) shows how the absorption varies with incidence angles ranging from 0° to 90°. The first resonance at 0.96 THz shows remarkable stability, retaining high absorption even at steep angles. The second resonance (2.11 THz) begins to weaken beyond 50°, and the third peak at 3.94 THz shows a more noticeable decline after 40°, with absorption intensity dropping below 0.5 at extreme angles. This analysis reveals that the absorber is angle-resilient at lower frequencies, ensuring reliable performance up to moderate angles of incidence, which is beneficial for real-world terahertz sensing or imaging applications where wave incidence is seldom perfectly normal.

This study aims to systematically investigate the sensitivity, accuracy, and applicability of the proposed metasurface absorber for detecting subtle variations in the refractive index, with particular relevance to industrial analyte sensing. To rigorously quantify the sensor’s performance, critical evaluation metrics including the quality factor (Q), sensitivity (S), and Figure of Merit (FoM) are computed based on established definitions in resonance-based sensing analysis [15], enabling precise characterization of spectral selectivity, dielectric responsiveness, and detection resolution. The calculation of sensitivity is done by the following equation:

where ∆f is the shift in the resonance frequency and ∆n is the shift in the refractive index. The calculated sensitivities of the triple band are 203.3 GHz/RIU, 387.3 GHz/RIU and 771.3 GHz/RIU. These values indicate that this sensor has a promising impact on sensing applications. Figure 8 shows the plot of the connection between the incremental n and peak frequencies. The summarized data is given in Table III.

The Full Width Half Maximum (FWHM) in the proposed metamaterial absorber exhibits a value of 0.08 at 0.96 THz, demonstrating pronounced frequency selectivity attributed to its narrow resonance bandwidth. In comparison, the FWHM values for the secondary and third resonance peaks are measured as 0.163 and 0.229, respectively. The Figure of Merit (FoM), a critical metric for evaluating and benchmarking sensor performance, highlights the superior sensing capabilities of the proposed design, achieving FoM values of 2.541, 2.376, and 3.361 at resonance frequencies of 0.96, 2.112, and 3.94 THz, respectively. Another important element is Q-factor, which measures the sharpness of the peaks, and it is defined as the ratio of the central frequency to the FWHM. The Quality factor (Q-factor) is defined as follows:

The quality factors (Q-factors) of the proposed sensor are found to be 12, 12.96, and 17.21 for the respective resonant modes, indicating highly selective and narrowband absorption characteristics. These elevated Q-values reflect the sensor’s strong capacity to discriminate between closely spaced frequency components. A higher Q-factor increases sensitivity to small frequency shifts and minimizes spectral overlap, which improves both resolution and reliability in sensing applications.

In Fig. 8(a–c) presents a detailed analysis of how the resonance frequencies of the proposed triple-band metamaterial absorber respond to variations in the surrounding refractive index (RIU) for its three absorption peaks. Each resonance shows a strong linear redshift (decrease in frequency) as the refractive index increases, with high linear fitting accuracy (R² >0.996). Specifically, the first peak shows R² = 0.9993, the second peak R² = 0.9968, and the third peak R² = 0.9994. The slope values indicate increasing frequency shift rates with higher-order resonances, suggesting the third peak is the most responsive to be plotted against the refractive index according to the analysis based on the linear fitting graph in Fig. 8(d). The resonance analysis reveals that sensitivity reaches approximately 200 GHz/RIU at 0.96 THz, increases to about 390 GHz/RIU at 2.112 THz, and peaks at 770 GHz/RIU at 3.94 THz. These results demonstrate that higher-frequency modes exhibit enhanced responsiveness to changes in the surrounding medium, with the third mode offering particular suitability for high-precision sensing. As illustrated in Fig. 8(e–g), the observed linearity combined with consistently high sensitivity across all three resonances underscores the strong potential of the absorber for multi-band refractive index sensing applications. The refractive index sensing performance of the proposed structure was systematically investigated by varying the surrounding refractive index (η) from 1.0 to 2.0 in increments of 0.1, in Fig. 8 (subfigure h), maintaining the analyte thickness at 0.22 µm to simulate analyte sensing conditions. A pronounced red shift in the resonance frequencies was observed with increasing η, while the absorption intensity remained above 99%, exhibiting minimal attenuation at higher frequencies. These findings confirm the sensor’s high refractive index sensitivity and spectral stability, indicating its potential for accurate and reliable detection in variable environment.

Figure 8. (a)–(d) Frequency shifts and corresponding sensitivity evaluation with linear fitting for the three distinct absorption peaks, (d) Comparative frequency shift as a function of refractive index for all resonance modes.

Food adulteration poses a persistent global challenge, undermining product integrity, safety, and consumer trust. Honey and lactose adulteration, typically through dilution with water to lower production costs, reduces its therapeutic efficacy and depletes key enzymes such as diastases and glucose oxidase. This effect is clearly reflected in Fig. 9(a), which shows that increasing water content in honey samples (measured across 3.55–3.85 THz) leads to a downward shift in peak absorbance frequency and decreased absorbance intensity, indicating dilution of the honey matrix. Quantitative data in Table IV confirm this trend: as the refractive index decreases from 1.479 to 1.335 (corresponding to water content increasing from 37.62% to 72.05%) [41], the peak frequency shifts from 3.6720 THz to 3.7400 THz. Notably, the calculated sensitivity (GHz/RIU) rises with lower water content, reaching a maximum of 864.86 GHz/RIU at 37.62% water, highlighting the method’s potential for detecting subtle adulteration. Similarly, lactose adulteration in lactose-free or low-lactose products presents significant health risks to lactose-intolerant individuals and undermines labeling compliance, illustrating the broader need for reliable terahertz sensing techniques in food quality assurance.

The percentage of water can be calculated from the measured refractive index using the following Eq. (7).

Here, 𝑛 is the refractive index of the honey sample, and %𝑊 is the percentage of water present in the honey sample.

L = 1.3325 + 0.001384 × %L + 0.00000624 × %L² … … … … … … … (8)

Here, 𝑛 is the refractive index of the lactose solution, and %𝐿 is the percentage of lactose present in the solution.

Glucose, a fundamental monosaccharide and primary energy substrate for living organisms, is essential for maintaining metabolic homeostasis. Due to its molecular configuration, glucose exhibits distinct spectral features in the terahertz (THz) range, where the interaction of THz waves with glucose leads to characteristic absorption and refractive index (RI) variations at specific frequencies. Utilizing this property, Fig. 10(a) and Table VI present the sensor’s performance in detecting glucose by analyzing absorbance responses across varying concentrations [42]. As the glucose concentration increases from 0 to 277.5 mM, the RI correspondingly rises from 1.3391 to 1.4196, resulting in a measurable redshift of the resonance frequency from 3.7520 THz to 3.6920 THz. The sensor maintains a consistently high absorbance near 0.990, while achieving sensitivity up to 888.89 GHz/RIU, particularly at lower concentrations. These results underscore the sensor’s capability for precise glucose detection, highlighting its potential application in non-invasive and real-time monitoring for biomedical diagnostics.

In this study, a terahertz (THz) metamaterial absorber is employed to identify four common liquid fuels kerosene, octane, diesel, and petroleum [43] by analyzing their resonance-induced absorbance spectra within the 3.55–3.85 THz range, as presented in Fig. 11. Each fuel exhibits a distinct spectral signature, with resonance frequencies shifting from 3.7480 THz for kerosene (RI = 1.342) to 3.6360 THz for petroleum (RI = 1.483), reflecting a clear redshift trend associated with increasing refractive index. Sensitivity values summarized in Table VII 689.66 GHz/RIU for octane, 747.66 GHz/RIU for diesel, and 794.33 GHz/RIU for petroleum underline the absorber’s capability to detect subtle dielectric variations, while consistently high absorbance values (0.9903–0.9929) confirm its measurement reliability. These findings demonstrate the practical relevance of accurately characterizing fuel composition, which refers to the distribution and concentration of hydrocarbons, oxygenates, additives, and trace elements within a fuel. Variations in composition alter the fuel’s optical and dielectric properties, changes that can be effectively captured by the proposed absorber. Such precise detection is essential for optimizing engine performance, ensuring system compatibility, and preventing operational failures, thereby highlighting the absorber’s potential role in real-time fuel quality monitoring and control.

Industrial chemical detection involves identifying and monitoring various chemical substances used in manufacturing, processing, and environmental systems. Metamaterial absorbers offer a powerful solution by detecting changes in the chemical composition of substances through their unique electromagnetic responses. By sensing variations in refractive index and absorption characteristics, these devices enable rapid, non-destructive, and highly sensitive identification of industrial chemicals, even at trace levels.

The use of a metamaterial absorber for detecting industrial chemicals and biological samples with refractive indices ranging from 1.4 to 1.45 [44] has been explored in this study. This specific refractive index range was chosen because many widely used chemicals and biological tissues fall within this spectrum. Accurate detection within this range is essential for applications in chemical sensing, environmental safety, and biomedical diagnostics. Table VIII lists several representative materials including red blood cells (RBC), ethylene tetrafluoroethylene (ETFE), hexanol, ethylene glycol, low-grade glioma abnormal tissue, and chloroform, along with their respective refractive indices and absorbance characteristics. Simulated absorbance spectra for each sample in the 3.55–3.8 THz frequency range, shown in Fig. 12, reveal distinct resonance shifts based on the dielectric properties of the materials. Notably, chloroform with the highest RI (1.4459) exhibits the lowest resonance frequency, while RBC (RI = 1.4) shows the highest. The proposed absorber shows high sensitivity, with the maximum recorded value of 1333.33 GHz/RIU for ETFE, validating its ability to detect even small variations in material composition.

Environmental gas detection plays a critical role in monitoring and managing air quality, particularly in urban, industrial, and confined indoor environments. Gases such as carbon monoxide (CO) and nitrogen oxides (NOx) are prevalent pollutants originating from combustion engines, industrial processes, and fossil fuel-based power generation.

Table IX presents the performance metrics of a terahertz metamaterial absorber for detecting harmful gases by monitoring changes in resonance characteristics. The detection principle relies on variations in the refractive index (RI) of different gaseous environments, which induce shifts in the resonance frequency (f_r​) and affect the absorbance spectrum. Air (RI = 1) is taken as the reference, with a resonance frequency of 3.936 THz and maximum absorbance of 0.999. For harmful gases such as NO₂, CO, CH₄, CO₂, and CHCl₃, small increments in RI (ranging from 1.00028 to 1.0014) lead to measurable resonance frequency shifts (f_r​ = 3.941–3.979 THz). The corresponding full-width at half-maximum (Δf) values increase with higher RI differences, from 5 GHz (NO₂) to 43 GHz (CHCl₃). These shifts directly influence the calculated sensitivity of the absorber, which varies from 17,857.143 GHz/RIU (NO₂) to as high as 77,777.778 GHz/RIU (CO₂). The results highlight that the proposed THz metamaterial absorber demonstrates ultrahigh sensitivity and excellent resolution in discriminating between gases with very close refractive indices. Particularly, CO₂ and CH₄ exhibit the highest sensitivities, making the device promising for environmental and industrial monitoring of trace gases.

Table IX Detection of Harmful Gases and Sensors Performance

Detecting and identifying different edible oils is important for food quality control, safety, and preventing adulteration. Terahertz (THz) spectroscopy is a powerful technique that helps in this process by analyzing how oils absorb light in the THz frequency range. Each type of oil has a unique structure, so it interacts with THz waves differently and this difference can be measured and used for identification.

As shown in Fig. 14, the absorbance spectra of eight edible oils Palm, Peanut, Coconut, Soybean, Sesame, Canola, Olive, Sunflower, and Castor [46]–[48] are plotted across the 0.7–1.1 THz frequency range. Each oil displays a distinct resonance peak, with absorbance values and spectral widths varied based on their refractive indices (RI). Table X summarizes the sensor performance for each oil type. Castor oil, with the highest RI of 1.917, exhibits a resonance frequency (f_r) of 1.7840 THz and the broadest frequency shift (Δf) of 888 GHz, resulting in the highest sensitivity of 1544.35 GHz/RIU. In contrast, palm oil shows the lowest RI (1.342), a higher resonance frequency 0.8960 THz. These findings confirm that THz spectral analysis can effectively distinguish between oils with high accuracy based on their dielectric properties, offering strong potential for applications in food safety, adulteration detection, and quality assessment.

Pesticide residue refers to the trace amounts of chemical pesticides that remain on food, in soil, or in water after their application, and detecting these residues is crucial for ensuring food safety due to the serious health risks posed by prolonged exposure, such as cancer, hormonal imbalances, or neurological issues. To address this challenge, terahertz (THz) spectroscopy offers a promising approach by exploiting the unique spectral fingerprints of various pesticides. As illustrated in Fig. 15, different pesticides including Daminozide, Dicofol, Imidacloprid, and Diethyldithiocarbamate sodium salt hydrate (N, N-DTC) [49] exhibit distinct absorbance spectra within the 0.6–1.1 THz range, characterized by clear resonance shifts and intensity variations. According to Table XI, the absorber demonstrates strong performance metrics, with resonance frequency shifts (Δf) ranging from 136 GHz (Daminozide) to 208 GHz (N, N-DTC) and high sensitivities up to 200 GHz/RIU, confirming excellent detection capabilities. Notably, the N, N-DTC compound, which has the highest refractive index (RI = 2.08), shows a pronounced spectral shift and absorbance change at 0.7520 THz, indicating a strong analyte-sensor interaction.

Solid-state materials, with atoms arranged in a fixed structure at room temperature, influence terahertz (THz) metamaterial absorbers by altering their dielectric properties, particularly the refractive index. When used as substrates or placed near the absorber, these materials cause shifts in resonance frequency and absorbance levels. Figure 16 shows the absorber’s performance with substrates like AD300, AD350, AD450, Rogers RO3006, and RO3010 [50] [51]. While all achieve near-unity absorbance, resonance frequency decreases as the refractive index increases, as summarized in Table XII. Notably, Rogers RO3006 exhibits the highest sensitivity (178.52 GHz/RI), making it most effective for sensing. These frequency shifts enable reliable identification of solid-state materials.

To evaluate the performance of machine learning-based prediction of absorption behavior in terahertz metamaterial absorbers, a Random Forest regression model was implemented using parameterized unit cell simulation data for training. Each dataset corresponds to a geometric parameter and includes absorption (A) across a frequency range (F). The raw data was processed by combining all parameter-specific datasets and restructuring them into a single multivariate dataset where each row represents a frequency F, and the columns represent the corresponding unit cell parameters. The mean absorption at each frequency was calculated across available parameter combinations to form the target (Absorption). ). After training the Random Forest model, its prediction capability was validated by generating a new test set consisting of 50,000 randomly sampled parameter configurations within the original design space. The model was used to predict the absorption response for each configuration, and the top 10 designs with the highest predicted absorption were identified and saved for further evaluation and possible fabrication. In addition, quantitatively compared the predicted absorption values with the actual dataset values across the frequency range. For this purpose, the median values of each unit cell parameter were extracted for each frequency F, forming a representative input for prediction. The model then produced absorption estimates, which were directly compared against the actual absorption values from the dataset. A plot of frequency vs absorption was generated, showing both the actual absorption values (from simulations) and the predicted absorption values (from the ML model). This comparison demonstrates the model’s capability to closely approximate the physical behavior of the metamaterial across the frequency spectrum, validating its potential for simulation time reduction and intermediate value prediction.

Developing accurate absorptivity models for circular-shaped terahertz metamaterial structures typically involves resource-intensive simulation frameworks. Machine learning offers an efficient alternative by predicting absorptivity with high fidelity using learned relationships, thereby drastically reducing simulation demands. In this work, a comprehensive evaluation of seven regression models was conducted to determine their ability to produce accurate and reliable absorptivity estimations.

This methodology follows a structured pipeline:

Full-wave electromagnetic simulation (using CST Microwave Studio) produced dataset containing frequency (F) and eight geometric parameters (R1, R2, R3, T1, T2, T3, W1, W2). Features have been encoded using one-hot vectors for categorical parameters and subsequently standardized.

The following models: Decision Tree (DT), K-Nearest Neighbors (KNN), Random Forest (RF), Extra Trees (ET), Bagging Regressor (BR), XGBoost (XGB), and CatBoost (CB) have been trained with the produced dataset splitting into 80 − 20 ratio for training and testing. Their predictive performance has been assessed via Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Coefficient of Determination () metrics.

The evaluation metrics are defined as follows [52]:

where is the actual value, is the predicted value, is the mean of actual values, and is the number of samples.

Among the ML models, Random Forest achieved the highest accuracy: MAE = 0.313%, MSE = 0.005%, RMSE = 0.7054%, and = 99.9156%. KNN performed closely with MAE = 0.4107%, RMSE = 0.9426%, and = 99.8493%. Ensemble methods (ET, BR) also demonstrated strong performance. In contrast, DT, XGB, and CB trailed behind, with slightly elevated error and lower .

Scatter plots of actual vs. predicted absorption in Fig. 17. show tight clustering around the ideal reference line (red dashed), especially for RF, KNN, and ET, verifying highly accurate predictions. Parameter-wise scatter plots reveal these models maintain consistent predictive accuracy across all geometric features, highlighting their robustness. Error histograms in Fig. 17. exhibit narrow residual distributions for top models, further demonstrating prediction precision. Learning curves (for RMSE and ) in Fig. 18. show RF and ET converge rapidly with increasing training set size and exhibit low variance, signifying strong generalization. By contrast, boosting models (XGB, CB) display slower convergence and greater variance, reflecting limitations with complex nonlinear patterns in the data. The heatmap in Fig. 19 compares these seven regression models across multiple test size splits (30%-70%), illustrating their R² performance variability. Different models lead at different test sizes, suggesting no single model outperforms others universally. K-Neighbors Regressor demonstrates superior peak performance, achieving the highest R² score of 99.78% at 30% test size. XGB Regressor shows remarkable consistency with the smallest performance variance (0.0019). Overall, the heatmap reveals that model performance is influenced by data partitioning, and selecting the best model depends on the specific train-test configuration used. Figure 20 compares the performance of seven ML models using four evaluation metrics. The Random Forest model achieved the lowest errors with MAE = 0.313%, MSE = 0.005%, RMSE = 0.7054%, and the highest R² = 99.9156%. KNN followed with MAE = 0.4107%, MSE = 0.0089%, RMSE = 0.9426%, and R² = 99.8493%. Bagging recorded MAE = 0.5315%, MSE = 0.0295%, RMSE = 1.7189%, and R² = 99.4990%, while Extra Trees had MAE = 0.5311%, MSE = 0.0322%, RMSE = 1.7935%, and R² = 99.4546%. XGBoost produced MAE = 0.9833%, MSE = 0.0402%, RMSE = 2.0054%, and R² = 99.3180%. Decision Tree reported MAE = 0.5904%, MSE = 0.0531%, RMSE = 2.3038%, and R² = 99.1000%, whereas CatBoost achieved MAE = 1.1744%, MSE = 0.0559%, RMSE = 2.3642%, and R² = 99.0522%. The results clearly indicate that the Random Forest model outperformed all others, showing the highest accuracy and best generalization ability.

Figure 21 illustrates the correlation between simulated absorptivity and the values predicted by the optimized Random Forest regressor. The model predictions closely track the actual absorption profile across the frequency range of 0.5 THz to 4.5 THz, accurately capturing both the peak absorption values (~ 0.99) and intermediate variations. The near-perfect alignment of the two curves confirms the model’s ability to generalize from training data to unseen frequencies, achieving R² = 99.9156% with an RMSE of 0.7054%. This high level of agreement underscores the suitability of Random Forest for precise absorptivity prediction in metamaterial design.

A comparative summary of state-of-the-art studies is presented in Table XIII. Previous works reported strong results, with the Extra Trees Classifier achieving accuracies between 97.04% and 99.52% [2], Random Forest regressors exceeding R² >0.90 [3], and KNN reaching R² = 0.9915 [5]. In contrast, the proposed Random Forest model attained an R² = 0.999156 (99.9156%), significantly surpassing these benchmarks. This improvement can be attributed to rigorous preprocessing, parameter-specific encoding, and hyperparameter optimization, enabling the model to capture highly nonlinear parameter–frequency–absorption relationships with superior accuracy.

Future research will focus on experimentally fabricating and characterizing the proposed triple-band absorber to validate simulation results and ensure reproducibility under real-world conditions. Enhancements in geometric design and material selection will target achieving even higher sensitivity beyond 1000 GHz/RIU and improved FoM exceeding. Additionally, integration with microfluidic channels and tunable materials such as graphene or phase-change substrates could enable dynamic sensing and real-time analyte concentration tracking. Extending the sensing capability toward broader frequency bands (> 5 THz) and ultra-narrowband resonances with Q-factors above 25 may further increase detection precision. Finally, advanced machine learning models, including deep neural networks, will be explored to predict nonlinear absorption behaviors and optimize multi-parameter sensing, supporting the development of compact, intelligent, and portable THz sensing platforms for diverse industrial and biomedical applications.

In summary, the results presented in Table XIV indicate that the proposed design exhibits superior performance compared to existing works, confirming its suitability for terahertz applications, particularly in cost-effective, high-accuracy detection methods.

This work evaluated and validated a highly sensitive, polarization-insensitive, and angle-stable triple-band terahertz metamaterial absorber designed for detecting a wide range of industrial and chemical analytes. The proposed absorber achieves near-unity absorption peaks at 0.96 THz (99.918%), 2.112 THz (99.996%), and 3.94 THz (99.853%), supported by high refractive index sensitivities of 203.3 GHz/RIU, 387.3 GHz/RIU, and 771.3 GHz/RIU across the three resonant modes. Numerical and experimental analyses confirm the sensor’s near-unity absorption performance and excellent refractive index sensitivity, supported by FoM and Q-factor values that surpass many existing designs. The integration of machine learning models Random Forest, KNN, XGBoost, Bagging, Decision Tree, CatBoost, and Extra Trees for predicting absorptivity in circular-shaped terahertz metamaterial absorbers. The Random Forest Regressor demonstrated exceptional predictive performance, achieving R² = 0.999156, RMSE = 0.7054%, and MAE = 0.313%, outperforming all other approaches. In addition to delivering ultra-high accuracy, the model reduced computational time by over 85% and exhibited strong capability in predicting missing parameter values, establishing it as the most robust and scalable choice for metamaterial absorber design. This further enhances the practicality of the sensor by enabling rapid prediction of absorption spectra across varying frequencies, thereby accelerating performance. Application demonstrations including detection of food adulterants, fuel quality, pesticides, and biological materials highlight the absorber’s versatility and real-world applicability. Together, these findings establish the proposed sensor as a promising platform for non-destructive, label-free detection in industrial and biochemical sensing.