A tunable graphene terahertz sensor with high sensitivity and figure of merit for refractive index biosensing

Abstract

This study presents the design, numerical modeling, and performance analysis of a tunable graphene-based terahertz (THz) sensor exhibiting multiband resonance behavior. The proposed device leverages the unique electro-optical properties of graphene, where modulation of the chemical potential (V) enables dynamic control over the electromagnetic response. This tunability allows real-time ON/OFF operation and precise frequency reconfiguration, resulting in enhanced adaptability for diverse sensing scenarios. The sensor supports four distinct resonance modes at 0.22, 0.35, 0.70, and 0.88 THz, covering a wide portion of the THz spectrum and making it particularly suitable for multiband detection. Simulation results reveal that increasing the chemical potential shifts all resonance modes toward higher frequencies, a consequence of enhanced graphene conductivity and improved impedance matching between the sensor and the surrounding medium. This frequency agility is critical for applications where detection bands need to be dynamically selected or reconfigured. The proposed design exhibits sharp resonance dips, high spectral selectivity, and elevated sensitivity, leading to an impressive figure of merit (FOM) of up to 5.30 RIU⁻¹ across all operational modes. For a refractive index range of 1.0–1.1, the device achieves sensitivities of 0.51, 0.85, 1.87, and 0.212 THz/RIU for the first to fourth modes, respectively, all within the 0.1–1.0 THz operational window. Such performance metrics position the sensor as a promising candidate for next-generation THz biosensing, non-invasive medical imaging, and chemical or environmental detection, where rapid, reconfigurable, and label-free measurements are essential. Moreover, the multiband capability and tunable nature of the graphene platform open avenues for integrated lab-on-chip sensing systems with adaptive, high-precision operation.

Introduction

The terahertz (THz) frequency band, typically defined from 0.1 to 10 THz, has attracted growing interest in recent years due to its unique capabilities in next-generation technologies. Applications range from high-speed wireless communication and non-invasive medical diagnostics to security screening, spectroscopic analysis, and biomedical imaging^1,2. The development of reconfigurable components operating in the THz domain has become essential to support the increasing demand for adaptive, high-performance systems. Among these components, reconfigurable antennas capable of dynamically altering their operating frequency, polarization, or radiation pattern have emerged as key enablers of flexible communication and sensing platforms^3,4. Conventional switching technologies, such as PIN diodes, MEMS, and varactor diodes, offer reliable solutions at microwave frequencies but face serious challenges in the THz range. These include increased losses, impedance mismatches, limited tuning speed, and manufacturing complexity^5,6. To overcome these issues, various novel THz antenna topologies have been proposed, including Yagi-Uda, bowtie, dipole, and slot-based structures, each tailored for miniaturization and spectral efficiency^7–9. Additionally, recent advances in flexible electronics have led to compact and conformal THz antennas suitable for wearable biomedical devices, automotive radar, and wireless body area networks (WBANs)^10–13. Researchers have also explored multi-band and beam-steerable solutions by incorporating parasitic elements, switchable geometries, or metasurfaces^14,15, demonstrating the growing need for tunable, integrated solutions in the THz regime.

At the material level, graphene has emerged as a groundbreaking candidate for THz applications due to its unique electrical, optical, and plasmonic properties^16,17. Its surface conductivity can be dynamically tuned via chemical potential modulation (by electrical gating or chemical doping), enabling real-time control of the device’s electromagnetic behavior^18,19. Graphene has been employed in various configurations such as radiating patches, switches, or conductive elements in hybrid metal–graphene structures to enhance both radiation efficiency and tunability^20–24. These features have led to the development of tunable antennas and metamaterial-based structures with capabilities including beam steering, polarization control, dual-band operation, and wideband frequency agility^25–30. Furthermore, graphene-integrated sensors have demonstrated impressive performance for detecting refractive index variations in complex media, thanks to their high-Q resonances and strong field localization effects^31–35. Experimental and numerical studies have reported sensitivity values exceeding 280 GHz/RIU and figure-of-merit (FOM) values up to 20 by tuning the chemical potential from 0.1 eV to 0.6 eV^36,37. Modern sensing architectures now combine graphene with engineered metasurfaces, multilayer configurations, and hybrid biasing schemes to enable intelligent detection and imaging at terahertz frequencies^38–41. These approaches aim to maximize sensitivity, miniaturization, and reconfigurability in devices targeting biomedical, biochemical, and environmental monitoring.

In this study, we present a novel hybrid graphene–gold terahertz (THz) sensor tailored for high-performance refractive index detection. The proposed structure incorporates a compact spiral-inspired resonator integrated with chemically tunable graphene elements on a SiO₂ substrate, combining plasmonic enhancement with electrical reconfigurability. By modulating the chemical potential of graphene, the sensor achieves real-time control over its electromagnetic response, resulting in dynamic spectral tunability and distinct multi-resonant behavior within the 0.1–1.0 THz range. Unlike conventional THz sensors that rely on fixed geometries or limited tuning mechanisms, our design leverages the synergy between metallic and graphene layers to optimize both sensitivity and bandwidth. Electromagnetic simulations confirm that the sensor exhibits sharp resonance dips, high sensitivity values, and competitive FOM across multiple operating modes. Furthermore, parametric analysis of key geometrical features and material properties provides deep insights into the underlying resonance mechanisms. These findings highlight the potential of the proposed structure for integration into compact, scalable platforms for next-generation biosensing, environmental monitoring, and chemical detection applications in the terahertz regime.

Graphene sensor design

The proposed terahertz (THz) sensor is composed of a multilayer structure that integrates metallic and graphene-based elements on a dielectric SiO₂ substrate. As illustrated in Fig. 1, the sensor features a spiral-shaped gold resonator (shown in yellow) patterned on the surface of the substrate (in red), with strategically embedded graphene layers (in black) positioned between key resonant segments. A normally incident THz wave is applied from above, interacting with the patterned surface to generate multiple resonance dips within the 0.1–1 THz band. These resonances arise due to strong electromagnetic confinement and field coupling, offering the potential for frequency-selective or multispectral sensing.

Fig. 1.

Schematic illustration of the sensor configuration and physical parameters.

The detailed geometry of the sensor is provided in Fig. 2, where part (a) shows the top view of the resonator layout, including labeled design parameters such as resonator widths (W_G1, W_G2, W_G3), and inter-resonator gaps (Gap₁, Gap₂, Gap₃). These geometrical features critically influence the device’s resonant modes and coupling efficiency. The embedded graphene strips, symmetrically integrated between gold segments, act as tunable elements whose electromagnetic response can be dynamically adjusted via chemical potential modulation.

Fig. 2.

Geometry of (a) Top view with parameters and (b) Front view of the Sensor.

The numerical simulations employed unit cell boundary conditions in the periodic directions and open boundary conditions along the propagation axis. A mesh convergence study confirmed numerical stability, with frequency variations below 0.4% at the chosen mesh density of ~500,000 cells. The simulation domain size ensured minimal boundary coupling effects (<1%) through adequate spacing (≥λ/2) from the metasurface.

In our design, all results correspond to x-polarized excitation (E-field parallel to graphene strips), which maximizes plasmonic coupling and sensitivity. Under y-polarization, resonances persist but with weaker graphene contribution, reducing reflection contrast and sensitivity while maintaining frequency shifts below 5%. This polarization dependence arises from the alignment between the E-field and the primary current path in graphene. For practical applications, polarization control is essential, though polarization-insensitive designs could be realized with symmetric layouts at the cost of peak sensitivity.

Fig. 2(b) presents the cross-sectional (front) view of the sensor. The gold resonator layer, with thickness t_G, sits atop a dielectric SiO₂ layer of thickness t_S, forming a vertically stacked architecture. This configuration enables strong excitation of localized surface plasmon polaritons (SPPs) at the graphene interface, which enhances frequency selectivity and sensitivity to environmental refractive index changes.

Eigenmode and field distribution analyses clarify the physical origin of all four resonance modes (comprehensively summarized in Table 1). Mode 1 (≈0.42 THz) acts as a fundamental electric dipole resonance of the outer metallic loop. Mode 2 (≈0.66 THz) is identified as a hybridized magnetic-loop resonance, arising from near-field coupling between metallic segments. Mode 3 (≈0.88 THz) is the dominant metal-graphene hybrid plasmonic mode, characterized by strong field localization at the graphene-metal interface and a high Q-factor (≈112), establishing it as the principal sensing channel. Mode 4 (≈1.02 THz) behaves as a higher-order quadrupolar resonance with more radiative behavior.

Table 1.

Summary of the physical origin and characteristics of the four resonance modes identified through eigenmode and surface current analysis.

Mode	Frequency (THz)	Physical origin	Field/current pattern	Type of resonance	Q-factor	Remarks (sensitivity/coupling)
Mode 1	≈ 0.22	Fundamental electric dipole resonance of the outer metallic loop	In-phase surface currents, strong E-field at outer gaps	Geometric (weak plasmonic)	~68	Moderate confinement; low RI sensitivity
Mode 2	≈ 0.34	Hybridized magnetic-loop resonance from near-field coupling	Circulating currents producing localized H-field inside cavity	Partially geometric	~84	Enhanced confinement; magnetic coupling dominant
Mode 3	≈ 0.7	Metal–graphene hybrid plasmonic mode	Strong E-field at graphene–metal interface, high sheet current in graphene	Hybrid plasmonic	~112	Principal sensing mode; highest field enhancement and RI sensitivity
Mode 4	≈ 0.89	Higher-order quadrupolar/slot-like resonance	Multiple current nodes; confined to inner arms	Radiative (higher order)	~57	Broader linewidth; secondary sensing channel

Following the structural design, the electromagnetic behavior of the sensor was analyzed under varying chemical potential (V) of graphene. Simulation results confirm that increasing V significantly enhances the surface conductivity of graphene, reducing its surface resistance. This in turn improves impedance matching between the sensor and the surrounding medium, resulting in lower reflection coefficients (S₁₁) and greater energy coupling. These effects are central to achieving dynamic tunability and high-performance sensing behavior in the proposed device.

The dielectric substrate (SiO₂) has a thickness of 20 μm and relative permittivity ε_r = 3.9, backed by an optically thick gold ground plane (7 μm, modeled as perfect conductor). Additionally, all spacing parameters and periodic boundary conditions applied in the CST simulation domain have been clearly stated, enabling complete reproduction of the simulated environment. A schematic with labeled dimensions has also been added in the revised Figure 2 to visually convey the structure layout. The complete list of structural parameters used in the design and simulation of the sensor is summarized in Table 2.

Table 2.

Design parameters and their values.

Parameter	Value	Parameter	Value	Parameter	Value
WS	250 µm	Q3	15 µm	p1	5 µm
WG1	200 µm	Gap1	25 µm	p2	5 µm
WG2	120 µm	Gap2	35 µm	p3	6 µm
WG3	50 µm	Gap3	30 µm	Lgr1	23.3 µm
tG	7 µm	g1	20 µm	Lgr2	11.6 µm
ts	14 µm	g2	20 µm	Q2	18 µm
Q1	16 µm	g3	20 µm	Wgr	4 µm

The graphene surface conductivity σ(ω, μ_c, Γ, T) was calculated using the full Kubo formula, which includes both intraband and interband contributions⁴⁴:

1

where the term is defined by:

2

Here, μ_c is the graphene chemical potential (ranging from 0 to 0.8 eV in our simulations), Γ = represents the scattering rate with relaxation time τ = 0.5 ps, Γ= 2×10¹² s⁻¹, and T = 300 K denotes the ambient temperature. The frequency-dependent complex conductivity σ(ω) was implemented in the simulation tool (CST Microwave Studio) via a surface impedance boundary condition, Z_s = , which allows dynamic tuning of graphene’s optical response. In our results, the reflection spectra for μ_c values of 0.1, 0.3, 0.5, and 0.8 eV clearly show progressive blue-shifting of the resonances, consistent with the theoretical dependence ω_p ∝ . This demonstrates that the claimed tunability is fully supported by a physical and computationally consistent conductivity model. The resulting surface impedance, was calculated across the tunable chemical potential range. At 0.9 THz, the magnitude of the surface impedance decreased from approximately 420 Ω at μ_c= 0.1 eV to about 260 Ω at μ_c=0.6 eV. This reduction of nearly 40% improves the impedance matching between the metasurface and free space, leading to stronger field confinement and the observed enhancement in resonance coupling efficiency. The quantitative agreement between the calculated impedance trend and the simulated reflection spectra confirms that the tunability mechanism is governed by the gate-dependent surface conductivity of graphene.

Results and discussions

In this section, the electromagnetic performance of the proposed graphene-based terahertz sensor is analyzed based on full-wave simulation results. The study focuses on key performance indicators such as resonance behavior, field distribution, sensitivity, and tunability. By systematically varying the chemical potential of graphene and the structural parameters, the influence on the sensor’s reflection characteristics and resonance frequencies is examined. The results demonstrate the sensor’s capability to operate in multiple resonant modes with high precision and reconfigurability, making it a promising candidate for THz sensing applications. Fig. 3 presents the simulated reflection spectrum of the proposed sensor under normal incidence of a THz wave. The results clearly exhibit multiple pronounced resonance dips across the 0.1–1.0 THz frequency band. Each dip corresponds to a distinct resonant mode arising from strong coupling between the incident THz field and the resonator geometry. These minima in the reflection coefficient (|S₁₁|) indicate efficient impedance matching and effective energy transfer into the structure. The observed behavior confirms the sensor’s multiband response, which is essential for multi-analyte detection or enhanced resolution in spectroscopic and biosensing applications.

Fig. 3.

Results of reflection and absorption of sensor simulated in CST.

In this work, the absorption characteristics are derived from reflection measurements under specific boundary conditions that are standard for absorber-type configurations. The simulated structure incorporates a Perfect Electric Conductor (PEC) layer at the substrate bottom, which serves as a perfect back-reflector. This boundary condition ensures that transmission through the structure is zero (T = 0). Therefore, the power conservation equation simplifies to: A(ω) + R(ω) = 1, where A(ω) is absorption and R(ω) is reflection. The observed reflection dips in our results thus directly correspond to absorption peaks, as any reduction in reflected power necessarily indicates energy dissipation within the graphene layer and dielectric environment, primarily through ohmic losses modeled via the Kubo formalism. This approach is widely adopted in computational electromagnetics for analyzing metamaterial absorbers and graphene-based absorbing structures.

The integration of graphene plays a key role in the tunability of these resonances. By modulating the chemical potential of graphene, the position of each resonance dip can be dynamically shifted, enabling real-time reconfiguration of the sensor’s spectral characteristics. This tunable, multi-resonant behavior offers a strategic advantage for designing compact and versatile THz sensing platforms. Fig. 4 illustrates the simulated electromagnetic field distributions at resonance, highlighting both (a) magnetic field intensity (A/m) and (b) electric field intensity (V/m). In Fig. 4(a), the magnetic field is primarily confined along the inner edges of the spiral-shaped metallic resonator, indicating the formation of strong surface current loops. This localization enhances inductive coupling, which contributes to the high-Q nature of the resonant modes.

Fig. 4.

(a) Normalized Magnetic field intensity (A/m) and (b) Electric (V/m) field intensity distributions.

In Fig. 4(b), the electric field is highly concentrated in the narrow gaps between metallic segments, particularly in regions adjacent to the embedded graphene strips. This strong electric field confinement increases the sensor’s sensitivity to changes in the surrounding refractive index. Even slight variations in the dielectric environment can perturb the localized fields, resulting in measurable shifts in the resonance frequency. Fig. 4 illustrates the simulated electromagnetic field distributions at the B4 resonance (0.88 THz), highlighting both Fig. 4(a) magnetic field intensity and Fig. 4(b) Electric field intensity. The electric field demonstrates a pronounced localization, with an enhancement factor exceeding 80 relative to the incident field, concentrated in the narrow gaps adjacent to the graphene strips. Simultaneously, the magnetic field circulates strongly within the metallic loops, with an enhancement factor of approximately 40. These quantified field confinements are the primary mechanism behind the high sensitivity, as they drastically increase the light-matter interaction with the analyte and the tunable graphene elements. Despite graphene occupying less than 2% of the unit cell area, its strategic placement within these electromagnetic hotspots ensures that perturbations to the local dielectric environment or to graphene’s own conductivity result in substantial and detectable resonance shifts. Furthermore, the tunable behavior of the sensor becomes evident when the chemical potential (V) of the graphene is varied. As V increases, graphene’s surface conductivity rises, reducing its resistive loss and enhancing absorption. This results in an upward shift in resonance frequencies and a further reduction in the reflection coefficient (|S₁₁|). Conversely, at lower V values, the graphene transitions to a more resistive (OFF) state, degrading the impedance matching and increasing reflection. These findings underscore the effectiveness of chemical potential modulation as a powerful method for actively tuning the resonance behavior and overall performance of THz devices.

In summary, the field distribution profiles and reflection characteristics together validate the sensor’s ability to confine electromagnetic energy, achieve dynamic spectral tuning, and detect refractive index changes with high precision. These properties make the proposed structure a strong candidate for future THz applications, including tunable absorbers, smart filters, and compact biosensors.

To further investigate the tunability of the sensor, a parametric analysis was performed by varying the geometrical gaps between the resonator segments. The effect of these structural changes on the reflection spectrum provides valuable insight into the coupling dynamics and resonant behavior of the device. Fig. 5 illustrates the effect of changing Gap₂, which is the spacing between two adjacent metallic segments in the spiral resonator. As Gap₂ increases, a blue-shift in the resonance frequencies is observed, indicating a shift toward higher frequencies. This behavior is attributed to the weakened capacitive coupling between the metallic arms, which reduces the effective capacitance of the resonant structure. In contrast, reducing Gap₂ enhances capacitive interaction, resulting in a red-shift of the resonance and potentially sharper resonance dips. These trends suggest that Gap₂ serves as a critical tuning parameter for adjusting the spectral location and sharpness of the resonances.

Fig. 5.

Effect of Gap₂ variation on the reflection response of the sensor.

Fig. 6 shows the effect of varying Gap₁, another inter-resonator spacing in the structure. Similar to Gap₂, decreasing Gap₁ leads to stronger capacitive coupling, which shifts the resonance frequencies toward the lower end of the spectrum. Conversely, increasing Gap₁ weakens the interaction between segments, resulting in a shift toward higher frequencies. The observed spectral shifts with respect to Gap₁ demonstrate that careful control of the structural gaps can enable fine-tuning of the resonant modes, allowing the sensor to be adapted for specific detection ranges or resolution requirements.

Fig. 6.

Effect of Gap₁ variation on the reflection response of the sensor.

The electromagnetic skin depth of gold at terahertz frequencies (δ ≈ 100–200 nm at 1 THz) is much smaller than the 7 μm thickness used in our initial model. The choice of 7 μm was made purely for numerical convenience to ensure complete field confinement and to avoid artificial transmission through the metallic ground plane in CST. To address this concern, we conducted additional simulations by varying the gold thickness from 0.2 μm to 7 μm. The resulting resonance frequencies, reflection magnitudes, and Q-factors changed by less than 1.5%, confirming that the device performance is independent of metal thickness beyond ~0.3–0.5 μm. This behavior is consistent with the fact that once the metal thickness exceeds approximately five times the skin depth, further increase has negligible electromagnetic effect.

These results collectively highlight the role of geometric engineering in enhancing the performance and flexibility of the proposed THz sensor. The ability to tune resonance frequencies by simply adjusting physical parameters, in addition to electrical tuning via graphene’s chemical potential, offers a dual-mode control strategy for high-precision, application-specific sensing.

The gap-dependent analyses in Figs. 5 and 6 were conducted using discrete full-wave electromagnetic simulations. For Gap₂ variation (170–210 μm), five simulations were performed at 10 μm intervals. For Gap₁ variation (1–9 μm), five simulations were conducted at 2 μm intervals. This approach ensures computational efficiency while capturing the essential physical trends, with the observed behaviors consistent with fundamental LC resonator principles.

Precise alignment is critical as the graphene strips are positioned within the SRR gaps at the electric field maxima. Lateral misalignment (Δx) modifies the effective coupling capacitance, C_eff, and consequently the resonance frequency. Analytical estimates confirm that for a ±5 μm misalignment within standard CVD transfer tolerances, the resonance frequency detuning remains below ~5%, corresponding to a sensitivity variation of <10%. This robustness arises because the strongest fields remain confined near the gap edges. Furthermore, standard photolithography can achieve alignment accuracy better than 3 μm, ensuring the structure’s experimental feasibility.

Fig. 7 illustrates the effect of two critical parameters - the refractive index (n) of the surrounding medium and the graphene’s carrier concentration - on the sensor’s reflection response. As the refractive index increases from 1.0 to 1.1, all resonance frequencies exhibit a red-shift, demonstrating strong sensitivity to dielectric environment changes. This shift originates from enhanced interaction between the localized electric field and surrounding medium, confirming the sensor’s capability to detect subtle refractive index variations - crucial for biosensing applications. While Fig. 7 focuses on refractive index effects, the sensor’s design inherently supports electrical tunability through graphene’s carrier concentration modulation. The carrier concentration (directly related to chemical potential μ) fundamentally determines graphene’s surface conductivity and thus the resonance characteristics. These combined effects, optical tunability via refractive index and electrical tunability via chemical potential, demonstrate the powerful dual-mode reconfigurability of the proposed sensor. The graphene layer not only serves as a passive conductive material but actively contributes to dynamic frequency tuning. This makes the structure highly adaptable for real-time sensing applications where environmental and electrical parameters may change simultaneously.

Fig. 7.

Effect of the refractive index (n) of the surrounding medium on the reflection response.

In addition to sensitivity, the FOM is another critical metric in assessing sensor performance. The FOM incorporates both sensitivity and the sharpness of the resonance by dividing S by the full width at half maximum (FWHM) of the corresponding resonance dip. This is expressed in Equation (3):

3

Where, S is the sensitivity, FWHM stands for Full Width at Half Maximum of the resonance curve. FOM quantifies a sensor’s performance by balancing sensitivity and spectral resolution (FWHM). In our study, the high FOM (~5.30 RIU⁻¹) stems from combining strong sensitivity with a sharp resonance peak, outperforming conventional plasmonic sensors. This enables precise detection of tiny refractive index changes, critical for biosensing applications like early disease diagnosis. For the dominant B4 resonance (≈ 0.88 THz), the numerical results are as follows: Sensitivity S = 0.212 THz/RIU and FWHM = 0.0042 THz, resulting in an FOM of 5.30 RIU⁻¹. This high FOM arises from the hybrid metal–graphene coupling mechanism that enhances the quality factor (Q ≈ 112 for B4), leading to a sharper resonance. As shown in Table 3, the proposed sensor demonstrates relatively high and consistent FOM values across different resonance modes and refractive index conditions.

Table 3.

Calculated FOM for the proposed sensor at different resonance modes.

Resonance mode	Resonance frequency (THz)	FWHM (THz)	FOM (RIU⁻1)
B1	0.23	0.10	0.51
B2	0.35	0.07	1.21
B3	0.70	0.35	0.53
B4	0.88	0.04	5.30

A higher FOM implies a sharper and more distinct resonance peak, improving the ability to detect small changes with high resolution. It enhances the selectivity and accuracy of the sensor, minimizing errors due to noise or overlapping signals. In practical applications, especially in biomedical and chemical environments, a high FOM ensures robust and reliable performance. In the design of terahertz (THz) devices such as antennas, sensors, and absorbers, achieving a multiband response is highly desirable. A multiband structure can operate effectively at multiple distinct frequencies, which is beneficial for applications like multi-channel communication, spectroscopy, and biological sensing. In this work, we evaluate the FOM using the frequency shift (Δf) corresponding to a given change in the refractive index (Δn), over the bandwidth of the resonance. The narrower the resonance and the higher the shift, the greater the FOM, indicating better detection resolution.

FOM quantifies a sensor’s performance by balancing sensitivity and spectral resolution (FWHM). In our study, the high FOM (~5.30 RIU⁻¹) stems from combining strong sensitivity (0.212 THz/RIU) with a sharp resonance peak, outperforming conventional plasmonic sensors. This enables precise detection of tiny refractive index changes, critical for biosensing applications like early disease diagnosis.As shown in Fig. 8, the proposed sensor demonstrates relatively high and consistent FOM values across different resonance modes and refractive index conditions. This performance is primarily attributed to the strong electromagnetic field confinement achieved by the hybrid graphene–metal architecture and the sharp resonance dips resulting from precise structural optimization. A high FOM is a key indicator of the sensor’s ability to detect subtle variations with high resolution and minimal noise, which is critical in biomedical and chemical sensing scenarios where even small changes in material properties must be reliably distinguished. Sensitivity is a crucial performance metric in terahertz sensors, especially those based on graphene. It is typically defined as equation (4):

4

Fig. 8.

Calculated FOM for the proposed sensor at different resonance modes.

Where, Δf is the shift in resonance frequency, Δn is the change in the surrounding refractive index. In Table 4, this relationship is calculated for different n in different bands. FOM is a critical performance metric in sensing systems, defined as the ratio of sensitivity (Δf/Δn) to the full width at half maximum (FWHM) of the resonance curve. It quantifies the resolution and selectivity of the sensor, where higher values indicate sharper and more distinguishable resonance peaks.

Table 4.

Sensitivity calculations performed for different refractive index (n).

n	1.1	1.2	1.3	1.4	1.5
	0.051	0.064	0.054	0.057	0.056
	0.085	0.102	0.088	0.093	0.092
	0.187	0.225	0.178	0.193	0.188
	0.212	0.225	0.215	0.210	0.209

The B4 resonance (≈0.88 THz) maintains consistently high sensitivity across the refractive index range (Table 3), resulting from its hybrid plasmonic characteristics. Modal analysis (Table 4) confirms strong field confinement at graphene-metal interfaces, where intense electric field localization within the sensing volume maximizes analyte interaction and resonance perturbation per Δn. The spiral geometry and graphene jointly suppress radiative losses, preserving a high Q-factor despite its higher-order nature. As the mode’s energy remains concentrated in the analyte-sensitive region, its effective mode volume and field distribution show minimal variation with changing refractive index, explaining the observed sensitivity stability.

As shown in Table 4, the sensitivity calculations were performed across five refractive index ranges (n=1.1 to n=1.5). The results reveal a non-uniform sensitivity response to refractive index changes. The maximum sensitivity (0.064) occurs in the n=1.1 to 1.2 range, while higher Δn ranges (1.3–1.5.3.5) show slightly reduced sensitivity (0.054–0.056.054.056). This suggests optimal performance for detecting small refractive index variations (Δn ≈ 0.1), with decreasing effectiveness at larger Δn values. The observed peak sensitivity at n = 1.2 stems from optimal hybrid plasmonic coupling in the graphene-metal system. The resonance frequency follows f_res​∝ , where L_eff is the effective inductance, C_m the metallic capacitance, and where the dielectric-dependent capacitance C_g(n) increases with the refractive index. Initially, this enhances field confinement and sensitivity, but beyond n≈ 1.2, excessive field penetration into the dielectric reduces plasmonic coupling. At lower n, metallic behavior dominates with weaker sensitivity, while at higher n, field leakage diminishes the response. This non-monotonic trend reflects a known physical balance in hybrid resonances between field confinement and dielectric loading, rather than a simulation artifact. The observed nonlinearity likely stems from graphene’s plasmonic interactions with the terahertz field. These findings emphasize the importance of operational range optimization for practical biosensing applications.

The observed narrow resonance linewidth (FWHM ≈ 4.5 GHz) is a direct consequence of hybrid plasmonic coupling in the graphene-metal system. This coupling enhances field confinement, increasing the effective inductance (L_eff), while graphene’s tunable conductivity reduces radiative losses, effectively lowering the equivalent resistance (R_eff). The resulting high quality factor (Q = = where R_eff and L_eff represent the equivalent resistance and inductance of the coupled graphene–metal resonant) leads to the substantial FOM values reported. Such narrow linewidths are consistent with established findings in graphene-based hybrid metasurfaces and confirm the physical plausibility of our sensing performance.

High sensitivity means the sensor can detect very small changes in the environment (e.g., slight variations in concentration or refractive index), resulting in a significant shift in the resonance frequency.

Although our Table 4 uses Δn = 0.1 RIU steps to quantify the overall sensitivity trend (S = 0.212 THz/RIU), the claim that the sensor can detect smaller changes (Δn = 0.01–0.05 RIU) relies on the resonance center frequency resolution, rather than the coarse simulation step. In resonance-based THz sensing, the minimum resolvable frequency shift is determined by how precisely the resonance position (f₀) can be identified, which can be significantly smaller than the FWHM. By fitting the resonance profile to a Lorentzian or Fano function, the resonance center can typically be extracted with uncertainty much less than the linewidth (sub-GHz), even if FWHM ≈ 4.5 GHz. This allows Δn ≈ 0.01 RIU to produce a detectable frequency shift of ~2.25 GHz, well above the measurement uncertainty. This principle is consistent with the physics of high-Q plasmonic resonators: the sharp electric-field confinement provided by the hybrid graphene–metal structure ensures a smooth, well-defined resonance that enables sub-linewidth frequency discrimination. The relationship between detectable RI variation Δn and resonance shift Δf can be expressed as: Δf_min​= S × Δn_min​, Δn_min​ = ​​, where S is the sensitivity (THz/RIU) and Δf_min is the minimum resolvable frequency shift, set by the resonance fitting precision and the experimental signal-to-noise ratio (SNR). For our sensor, a Δf_min of 2–3 GHz corresponds to Δn_min ≈ 0.01–0.015 RIU, demonstrating that small RI changes are physically distinguishable from noise, even without reducing the FWHM. Finally, modern THz measurement instruments, such as vector network analyzers or time-domain spectroscopy systems, routinely achieve frequency resolution below 1 MHz, far finer than both the FWHM and the required Δf_min. Therefore, the claimed detection limit of Δn = 0.01–0.05 RIU is experimentally feasible, determined by resonance fitting and noise considerations rather than simulation step size, making the sensor practically suitable for biomedical applications such as cancer or virus detection. This is highly desirable for applications in biosensing and chemical detection. Low sensitivity indicates a weaker response to environmental changes, limiting the sensor’s effectiveness in high-precision tasks. Thus, higher sensitivity translates directly to better detection accuracy and resolution, making it a key parameter for evaluating the quality of a THz sensor. Finally, Fig. 9 provides an overview of the calculated sensitivity values (S) for each resonance mode. It can be observed that the sensor demonstrates a linear and stable increase in sensitivity with higher frequency modes, making it suitable for multi-band, high-precision refractive index sensing. The integration of tunable graphene ensures that these characteristics can be dynamically adjusted based on the operational requirements, offering reconfigurability and adaptability not commonly found in traditional fixed-geometry sensors. These results collectively validate the effectiveness of the proposed design in delivering high sensitivity, tunability, and resolution, three critical requirements for biosensing, chemical detection, and real-time environmental monitoring in the terahertz regime.

Fig. 9.

Sensitivity (S) of the sensor at different resonance modes.

Table 5 provides a comparative overview of the proposed sensor alongside several recently reported terahertz (THz) designs, focusing on material composition, structure, footprint, and sensitivity (S). A critical analysis of these references highlights the distinct advantages of our approach. While many prior studies employed geometries such as split-ring resonators (SRRs), I-shaped structures, or hole-type metasurfaces, most suffer from limited sensitivity or large device footprints. For example, the sensors in^42,43, and⁴⁸ achieve sensitivities below 0.3 THz/RIU despite utilizing hybrid material systems. Similarly, the compact designs in^46–51 are not suitable for high-precision sensing due to inadequate sensitivity levels. Although certain high-performance designs like⁴⁴ and⁵³ report impressive sensitivities (e.g., 2.372 and 3.963 THz/RIU), they often rely on complex geometries or extremely small footprints, making fabrication difficult and scalability impractical for real-world deployment. In contrast, our sensor achieves a balanced performance, offering a sensitivity of 0.212 THz/RIU and a moderate footprint of 250 × 250 µm. This balance ensures manufacturability, scalability, and adequate performance for practical applications. The integration of graphene with gold and SiO₂ enables real-time tunability through chemical potential modulation, an advantage not widely leveraged in previous designs. Moreover, the use of a straightforward SRR-based geometry simplifies fabrication while maintaining multi-band operation and high field confinement. To assess biosensing potential, realistic refractive index (RI) values associated with biological analytes were considered. Typical RI values for healthy tissues range from 1.33 to 1.55⁵⁵, with normal cells around n ≈ 1.368 and cancerous cells reaching up to n ≈ 1.401⁵⁶. For viral detection, the effective RI of SARS-CoV-2 has been reported as 1.2566, with RNA and membrane protein components exhibiting indices of approximately 1.5468 and 1.46 ± 0.006, respectively⁵⁷. Given the sensor’s demonstrated sensitivity, it is capable of detecting RI variations as small as 0.01–0.05 RIU. This level of performance supports its applicability in identifying pathological tissue changes and viral presence, confirming its suitability for advanced biosensing and diagnostic systems. To explicitly validate the sensor’s performance for biomedical applications, its response was also examined within the biologically critical refractive index range of 1.3 to 1.5, which encompasses values for blood plasma, cells, and viral particles^55–57. The sensitivity within this specific window remained consistently high, at approximately 0.212 THz/RIU for the B4 mode, confirming the device’s direct applicability for detecting relevant biological analytes.

Table 5.

Comparison of the reported design with other works.

References	Materials	Design	Footprint	S (THz/RIU)	FOM (RIU⁻1)	Bands/tunability
42	Metal, graphene	SRR	188μm× 188μm	0.282	4.5	Single/Electrically Tunable
43	Silicon dioxide, gold	I Shape	180μm× 180μm	0.105	2.8	Single/Not Tunable
44	Gold, silicon dioxide, graphene	Hole	4.8μm× 4.8μm	2.372	9.2	Single/Electrically Tunable
45	Gold, gallium arsenide	CRR	102μm× 102μm	1.447	4.1	Single/Not Tunable
46	Aluminum, silicon	SRR	96μm× 96μm	0.076	2.1	Single/Not Tunable
47	Aluminum, silicon	SRR	60μm× 60μm	0.085	3.8	Quad-band/Not Tunable
48	Gold, silicon dioxide	Strip and SRR	144μm× 144μm	0.135	4.2	Dual-band/Not Tunable
49	Gold, Polydimethylsi--loxane (PDMS)	SRR	370μm× 370μm	0.0294	1.5	Single/Not Tunable
50	Silicon dioxide,Indium antimonide	H Shape	400μm× 400μm	0.264	3.5	Single/Thermally Tunable
51	Aluminum	SCR	200μm× 200μm	0.214	3.1	Single/Not Tunable
52	Gold, silicon dioxide	RCR	37μm× 74μm	0.420	8.3	Single/Not Tunable
53	Cyclic olefin copolymer, gold	CSRR	200μm× 200μm	3.963	16.5	Single/Not Tunable
54	Gold, silicon dioxide	SRR	200μm× 200μm	0.23	2.8	Dual-band/Not Tunable
This work	Gold, Sio2, Graphene	SRR	250μm× 250μm	0.212	5.3	Quad-band/Electrically Tunable

While state-of-the-art sensitivities often rely on complex nanogap structures requiring sub-100 nm fabrication tolerances^44,53, the present design prioritizes manufacturability and tunability. The key differentiator is not the minimum feature size per se, but the orders-of-magnitude larger alignment tolerances and the single-layer fabrication process, making this design particularly suited for scalable and reproducible production. The electrostatic tunability of our device, achieved through a simple gating architecture, offers a practical advantage over some multi-resonant fixed-frequency designs^58,59, while the multi-band operation aligns with the trend towards versatile THz components as seen in recent absorber designs⁶¹.

While other designs achieve higher sensitivity using sub-micrometer nanogaps (<0.5 μm) requiring e-beam lithography, our sensor prioritizes manufacturability through larger resonator gaps (25–35 μm) compatible with standard photolithography (±5 μm tolerance). The single-layer graphene-metal structure eliminates complex multilayer stacking, ensuring reproducibility. Our reported sensitivity of 0.212 THz/RIU therefore represents a practical trade-off between performance and scalable fabrication for real-world applications.

The refractive index (RI) range of 1.0–1.5 was chosen to demonstrate the sensor’s versatility across both realistic and hypothetical analytes. This range covers biologically relevant materials including blood, plasma (RI ≈ 1.33–1.55.33.55), viruses, and proteins (RI ≈ 1.25–1.55.25.55), while the extended lower end (down to 1.0) enables benchmarking of low-index analytes and future applications. The selected range ensures robust performance across diverse sensing scenarios without compromising sensitivity or FOM, highlighting the sensor’s adaptability beyond conventional biological detection.

The proposed sensor is designed for experimental feasibility. The structure can be fabricated using standard processes: patterning gold resonators on a high-resistivity Si substrate via lithography, followed by the transfer and etching of CVD graphene. Tunability can be achieved using a dielectric or ion-gel gate. While challenges like uniform graphene transfer and precise alignment exist, they are addressable with current technology, making the design experimentally viable for future fabrication and characterization.

The sensor demonstrates direct applicability to practical biosensing scenarios including glucose detection in blood plasma (RI: 1.33–1.35.33.35) and viral particle detection in cellular environments (RI: 1.35–1.50.35.50). The high-Q B4 resonance provides sharp frequency shifts capable of resolving small refractive index variations (Δn≈ 0.01–0.05.01.05 RIU) relevant to physiological changes. Multi-band operation enables simultaneous monitoring of multiple spectral channels for analyte discrimination, while graphene-based electrical tuning (μ_c= 0.1–0.6.1.6 eV) offers dynamic optimization for specific biomarker detection. This combination of features ensures the sensor’s experimental relevance for diverse biochemical sensing applications.

To isolate graphene’s role, a control structure with gold strips (no graphene) was simulated. This reference showed no measurable resonance shift (<1 GHz), confirming the observed tunability is solely due to graphene. In contrast, the graphene-gold hybrid exhibited a pronounced^50–60 GHz blue-shift for the B4 mode when the chemical potential was increased from 0.1 eV to 0.6 eV. This shift, constituting 22–27% of the resonance linewidth, enables robust dynamic control. The significant impact from the minimal graphene coverage (<2% of the unit cell) results from its strategic placement within regions of maximum electric field intensity, where it efficiently perturbs the electromagnetic energy distribution and the resonant mode’s effective impedance.

Fabrication imperfections, graphene quality, and substrate variations mainly affect the sensitivity and FOM by altering field confinement and increasing losses. Misalignment, reduced graphene coverage, or rough edges slightly lower the near-field overlap with the analyte, modestly reducing sensitivity. Substrate inhomogeneity can shift resonance frequencies but has limited effect on S. The FOM is more sensitive to additional losses and FWHM increases with dissipated power. Lower-quality graphene increases resistive loss and broadens the resonance, while metal roughness and lossy substrates also reduce Q and FOM. These effects can be mitigated with standard fabrication strategies: using high-quality graphene, low-loss substrates, precise alignment, smooth metal deposition, and thin dielectric or ion-gel gating. For practical electrostatic gating, the thick SiO₂ substrate is supplemented with a thin high-κ dielectric (e.g., 20 nm HfO₂) or an ion-gel layer. This enables efficient modulation of the graphene chemical potential up to μc = 0.6 eV with applied voltages below 5 V, in contrast to the >1000 V required through the SiO₂ substrate alone. Two feasible architectures are proposed: a back-gate with thin high-κ oxide or a top-gate/ion-gel configuration, both compatible with standard device fabrication.

SiO₂ exhibits a small but finite loss tangent (tan δ ≈ 0.001–0.01) at THz frequencies, which contributes to damping of resonances. The total quality factor can be approximated as equation (5)⁴²:

5

where For typical parameters, this yields a dielectric-limited Q ≈ 250, reducing the overall resonator Q from ~120 (lossless case) to ~105, a modest degradation that preserves the high-Q nature of the hybrid modes. The resonance frequency shifts by less than 0.3%, confirming that substrate losses slightly reduce reflection amplitude but do not compromise tuning capability or sensing sensitivity, as energy dissipation remains dominated by the graphene and metallic components.

The graphene chemical potential (μ_c) was varied from 0.1 eV to 0.8 eV to demonstrate electrical tunability. The OFF state (low conductivity) corresponds to μ_c= 0.1 eV, while the ON state (high conductivity) is defined at μ_c= 0.6 eV. These values align with experimentally achievable ranges using back-gating with high-κ dielectrics (e.g., 20 nm HfO₂ requiring <10 V bias for μ_c = 0.6 eV) or ion-gel gating, ensuring practical feasibility while maintaining significant modulation contrast.

The practical sensing performance of the proposed device is influenced by ohmic losses and environmental noise. In the hybrid graphene-gold structure, losses originate primarily from the finite conductivity of graphene, especially at lower chemical potentials (μ_c ≈ 0.1–0.2 eV) where its higher sheet resistance leads to broader resonance linewidths. As μc increases, graphene’s conductivity improves, sharpening the resonances and enhancing the figure of merit. While the gold metasurface contributes to background loss, its impact remains relatively constant across the tuning range. Regarding detection limits, environmental noise, including thermal and instrumental fluctuations, sets the minimum resolvable frequency shift. However, with a typical signal-to-noise ratio >30 dB and a resonance linewidth (FWHM) of approximately 4.5 GHz for the B4 mode, a frequency shift of about 2 GHz, corresponding to a refractive index change of Δn = 0.01 RIU, can be reliably detected using standard resonance fitting techniques. This confirms the sensor’s robustness and practical utility under real-world operating conditions.

Graphene’s absorption dominates the power dissipation, particularly at low chemical potentials (μc) where its resistive losses are high. The absorbed power follows P_abs,gr = Re() | A (where σ is the graphene surface conductivity, E_gr is the local electric field at the graphene, and A is the graphene área), leading to broader resonances and lower quality factors (Q). As μ_c increases, graphene becomes more conductive, reducing its absorption share and sharpening the resonances. This tunable loss mechanism, quantified by the evolution of the Q-factor (Q= ω ​), allows the sensor to balance between high sensitivity (at low μ_c) and high spectral resolution (at high μ_c). Furthermore, the blue-shift in resonance with increasing μc enhances the refractive index sensitivity (S= ​​) by strengthening the field confinement at the graphene-dielectric interface, without compromising the detection capability.

The proposed sensor is highly adaptable for complex biosensing. Its linear response to refractive index change enables precise concentration monitoring of specific biomarkers. Furthermore, the distinct multi-resonant spectrum allows for multi-analyte discrimination by functionalizing different sensor regions or analyzing unique spectral shift patterns for different biomolecules.

Our tunable graphene-metal hybrid sensor advances the growing field of functional terahertz metasurfaces. Recent research demonstrates several key directions: ultra-wideband polarization converters with integrated biosensing^62,71, hybrid 2D material sensors for cancer and disease biomarkers^{63,65,66,68,70}, and machine learning-enhanced detection platforms^63,69,71,72. Further innovations include specialized configurations like metamaterial-clad fibers⁶⁴ and electrochemical sensors for non-invasive monitoring⁶⁷. Furthermore, developments in graphene metasurface lenses⁷³ and tunable multi-beam antennas⁷⁴ highlight the expanding capabilities of reconfigurable THz devices, while advances in additive manufacturing of metasurfaces⁷⁵ offer new fabrication pathways. Our design synthesizes elements from these approaches, offering multi-resonant operation, straightforward graphene-based tunability, and a fabrication-friendly geometry, while maintaining focus on practical refractive index sensing applications.

Conclusion

In this study, a tunable graphene–gold terahertz (THz) sensor was designed and analyzed for high-performance refractive index sensing. The proposed structure demonstrates multi-band resonance behavior within the 0.1–1.0 THz range, enabled by a spiral resonator with embedded graphene strips on a SiO₂ substrate. By modulating the chemical potential of graphene, the sensor achieves real-time spectral reconfigurability, with sensitivity values reaching up to 0.212 THz/RIU and figure-of-merit (FOM) values confirming high-resolution performance. Such characteristics make the device well-suited for a range of practical applications. In biosensing, the sensor can detect small dielectric changes associated with biomolecules, pathogens, or variations in body fluids, making it ideal for early-stage diagnostics such as cancer detection or viral identification. Its high field confinement and spectral precision also make it applicable in THz imaging and non-invasive medical analysis. Furthermore, the sensor’s ability to detect materials based on their spectral signatures highlights its usefulness in chemical detection and material characterization, particularly in environmental monitoring and security screening. Simulation results and performance evaluations confirm that varying the chemical potential of graphene leads to measurable shifts in resonance frequencies and reflection coefficients, reinforcing the concept of electrical tunability. The compact footprint, fabrication-friendly geometry, and dynamic response of the proposed design support its integration into real-world THz sensing platforms, particularly in scenarios where adaptability, miniaturization, and sensitivity are critical.

Author contributions

MA:Conceptualization, methodology, formal analysis, writing – original draft, review, and editing. AHA, AE:Methodology, formal analysis, software, Validation,writing – review. HH: Visualization, writing – review, and editing. 

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Conflicts of interest

The authors declare no competing interests.