A dual-tunable terahertz absorber using graphene-ZnO-VO 2 hybrid structure for quad-band absorption, broadband-narrowband switching, and refractive-index sensing

1 Introduction

1.1 Terahertz absorbers and their applications

Terahertz (THz) technology has emerged as a rapidly growing research field because of its unique spectral position between the microwave and infrared regions of the electromagnetic spectrum. THz waves exhibit several advantageous properties, including non-ionizing radiation, high spectral resolution, and strong interaction with molecular vibrations and dielectric properties, making them highly suitable for sensing, imaging, and biosensing applications (Wei et al., 2025; Zhang et al., 2024). Consequently, THz technology has been extensively investigated for biomedical diagnostics, environmental monitoring, chemical detection, and security screening (Wang X. et al., 2022). However, conventional THz sensing systems suffer from weak light-matter interactions and low sensitivity because THz wavelengths are considerably larger than nanoscale analytes (Zhou et al., 2025; Soltani Zanjani and Sadrnia, 2024). To overcome these limitations, metamaterials (MMs) composed of artificially engineered subwavelength resonators have been extensively explored because of their ability to localize electromagnetic fields, manipulate wave propagation, and significantly enhance light-matter interactions and absorption performance (Yin et al., 2022).

Metamaterial absorbers have attracted considerable research interest owing to their ability to achieve near-unity absorption through engineered subwavelength resonances and impedance matching, enabling applications in terahertz sensing, imaging, wireless communications, energy harvesting, and photonic devices (Asif et al., 2025; Munir et al., 2026; Asif et al., 2026). Their unique electromagnetic characteristics, including strong field confinement, spectral selectivity, and impedance matching, have established THz metamaterial absorbers as promising platforms for high-performance sensing, filtering, modulation, and reconfigurable photonic systems (Upender and Kumar, 2023; Chen et al., 2024; Karthikeyan et al., 2022; Banerjee et al., 2023). Among these applications, refractive-index sensing has received particular attention because localized electromagnetic fields substantially enhance the interaction between THz waves and the surrounding analytes, resulting in improved sensing sensitivity. These absorbers detect variations in the resonance frequency, absorption amplitude, and phase response caused by changes in the refractive index or dielectric constant of the analytes (Karthikeyan et al., 2022). Recent advancements in resonance engineering and dielectric metasurfaces have further improved the sensing sensitivity, quality factor (Q-factor), and figure of merit (FOM), where narrowband absorbers provide high sensitivity, whereas multiband absorbers enhance the sensing selectivity through multiple resonances (Banerjee et al., 2023; Khodadadi et al., 2025; Samy et al., 2023).

Recently, actively tunable terahertz metasurfaces have attracted significant attention because they enable the dynamic control of the amplitude, phase, polarization, and spectral characteristics. These capabilities are essential for realizing adaptive optical devices, beam steering, optical switching, dynamic filtering, and next-generation sensing platforms. By integrating tunable functional materials into metamaterial architectures, the electromagnetic response can be actively manipulated, thereby enabling multifunctional and reconfigurable THz devices with enhanced operational flexibility.

Graphene has emerged as one of the most promising tunable materials for THz metamaterials because of its exceptional electrical conductivity, ultrahigh carrier mobility, and electrically controllable plasmonic properties (Zakir et al., 2022). The conductivity and chemical potential of graphene can be dynamically tuned using an external bias voltage or chemical doping, allowing for adaptive resonance control and reconfigurable device operation (Upender and Yadav, 2025). Consequently, graphene-based resonator configurations, including nanoribbons, meta-rings, and maze-shaped structures, have demonstrated excellent absorption efficiency, polarization insensitivity, and wide-angle stability (Miah et al., 2025; Verma and Meena, 2024; Fu et al., 2024). Furthermore, hybrid material platforms based on graphene, such as bulk Dirac semimetals and MoS₂/graphene heterostructures, have been investigated to further improve their tunability and sensing performance (Squires et al., 2022; Wei et al., 2022).

Among various phase-change materials, vanadium dioxide (VO₂) has attracted considerable interest because of its reversible insulator-to-metal phase transition, which enables the dynamic modulation of electromagnetic responses (Li et al., 2023). The conductivity of VO₂ can be significantly altered by thermal, optical, or electrical excitation, providing an effective mechanism for actively tuning THz absorbers and sensors (Lu et al., 2023). Consequently, graphene/VO₂ hybrid metamaterial structures have emerged as attractive candidates for tunable absorbers, polarization-insensitive devices, and multifunctional sensing applications (Cheng et al., 2022; Kumar and Varshney, 2023; Zhou et al., 2021). Previous studies have demonstrated that VO₂-assisted absorbers can realize broadband, narrowband, and switchable THz absorption characteristics through conductivity modulation and phase-transition behavior (Feng et al., 2021; Cyrus and Biabanifard, 2021; Liu et al., 2024). Recently, graphene-based metamaterial absorbers and graphene/VO₂ hybrid structures have demonstrated actively tunable absorption characteristics, broadband-to-multiband switching, polarization-insensitive operation, and enhanced sensing performance through the combined effects of electrical and phase-change modulation (Munir et al., 2026; Asif et al., 2026; Asif et al., 2024; Ahsan et al., 2025). In addition, multifunctional THz metasurfaces incorporating dual-tunable materials have been reported for dynamic resonance tuning, refractive index sensing, and switchable electromagnetic responses, highlighting their considerable potential for adaptive THz photonic systems (Asif et al., 2025; Munir et al., 2026; Asif et al., 2026; Asif et al., 2024; Ahsan et al., 2025).

Despite these significant advances, several challenges remain, including water absorption losses, fabrication complexity, limited multifunctionality, restricted tunability, and difficulties associated with large-scale device integration (Barzegar-Parizi et al., 2024; Wang G. et al., 2022). Although remarkable progress has been achieved in graphene-based absorbers, VO₂-assisted phase-change devices, and hybrid metasurfaces, the simultaneous realization of broadband-to-narrowband switching, high absorption efficiency, excellent sensing performance, polarization stability, and compact multilayer implementation within a single platform remains a significant challenge. Consequently, current research efforts are directed toward the development of compact, highly efficient, tunable, and multifunctional THz absorbers capable of providing dynamic electromagnetic control and stable performance (Liu et al., 2021). Continuous advancements in metamaterial engineering, graphene plasmonics, and VO₂ phase-change materials are expected to further enhance the performance of THz absorbers for sensing, imaging, filtering, modulation, and reconfigurable photonic applications (Gong et al., 2022; Zhang and Song, 2020).

To identify the current research trends and existing limitations of graphene- and VO₂-based terahertz metamaterial absorbers, Table 1 summarizes representative studies reported in the literature. The comparison shows that graphene, VO₂, and graphene-VO₂ based absorbers have been extensively investigated for tunable absorption, switching, multiband operation, and sensing applications. However, most reported designs primarily emphasize individual functionalities rather than integrating multiple reconfigurable capabilities within a single absorber platform. Only a limited number of studies simultaneously investigate dual tunability, broadband-narrowband switching, refractive-index sensing, polarization-insensitive operation, wide-angle stability, and the underlying electromagnetic resonance mechanisms. These observations reveal the need for multifunctional and highly reconfigurable THz absorbers capable of integrating these capabilities within a unified platform. Motivated by this research gap, the present work proposes a compact graphene-ZnO-VO₂ absorber that integrates quad-band high-efficiency absorption, dual tunability, broadband-narrowband switching, refractive-index sensing, and a comprehensive investigation of the underlying resonance mechanisms.

TABLE 1. Comparison of recent graphene- and VO₂-based THz absorbers.

1.2 Graphene-based tunable THz devices

Graphene has emerged as one of the most promising materials for terahertz (THz) absorbers and metamaterial devices owing to its exceptional electrical conductivity, high carrier mobility, and electrically tunable plasmonic response. Unlike conventional metallic resonators, graphene enables the dynamic control of resonance characteristics by modulating its chemical potential and surface conductivity. These unique properties allow graphene-based absorbers to achieve high absorption efficiency, broadband operation, polarization insensitivity, and active tunability, making them attractive for next-generation THz sensing, filtering, modulation, and reconfigurable photonic applications (Zakir et al., 2022; Upender and Yadav, 2025; Miah et al., 2025; Verma and Meena, 2024).

Several graphene-based absorbers have demonstrated broadband absorption, multiband operation, and active tunability through Fermi-level engineering, external biasing, and chemical doping (Zakir et al., 2022; Upender and Yadav, 2025; Miah et al., 2025; Verma and Meena, 2024; Fu et al., 2024; Squires et al., 2022). By dynamically controlling the conductivity of graphene, the resonance frequency, absorption intensity, and spectral response can be effectively tuned, enabling adaptive and reconfigurable THz devices. Various resonator geometries, including graphene nanoribbons, meta-rings, slotted structures, and hybrid metasurfaces, have been employed to enhance plasmonic coupling, electromagnetic confinement, and impedance matching, resulting in absorption levels exceeding 90% over wide frequency ranges while maintaining polarization-insensitive performance (Miah et al., 2025; Verma and Meena, 2024; Fu et al., 2024; Squires et al., 2022).

In addition to broadband operation, graphene nanostructures have enabled the realization of multiband THz absorbers with independently controllable resonance modes (Wei et al., 2022; Li et al., 2023). By carefully engineering the resonator geometry and graphene conductivity, multiple absorption bands can be generated within a compact footprint, improving the spectral selectivity and multifunctionality. Such multiband absorbers are particularly attractive for sensing, filtering, frequency-selective surfaces, and integrated photonics applications. Recent studies have also demonstrated that graphene-based resonators can provide enhanced quality factors, strong field localization, and improved sensitivity, making them suitable candidates for THz-sensing platforms (Wei et al., 2022; Li et al., 2023).

To further enhance tunability and multifunctionality, hybrid graphene-based architectures incorporating phase-change materials have attracted increasing attention (Lu et al., 2023; Cheng et al., 2022). In particular, graphene-VO₂ hybrid absorbers combine electrically tunable plasmonic resonances with conductivity-controlled phase-transition behavior, enabling the dynamic manipulation of absorptance, reflectance, and transmittance. Such hybrid structures provide a promising route for multifunctional THz devices capable of switching, modulation, sensing, and adaptive electromagnetic control (Lu et al., 2023; Cheng et al., 2022). A high-performance metamaterial absorber exhibiting enhanced field confinement, resonance tunability, and sensing capability was demonstrated, highlighting the potential of such structures for advanced terahertz sensing, and filtering applications (Liu et al., 2021; Tamrakar et al., 2026; Tamrakar et al., 2025; Patel et al., 2025).

Despite these advances, most graphene-based absorbers primarily focus on broadband absorption, multiband operation, or sensing functionality. The simultaneous realization of high absorption efficiency, dual tunability, broadband-narrowband switching capability, polarization-insensitive behavior, wide-angle stability, and sensing performance within a single compact platform remains challenging. Consequently, graphene-VO₂ hybrid architectures have emerged as promising candidates for the development of highly reconfigurable and multifunctional THz absorbers.

1.3 VO₂-assisted tunable absorbers

VO₂ and graphene-based absorbers have gained significant attention for tunable terahertz (THz) applications owing to their strong electromagnetic modulation capabilities and reconfigurable material properties. While graphene provides electrically tunable plasmonic resonances through chemical potential modulation, VO₂ enables dynamic control of absorption through its reversible insulator-to-metal phase transition (Zakir et al., 2022; Fu et al., 2024; Squires et al., 2022; Wei et al., 2022; Li et al., 2023; Lu et al., 2023; Cheng et al., 2022). During this transition, the electrical conductivity of VO₂ changes by several orders of magnitude, resulting in substantial variations in the resonance frequency, absorption bandwidth, impedance matching, and electromagnetic energy confinement.

Several studies have demonstrated that VO₂-assisted metamaterial absorbers can achieve dynamically tunable absorption, switchable resonance characteristics, and broadband-narrowband operation through conductivity modulation (Fu et al., 2024; Li et al., 2023; Lu et al., 2023; Cheng et al., 2022). By exploiting the transition between insulating and metallic states, these absorbers provide adaptive control of electromagnetic responses and enhanced operational flexibility. In particular, hybrid graphene-VO₂ structures have attracted increasing attention because they combine the electrically tunable plasmonic properties of graphene with the phase-transition-assisted tunability of VO₂, enabling multifunctional THz devices with improved spectral reconfigurability and switching performance (Li et al., 2023; Lu et al., 2023; Cheng et al., 2022).

Recent research has focused on improving the bandwidth, tunability, compactness, and multifunctionality of VO₂ by integrating it with advanced metamaterials and plasmonic structures. The conductivity variation of VO₂ across its phase transition provides a unique opportunity to investigate both metallic-state resonance mechanisms and insulating-state tunability within a single absorber platform. Consequently, graphene-VO₂ hybrid absorbers have emerged as promising candidates for THz modulation, filtering, sensing, optical switching, and reconfigurable photonic applications.

1.4 Research gap

Although graphene, VO₂, and graphene-VO₂ based terahertz absorbers have been extensively investigated for tunable absorption, switching, multiband operation, and sensing applications, several challenges remain to be addressed. Most reported absorbers primarily employ either graphene-based electrical tuning or VO₂-based phase-transition tuning, which limits the achievable level of spectral reconfigurability and multifunctional performance. Furthermore, many existing designs focus on broadband absorption, switching behavior, or sensing performance separately without systematically investigating the combined influence of resonator geometry, dielectric optimization, graphene relaxation time, graphene chemical potential, and VO₂ conductivity variation on the absorber performance.

While hybrid graphene-VO₂ absorbers have demonstrated promising tunability, the underlying resonance mechanisms associated with different conductivity states of VO₂ remain largely unexplored. In particular, comprehensive analyses of electric-field confinement, magnetic-field localization, and power-loss distribution under different VO₂ conductivity states have rarely been reported. Moreover, the simultaneous realization of dual tunability, quad-band high-efficiency absorption, broadband-narrowband switching, refractive-index sensing, polarization-insensitive operation, and wide-angle stability within a single compact absorber platform remains a significant challenge.

Therefore, there remains a need for a compact graphene-ZnO-VO₂ terahertz absorber that integrates dual tunability, quad-band high-efficiency absorption, broadband-narrowband switching, refractive-index sensing, and comprehensive electromagnetic resonance analysis within a unified design framework.

1.5 Novelty of the proposed work

The novelty of the present work is not in the single use of graphene, nor in the single use of VO₂, as they have been employed in several previously reported THz absorbers (as summarized in Table 1) (Asif et al., 2025; Asif et al., 2026; Upender and Yadav, 2025; Miah et al., 2025; Verma and Meena, 2024; Cheng et al., 2022; Zhou et al., 2021) but rather in the combination of the two materials, which allows for dual tunability. The novelty of the present work resides in the following combination: (i) quad-band near-unity absorption obtained from a single connected four-cut graphene resonator, (ii) dual tunability that covers both an electrically tunable graphene plasmonic mechanism and a thermally/electrically tunable VO₂ phase-transition mechanism, (iii) a systematic broadband-to-narrowband switching characterization of the whole VO2 insulator-to-metal transition, and (iv) a combined resonance-mechanism analysis (electric-field, magnetic-field and power-loss distributions) and a refractive-index-sensing analysis performed across all four absorption bands within one absorber platform. In contrast to most previously reported THz absorbers that were based on tuning, VO2-assisted switching, or sensing one at a time, the proposed work combines all these features in a single compact structure and an in-depth study of the underlying electromagnetic resonance mechanisms.

A distinguishing feature of this study is the systematic investigation of the absorber performance under both metallic-state and conductivity-modulated VO₂ conditions. The metallic-state VO₂ configuration is first employed to establish the fundamental absorption characteristics through graphene relaxation-time optimization, equivalent LC-resonance modeling, impedance analysis, and electromagnetic field analysis. Subsequently, the influence of VO₂ conductivity variation together with graphene chemical-potential tuning is investigated to explain the phase-transition-assisted tunability, broadband-narrowband switching behavior, and spectral reconfigurability of the absorber.

Furthermore, the resonator geometry, ZnO dielectric-spacer thickness, graphene relaxation time, graphene chemical potential, and VO₂ conductivity are systematically optimized to maximize absorption efficiency, impedance matching, and electromagnetic-field confinement. Comprehensive electric-field, magnetic-field, and power-loss analyses are employed to elucidate the physical mechanisms governing resonance formation and absorption enhancement. Collectively, these features establish the proposed graphene-ZnO-VO₂ absorber as a versatile multifunctional platform for terahertz sensing, modulation, filtering, imaging, and reconfigurable photonic applications.

1.6 Main contributions

This study presents a compact graphene-ZnO-VO₂ hybrid terahertz (THz) absorber designed for tunable absorption, switching, and high-performance sensing applications across multiple terahertz frequency bands. The proposed structure consists of a graphene resonator layer, ZnO dielectric spacer, and VO₂ ground layer to achieve dynamic tunability and high-efficiency THz absorption. The major contributions of this study are summarized as follows.

• A parameter-optimized graphene-ZnO-VO₂ terahertz absorber was designed and investigated, exhibiting four near-unity absorption resonances at 0.34, 5.14, 10.11, and 15.27 THz, respectively.
• Dual tunability is achieved through graphene chemical-potential modulation (0.1–1.0 eV) and VO₂ conductivity variation (10–1 × 10⁵ S/m), enabling dynamic control of the absorption response and reversible broadband-narrowband switching behavior.
• The optimized absorber demonstrated a maximum tunability factor of 152.2% and a modulation depth of 74.26%, indicating excellent spectral reconfigurability and active electromagnetic control.
• Polarization-insensitive absorption characteristics were maintained over a wide range of polarization angles, whereas stable absorption performance was preserved for incident angles up to 80°, confirming robust operational stability.
• The refractive-index sensing capability is demonstrated over the refractive-index range of 1.0–2.0, achieving a maximum sensitivity of 1.03 THz/RIU, a figure of merit (FOM) of 0.26 RIU⁻¹, and a Q-factor of 3.83 at the 15.27 THz resonance.
• The proposed absorber integrates quad-band absorption, dual tunability, broadband-narrowband switching, and sensing functionality within a compact platform, making it suitable for THz sensing, filtering, modulation, imaging, and reconfigurable photonics applications.

It should be noted that the present study is a numerical/simulation investigation; no experimental fabrication or characterization was performed, and the proposed absorber’s practical performance remains to be validated experimentally, as discussed in Section 7.

1.7 Paper organization

The remainder of this paper is organized as follows. Section 2 presents the geometry, material properties, and absorption theory of the proposed graphene-ZnO-VO₂ terahertz absorber. Section 3 describes the absorber evolution process and the parameter optimization. Section 4 discusses the absorption characteristics, resonance mechanism, and tunability of the proposed absorber. Section 5 investigates the polarization-insensitive behavior and angular stability of the proposed structure. Section 6 evaluates the refractive-index sensing performance in terms of sensitivity, figure of merit (FOM), and Q-factor. Finally, Section 7 concludes the paper and highlights the potential applications of the proposed absorber in terahertz sensing, filtering, modulation, and reconfigurable photonic systems.

2 Proposed absorber design and theoretical modelling

2.1 Geometry of the proposed graphene-ZnO-VO₂ absorber

The proposed terahertz absorber consists of a graphene-based connected-cut resonator patterned on a ZnO dielectric spacer and backed by a VO₂ ground layer. As shown in Figure 1, the incident THz wave is normally incident on the graphene resonator layer, whereas the VO₂ layer acts as a reflective backplane that suppresses transmission and promotes electromagnetic energy confinement within the absorber. The ZnO dielectric spacer facilitates a strong coupling between the resonator and ground plane, thereby enhancing the impedance matching and absorption efficiency.

The graphene resonator was designed to support strong plasmonic oscillations and enhanced surface current confinement, whereas the connected-cut geometry increased the effective current path length and capacitive coupling within the resonator. The tunable conductivity of the VO₂ layer further contributes to the dynamic control of the absorber response and electromagnetic energy dissipation. By combining a connected-cut graphene resonator, optimized ZnO spacer thickness, and graphene relaxation-time engineering, the proposed structure achieves strong field localization, reduced reflection losses, and high absorption efficiency in the terahertz region. The synergistic interaction among these components enables multi-band resonances with absorption exceeding 90%, making the absorber highly suitable for terahertz sensing, filtering, and modulation applications.

2.2 Material properties

2.2.1 Graphene properties

2.2.1.1 Conductivity

Graphene possesses excellent electrical conductivity and strong plasmonic behavior, which make it highly suitable for tunable terahertz (THz) absorbers. Its conductivity can be dynamically controlled through an external bias voltage, chemical doping, and variation of the Fermi energy level (Liu et al., 2024; Barzegar-Parizi et al., 2024; Wang G. et al., 2022; Liu et al., 2021; Gong et al., 2022; Zhang and Song, 2020; Koulouklidis et al., 2019; Tasolamprou et al., 2019; Mittendorff et al., 2014; Galiffi et al., 2018). The electrical conductivity of graphene was modeled using the Kubo formalism expressed in Equation 1, where the total conductivity consists of intraband and interband contributions. In the terahertz frequency range, the intraband component dominates and governs graphene’s plasmonic response. The conductivity depends on the chemical potential, operating frequency, temperature, and carrier relaxation time, enabling the dynamic tuning of the resonance characteristics through external biasing or chemical doping.

σ g = σ i n t r a + σ i n t e r (1)

The intraband conductivity expressed in Equation 2, dominates in the THz region and can be expressed as (Cyrus and Biabanifard, 2021; Liu et al., 2024)where e is the electron charge, k B is Boltzmann’s constant, T is temperature, ω is angular frequency, τ is relaxation time, and μ_c is the chemical potential. Both the chemical potential and carrier relaxation time strongly influence the conductivity of graphene, thereby affecting the resonance frequency, impedance matching, and absorption characteristics of THz absorbers. Because of these tunable properties, graphene enables efficient impedance matching and enhanced absorption performance in THz absorbers (Liu et al., 2024; Barzegar-Parizi et al., 2024; Wang G. et al., 2022; Liu et al., 2021; Gong et al., 2022; Zhang and Song, 2020).

σ i n t r a = j e 2 k B T π ħ 2 ω + j τ μ c k B + 2 ⁡ ln e − μ c k B T + 1 (2)

2.2.1.2 Chemical potential

The chemical potential of graphene, also referred to as the Fermi energy level, plays a crucial role in determining the resonance frequency and absorption characteristics of THz absorbers. The chemical potential can be adjusted through the gate voltage, external biasing, or chemical doping (Liu et al., 2024; Barzegar-Parizi et al., 2024; Wang G. et al., 2022; Liu et al., 2021; Gong et al., 2022; Zhang and Song, 2020). By varying the chemical potential, the absorption spectrum can be actively tuned, providing enhanced spectral reconfigurability and an adaptive electromagnetic response. The relationship between the chemical potential and the applied gate voltage is expressed aswhere v F is the Fermi velocity, C g is the gate capacitance, V g is the applied gate voltage, and e is the electron charge. Equation 3 indicates that the chemical potential can be effectively controlled by an external voltage bias, thereby enabling the active tuning of the absorber response.

μ c = ħ v F π C g V g e (3)

2.2.1.3 Relaxation time

The relaxation time (τ) is an important parameter that governs carrier scattering, plasmon damping, and surface conductivity in graphene-based THz absorber. It directly influences the resonance sharpness, absorption bandwidth, and electromagnetic energy dissipation, thereby playing a significant role in determining the absorber performance. The graphene relaxation time can be expressed as follows (Liu et al., 2024):where μ is carrier mobility, E_f is Fermi energy, and v F is Fermi velocity. Equation 4 indicates that the relaxation time is directly proportional to the carrier mobility and Fermi energy. An increase in the relaxation time reduces carrier scattering and plasmon damping, resulting in sharper resonances, improved impedance matching, and enhanced absorption performance (Cheng et al., 2023; Qi et al., 2021; Hossain and Khaleque, 2024; Fan et al., 2019; Maurya et al., 2024; Xing et al., 2010). Therefore, the relaxation time is an important design parameter for controlling the spectral response of graphene-based THz absorbers.

τ = μ E f e v F 2 (4)

2.2.2 VO₂ properties

VO₂ is a phase-change material that exhibits a reversible insulator-to-metal transition under thermal, electrical, and optical excitations. In the insulating state, VO₂ behaves as a dielectric material with relatively low conductivity, whereas in the metallic state, its conductivity increases by several orders of magnitude. (Liu et al., 2024; Barzegar-Parizi et al., 2024; Wang G. et al., 2022; Liu et al., 2021; Gong et al., 2022; Zhang and Song, 2020). This unique phase-transition behavior enables the dynamic tuning of the resonance frequency, absorption bandwidth, and impedance characteristics of terahertz absorbers.

In the insulating phase, the complex permittivity of VO₂ can be represented by Equation 5 as follows:

ɛ ω = ε 1 ω + j ε 2 ω (5)

The dielectric response of VO₂ is described by the Drude model represented in Equation 6:where ε ∞ is the high-frequency permittivity, ω p is plasma frequency, and γ is collision frequency. When subjected to thermal, electrical, or optical stimulation, VO₂ transitions to a metallic state with significantly enhanced conductivity. The conductivity of metallic VO₂ can be as expressed in Equation 7:where σ₀ represents the DC conductivity, and τ denotes the carrier relaxation time.

ɛ ω = ε ∞ − ω p 2 ω 2 + j γ ω (6)

σ ω = σ 0 1 + j ω τ (7)

For thermal excitation, VO₂ undergoes a reversible temperature-induced insulator-to-metal transition. At temperatures below the transition region, VO₂ remains predominantly in its low-conductivity insulating phase. As the temperature increases through the transition region, metallic domains progressively form and develop within the insulating matrix, resulting in a substantial increase in the effective electrical conductivity. Above the transition region, the metallic phase becomes dominant and VO₂ exhibits a highly conductive electromagnetic response (Liu et al., 2024; Zhang and Song, 2020; Dong et al., 2021).

The temperature-dependent metallic-phase volume fraction can be described by the Boltzmann-type relation as given in Equation 8; (Liu et al., 2024; Dong et al., 2021):where V(T) represents the metallic-phase volume fraction, V max is the maximum metallic-phase fraction, T 0 is the characteristic phase-transition temperature, and Δ T represents the transition width. (Dong et al., 2021)

V T = V max 1 − 1 1 + exp T − T 0 Δ T (8)

The temperature-dependent effective conductivity can subsequently be related to the effective complex permittivity as per Equation 9; (Dong et al., 2021)

σ e f f ω , T = − i ε 0 ω ε e f f ω , T − 1 (9)

Therefore, increasing the temperature through the phase-transition region increases the metallic-phase fraction and modifies the effective permittivity and conductivity of VO₂, which can be summarized as.

T↑⇒V(T)↑⇒ σ V O 2 ↑⇒insulating state→metallic state.

The conductivities used in the present parametric analysis (σ = 10, 100, 1,000, 5,000, 10000, and 1 × 10⁵ S/m) were chosen as representative fixed values that cover the insulating, transition and metallic regions of VO₂ based on the literature-reported limiting conductivities (Liu et al., 2024; Barzegar-Parizi et al., 2024; Wang G. et al., 2022; Zhang and Song, 2020; Dong et al., 2021) rather than a continuous temperature sweep of the Boltzmann-type phase-transition model of Equations 8, 9. Equations 8, 9 represent the physical connection between temperature and the effective conductivity of VO₂, but do not provide a mapping of each conductivity value to a corresponding film temperature and do not include the thermal hysteresis of the VO₂ insulator to metal transition that occurs in the range of about 300–340 K in typical VO₂ thin films. This is a simplification that is used so that the electromagnetic response of the absorber can be isolated and studied as a function of conductivity only. An important direction for future research is to use the measured V(T) hysteresis data, which depends on the composition of the VO₂ film to be used in the device fabrication, to develop a temperature-resolved treatment that would allow one to predict the switching speed and thermal stability of the proposed device under realistic operating conditions.

In this study, the conductivity of VO₂ was varied from 10 S/m to 1 × 10⁵ S/m to investigate the transition between insulating and metallic states and its influence on absorption characteristics from the low-conductivity insulating regime toward the high-conductivity metallic regime. Temperature itself is not directly swept as an independent parameter in the full-wave simulations; instead, the conductivity variation is employed to represent the corresponding change in the electromagnetic state of VO₂. This conductivity modulation plays a critical role in controlling the resonance intensity, absorption bandwidth, impedance matching, and broadband-narrowband switching behavior of the proposed absorber. The resulting conductivity-dependent response of the complete graphene-ZnO-VO₂ absorber is subsequently investigated in Section 4.5.1.

2.2.3 ZnO dielectric characteristics

ZnO is widely employed as a dielectric spacer material in THz and electromagnetic structures owing to its dielectric characteristics, thermal stability, and suitability for electromagnetic-field confinement (Liu et al., 2024; Barzegar-Parizi et al., 2024; Wang G. et al., 2022; Dong et al., 2021). In the proposed graphene-ZnO-VO₂ absorber, the ZnO layer acts as the dielectric spacer between the patterned graphene resonator and the VO₂ ground layer. It plays an important role in controlling the capacitive coupling, electromagnetic-field confinement, impedance matching, and resonance characteristics of the absorber.

In the present numerical model, ZnO is defined using the “Zinc Oxide (Postava) (optical)” material model available in CST. Rather than assigning a single constant value of relative permittivity, the material is represented using a frequency-dependent complex dielectric response. The complex relative permittivity can be expressed in Equation 10 as:where ε ′ ω represents the dispersive dielectric response and ε ″ ω accounts for dielectric loss. In the employed CST material definition, ZnO is considered nonmagnetic with μ r = 1, and no additional electrical conductivity is assigned (σ = 0 S / m. The dielectric-dispersion data are represented using CST’s nth-order fitting scheme with a maximum fitting order of six and an error limit of 0.05.

ε r ω = ε ′ ω − j ε ″ ω (10)

The dielectric characteristics of ZnO influence the effective capacitance and electromagnetic coupling between the graphene resonator and the VO₂ ground layer. Consequently, the ZnO spacer affects the resonance frequencies, absorption amplitudes, impedance-matching condition, and electromagnetic-field localization. Its influence is also demonstrated by the spacer-thickness optimization presented in Section 3.3.A, where the ZnO thickness is varied from 10 to 16 µm. The optimized thickness of 14 µm provides the most favorable overall absorption response and is therefore employed in the final absorber configuration.

The frequency-dependent dielectric behavior of ZnO is particularly relevant to the higher-order resonances because dielectric loading and loss contribute to the effective resonance condition and electromagnetic energy confinement within the graphene-ZnO-VO₂ structure. The electric-field, magnetic-field, and power-loss distributions presented in the Results section further support the role of the ZnO spacer in the resonant electromagnetic response. For transparency and reproducibility, the complex dielectric dataset associated with the ZnO material definition employed in CST is provided in the Supplementary Information.

2.3 Absorption theory

The absorption performance of a terahertz (THz) absorber is determined by the interaction between the incident electromagnetic wave and resonant structure. The absorption can be expressed as in Equation 11:where A ω , R ω and T ω represent absorption, reflection, and transmission, respectively. Because the VO₂ ground layer thickness is greater than the electromagnetic skin depth in the operating frequency range, the transmission coefficient is approximately zero (T ≈ 0). Therefore, the absorption can be simplified as Equation 12; (Munir et al., 2026):

A ω = 1 − R ω − T ω (11)

A ω = 1 − R ω (12)

This indicates that high absorption is achieved by minimizing the reflection through impedance matching with free space. It is clarified here that in all the results presented in this work, transmission was not assumed as zero. The absorption spectrum shown in this study (in the VO₂-conductivity sweep, graphene chemical-potential sweep, and in the refractive-index-sensing analysis of Section 6), was calculated directly from the full-wave electromagnetic simulation of the reflection and transmission coefficients R ω = S 11 2 , T ω = S 21 2, and then using the formula A ω = 1 − R ω − T ω. Analogously to the well-known continuous metallic perfect absorber, the VO₂ also suppresses transmission for a large portion of the operating frequency range because of its thickness d = 0.5 μm compared to the electromagnetic skin depth, δ = √ 2 / ω μ 0 σ, where μ 0 is the vacuum permeability, and σ is the electrical conductivity.

In the proposed graphene-ZnO-VO₂ absorber, electromagnetic absorption was achieved through the combined effects of plasmonic resonance in the graphene layer, capacitive coupling within the connected-cut resonator, and impedance matching provided by the ZnO spacer and VO₂ ground layer. The graphene resonator supports strong localized surface plasmon oscillations, whereas the VO₂ layer suppresses transmission and enhances electromagnetic energy confinement. The interaction among these components results in efficient absorption and quad-band resonance behavior in the terahertz frequency range.

The normalized input impedance of the absorber can be calculated from the reflection coefficient as expressed in Equation 13; (Munir et al., 2026):

Z = 1 + S 11 1 − S 11 (13)

At the resonance frequencies, the normalized input impedance approaches the free-space impedance, where the real part tends toward unity and the imaginary part tends toward zero. Under this near-impedance-matching condition, the reflection coefficient is significantly reduced. Since the VO₂ ground layer suppresses transmission (S 21 ≈ 0), most of the incident electromagnetic energy is confined within the resonator and dissipated through graphene ohmic losses and dielectric losses in the ZnO layer, resulting in near-perfect absorption.

2.4 Boundary conditions and simulation configuration

The proposed graphene-ZnO-VO₂ absorber was simulated using the CST frequency-domain solver. To represent an infinitely periodic absorber array, unit-cell boundary conditions with adaptive tetrahedral messing were applied at X_min/X_max and Y_min/Y_max, corresponding to periodic repetition of the unit cell along the x and y directions. Along the wave-propagation direction, open add space boundary conditions were applied at Z_min and Z_max to emulate an unbounded free-space region and minimize artificial reflections from the computational boundaries. Floquet excitation with two fundamental modes (TE and TM) was employed for the periodic unit-cell analysis. At normal incidence, the scan angles were set to θ = 0 ° and φ = 0 °, while these parameters were varied for the polarization and oblique-incidence analyses.

At the individual material interfaces, the fields satisfy the conventional electromagnetic interface conditions derived from Maxwell’s equations, including continuity of the appropriate tangential electric and magnetic field components and normal electric and magnetic flux components (Bhati and Malik, 2023). At the air/graphene interface, the incident THz field excites conductivity-dependent currents in the graphene resonator. At the graphene/ZnO interface, the dielectric contrast and field continuity support capacitive coupling and electromagnetic-field confinement within the ZnO spacer. At the ZnO/VO₂ interface, the conductivity-dependent VO₂ backplane governs electromagnetic penetration, loss, and reflection; consequently, increasing the VO₂ conductivity toward its metallic state strongly suppresses transmission and modifies the impedance-matching and resonance conditions. These boundary conditions collectively represent the periodic propagation, interlayer electromagnetic coupling, and absorption behavior of the proposed graphene-ZnO-VO₂ structure.

3 Evolution and parameter optimization of the proposed graphene-ZnO-VO₂ absorber

3.1 Design flow and optimization strategy

Figure 2 illustrates the design and optimization workflow of the proposed graphene-ZnO-VO₂ terahertz absorber. The optimization objective was to achieve an absorption greater than 90% while maintaining stable resonance characteristics and tunability. Initially, the unit cell structure and material configuration were established, followed by the systematic evolution and geometric optimization of the graphene resonator to enhance the electromagnetic confinement and absorption performance. Because the initial absorber configurations did not achieve the target absorption level, two optimization approaches were investigated: graphene relaxation-time variation and VO₂ electrical conductivity modulation. Both approaches improved the absorption performance; however, VO₂ conductivity tuning provided a broader absorption response and superior tunability. Therefore, the VO₂ conductivity optimization strategy was selected for subsequent absorber development and employed in the final absorber configuration for tunability, polarization, angular stability, and sensing investigations.

3.2 Evolution of the proposed graphene-based absorber

The evolution of the proposed terahertz absorber, shown in Figure 3, demonstrates the progressive enhancement of the absorption performance through the systematic modification of the graphene resonator geometry while maintaining the ZnO dielectric layer as the primary tuning medium. Three configurations were investigated: a simple graphene sheet resonator (Abs 1), symmetric 4-cut graphene resonator (Abs 2), and connected 4-cut graphene resonator (Abs 3).

In the first design (Abs 1), the graphene sheet acts as a resonating element, and the absorber performance is primarily controlled by the ZnO dielectric thickness. The variation in the ZnO thickness significantly influences the effective capacitance and electromagnetic confinement within the structure. The optimized graphene sheet resonator exhibited a resonance near 2.97 THz with a maximum absorption of approximately 0.57, serving as the baseline configuration for subsequent absorber evolution. The graphene sheets supported plasmonic oscillations and enhanced electromagnetic energy localization, resulting in tunable absorption characteristics and controllable resonance shifts. The resonance behavior follows the LC resonance relation as expressed in Equation 14 as:where L represents the equivalent inductive response of the resonator, and C corresponds to the effective capacitance arising from graphene coupling and ZnO dielectric confinement. The ZnO spacer thickness directly influences the equivalent capacitance and consequently shifts the resonance frequency according to Equation 14.

f r = 1 2 π L C (14)

To further improve the absorption characteristics, a symmetric 4-cut graphene resonator was introduced (Abs 2) in the design. The incorporation of the four cuts modifies the surface current distribution and increases the interaction between the incident electromagnetic wave and the resonator. This geometry improves the field localization and impedance matching, leading to a distinct resonance peak with a maximum absorption of approximately 0.64 at 3.09 THz. Compared with a simple graphene sheet resonator, the 4-cut configuration provides stronger confinement of electromagnetic energy and enables operation in a lower terahertz frequency region. Although the increase in peak absorption was moderate, the introduction of the four-cut geometry improved resonance localization and established a foundation for further enhancement through resonator connectivity. The final stage of the absorber evolution is represented by the connected 4-cut graphene resonator (Abs 3). By connecting the cut sections, the effective current path length and capacitive coupling within the resonator were significantly increased. This modification enhances the plasmonic coupling, strengthens the electromagnetic field confinement, and reduces the reflection losses. Consequently, the absorber exhibited a substantially improved maximum absorption of approximately 0.86 at 2.68 THz. The resonance frequency shifted toward lower frequencies due to the increase in the equivalent inductance and capacitance introduced by the connected-cut geometry. A stronger and sharper resonance peak indicates more efficient trapping and dissipation of the incident electromagnetic energy within the absorber.

Overall, the absorber evolution demonstrates that the geometric modification of the graphene resonator significantly influences the resonance frequency, electromagnetic confinement, and absorption performance. Although Abs 2 exhibited only a moderate increase in peak absorption compared with Abs 1, it improved field localization and resonance confinement, thereby facilitating further enhancement through resonator connectivity. The connected 4-cut resonator (Abs 3) provides the highest absorption of 0.86 at 2.68 THz due to its extended current path length and enhanced capacitive coupling. As shown in Figure 4 and Table 2, the progressive resonator evolution leads to substantial improvement in absorption performance, confirming the effectiveness of the connected-cut geometry of the resonator. Because the maximum absorption remained below the target value of 0.9, additional parameter optimization and tunable-material engineering were performed to achieve near-unity absorption.

TABLE 2. Evolution of the proposed absorber and comparison of resonance characteristics.

3.3 Parameter optimization of the proposed THz absorber

The proposed THz absorber employs a graphene-ZnO-VO₂ multilayer architecture consisting of a graphene resonator (t_g = 0.00034 μm), ZnO dielectric spacer, and VO₂ ground layer (t V O 2 = 0.5 μm). To achieve near-unity absorption, key geometrical parameters, including the dielectric spacer thickness, square-cut dimension, and connecting-arm width, were systematically optimized through parametric simulations. Graphene supports tunable plasmonic resonances, the ZnO spacer enhances electromagnetic coupling and field confinement, while the VO₂ layer acts as a conductive ground plane that improves absorption through energy dissipation.

3.3.1 Optimization of dielectric thickness

The thickness of the dielectric spacer is crucial for determining the impedance matching and resonance characteristics of the absorber. The initial thickness range was estimated using the quarter-wavelength condition, according to Equation 15:where (c) is the speed of light, (f) is the operating frequency, and ε_r is the relative permittivity of the ZnO. For the target frequency range of 1–3 THz, the calculated thickness varied from approximately 8.6–25.7 μm. Based on this range, the ZnO thickness was varied from 10μm to 16 μm through parametric simulations. As shown in Figure 5, increasing the dielectric thickness caused a noticeable shift in the resonance frequency and modified the absorption magnitude. This behavior is attributed to changes in the effective capacitance and electromagnetic confinement of the absorber cavity.

t d i e l e c t r i c = c 4 f ϵ r (15)

The results show that increasing the spacer thickness improves the electromagnetic confinement and resonance stability. Among the investigated values, a dielectric thickness of 14 μm provides the most favorable compromise between resonance strength, frequency stability, and impedance matching. Therefore, t_dielectric = 14 μm was selected as the optimum spacer thickness for the proposed absorber.

3.3.2 Optimization of square-cut size (a)

To enhance the resonant characteristics of the second evolution stage (Abs-2), the square-cut size (a) was varied from 1μm to 2.5 μm. As illustrated in Figure 6, the resonance near 3 THz exhibits significant sensitivity to the cut dimension, whereas the resonance around 8 THz remains comparatively stable. This behavior indicates that the square defects primarily control the localized current distribution associated with the low-frequency resonance mode. Increasing (a) improves the field localization around the cut edges and enhances the absorption. The maximum absorption of approximately 0.64 is achieved at (a = 2 μm). Further increasing the cut size produced negligible improvement and slightly broadened the resonance. Therefore, (a = 2 μm) was selected as the optimum defect dimension for the final design.

3.3.3 Optimization of arm width (c)

For the final absorber configuration (Abs-3), the width of the connecting arms (c) was varied from 0.5μm to 2 μm. As shown in Figure 7, increasing the arm width initially enhances the absorption because of the improved current circulation and stronger capacitive coupling between adjacent resonator sections. However, excessive arm width weakens the resonance by altering the impedance-matching conditions. The absorption peak reached a maximum value of approximately 0.89 at c = 1μm, indicating an optimal balance between capacitive coupling, current distribution, and impedance matching. A further increase in the arm width weakens the resonance and reduces the absorption level. Consequently, (c = 1 μm) was selected as the optimum arm width for the proposed absorber.

3.3.4 Final dimensions of the proposed absorber

The parameter optimization study confirmed that the dielectric thickness, square-cut dimension, and connecting-arm width significantly influenced the resonance characteristics and absorption performance of the absorber. The optimized parameter combination provided improved impedance matching, enhanced electromagnetic confinement, and stronger plasmonic coupling, resulting in a maximum absorption approaching 0.9. The optimized dimensions listed in Table 3 were adopted for the final absorber design and served as the basis for subsequent investigations of tunability, polarization insensitivity, angular stability, impedance matching, and refractive-index sensing performance.

TABLE 3. Optimized geometrical parameters of the proposed graphene-ZnO-VO₂ terahertz absorber.

4 Results and analysis

Following the geometrical optimization presented in Section 3, the absorber performance was first investigated under the metallic-state condition of VO₂, corresponding to a high electrical conductivity of σ V O 2 = 10 5 S / m. In this state, the VO₂ layer behaves as an effective metallic reflector, providing strong electromagnetic confinement and stable resonant characteristics. This operating condition was selected as the baseline configuration for analyzing the intrinsic absorption mechanism of the proposed graphene-ZnO-VO₂ absorber. Accordingly, the effects of graphene relaxation time, resonance behavior, electric-field distribution, magnetic-field distribution, and power-loss characteristics were first examined under metallic-state conditions to establish the fundamental absorption mechanism. Subsequently, the conductivity of VO₂ was varied to investigate the phase-transition-induced tunability and switching behavior of the absorbers.

4.1 Optimization of graphene relaxation time and absorption analysis

To establish the fundamental absorption characteristics of the proposed absorber, the VO₂ conductivity was initially fixed at σ V O 2 = 10 5 S / m, corresponding to its metallic phase. Under these conditions, the absorber exhibited strong electromagnetic confinement and near-zero transmission due to the metallic behavior of the VO₂ ground layer. The influence of the graphene relaxation time was subsequently investigated to optimize the resonance strength and absorption performance of the structure.

Although the connected-cut graphene resonator (Abs-3) significantly enhanced the absorption performance compared with the previous absorber configurations, the maximum absorption remained below the desired level of 0.9. Therefore, the graphene relaxation time (τ) was introduced as an additional optimization parameter to further improve the absorption characteristics.

The influence of the graphene relaxation time on the absorber performance was investigated through parametric simulations. Because the relaxation time controls carrier scattering and plasmon damping, varying τ modifies the resonance strength, spectral sharpness, and impedance-matching characteristics of the absorber. In this study, τ was varied from 1ps to 9ps while maintaining all geometrical and material parameters unchanged. The objective of this analysis was to determine the optimum relaxation time capable of achieving the target absorption level (A ≥ 0.9) while preserving stable multiband resonance characteristics.

As shown in Figure 8, increasing the relaxation time from 1ps to 6 ps substantially enhances the resonance intensity at the lower-frequency modes. For τ = 1ps, the strongest resonance exhibited an absorption below 0.9. In contrast, τ = 6ps produces three distinct resonance modes exceeding the target absorption level of 0.9, representing a substantial improvement in the absorber performance through relaxation time optimization. This represents a substantial improvement in the absorber performance through relaxation time optimization. The resonance peaks also became significantly narrower. The narrowing of the resonance linewidth also suggests an increase in the effective Q-factor, which is advantageous for frequency-selective filtering and high-sensitivity sensing applications. These observations confirm that longer relaxation times promote stronger plasmonic confinement, improved impedance matching, and more efficient electromagnetic energy dissipation within the absorber.

Although increasing the relaxation time beyond 6 ps further sharpens some resonance features, the overall absorption enhancement becomes negligible. The absorption spectra for τ = 6ps and τ = 9ps exhibit very similar characteristics, indicating the saturation of the plasmonic response. Therefore, τ = 6ps was selected as the optimum value because it achieved near-unity absorption while avoiding unnecessary increases in the carrier lifetime.

The optimization results demonstrate that graphene relaxation-time engineering is an effective method for enhancing the performance of absorbers. By selecting τ = 6ps, the proposed Graphene-ZnO-VO₂ absorber achieves multiple high-quality resonances with absorption levels exceeding 90%, thereby satisfying the design objective established in Section 3. Accordingly, τ = 6ps was adopted as the optimized graphene relaxation time throughout the remainder of this study and served as the baseline operating condition for tunability, polarization insensitivity, angular stability, and refractive index sensing analyses.

4.2 L-C resonance model

Based on the optimized absorber under metallic-state VO₂ condition, an equivalent LC circuit model was developed to explain the origin of the observed resonance modes, as shown in Figure 9. The graphene resonator is represented by an equivalent capacitance C g, while each resonance mode is modeled by an RLC branch R i , L i , C i. The resonance frequency of each branch is given by Equation 16:where L i and C i are the equivalent inductance and capacitance, respectively. The resistive elements R i account for electromagnetic losses. The LC model confirms that the absorption peaks originate from inductive-capacitive resonances and provides a simplified theoretical explanation for absorber operation.

f i = 1 2 π L i C i (16)

4.3 Impedance matching analysis

To further explain the absorption mechanism, the normalized input impedance was retrieved from the simulated complex S-parameters using Equation 13. The real and imaginary parts of the normalized impedance are shown in Figure 10. The enlarged view highlights the impedance behavior at the three resonance frequencies of 1.20, 1.49, and 2.63 THz. At 1.20 THz, the normalized impedance is Re(Z) = 1.20 and Im(Z) = 0.57, while at 1.49 THz, it is Re(Z) = 1.16 and Im(Z) = 0.63. For the third resonance at 2.63 THz, the impedance becomes Re(Z) = 0.70 and Im(Z) = −0.01, where the imaginary part is nearly zero, indicating excellent reactive impedance matching. Although slight deviations from the ideal condition (Re(Z) = 1 and Im(Z) = 0) are observed, the normalized impedance approaches the free-space impedance at all three resonances, thereby significantly reducing electromagnetic reflection. Since the VO₂ ground layer effectively suppresses transmission (S 21 ≈ 0), the incident THz energy is efficiently confined and dissipated through graphene ohmic losses and dielectric losses in the ZnO spacer, resulting in near-unity absorption.

4.4 Electromagnetic resonance mechanism analysis

4.4.1 Electric field distribution

The resonance characteristics identified in Section 4.1 were further investigated using electromagnetic field analysis. All field distributions presented in this section correspond to the optimized absorber operating under the metallic-state VO₂ condition, which was selected as the baseline-absorber state.

The electric field (E-field) distributions at the three principal resonance frequencies (1.20, 1.49, and 2.63 THz) under both TE and TM polarizations are presented in Figures 11, 12. These distributions provide insights into the electromagnetic energy confinement and resonance mechanisms responsible for the high absorption performance of the proposed graphene-ZnO-VO₂ absorber.

At 1.20THz, a strong electric-field concentration was observed along the outer edges and corner regions of the connected graphene resonator. The localized field enhancement indicates the excitation of a fundamental localized surface plasmon resonance (LSPR), in which the electromagnetic energy is strongly confined around the discontinuities and edge regions of the resonator. The side-view distribution further shows that the field is concentrated near the graphene-ZnO interface and rapidly decays toward the VO₂ ground layer, confirming efficient energy trapping within the absorber structure.

At 1.49THz, the electric field was more uniformly distributed around the resonator arms and connecting sections. Compared with the first resonance mode, a stronger coupling was observed between adjacent resonator segments, indicating enhanced capacitive interaction and current circulation. Therefore, this resonance mode is associated with a hybrid plasmonic-LC resonance, which improves the impedance matching between the absorber and free space, leading to enhanced electromagnetic energy confinement and high absorption efficiency.

At 2.63THz, intense field hotspots appeared predominantly along the resonator boundaries and connecting-arm regions. Stronger localization and increased field intensity indicate the excitation of a higher-order resonance mode. The concentration of electromagnetic energy near the connecting arms confirms that the connected-cut geometry plays a critical role in extending the current path length and strengthening the plasmonic coupling. Consequently, efficient electromagnetic energy confinement within the resonator and enhanced ohmic dissipation in the graphene layer were achieved at this frequency, resulting in the strongest absorption response among the investigated resonance modes. These resonance-dependent field distributions are illustrated in the top-view profiles in Figure 11.

The top-view E-field distributions presented in Figure 11 reveal the spatial localization of the resonance modes on the graphene resonator surface, whereas the side-view profiles in Figure 12 illustrate the vertical confinement of the electromagnetic energy within the multilayer absorber structure.

The side-view E-field distributions shown in Figure 12 demonstrate that the electromagnetic energy is primarily confined within the graphene resonator and ZnO dielectric spacer, whereas only a weak field penetrates the VO₂ layer. This behavior confirms that the VO₂ ground plane effectively suppresses transmission and enhances absorption through energy dissipation. Furthermore, the similarity of the field distributions under both TE and TM polarizations indicates that the absorber maintains nearly identical resonance behavior for different polarization states. Such polarization-insensitive characteristics arise from the geometric symmetry of the connected four-cut resonator and contribute to the stable absorption performance of the proposed design.

Overall, the electric field distributions confirm that the absorption peaks at 1.20, 1.49, and 2.63 THz originate from distinct plasmonic resonance modes with different field localization characteristics. The observed energy confinement within the graphene resonator and ZnO spacer, together with the transmission suppression effect of the VO₂ ground layer, verified the physical mechanism responsible for the high absorption performance and polarization-insensitive behavior of the proposed absorber.

4.4.2 Magnetic field distribution

The magnetic-field (H-field) distributions at the three principal resonance frequencies (1.20, 1.49, and 2.63 THz) under both TE and TM polarizations are presented in Figures 13, 14. These distributions provide physical insights into the magnetic resonance modes and energy confinement mechanisms responsible for the high absorption performance of the proposed graphene-ZnO-VO₂ absorber.

At 1.20THz, the magnetic field is concentrated around the outer perimeter of the resonator structure, with an enhanced intensity observed near the edge regions. This distribution indicates the excitation of the fundamental magnetic resonance mode associated with the circulating surface currents induced by the incident electromagnetic wave. The magnetic energy remains primarily localized around the resonator boundaries, contributing to efficient electromagnetic confinement and absorption of energy.

At 1.49THz, a stronger magnetic-field intensity was observed around the resonator edges and dielectric interface compared with the lower-frequency mode. The enhanced magnetic confinement suggests an increased coupling between the graphene resonator, ZnO dielectric spacer, and VO₂ ground layer. This enhanced magnetic coupling promotes improved impedance matching between the absorber and free space, thereby increasing electromagnetic energy dissipation and contributing to the observed high-absorption efficiency.

At 2.63THz, the magnetic-field distribution becomes more extensive across the resonator region, indicating the excitation of a higher-order magnetic resonance mode. A strong magnetic-field concentration was observed along the resonator boundaries and surrounding the dielectric region, reflecting enhanced current circulation and increased inductive effects. The stronger magnetic confinement at this frequency contributed to the highest absorption response among the investigated resonance modes.

The top-view magnetic field distributions shown in Figure 13 reveal the spatial localization of the magnetic resonance modes across the resonator surface at the three resonance frequencies. The observed field patterns confirm that the connected four-cut resonator supports multiple magnetic resonance modes, enabling efficient electromagnetic energy trapping within the operating frequency range.

The side-view H-field distributions presented in Figure 14 further reveal the vertical confinement of the magnetic energy within the multilayer absorber structure. Most of the magnetic energy remains confined within the graphene resonator and ZnO dielectric spacer region, whereas only weak field penetration occurs toward the VO₂ ground layer. This behavior indicates the effective suppression of transmission and strong confinement of the incident THz energy within the absorber cavity. Furthermore, the similarity of the magnetic field distributions under TE and TM polarizations confirms that the absorber exhibits nearly identical magnetic resonance characteristics for different polarization states. This behavior originates from the geometrical symmetry of the connected four-cut resonator and contributes to the polarization-insensitive absorption performance of the proposed design.

Overall, the magnetic field distributions confirm that the absorption peaks at 1.20, 1.49, and 2.63 THz originate from distinct magnetic resonance modes characterized by different magnetic energy confinement patterns. The combined magnetic confinement within the graphene-ZnO-VO₂ multilayer structure, together with the enhanced current circulation enabled by the connected four-cut resonator geometry, facilitated efficient electromagnetic energy trapping and dissipation. These results complement the electric-field analysis and verify the physical mechanisms responsible for the high absorption efficiency, multiband response, and polarization-insensitive performance of the proposed absorber.

4.4.3 Power loss

The power-loss distributions at the three principal resonance frequencies (1.20, 1.49, and 2.63 THz) under both TE and TM polarizations are presented in Figure 15. The power-loss profiles provide direct evidence of the locations where the incident electromagnetic energy is dissipated within the graphene-ZnO-VO₂ absorber, revealing the physical origin of the absorption resonances.

At 1.20THz, the power loss was primarily concentrated within the central region of the connected graphene resonator and along the connecting-arm sections. The localized loss distribution indicates the effective excitation of the fundamental plasmonic resonance mode, where the incident electromagnetic energy is confined and dissipated through the conductive losses in graphene. Similar loss patterns were observed under both TE and TM polarizations, demonstrating polarization-independent energy dissipation.

At 1.49THz, the power-loss intensity increases significantly and becomes more localized around the resonator boundaries and coupling regions. The enhanced loss localization indicates a stronger interaction between the graphene resonator, ZnO dielectric spacer, and VO₂ ground layer. This resonance mode exhibited efficient electromagnetic energy dissipation, which was consistent with the high absorption level observed near this frequency.

At 2.63THz, multiple loss-concentration regions appeared around the resonator boundaries and connecting-arm structures. A broader loss distribution indicates the excitation of a higher-order resonance mode associated with stronger plasmonic oscillations and increased current circulation. The enhanced conductivity and dielectric losses at this frequency contribute to efficient electromagnetic energy confinement and absorption.

The top-view power loss distributions shown in Figure 15 reveal the spatial locations of electromagnetic energy dissipation across the resonator surface. The observed loss patterns confirm that different resonance frequencies are associated with distinct energy confinement mechanisms and plasmonic resonance modes. Furthermore, the similarity of the power-loss distributions under the TE and TM polarizations confirms that the absorber exhibits nearly identical energy dissipation characteristics for different polarization states, thereby supporting its polarization-insensitive absorption performance.

Overall, the power-loss distributions confirm that the high absorption performance of the proposed absorber originates from the efficient electromagnetic energy confinement and dissipation within the graphene-ZnO-VO₂ multilayer structure. The combined effects of plasmonic resonance, enhanced current circulation, and dielectric coupling enable the effective conversion of incident THz energy into conductive and dielectric losses, thereby producing the observed multiband high-absorption response.

4.5 Dual-tunability analysis of the proposed absorber

After establishing the resonance mechanism of the optimized absorber under the metallic-state VO₂ condition (σ V O 2 = 10 5 S / m), the conductivity of VO₂ was progressively reduced to investigate the influence of the insulator-to-metal phase transition on the absorption response. The conductivity was varied from 10 to 1 × 10⁵ S/m, covering the insulating, transition, and metallic phases of VO₂.

4.5.1 Effect of VO₂ electrical conductivity

As discussed in Section 2.2.2, the temperature-induced insulator-to-metal transition of VO₂ is accompanied by a substantial increase in its electrical conductivity. In the present full-wave simulations, this thermally induced material transition is represented through the variation of VO₂ conductivity rather than by directly sweeping temperature. Accordingly, the conductivity is varied from 10 S/m to 1 × 10⁵ S/m, representing the evolution from the low-conductivity insulating regime toward the high-conductivity metallic regime. The corresponding influence of this conductivity evolution on the electromagnetic response of the proposed graphene-ZnO-VO₂ absorber is demonstrated in Figures 16, 17.

As the VO₂ conductivity increases, the electromagnetic characteristics of the VO₂ ground layer change, thereby modifying the loss, field penetration, and impedance-matching conditions of the complete absorber. Consequently, variations in the resonance frequency, absorption magnitude, and bandwidth are observed across the investigated conductivity range. Therefore, the conductivity-dependent absorption characteristics in Figures 16, 17 provide the absorber-level representation of the thermally induced VO₂ phase transition described in Section 2.2.2.

Figure 16 shows the absorption heatmap of the proposed graphene-ZnO-VO₂ absorber as a function of the operating frequency and VO₂ electrical conductivity. The conductivity was varied from 10 S/m to 1 × 10⁵ S/m to investigate the influence of the VO₂ insulator-to-metal transition on the absorption characteristics of the structure. The heatmap provides a comprehensive visualization of the resonance evolution across the entire conductivity range, where the brighter regions correspond to higher absorption values approaching unity.

At low conductivity values (10–10³ S/m), corresponding to the insulating phase of VO₂, several well-defined narrowband absorption resonances were observed near 0.34, 5.14, 10.11, and 15.27 THz. These resonances exhibited absorption values close to unity, indicating efficient impedance matching and strong electromagnetic confinement within the absorber cavity.

As the conductivity increased into the transition region (approximately 5 × 10³–10⁴ S/m), noticeable resonance migration and spectral broadening occurred. The resonant frequencies gradually shifted, while the resonance linewidth increased due to conductivity-induced changes in the effective permittivity and surface impedance of VO₂. This behavior reflects the progressive transformation of VO₂ from a dielectric material to a metallic state.

In the highly conductive metallic regime around 10⁵ S/m, the resonance response becomes broader and less localized. The absorber exhibited enhanced reflection and reduced field penetration, leading to resonance damping and absorption degradation for several resonance modes. The heatmap clearly demonstrates the conductivity-controlled evolution from strongly localized narrowband resonances to broader absorption characteristics. The conductivity-dependent absorption behavior can be interpreted using the absorption theory presented in Section 2.3. Since the VO₂ ground layer suppresses transmission T ≈ 0, variations in absorption primarily originate from conductivity-induced changes in reflection and impedance matching characteristics.

To quantitatively evaluate the resonance migration and absorption variation observed in the heatmap, Figure 17a presents the evolution of resonance frequencies, while Figure 17b illustrates the corresponding peak absorption values as a function of VO₂ electrical conductivity.

4.5.1.1 Resonance frequency evolution

Figure 17a illustrates the variation in the four principal resonance frequencies with respect to the electrical conductivity of VO₂. In the insulating region (10–10³ S/m), all resonance modes remain nearly unchanged, indicating that the effective electromagnetic properties of the absorber experience only minor variations under low-conductivity conditions. The resonance frequencies were maintained at approximately 0.34, 5.14, 10.11, and 15.27 THz, confirming stable resonance behavior and strong electromagnetic confinement.

As the conductivity increases into the transition region (5 × 10³–10⁴ S/m), noticeable resonance migration occurs due to conductivity-induced modifications in the effective permittivity and surface impedance of VO₂. Among the four resonance modes, Peak 1 increases from approximately 0.34 THz at 10³ S/m to 0.66 THz at 5 × 10³ S/m and 1.04 THz at 10⁴ S/m, reaching approximately 1.23 THz at 10⁵ S/m. This corresponds to an overall increase of approximately 215% relative to its value at 10³ S/m, demonstrating the strong conductivity sensitivity of the low-frequency mode. Similarly, Peaks 2, 3, and 4 gradually shifted toward lower frequencies, demonstrating the strong influence of the VO₂ conductivity on the spectral response of the absorber.

In the metallic regime (σ = 10⁵ S/m), the resonance frequencies became comparatively stable, indicating that the absorber reached a conductivity-saturated state, where further increases in conductivity produced only minor changes in resonance behavior.

4.5.1.2 Peak absorption evolution

Figure 17b illustrates the variation of the peak absorption magnitude of the four principal resonance modes as a function of the electrical conductivity of VO₂. In the insulating region (10–10³ S/m), all four resonance modes exhibit absorption values close to unity, with Peak 1, Peak 2, Peak 3, and Peak 4 maintaining values of approximately 0.98, 0.99, 1.00, and 0.98, respectively. This indicates efficient electromagnetic coupling and favorable impedance matching in the low-conductivity state of VO₂. As the conductivity increases into the transition region, the absorption response becomes mode-dependent. Peak 1 decreases progressively from approximately 0.98 at 10³ S/m to 0.89 at 5 × 10³ S/m and 0.84 at 10⁴ S/m, whereas Peaks 2–4 retain relatively high absorption values close to unity over a substantial portion of the transition region. At 10⁵ S/m, corresponding to the highly conductive metallic-like regime, a pronounced reduction in absorption is observed for all modes. The absorption of Peak 1 decreases to approximately 0.69, while Peaks 2, 3, and 4 decrease to approximately 0.84, 0.56, and 0.60, respectively. The stronger degradation observed for Peaks 3 and 4 can be attributed to the increased conductive response of VO₂, which modifies the surface-current distribution, electromagnetic coupling, and impedance-matching condition, thereby increasing reflection and reducing the field confinement within the resonant region.

These results demonstrate that VO₂ electrical conductivity provides an effective means of controlling both the resonance frequency and absorption magnitude of the proposed absorber. The relatively high absorption maintained over the insulating and transition states, followed by a substantial reduction in the metallic-like state, enables conductivity-controlled modulation and switching of the absorption response. Thus, the proposed structure exhibits electrically reconfigurable absorption characteristics associated with the VO₂ conductivity transition, which can be useful for adaptive THz switching, modulation, filtering, and sensing applications.

While VO₂ conductivity tuning provides phase-transition-induced spectral reconfiguration, additional tunability can be achieved through the electrical modulation of graphene conductivity. Therefore, the influence of the graphene chemical potential on the absorption characteristics of the proposed absorber was investigated in the following subsection.

4.5.2 Graphene chemical potential tuning

Figure 18 presents the absorption heatmap of the proposed Graphene-ZnO-VO₂ absorber as a function of operating frequency and graphene chemical potential (μ c). The chemical potential was varied from 0.1 to 1.0 eV to investigate the electrically tunable absorption characteristics of the structure. Four distinct absorption bands were observed throughout the tuning range, indicating stable multiband operation and strong electromagnetic confinement.

As the graphene chemical potential increases, all resonance modes remain highly absorptive while exhibiting different levels of frequency tunability. Among the four resonances, Among the four resonances, Peak 1 exhibits the highest relative frequency tunability, shifting from approximately 0.38 THz to 0.96 THz, corresponding to an increase of about 153%. Peak 2 also exhibited noticeable tuning behavior, migrating from 4.99 to 5.99 THz, whereas Peaks 3 and 4 remained comparatively stable. These results indicate that the lower-frequency resonance modes are more sensitive to the chemical potential modulation of graphene than the higher-frequency modes.

Despite the frequency tuning, the absorption magnitude remained above 93% across the entire chemical-potential range, demonstrating excellent absorption stability and robust impedance matching. The ability to maintain near-unity absorption while simultaneously achieving electrical tunability is advantageous for reconfigurable THz devices and sensing applications.

Increasing the graphene chemical potential increases the carrier density and surface conductivity of graphene, thereby strengthening the plasmonic oscillations and modifying the effective inductive-capacitive resonance of the absorber. The enhanced plasmonic interaction alters the effective electromagnetic path length and resonance condition, leading to conductivity-dependent frequency tuning while preserving the strong electromagnetic confinement and efficient absorption.

The three-dimensional absorption surface shown in Figure 19 provides an alternative visualization of the tunability behavior observed in Figure 18. It can be observed that all four resonance modes maintain high absorption throughout the investigated chemical-potential range, confirming the robustness of the absorber response. The gradual displacement of the resonance surfaces with increasing graphene chemical potential further demonstrates the capability of electrical tuning without significant degradation of the absorption performance.

Overall, graphene chemical-potential tuning provides an effective electrical control mechanism for dynamically adjusting the resonance frequencies while preserving the high absorption performance. When combined with the phase-transition-induced conductivity modulation of VO₂, graphene chemical-potential tuning enables independent electrical control of the absorber response, providing a versatile dual-tunable platform for adaptive THz sensing, filtering, modulation, switching, and reconfigurable photonic applications.

4.5.3 Absorption modulation and switching behavior

• Absorption Modulation

The tunability characteristics of the proposed graphene-based THz absorber were investigated by varying the graphene chemical potential (μ c) from 0.1 eV to 1.0 eV. As (μ c) increased, all absorption resonances exhibited noticeable frequency shifts, demonstrating the active reconfigurability of the proposed structure. The first resonance frequency shifted from 0.379 to 0.956 THz, whereas the second, third, and fourth resonances shifted from 5.07 to 5.99THz, 10.08 to 10.58 THz, and 15.24 to 15.59 THz, respectively. These results confirm the realization of an electrically controlled quadrature-band operation.

Among the four resonance modes, Peak 1 exhibited the largest frequency variation, corresponding to a frequency shift of 0.577 THz. The tunability factor (TF) is defined as, as shown in Equation 17:where f min and f max denote the maximum and minimum resonance frequencies, respectively. For the lower resonance mode, the frequency shifts from 0.37 to 0.95 THz, resulting in a tunability factor of 152.2%, which indicates the excellent electrical reconfigurability of the proposed absorber. To quantitatively compare the frequency tuning performance of the individual resonance modes, the minimum resonance frequency (f min, maximum resonance frequency (f max, and corresponding tunability factor (TF) are summarized in Table 4.

T F % = f max − f min f min × 100 (17)

TABLE 4. Frequency tunability of the proposed graphene-ZnO-VO₂ absorber under graphene chemical-potential variation.

The tuning sensitivity of the proposed absorber can be evaluated as expressed in Equation 18:where (f r) denotes the resonance frequency and (μ c) represents the graphene chemical potential. The calculated tuning sensitivity for Peak 1 was approximately 0.64 THz/eV, confirming the strong electrical tunability of the proposed absorber.

S μ = ∂ f r ∂ μ c (18)

In addition to frequency tunability, the modulation depth (MD) was evaluated to quantify the absorption amplitude modulation capability of the absorber. The modulation depth is calculated using Equation 19:where A_max and A_min represent the maximum and minimum absorption values.

M D % = A max − A min A max × 100 (19)

As shown in Figure 20, the modulation depth increases monotonically with graphene chemical potential, rising from 42.39% at μ c = 0.1 eV to 74.26% at μ c = 1.0 eV. A rapid increase was observed in the low chemical-potential region (0.1–0.3 eV), followed by a more gradual enhancement between 0.3 and 0.7 eV. Beyond 0.7 eV, the modulation depth approaches saturation, indicating that the graphene conductivity has reached a level at which further increases in the carrier concentration produce only marginal changes in the absorption performance. This behavior confirms the strong influence of graphene conductivity on the modulation characteristics of the absorber.

For clarity, the key modulation and tuning performance metrics of the proposed absorber are summarized in Table 5, including the frequency shift, tuning sensitivity, tunability factor, and maximum modulation depth.

TABLE 5. Summary of graphene chemical-potential tuning and absorption-modulation performance.

To evaluate the effectiveness of the proposed design, a comparison with previously reported graphene-based tunable THz absorbers is presented in Table 6. This comparison highlights the frequency tunability, multiband response, and modulation capability achieved by different graphene-enabled absorber configurations.

TABLE 6. Comparison of graphene-tunable THz absorbers with the proposed graphene-ZnO-VO₂ absorber.

As observed from Table 6, the proposed Graphene-ZnO-VO₂ absorber achieves competitive frequency tunability while simultaneously providing quad-band operation and a modulation depth of 74.26%. Compared with previously reported graphene-based absorbers, the proposed design offers the additional advantage of dual tunability through the combined use of graphene chemical potential modulation and VO₂ phase-transition control.

Overall, the proposed Graphene-ZnO-VO₂ absorber exhibited strong electrically controlled reconfigurability through graphene chemical-potential modulation. A maximum frequency shift of 0.57 THz, tuning sensitivity of 0.64 THz/eV, tunability factor of 152.2%, and modulation depth of 74.26% were achieved. The results demonstrate that graphene chemical potential tuning effectively controls both the spectral position and absorption strength of the resonance modes. When combined with VO₂ phase-transition-induced conductivity modulation, the proposed structure realizes a dual-tunable THz platform capable of adaptive filtering, modulation, switching, and reconfigurable photonic operation. The performance comparison presented in Table 7 indicates that the proposed design combines dynamic absorption control and refractive index sensing within a single compact platform.

TABLE 7. Comparison of recent VO₂-Based tunable THz absorbers and the proposed graphene-ZnO-VO₂ absorber.

4.6 L-C equivalent circuit with VO₂ electrical conductivity effect

To explain the conductivity-dependent resonance behavior of the proposed graphene-ZnO-VO₂ absorber, an equivalent LC circuit model is shown in Figure 21. The graphene resonator is represented by an inductance L g and capacitance C g, while the ZnO spacer is modeled as a coupling capacitance C d. The VO₂ layer is represented by a tunable resistance R V O 2, whose value varies with electrical conductivity. The resonance frequency can be expressed as in Equation 20:

f r = 1 2 π L g C g + C d (20)

The equivalent impedance is given by Equation 21:

Z e q ω = R V O 2 + j ω L g + 1 j ω C g + C d (21)

As the conductivity of VO₂ increases, R V O 2 decreases, modifying the impedance matching condition and damping characteristics of the resonator. Consequently, resonance shift, bandwidth variation, and absorption modulation were observed. Therefore, the LC equivalent circuit provides a simple physical explanation for the conductivity-controlled tuning and switching behaviors of the proposed absorber.

In this section, two different VO₂ conductivity regimes are analyzed for clarity. The fully metallic-state VO₂ condition (σ V O 2 = 1 × 10 5 S / m) is used as the baseline for the graphene relaxation-time optimization, the LC-resonance model, the impedance-matching analysis, and the electromagnetic field and power-loss analysis discussed above, in order to establish the resonance mechanism of the absorber. Section 4.5 then examines the absorber under the low-conductivity insulating-state condition (σ V O 2 = 10 t o 10 3 S / m), which exhibits four principal near-unity resonances at 0.34, 5.14, 10.11, and 15.27 THz, and traces the evolution of the absorption response as the VO₂ conductivity is varied across the full insulator-to-metal transition. The different number and frequency of resonances reported for these two regimes reflect two distinct, deliberately analyzed electromagnetic operating conditions of the same absorber structure, rather than an inconsistency in the design.

5 Polarization and angular stability analysis

5.1 Angular stability analysis (θ variation)

Figure 22 shows the absorption heatmap of the proposed graphene-ZnO-VO₂ absorber as a function of the operating frequency and incidence angle (θ), which varied from 0° to 89°. The heatmap illustrates the angular evolution of the previously identified resonance modes and provides a comprehensive view of the stability of the absorber under oblique incidence conditions. High-absorption regions are represented by bright yellow bands, corresponding to absorption values approaching unity.

The high-absorption bands remained nearly unchanged over a broad angular range, indicating excellent angular stability of the absorber. Only minor resonance migration and bandwidth variations were observed as the incidence angle increased from normal incidence to approximately 75°–80°. Beyond this range, gradual absorption degradation occurs due to reduced electromagnetic coupling and increased reflection losses under highly oblique incidence conditions.

The persistence of the high-absorption regions demonstrates that the absorber maintains efficient impedance matching and strong electromagnetic confinement over a wide range of incidence angles. This behavior confirms the robustness of the proposed graphene-ZnO-VO₂ absorber for practical terahertz applications, where the direction of the incident electromagnetic wave cannot be precisely controlled.

To further evaluate the angular stability performance of the proposed absorber, a comparison with previously reported polarization-insensitive THz absorbers is presented in Table 8. As shown in Table 8, the proposed absorber maintained stable absorption up to approximately 80°, which is comparable to or better than several recently reported graphene- and metasurface-based THz absorbers. This wide-angle stability is advantageous for sensing, imaging, and free-space THz applications.

TABLE 8. Comparison of angular stability performance between the proposed graphene-ZnO-VO₂ absorber and previously reported polarization-insensitive THz absorbers.

5.2 Polarization stability analysis (Φ variation)

Figure 23 shows the absorption heatmap of the proposed graphene-ZnO-VO₂ absorber as a function of the operating frequency and polarization angle (Φ), which varied from 0° to 89°. The heatmap illustrates the evolution of the absorption response under different polarization orientations of an incident electromagnetic wave.

The high-absorption bands remained virtually unchanged throughout the entire polarization range. No noticeable resonance migration, absorption degradation, or bandwidth variation was observed as the polarization angle increased from 0° to 89°. The absorption response remained nearly identical for all polarization states, indicating the excellent polarization-insensitive behavior of the proposed absorber.

The observed polarization stability originates from the geometric symmetry of the resonator configuration, which produces nearly identical electromagnetic responses for different polarization orientations. Consequently, the absorber maintains stable impedance matching and strong electromagnetic confinement, regardless of the polarization state of the incident wave.

The results demonstrate that the proposed absorber is highly robust against polarization variations and can maintain stable multiband absorption characteristics under arbitrary polarization. Together with the wide-angle stability demonstrated in Section 5.1, this confirms the suitability of the proposed graphene-ZnO-VO₂ absorber for practical terahertz sensing, imaging, and filtering applications.

The negligible variation in the absorption response indicates that the proposed absorber can maintain a stable performance under arbitrary polarization states, which is highly desirable for practical free-space terahertz systems. The combined angular and polarization stability confirm that the proposed absorber can maintain a high absorption performance under realistic operating conditions, where both the incidence angle and polarization state of the incoming terahertz wave may vary dynamically.

6 THz absorber sensing performance analysis

To evaluate the sensing capability of the proposed Graphene-ZnO-VO₂ absorber, an analyte layer was introduced above the graphene resonator, as illustrated in Figure 24. The sensing principle relies on the interaction between the localized electromagnetic fields generated by the resonant graphene structure and the dielectric environment of the analyte. Because part of the localized field extends into the analyte region, variations in the analyte properties perturb the effective dielectric loading of the resonator and consequently modify its resonance characteristics. Therefore, the sensing performance is investigated through two complementary analyses: (i) analyte-thickness variation to evaluate the stability of the sensing response and (ii) refractive-index variation to quantify the resonance-frequency shift and sensing performance.

6.1 Analyte thickness variation

Figure 25 presents the absorption heatmap of the proposed graphene-ZnO-VO₂ absorber as a function of the operating frequency and analyte thickness (ta), which varied from 0.2 to 2.0 μm. The heatmap provides a comprehensive visualization of the influence of analyte layer thickness on the absorption characteristics of the proposed multi-band absorber.

Four prominent absorption bands were observed at 0.34, 5.14, 10.11, and 15.27 THz, corresponding to the previously identified resonance modes of the absorber. The bright yellow regions indicate absorption values approaching unity, confirming strong electromagnetic confinement and efficient energy dissipation within the resonator.

It can be observed that increasing the analyte thickness results in only negligible changes in the resonance frequencies. The resonance bands remained nearly horizontal throughout the investigated thickness range, indicating excellent frequency stability and weak dependence on the analyte thickness. In addition, the absorption magnitude remained above 95% for all resonance modes, demonstrating that the impedance-matching condition was largely preserved even when the analyte thickness was varied.

The limited frequency variation suggests that the resonance behavior of the proposed absorber is primarily governed by the intrinsic resonator geometry and electromagnetic properties of the graphene-ZnO-VO₂ structure rather than by the physical thickness of the analyte layer. Consequently, variations in the analyte thickness do not significantly perturb the localized electromagnetic fields responsible for resonance formation.

From a sensing perspective, this behavior is highly advantageous because it indicates that the absorber response is relatively insensitive to the thickness fluctuations of the deposited analyte layer. Such stability minimizes measurement uncertainty and improves sensing reliability, particularly in practical environments where precise control of the analyte thickness may be difficult to achieve.

Overall, the results confirm that the proposed absorber maintains stable multiband absorption characteristics over a wide analyte thickness range while preserving near-unity absorption performance. This robustness renders the structure suitable for reliable terahertz sensing, filtering, and spectroscopic applications.

6.2 Refractive-index sensing mechanism and performance analysis

The refractive-index sensing mechanism originates from the interaction between the localized electromagnetic fields of the resonant structure and the analyte placed above the graphene layer. When the incident THz wave excites the resonant modes, electromagnetic energy is localized around the patterned graphene resonator and within the graphene-ZnO region. A portion of the localized field extends into the analyte region; consequently, changes in the analyte refractive index modify the effective dielectric environment experienced by the resonator.

The physical origin of the resonance shift can be understood from the equivalent LC resonance model previously described by Equation 20. According to Equation 20, the resonance frequency depends on the inductive contribution L g and the capacitive contributions C g and C d of the resonant structure. When the dielectric environment surrounding the resonator changes, the effective capacitive loading is modified, which consequently alters the resonance frequency.

For refractive-index sensing, this dielectric dependence can be represented as given by Equation 22:where f r represents the resonance frequency, and ε e f f denotes the effective dielectric permittivity experienced by the resonant electromagnetic field. For a nonmagnetic analyte μ r ≈ 1, the refractive index is related to the dielectric permittivity, as expressed in Equation 23:

f r ∝ 1 ε e f f (22)

n = ε r (23)

Therefore, increasing the analyte refractive index increases its dielectric permittivity and consequently increases the effective dielectric loading surrounding the graphene resonator. Because part of the localized resonant field interacts with the analyte layer, this dielectric perturbation modifies the effective capacitive contribution of the resonant structure. According to Equations 20, 22, increased capacitive/dielectric loading results in a reduction in the resonance frequency. The sensing mechanism can therefore be summarized as. n ↑ ⇒ ε r ↑ ⇒ ε e f f ↑ ⇒ C e f f ↑ ⇒ f r ↓. Thus, an increase in analyte refractive index produces a red shift of the absorption resonance. The magnitude of this frequency shift depends on the interaction between the localized electromagnetic field and the analyte.

The simulated absorption heatmap of the proposed Graphene-ZnO-VO₂ absorber results in Figure 26 support this mechanism. When the analyte refractive index is increased from 1.0 to 2.0, all four resonance modes exhibit systematic shifts toward lower frequencies while maintaining high absorption levels. The magnitude of the shift becomes larger for the higher-frequency resonances, with the resonance near 15.27 THz exhibiting the largest frequency displacement. This behavior indicates a strong interaction between the localized electromagnetic fields and the surrounding dielectric environment, confirming the refractive-index sensing capability of the proposed absorber.

The sensing sensitivity of the absorber was calculated using Equation 24:

s = Δ f Δ n (24)

The figure of merit (FOM) and quality factor (Q-factor) were determined using Equations 25, 26, respectively:andwhere s is the sensitivity (THz/RIU), Δ f is the resonance frequency shift, Δ n is the refractive index variation, and FWHM is the full width at half maximum of the resonance peak.

F O M = S F W H M (25)

Q = f 0 F W H M (26)

Since the sensing analysis is based on deterministic full-wave simulations, the principal numerical uncertainty originates from the frequency sampling interval used to extract the resonance peaks. The simulated frequency interval was approximately 0.0199 THz; therefore, the uncertainty in each extracted resonance frequency was estimated as half of this interval, namely, δ f = ± 0.00995 THz. The sensitivity uncertainty was calculated through standard propagation as expressed in Equation 27:where Δ n = 1 RIU for the investigated refractive-index range from 1.0 to 2.0. The resulting sensitivity uncertainty was approximately ± 0.0141 THz/RIU for all four resonance modes, since it depends only on the fixed frequency resolution and refractive-index interval rather than on the resonance frequency itself. Here, δ f 1 and δ f 2 denote the resolution-limited uncertainty of the two resonance-frequency readings used to compute Δf, both equal to δf.

δ S = δ f 1 2 + δ f 2 2 Δ n , (27)

The same base uncertainty was propagated into the quality factor and figure of merit, both of which are defined as ratios of frequency-domain quantities as defined in Equations 25, 26. Since Q depends on both the resonance position and the spectral width, the latter obtained as the difference between two half-maximum crossing frequencies and therefore carrying its own independent uncertainty of √ 2 δ f its uncertainty was obtained by standard quotient error propagation as expressed in Equation 28:whereas the FOM = S/FWHM uncertainty was dominated by the sensitivity term, with the FWHM contribution found to be less than 3% of the total and therefore neglected as expressed in Equation 29.

δ Q = Q δ f f 0 2 + 2 δ f F W H M 2 (28)

δ F O M = F O M · δ S / S (29)

The calculated sensing parameters for all four resonance modes are listed in Table 9.

TABLE 9. Refractive-index sensing performance of the proposed graphene-ZnO-VO₂ absorber for different resonance modes.

As summarized in Table 9, all the resonance modes exhibited measurable refractive index sensitivity. The resonance near 15.27 THz demonstrated the best sensing performance, achieving a maximum sensitivity of 1.03 THz/RIU, a figure of merit of 0.26 RIU⁻¹, and a Q-factor of 3.83. The enhanced performance at this resonance can be attributed to the stronger electromagnetic confinement and increased interaction between the evanescent field and analyte layer.

The resonance near 10.11 THz also exhibits high sensitivity and good spectral selectivity, whereas the 5.14 THz resonance provides moderate sensitivity suitable for practical biomedical and chemical sensing applications. Although the 0.34 THz resonance exhibits lower sensitivity, its deeper field penetration may be advantageous for bulk material characterization and low-loss sensing applications. These results confirm that the proposed absorber functions as an effective multifrequency THz sensing platform capable of detecting refractive-index variations over a broad frequency range.

Figures 27a–c further illustrates the sensing performance of the proposed Graphene-ZnO-VO₂ absorber in terms of sensitivity, figure of merit (FOM), and quality factor (Q-factor) for the four resonance modes. As shown in Figure 27a, the sensitivity increases progressively with the resonance frequency, rising from 0.09 THz/RIU at 0.34 THz to 1.03 THz/RIU at 15.27 THz. This trend indicates that the higher-frequency resonance modes exhibit stronger interactions between the localized electromagnetic fields and the surrounding analyte layer, resulting in an enhanced refractive-index sensing capability.

Similarly, Figure 27b shows that the FOM increases from 0.07 RIU⁻¹ to 0.26 RIU⁻¹ as the resonance frequency increases. Higher FOM values obtained at upper-frequency resonances indicate an improved sensing resolution and a greater ability to distinguish small refractive-index variations.

The variation in the quality factor is shown in Figure 27C. The Q-factor increased from 0.25 at the lowest-frequency resonance to 3.83 at the 15.27 THz resonance, demonstrating progressively sharper resonance characteristics and improved spectral selectivity. The simultaneous enhancement of the sensitivity, FOM, and Q-factor with increasing resonance frequency indicates that the higher-order resonance modes provide improved sensing performance and spectral selectivity.

Overall, the proposed graphene-ZnO-VO₂ absorber demonstrated a stable multiband-sensing performance with a maximum sensitivity of 1.03 THz/RIU, FOM of 0.26 RIU⁻¹, and a Q-factor of 3.83. Combined with dual tunability, polarization-insensitive behavior, and wide-angle stability, the proposed absorber represents a promising platform for multifunctional THz sensing and in reconfigurable photonic applications.

As shown in Table 10, the proposed graphene-ZnO-VO₂ absorber demonstrates competitive sensing performance while providing several additional functionalities that are not simultaneously achieved in most previously reported THz sensors. Although certain designs exhibit higher peak sensitivity, they are generally limited to single-, dual-, or triple-band operations and lack active reconfigurability. In contrast, the proposed absorber supports quad-band sensing, graphene chemical-potential tuning, VO₂ phase-transition-based switching, absorption modulation, polarization-insensitive operation, and wide-angle stability, all within a single compact platform. The combination of multi-frequency sensing capability and dual tunability enables adaptive operation across different THz frequency bands, making the proposed absorber particularly attractive for biomedical sensing, chemical detection, environmental monitoring and reconfigurable THz photonic applications.

TABLE 10. Comparison of the sensing performance of the proposed absorber with previously reported THz sensors.

7 Proposed experimental implementation, validation strategy and scope considerations

The numerical simulations indicate that the proposed absorber of graphene-ZnO-VO₂ can be fabricated by available thin-film deposition and graphene transfer and lithography techniques. The reflection coefficient (S₁₁) of the fabricated device can be measured with a THz vector network analyzer (THz-VNA) or with a THz time-domain spectroscopy (THz-TDS) system, and the VO₂ ground layer is able to provide a small transmission (S₂₁ ≈ 0). The absorption can then be checked by A = 1-∣S₁₁∣² and compared with the results simulated. Further validation of the proposed design is possible by electrical tuning of graphene and thermal tuning of VO₂. Due to the lack of THz characterization facilities, the absorber proposed in the present work was not necessarily demonstrated in an experimental setup, but the proposed validation methodology illustrates the practicality of the absorber.The experimental Setup is shown in Figure 28.

Several point to be explained in the numerical modelling, selection of the parameters and terminology used in this work are summarized below. This work is a numerical/simulation study as mentioned in Section 1.6 and Section 7. It is important to note that the VO₂ conductivity values (10, 100, 1,000, 5,000, 10000, and 1 × 10⁵ S/m) are values from the literature and are not points on a continuous temperature sweep and are not included in the range between insulating and metallic, as explained in Section 2.2.2. The transmission was not taken to be zero at any point and each of the absorption spectra reported was calculated from A(ω) = 1 − R(ω) − T(ω) with simulated S₁₁ and S₂₁, as described in Section 2.3. The three resonances listed in Sections 4.1–4.3 (metallic-state VO₂) and the four resonances listed in Section 4.5 (insulating-state VO₂) all refer to the same two deliberately studied operating conditions as detailed in Section 4.6.

The proposed experimental configuration therefore provides a practical pathway for validating the absorption characteristics and dual-tunable response of the graphene-ZnO-VO₂ absorber. Future work will focus on fabrication and experimental characterization of the proposed structure and quantitative comparison of the measured resonance frequencies, absorption levels, bandwidths, and tuning characteristics with the corresponding numerical results.

8 Conclusion

In this study, a parameter-optimized graphene-ZnO-VO₂ terahertz absorber was proposed and numerically investigated for tunable absorption and refractive index sensing applications. The absorber employs a connected four-cut graphene resonator integrated with a ZnO dielectric spacer and VO₂ ground layer to achieve strong electromagnetic confinement and dynamic spectral control. Through systematic optimization of the dielectric thickness, resonator dimensions, and graphene relaxation time, the absorber exhibited four near-unity absorption resonances at 0.34, 5.14, 10.11, and 15.27 THz.

Electromagnetic field and power-loss analyses revealed that the observed resonances originated from localized plasmonic and LC-resonance mechanisms supported by the graphene resonator and enhanced by the ZnO-VO₂ multilayer configuration. The optimized structure demonstrated excellent absorption performance, strong impedance matching, and efficient electromagnetic energy dissipation.

Dual tunability was achieved by modulating both the chemical potential of graphene and the electrical conductivity of VO₂. Graphene chemical-potential tuning from 0.1 to 1.0 eV enables active spectral reconfiguration with a maximum tunability factor of 152.2% and a modulation depth of 74.26%. In addition, the variation in the conductivity of VO₂ from 10 to 1 × 10⁵ S/m provides reversible broadband-narrowband switching behavior, enabling the adaptive control of the absorption response.

The proposed absorber further exhibits polarization-insensitive operation and maintains stable absorption characteristics for incidence angles of up to approximately 80°, confirming its robustness under practical operating conditions. Refractive-index sensing analysis demonstrated systematic resonance frequency red shifts as the analyte refractive index increased from 1.0 to 2.0. The highest-frequency resonance at 15.27 THz achieved a maximum sensitivity of 1.03 THz/RIU, a figure of merit of 0.26 RIU⁻¹, and a Q-factor of 3.83, indicating enhanced sensing performance and spectral selectivity.

Overall, the combination of quad-band absorption, dual tunability, broadband-narrowband switching capability, polarization-insensitive behavior, wide-angle stability, and refractive-index sensing establishes the proposed graphene-ZnO-VO₂ absorber as a versatile multifunctional platform for terahertz sensing, biochemical detection, environmental monitoring, filtering, modulation, imaging, and reconfigurable photonic applications. Future studies should focus on experimental validation, fabrication tolerance analysis, and integration with active THz devices for practical sensing and adaptive photonic applications.

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Footnotes

Edited by: Luca Varani, Université de Montpellier, France

Reviewed by: Rana Munir: Shenzhen University, China

Durgesh Kumar: D Y Patil International University, India