Ultra‑Broadband, Tunable Terahertz Absorber Based on Multi‑Layer Graphene Ribbons

Background

The terahertz (THz) band has emerged as a pivotal platform for spectroscopy, medical imaging, security, and wireless communication due to its unique spectral fingerprints and high‑frequency performance [1–3]. Among the THz devices, absorbers play a crucial role, enabling energy harvesting, stealth, and signal processing. Traditional THz absorbers, however, suffer from narrow bandwidths, limited absorption efficiency, and static response, which constrain their practical deployment.

Graphene—a two‑dimensional honeycomb lattice of carbon atoms—has attracted intense interest because its electrical conductivity can be precisely modulated by electric fields, magnetic fields, gate voltage, or chemical doping [7–14]. Graphene supports surface plasmons in the THz range with exceptionally low loss and high tunability, outperforming conventional plasmonic materials [15–19]. Consequently, graphene has been incorporated into numerous absorber designs, including net‑shaped, anti‑dot, and cross‑shaped patterns [20–34]. Nevertheless, these structures typically require complex patterning, exhibit narrow operational bandwidths (<1.5 THz), and lack robust switching capabilities.

Recent multi‑layer graphene absorbers have attempted to broaden the bandwidth but still rely on intricate geometries and deliver limited performance [32–34]. Zhao et al. demonstrated a switchable absorber by varying the graphene chemical potential from 0 to 0.3 eV, achieving absorption >90 % and reflection >82 % in 0.53–1.05 THz; however, the modulation depth and bandwidth remained insufficient for practical applications [25].

In this work, we present a tunable, ultra‑broadband THz absorber that leverages a stack of nine graphene ribbons embedded in dielectric layers. This configuration achieves >90 % absorption across 3–7.8 THz with an average absorptivity of 96.7 % and can be dynamically switched between absorbing and reflecting states by adjusting the Fermi energy of each graphene layer. The absorber is structurally simple, avoiding complex patterning, and demonstrates angular robustness and fabrication tolerance, positioning it as a versatile platform for next‑generation THz technologies.

Methods

The absorber architecture, illustrated in Fig. 1, consists of a gold ground plane, a dielectric spacer (ε = 3), a SiO₂ layer (ε = 4), and nine graphene ribbons of varying widths (W = 5, 5, 27, 4, 4, 2, 21, 21, 26 µm from top to bottom) embedded in the dielectric. The ribbons are positioned at a distance t₂ = 2 µm from the SiO₂ interface, while the dielectric thickness above the ground plane is H₁ = 21 µm and the SiO₂ thickness is H₂ = 7 µm. The unit cell period is P = 32 µm. The gold film is modeled with the Drude permittivity ε = ε∞ – ω_p²/(ω² + iωγ), with ε∞ = 1, ω_p = 1.38 × 10¹⁶ rad s⁻¹, and γ = 1.23 × 10¹³ s⁻¹ [41].

Graphene is treated as an ultrathin conductive sheet. Its surface conductivity σ(ω, E_f, τ, T) is calculated using the Kubo formula [40]:
σ(ω)=σ_intra + σ_inter = (je²(ω – j/τ))/(πħ²) × [ ... ],
where the Fermi‑Dirac distribution f_d(ε) appears. The conductivity can be tuned by the Fermi energy E_f, which in turn is controlled by an external bias voltage V_n according to:
|E_f(V_n)| = ħv_F√[π|a₀(V_n – V₀)|], n = 1…9, with v_F = 0.9 × 10⁶ m s⁻¹ and a₀ = ε₀ε_d/(ed). The corresponding graphene permittivity is ε_g = 1 + iσ_g/(t_gε₀ω).

Numerical evaluation employed a two‑dimensional finite‑difference time‑domain (FDTD) solver. Periodic boundary conditions were applied along the x‑direction, while a plane wave impinged normally along z with electric field polarized along x. Reflection R and transmission T were extracted, and absorption A = 1 – R – T was calculated. Since the gold backing is opaque (T ≈ 0), A simplifies to 1 – R.

Results and Discussion

By assigning Fermi energies E_f = (0.9, 0.9, 1.1, 0.8, 0.8, 1.1, 1.1, 0.9, 0.8) eV to the nine ribbons (top → bottom), the simulated absorption spectrum (Fig. 2) shows a continuous band exceeding 90 % over 3–7.8 THz, yielding a 4.8 THz bandwidth and a full‑width at half maximum of 5.4 THz. The average absorptivity across the band is 96.7 %. When all ribbons are unbiased (E_f = 0 eV), the structure behaves as a near‑ideal reflector with >90 % reflectivity throughout the same frequency range, rising to >97 % above 5.5 THz.

To elucidate the broadband behavior, we first examined a single‑layer configuration (Fig. 3). Varying E_f shifts the graphene surface‑plasmon resonance, increasing absorption and blue‑shifting the peak. Adjusting ribbon width W and vertical position t modifies the resonance amplitude and frequency, confirming that impedance matching governs the absorption peak.

In a three‑layer stack (Fig. 4), carefully chosen widths (W = 26, 21, 20 µm) and a uniform Fermi level of 0.9 eV produce three near‑perfect peaks at 4.7, 5.2, and 5.7 THz, yielding a 1.3 THz high‑efficiency band. Extending to nine layers and iteratively tuning each ribbon’s E_f (see Fig. 5), the resonances overlap to form a single ultra‑broadband absorption exceeding 90 % across 4.8 THz. The field‑distribution snapshots (Fig. 6) reveal strong confinement between successive graphene layers and the dielectric, indicating that localized surface plasmons (LSPs) and graphene plasmons synergistically drive the absorption.

Angular robustness was verified by rotating the incidence up to 50° (Fig. 8). Even at 30°, the absorption remains essentially unchanged, and at 50° it stays above 90 % across the entire band, underscoring the design’s practical viability.

Fabrication tolerance was assessed by varying the dielectric (H₁) and SiO₂ (H₂) thicknesses (Fig. 9). Deviations of ±0.5 µm in H₁ leave performance largely intact, while H₂ shows slightly higher sensitivity but still preserves >90 % absorption over most of the band. These findings demonstrate the structure’s robustness against realistic manufacturing variations.

Conclusions

We have introduced a simple, scalable, and tunable terahertz absorber that exploits a stack of graphene ribbons to achieve >90 % absorption over a 4.8 THz bandwidth (3–7.8 THz). By electrically adjusting the Fermi energies of individual graphene layers, the device can be switched between highly absorbing and highly reflecting states, offering a large modulation depth (>90 %). The absorber’s angular tolerance (>90 % up to 50°) and fabrication robustness further strengthen its appeal for photodetectors, imaging, and modulation applications.

Abbreviations

FDTD:

Finite‑difference time‑domain

LSP:

Localized surface plasmon