Ultra‑Narrow Discrete‑Frequency Dual‑ and Triple‑Band Terahertz Metamaterial Absorbers

Introduction

Metamaterial perfect absorbers (MPAs) are engineered structures that suppress both reflection and transmission, delivering near‑total absorption at target frequencies. Their appeal stems from ultrathin footprints (often < λ/35), tunable bandwidths, and the ability to tailor resonances through geometry [1–12]. The pioneering work by a Boston College group [13] introduced a sandwich architecture of an electric‑ring resonator, dielectric spacer, and metallic backplane, achieving > 88 % absorption at 11.5 GHz. Despite these advances, many MPAs suffer from narrow angular acceptance, polarization dependence, and single‑band operation—limitations that restrict practical deployment in sensing, imaging, and detection [14–23].

To address these shortcomings, researchers have explored wide‑angle, polarization‑insensitive, and multi‑band MPAs through structural optimization. Techniques such as 1‑D stacked arrays [18] and nested metallic ring resonators [19–23] have successfully produced multiple resonances. Such multi‑band devices are particularly valuable for detecting hazardous substances, spectroscopic imaging, and selective bolometry [24–30].

Three primary strategies exist for realizing multi‑band MPAs: (1) coplanar arrangements with resonators of varying sizes within a single unit cell [19–26]; (2) vertical stacking of distinct resonant layers [27–30]; and (3) hybrid combinations of the two [31–32]. Although effective, these approaches typically yield large frequency separations between adjacent peaks (often > 50 % relative). Large spacings leave substantial off‑resonance regions, compromising the device’s ability to interrogate closely spaced spectral features. Consequently, reducing the relative discrete distance, Δ, is essential for applications that rely on resolving subtle frequency differences.

In this work, we demonstrate dual‑ and triple‑band terahertz MPAs with remarkably small Δ values. By engineering the geometry of Au strip resonators and dielectric spacers, we achieve ultra‑narrow inter‑peak spacings of 0.30 THz (Δ = 13.33 %) in the dual‑band case and 0.14–0.17 THz (Δ ≈ 6–7 %) in the triple‑band configuration. These low Δ values result from the inherently narrow bandwidths of the constituent single‑band resonances, enabling high‑resolution spectral discrimination.

Methods/Experimental

Achieving a small Δ requires each constituent resonance to have a narrow full‑width at half‑maximum (FWHM). We first design a single‑band MPA using a standard sandwich geometry: a gold (Au) rectangular strip (length l = 39 µm, width w = 8 µm, thickness 0.4 µm, conductivity 4.09 × 10⁷ S m⁻¹) atop a 2 µm dielectric layer (ε = 3(1 + i0.001)) backed by a continuous Au ground plane. The unit cell period is 60 µm.

Side views of the single‑band, dual‑band, and triple‑band MPAs are shown in (a), (c), and (d); (b) depicts the top view of the Au strip resonator.

Electromagnetic simulations were performed with Lumerical FDTD Solutions, employing periodic boundary conditions in the transverse directions and perfectly matched layers along the propagation axis. The absorption is calculated as A = 1 – R, since the backplane renders transmission negligible. This framework allows us to evaluate the absorption spectra and field distributions for each design.

Results and Discussion

The single‑band MPA exhibits a sharp resonance at 2.25 THz with ≈100 % absorption and a bandwidth of 0.06 THz (2.67 % of the center frequency). The quality factor Q = f/Δf reaches 37.5, indicating an ultra‑narrow response. Field analysis reveals that the magnetic field |Hy| is concentrated within the dielectric spacer, while the electric field |E| shows strong enhancement at the strip edges—confirming magnetic resonance as the dominant absorption mechanism.

Absorption spectrum of the single‑band MPA (a); field distributions at 2.25 THz: |Hy| (b), |E| (c), and Ez (d).

Building on this narrow‑band foundation, we constructed a dual‑band MPA by vertically stacking two Au strip/dielectric pairs on the ground plane. The strip lengths are l₁ = 36 µm and l₂ = 39 µm, with dielectric thicknesses t₁ = 1.4 µm and t₂ = 2 µm. The resulting absorption spectrum (Fig. 3a) shows two ≈100 % peaks at 2.10 THz and 2.40 THz, with bandwidths of 0.05 THz (2.00 %) and 0.09 THz (3.75 %). The relative spacing Δ is 13.33 %—substantially lower than previously reported values. Field maps indicate that the first resonance originates from magnetic coupling in the second dielectric layer, while the second resonance arises from the first dielectric layer, confirming the role of strip length in tuning each peak.

Dual‑band MPA absorption (a); |Hy| distributions for the first and second modes (b, c); absorption curves for varying l₁ (d) and l₂ (e).

By varying l₁ and l₂, we demonstrate that Δ can be tuned from 17.41 % down to 6.45 %. For instance, decreasing l₂ to 36 µm yields the smallest Δ of 0.15 THz (6.45 %). This tunability underscores the practical flexibility of the design.

Extending the stack to a triple‑band MPA—adding a third Au strip/dielectric pair with lengths l₁ = 34 µm, l₂ = 36 µm, l₃ = 39 µm and dielectric thicknesses t₁ = 1.2 µm, t₂ = 1.4 µm, t₃ = 2.8 µm—produces three ≈100 % peaks at 2.06 THz, 2.27 THz, and 2.51 THz. The inter‑peak spacings of 0.21 THz and 0.24 THz correspond to Δ values of 9.70 % and 10.04 %, respectively. Off‑resonance absorption remains below 32 %. Field analysis confirms that each resonance is associated with magnetic coupling in its respective dielectric layer.

Triple‑band MPA absorption (a); |Hy| distributions for the first (b), second (c), and third (d) modes; tuning of absorption with varying l₁ (e), l₂ (f), l₃ (g).

Tuning the strip lengths allows precise control over Δ. Adjusting l₁ primarily shifts the third mode, enabling Δ between the last two peaks to be tuned from 12.66 % down to 7.22 %. Similarly, varying l₃ or l₂ adjusts the spacing between the first two peaks. This demonstrates the versatility of the design for application‑specific spectral tailoring.

Conclusion

We have fabricated dual‑ and triple‑band terahertz MPAs featuring ultra‑narrow discrete frequencies. The dual‑band device achieves two ≈100 % absorption peaks separated by 0.30 THz (Δ = 13.33 %), which can be reduced to 6.45 % by adjusting Au strip lengths. The triple‑band structure produces three ≈100 % peaks with spacings of 0.21 THz and 0.24 THz (Δ ≈ 9–10 %), again tunable through geometric control. These low Δ values, achieved via high‑Q single‑band resonances and vertical stacking, enable the interrogation of spectral features that are otherwise obscured in conventional multi‑band MPAs. The presented designs hold promise for high‑resolution sensing, imaging, and spectroscopic applications where resolving closely spaced frequencies is critical.

Abbreviations

FWHM:

Full width at half maximum

MPAs:

Metamaterial perfect absorbers

Q:

Quality factor