Terahertz (THz) technology—spanning 0.1–10 THz—represents a rapidly advancing field bridging microwave electronics and infrared photonics (Tonouchi 2007), (Siegel 2002). This spectral window is crucial for emerging technologies due to its coverage of molecular rotational/vibrational energy states and penetration capability through non-conductive materials (Ferguson and Zhang 2002). These properties enable transformative applications including ultra-high-speed wireless communications (6G and beyond) (Akyildiz et al. 2018; Rappaport et al. 2019); high-resolution medical imaging/spectroscopy for cancer detection (Li et al. 2022; Woodward et al. 2003); non-destructive material inspection (Jepsen et al. 2011); and stand-off security screening (Mittleman 2018). However, realizing these systems requires precise manipulation of THz wave properties, among which polarization control is paramount (Zheludev and Kivshar 2012). Efficient dynamic control of polarization states (e.g., TE/TM conversion) is essential for: enhancing communication signal-to-noise ratios (Cong et al. 2017); mitigating polarization-mismatch losses (He et al. 2015); and enabling polarization-sensitive imaging/spectroscopy to probe material anisotropy and surface textures (Rashid et al. 2023).

Historically, polarization control relied on conventional optical components exploiting natural material properties—such as birefringence in quartz/calcite waveplates or the Faraday effect in magneto-optical materials (Goldstein 2017). These approaches, however, prove ineffective at THz frequencies where most natural materials exhibit weak electromagnetic responses. Consequently, devices require interaction lengths spanning tens of wavelengths to achieve sufficient phase shifts (Masson and Gallot 2006), resulting in bulky, expensive systems with narrow operational bandwidths (Ako et al. 2020). To overcome these limitations, researchers have adopted metamaterials—artificially structured media with subwavelength "meta-atoms" engineered for bespoke electromagnetic responses (Pendry et al. 1999; Smith et al. 2000). Their 2D counterparts, metasurfaces, offer unprecedented control over wave amplitude, phase, and polarization within ultrathin profiles (Kildishev et al. 2013; Yu et al. 2011), enabling compact, efficient components (Glybovski et al. 2016).

For THz polarization conversion, metasurfaces are categorized as reflective or transmissive. Reflective designs typically achieve superior efficiency and bandwidth through simplified Fabry-Perot resonance mechanisms (Chen 2012).

Numerous resonator geometries have been explored for unit-cell designs, including V-shaped antennas (Grady et al. 2013), split-ring resonators (SRRs) (Cheng et al. 2014), cross-shaped structures (Ahmad et al. 2022)d shaped resonators (Xu et al. 2018). While demonstrating significant improvements over conventional approaches, these designs often face critical performance trade-offs. A persistent challenge remains the simultaneous achievement of high polarization conversion ratio (PCR), broad bandwidth, and angular stability across wide incidence angles (Zhang et al. 2022). For instance, single-layer designs typically achieve near-unity PCR at discrete resonant frequencies but exhibit rapid performance degradation under frequency detuning or oblique incidence (Yang et al. 2024). Multi-layer structures—proposed to broaden bandwidth through stacked resonators exciting adjacent resonances (Dong et al. 2016; Fei et al. 2020)—still suffer from fabrication complexity and pronounced angular sensitivity. These limitations necessitate further innovation.

This paper addresses these challenges through a novel three-layer passive metasurface polarization converter optimized for THz frequencies. The design employs vertically stacked copper ring resonators on a low-loss silicon substrate, enabling efficient bidirectional TE/TM conversion. The simple ring geometry ensures robustness, while numerical optimization of the tri-layer stack facilitates excitation of overlapping resonances. This strategy achieves > 90% polarization conversion efficiency across a 1–1.8 THz bandwidth while maintaining high performance for incidence angles up to 60°—a substantial improvement in angular stability over prior designs. Fabrication leverages established copper/SiO₂ deposition and photolithography techniques (Zhang et al. 2005), ensuring compact, robust, and system-integrable devices. This work provides a high-performance solution for dynamic polarization control in advanced THz communication, imaging, and sensing systems operating under variable angles.

The performance of the proposed FSS filter is governed by its geometric parameters and material composition. As illustrated in Fig. 1, the structure features four vertically stacked dielectric layers (thicknesses ℎ₁​ to ℎ₄) aligned along the z-axis. The top SiO₂ layer (ℎ_1​) functions as both protective coating and anti-reflection element, while the underlying silicon layers (ℎ₂​, ℎ₃​, ℎ₄​) embed copper resonators.

Unit cells are arranged periodically in the x-y plane with lattice constant p, a critical parameter controlling resonant frequency and bandwidth. Three sets of split-ring resonators (SRRs) embedded across different layers serve as the primary frequency-selective elements. Each SRR is defined by radius (R₁​, R₂​, R₃​), width (W₁​,W₂​, W₃​), and capacitive gap (C₁​, C₂​, C₃), with the incomplete loops creating gaps essential for resonant tuning.

The unit cell design, illustrated in top-down views (Fig. 1), positions each ring resonator at distinct depths within the stack, enabling vertical integration. This multi-layered configuration with varied ring dimensions achieves tailored frequency responses, specifically enabling broadband filtering across the THz range.

Optimization of layer thicknesses (ℎ₁​-ℎ₄​), periodicity (p), and ring geometric parameters (R_x​, W_x​, C_x​) is critical for resonance control. We numerically optimized these parameters to position resonances at target frequencies, with final design values listed in Table 1.

To support the full-wave numerical simulations, we develop a comprehensive multilayer analytical model based on classical thin-film interference theory and generalized Fresnel reflection principles. This theoretical framework elucidates the physical mechanisms by which the proposed vertically stacked split-ring resonator metasurface achieves broadband polarization conversion between TE and TM modes through strategic suppression of co-polarized reflection combined with enhanced anisotropic cross-polarization coupling.

The top SiO₂ layer functions as an AR coating. The quarter-wave optical thickness condition (Xiong et al. 2013) as where is the target wavelength and is the refractive index of the AR coating. The odd integer enforces a π-phase difference between reflections at the air–SiO₂ and SiO₂–Si interfaces, minimizing co-polar reflectance. Such destructive interference enhances the relative strength of cross-polarized components generated by the SRRs.

Transmit () field amplitudes in layer d follow the generalized Fresnel recursion (Parratt 1954):

Where denotes the polarization of wave (TE, TM (, and is the z component of the wavevector in layer d, and is the Fresnel reflection coefficient at the interface between layers d and (d + 1). The boundary condition at the bottom perfectly conducting ground plane (layer N) is Recursively solving Eq. (1) from the bottom layer upward yields the total reflection coefficient (Zhou et al. 2010) as .

The overall co-polar reflectance is given by the classical Airy thin-film formula (Sun et al. 2011):

Here, and are the Fresnel reflection and transmission coefficients at interface , respectively. The phase term is defined as and where are the reflection phase shift at each interface, accounts for transmission phase accumulation, is the effective complex permittivity of the multilayer AR coating, is the free space wave number, and is the incident angle in the substrate. Co-polar reflection is minimized when:

= (2N+1) π, N ∈ ℤ(4)

When these conditions are met, destructive interference occurs at the dielectric interfaces, suppressing the co-polarized reflection to near zero. Consequently, the split-ring resonators (SRRs) efficiently rotate the polarization of the incident field from TE to TM (and vice versa). This conversion arises from SRR-induced resonant surface currents at the target wavelength, which generates the required cross-polarized response at the interface.

Due to the circular shape of the SRRs, the surface current excited by the incident field exhibits both Jx and Jy component on the surface of the conductor (Fig. 5). Under resonant excitation, the Jx currents on the two split sections are out of phase and therefore cancel in the far field, whereas the Jy components remain in phase and add constructively. As a result, a pronounced cross-polarized response is produced, consistent with the strong polarization conversion observed in the extracted S-parameters.

As can be seen in the S-parameter S11 TE-TE versus frequency, (Fig. 3) in certain frequencies we observe deep spectral dips. These resonance frequencies correspond to regions where the above-mentioned conditions are satisfied, and co-polar reflection component approaches to zero.

The SRR layers are geometrically anisotropic (R₁<R₂<R₃, with differing capacitive gaps C_i), producing off-diagonal reflection terms (Ahmad et al. 2022):

When (2)– (4) suppress the diagonal terms ρ_TE,TE and ρ_TM,TM, the cross-polar terms dominate. Reciprocity gives ρ_TE,TM = ρ_TM,TE. This produces bidirectional conversion with near unity polarization conversion ratio (PCR > 0.95) and angular stability up to 60 incidence angles.

Figure 3 presents CST simulation results for the polarization converter under TE- and TM-polarized plane wave illumination across varying incidence angles.

As shown in Fig. 3a, resonant dips occur in the 1–1.8 THz range for co-polarized reflections (TE/TE and TM/TM), reaching approximately − 15 dB. These minima arise from destructive interference between incident and reflected waves. Conversely, cross-polarized reflections (TE/TM and TM/TE) exhibit near-unity magnitude (approaching 0 dB) across this bandwidth (Fig. 3a), confirming efficient polarization conversion. This demonstrates the FSS metasurface enables robust TE/TM mode conversion over 1–1.8 THz.

The stacked SRR layers create multiple reflection paths for incident waves. Phase oscillations result from interference between waves reflected from the top resonator layer and also from waves penetrating deeper layers and reflecting from subsequent resonators/substrates. Phase changes linearly between resonances (e.g., smooth slopes in Fig. 3b) represent propagation delays through dielectric layers and the slope magnitude (dω/dϕ) relates to the effective electrical length of the structure.

Figure 5 illustrates the surface current distributions across the three split-ring resonators (SRR₁, SRR₂, SRR₃) within the FSS metasurface at four resonant frequencies. At 1 THz (Fig. 5a), currents localize predominantly along SRR₃'s inner edges, indicating fundamental resonance excitation. Minimal activity occurs in SRR₁, while SRR₂ exhibits weak coupling. By 1.3 THz (Fig. 5b), the resonance shifts to SRR₂-dominant with symmetric current patterns, accompanied by diminished SRR₁/SRR₃ contributions. At 1.6 THz (Fig. 5c), strong hybrid resonance emerges between SRR₃ and SRR₁, with secondary SRR₂ excitation. Finally, at 1.8 THz (Fig. 5d), asymmetric currents intensify in SRR₂ and SRR₃, while SRR₁ participation remains negligible.

These distinct modal distributions confirm that coupled SRR resonances generate destructive interference, producing the sharp reflection minima at 1.0, 1.3, 1.6, and 1.8 THz observed in Fig. 3. This multi-resonator synergy enables precise spectral control across the 1–1.8 THz operational band.

Complementary field analyses (Fig. 6) elucidate wave-matter interactions. The electric field (Figs. 6a, 6c) concentrates at unit-cell boundaries, traversing SRRs as electric dipoles. At 1 THz, strong confinement occurs at SRR₃ (Fig. 6a), shifting to SRR₂ at 1.3 THz (Fig. 6c) consistent with current distributions. Conversely, the magnetic field (Figs. 6b, 6d) circulates around resonator edges, confirming distinct polarization-dependent coupling mechanisms.

To model the frequency-selective response of the metasurface, an equivalent circuit was developed that accounts for both Fabry-Perot resonances in the dielectric stack and split-ring resonator interactions. The circuit (Fig. 7a) employs four cascaded transmission line segments (TLIN₁–TLIN₄) corresponding to the SiO₂ cap (h₁) and silicon interval-layers (h₂–h₄), with electrical lengths proportional to physical layer thicknesses. Each split-ring resonator is represented by coupled LC networks where the conductive rings provide series inductance (L) and the capacitive gaps introduce shunt capacitance (C). Impedance discontinuities at dielectric interfaces are inherently modeled through transmission line impedance variations, not explicit grounding. The circuit is terminated with 377 Ω ports to emulate standard measurement conditions.

Validation in Fig. 7b demonstrates reasonable agreement between circuit simulations and full-wave results across the 1–1.8 THz operating band, confirming its ability to predict: 1) Fabry-Perot resonance frequencies governed by cumulative layer thicknesses, 2) resonance quality factors controlled by SRR LC ratios, and 3) cross-polarization efficiency linked to gap capacitance asymmetry. This model enables performance tuning through parameter adjustments: Increasing SRR gap widths (W₁, W₂, W₃) reduces shunt capacitance, broadening resonance bandwidths; modifying ring radii scales inductance, shifting coupled-resonance frequencies; and varying layer thicknesses (h₁–h₄) alters transmission line lengths, controlling Fabry-Perot mode spacing. Physical dimensions thereby map directly to circuit components for targeted THz spectral shaping.

Fabrication feasibility guided the metasurface design, with materials selected for THz-optimized dielectric properties and microfabrication compatibility. The process, detailed in Fig. 8, begins with a high-resistivity silicon substrate (> 10 kΩ·cm) to minimize THz absorption. A 5–10 nm chromium adhesion layer is deposited via e-beam evaporation, followed by 200 nm copper to form the base conductive plane.

The first SRR layer is patterned using photolithography: photoresist spin-coating, UV exposure through a photomask defining ring geometry (radius R₁ = 16.6 µm, gap C₁ = 2.25 µm), development, and 100 nm copper evaporation. Liftoff yields the defined SRRs. Low-pressure chemical vapor deposition (LPCVD) then grows a 10.0 µm crystalline silicon spacer (h₄).

The sequence repeats for subsequent layers: Photolithography patterns SRR₂ (R₂ = 23.0 µm, C₂ = 5.9 µm) followed by 100 nm copper evaporation and LPCVD of a 9.15 µm silicon layer (h₃). Precise alignment ensures functional integrity during SRR₃ patterning (R₃ = 31.6 µm, C₃ = 7.3 µm), copper evaporation, and deposition of the final 10.5 µm silicon spacer (h₂) via LPCVD.

A 26.3 µm silicon dioxide cap layer is deposited by plasma-enhanced CVD (PECVD) in staged cycles (< 5 µm/layer) with 300°C anneals to mitigate film stress. Alternatively, spin-on-glass (SOG) with pyrolysis annealing provides a stress-relieved oxide. Critical features—including subwavelength periodicity (p = 34.7 µm) and ring widths down to W₁=2.7 µm—are achievable through i-line photolithography or electron-beam patterning.

This fabrication framework enables physical realization of the broadband polarization converter, with design parameters aligning with standard microfabrication capabilities for THz system integration.

Figure 7. (a) Equivalent circuit model of the FSS metasurface featuring cascaded transmission lines (TLIN₁–TLIN₄) for SiO₂/Si dielectric layers and coupled LC networks modeling split-ring resonators. (b) Validation: Full-wave electromagnetic simulation (solid lines) versus equivalent circuit simulation (dashed lines) of reflection coefficient magnitudes across 1–1.8 THz.

This work demonstrates a multi-layer FSS metasurface achieving efficient, angularly stable TE-TM polarization conversion across 1–1.8 THz. By vertically stacking copper ring resonators on a silicon/silicon dioxide platform, the design enables > 90% conversion efficiency while maintaining robust performance for incidence angles up to 60°—significantly outperforming conventional single-layer converters. Three key advances underpin this breakthrough: Broadband operation stems from four coupled resonances (1.0, 1.3, 1.6, 1.8 THz) generated through Fabry-Perot modes in dielectric spacers and SRR hybridization; angular insensitivity arises from optimized periodicity (p = 34.7 µm) and substrate thicknesses; and CMOS-compatible fabrication employs lithographically patterned copper resonators (minimum feature width 2.7 µm) with LPCVD/PECVD dielectric stacking. Validated through full-wave simulations and equivalent circuit modeling, this architecture overcomes fundamental limitations of narrow bandwidth and angular sensitivity in THz polarization control. The design is readily integrable into 6G communication systems (beamforming arrays), polarization-sensitive imaging diagnostics, and material birefringence sensors. Future work will explore active tuning via vanadium dioxide interlayers and experimentally validate the staged PECVD fabrication process.