Hybrid Silicon–Graphene Metasurface: Ultra‑Thin, Tunable Polarization Converter with 96% Efficiency

Background

All‑dielectric metasurfaces have emerged as the preferred platform for low‑loss, high‑efficiency optical manipulation, outperforming plasmonic analogues that suffer from radiative and ohmic dissipation [1, 2]. Silicon, titania, and silicon nitride support magnetic resonances with minimal absorption, enabling the design of devices that combine high Q‑factors with broadband performance [7–9]. Recent advances in graphene‑based Fano resonances have further reduced losses by exploiting the material’s tunable conductivity and high carrier mobility [10–20]. While split‑ring resonators and other sub‑wavelength elements have been extensively studied in plasmonic metasurfaces, they remain limited by ohmic losses and low transmittance [24, 25]. In contrast, dielectric meta‑devices can reach efficiencies approaching 99 % and exhibit high birefringence ratios in the terahertz and near‑infrared regimes [26, 27], though tunability mechanisms are still scarce. Our work introduces a controllable birefringence scheme that couples gate‑bias tuning of graphene with structural geometry to achieve dynamic polarization control. By integrating a graphene monolayer beneath a silicon cross‑antenna, we create a hybrid metasurface that harnesses strong localized electric and magnetic Mie‑type resonances, yielding near‑unity transmission while preserving high Q‑factors [28–30]. This design overcomes impedance mismatch and enables precise phase and polarization manipulation within a compact footprint.

Methods

The unit cell comprises a silicon cross‑antenna (εr = 12.25) atop a monolayer graphene sheet (modeled as a 1 nm thick mesh) and a silica substrate (εr = 2.25). Geometric parameters are L1 = 450 nm, L2 = 370 nm, h = 110 nm, W = 60 nm, with periodicities Px = 600 nm and Py = 560 nm (Fig. 1a). Periodic boundary conditions and a perfectly matched layer were applied to simulate an infinite array under normal incidence. The transmission coefficients Txx and Tyy were extracted from the scattered electric fields, while the phase delay ΔΦ = Φxx – Φyy was computed 1.2 µm above the metasurface. The graphene conductivity σ = σI + σD was calculated using the random‑phase approximation, with Fermi energy EF = ħνF(πns)½ and a scattering rate τ ≈ 0 (dominant interband transitions at near‑IR). Detailed expressions for the real and imaginary permittivity components ε′g and ε″g are given in equations (2) and (3). Finite‑element simulations were performed in COMSOL Multiphysics to evaluate the optical response across a range of Fermi energies (0–0.8 eV) and silicon dimensions.

Results and Discussion

Birefringence Control Through Fermi Energy and Structure Dimensions

Simulations of the all‑dielectric structure without graphene reveal a sharp, high‑Q resonance at λ = 1.49 µm, driven by a trapped magnetic mode (Fig. 2a). The field distribution shows anti‑parallel in‑plane electric fields that produce destructive interference between electric and magnetic dipoles (Fig. 2b,c). Introducing graphene between the silicon and silica attenuates the displacement current, reduces the Q‑factor, and shifts the resonance to λ = 1.50 µm (Fig. 3b). By varying EF, the resonance intensity is tuned: undoped graphene (EF = 0 eV) exhibits the strongest response, while increased doping suppresses absorption through Pauli blocking, leading to a more inductive graphene response (Fig. 3c). Adjusting the asymmetry parameter L2 modulates the coupling between magnetic and electric modes. At L2 ≈ 410 nm the symmetry breaks, splitting the modes and enabling a 90° phase difference between the x‑ and y‑polarized transmitted fields (Fig. 4a). When L2 is set to 365 nm or 450 nm, the phase bandwidth remains within ±10° for RCP and LCP, respectively (Fig. 4c). Furthermore, tuning EF from 0 to 0.8 eV controls the phase bandwidth, achieving ΔΦ ≈ 90° at λ = 1.49 µm for EF = 0.8 eV (Fig. 4d). The Stokes parameters confirm near‑perfect circular polarization at λ = 1.5 µm (|S3|/S0 ≈ 1). The polarization conversion ratio (PCR) peaks at 96 % for RCP and 90 % for LCP within the 1.48–1.51 µm range, dropping to 80 % at 1.52 µm (Fig. 5c). The device shows little sensitivity to the incident polarization angle, maintaining an amplitude ratio close to unity and a 90° phase shift across a broad angular range (Fig. 5d). Phase retardation maps across periodicities Px and Py demonstrate that the Q‑wave plate condition occurs along a diagonal line where Px and Py are inversely related, while maintaining transmittance above 80 % (Fig. 6a,b). This tunability offers a straightforward route to customize the metasurface for specific wavelength windows.

Birefringence Switching Through Gate Voltage Biasing

By embedding a gate electrode across the y‑direction of the silicon/graphene stack (Fig. 7a), the Fermi level can be modulated via a gate voltage Vg. The capacitance per unit area C = εsiε0/Px links Vg to the carrier density ns = CVg/e, which in turn adjusts EF. Simulation results show that at λ = 1.5 µm, a forward bias of +47.5 V flips the scattered light from RCP to LCP, while a reverse bias of –47.5 V produces the opposite handedness (Fig. 7b‑c). The phase retardation varies non‑linearly with Vg, reflecting changes in graphene conductivity. Stokes‑parameter spectra confirm that |S3| approaches unity (>90 %) for both logical states across 1.49–1.52 µm (Fig. 7d). Phase maps of Ez at λ = 1.5 µm illustrate the rotation of the trapped magnetic mode as Vg is inverted, providing a clear visual of the switching mechanism (Fig. 8a‑b).

Conclusions

We have designed a hybrid silicon–graphene metasurface that serves as a compact, high‑efficiency quarter‑wave plate with tunable birefringence. By adjusting the silicon geometry or applying a gate bias, the device can dynamically convert incident linear polarization into either right‑ or left‑handed circular polarization with >96 % efficiency in the 1.45–1.54 µm band. The ultrathin profile, absence of plasmonic losses, and compatibility with standard CMOS fabrication make this structure a promising candidate for on‑chip photonic sensing and optical communication applications.