Electro-optic Modulator Based on a Graphene-embedded Metasurface
Optical metasurfaces, composed of subwavelength unit cells, are two-dimensional artificial platforms that enable exceptional electromagnetic wave manipulation unattainable in natural materials, playing pivotal roles in enhancing light-matter interactions [1]. Resonance, ubiquitous in both metallic and dielectric structures, is a fundamental physical mechanism that underpins the strong optical responses of metasurfaces. Leveraging these optical resonances, electromagnetic energy can be tightly confined within subwavelength meta-atoms, leading to substantial near-field enhancement [2]. Through judicious structural design, integrating such near-field enhancements with active materials can yield significant improvements in the efficiency of photodetection and optical modulation [3]. This approach thus provides an effective technological pathway toward realizing compact, planar, and reconfigurable photonic devices.
In this work, we propose a graphene-embedded metasurface, as schematically illustrated in Fig. 1. The structure comprises an array of high-index Si grating on a low-index SiO2 spacer, with a monolayer of graphene interposed between them. Beneath the spacer layer lies a 100-nm-thick Au film, which completely blocks the transmission of near-infrared light, thereby constituting a reflective-type metasurface. Leveraging the physical mechanism of bound states in the continuum (BICs), a near-perfect absorption resonance with a high quality factor (Q) is established by deliberately breaking the in-plane symmetry of the grating units. The resonance engenders a strong in-plane electric field that efficiently interacts with the graphene layer; consequently, high-contrast dynamic modulation of the resonance can be achieved by tuning the Fermi energy (Ef) of the graphene, as evidenced by the near-infrared reflectance spectra presented in the lower-right panel of Fig. 1.
The numerical simulations are performed using the Wave Optics Module in COMSOL Multiphysics, encompassing both full-wave wavelength-domain simulations and eigenmode analyses. The unit cell of the metasurface is modeled using Floquet periodic boundary conditions to simulate an infinite array, with periodic ports configured to excite plane-wave incidence. The graphene layer is modeled using the built-in transition boundary condition, with its surface conductivity defined as a function of Ef through an analytic function in the Global Definitions node based on the Kubo formula.
Together with the reflection spectra, our results confirm that near-perfect absorption is achieved under the critical-coupling condition, specifically when Qrad = Qdis. Upon increasing the Ef from 0 to 0.8 eV, the resonance dip undergoes a blue shift of approximately 3 nm, accompanied by a pronounced suppression of reflectance from ~0.7 to near-zero levels, yielding a modulation depth of nearly 100%. Collectively, these findings demonstrate that the metasurface reflectance can be dynamically and efficiently controlled through external voltage control of the graphene’s Ef.
This study validates the feasibility of achieving dynamically tunable optical responses in graphene-based metasurfaces via external voltage control, providing a theoretical foundation for the design of tunable optoelectronic devices such as modulators, filters, and detectors.
