Far-Field Pattern Evaluation for Magnetically Biased Graphene Resonators via Quasi-Normal Modes

This paper investigates the far-field response of magnetically biased graphene plasmonic resonators at THz frequencies using a quasi-normal mode approach. The supported resonant modes are first identified by reformulating Maxwell’s equations into a linear eigenvalue problem, where graphene is modeled as an equivalent surface current. The resulting eigenstates are then normalized through a non-trivial procedure that accounts for the anisotropic nature of graphene’s surface conductivity. This normalization enables accurate evaluation of the scattered fields, which are computed via the modal coefficients of the quasi-normal modes for a general incident plane wave. Then, the scattered surface current on the graphene is used to derive the magnetic potential in spherical coordinates at any point in the domain. Finally, the far-field is reconstructed by applying the far-field approximation, which neglects the radial component of the potential. The proposed methodology is validated using a graphene disk scatterer in the THz regime, under different incident wave scenarios, and exhibits excellent agreement with results from a full-wave solver. Furthermore, it is demonstrated that the main lobe direction of the scattered field can be effectively tuned by the applied magnetostatic bias, highlighting the applicability on modern adjustable metasurface systems.