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A multimode framework that can be utilized in the analysis and design of general, non-Hermitian periodic systems that comprise contemporary 2D materials is developed. The theoretical framework is based on the concept of Quasinormal Modes (QNMs) that can be used to efficiently retrieve the spectral response of periodic systems. Both sub- and super-wavelength lattice constants are examined with extra care to include propagating higher diffraction orders. The framework is employed in two indicative configurations, a graphene-based periodic metasurface that supports tightly confined graphene surface plasmons, and a periodic dielectric metasurface enhanced with a transition metal dichalcogenide layer that supports quasi bound states in the continuum. Both configurations are of fundamental and practical interest since they exhibit controllable resonant response and, in addition, the electromagnetic properties of the involved 2D materials can be electrically tuned. The Finite Element Method (FEM) is used to retrieve the QNMs, which are then fed to the framework to specify the spectral response for the zeroth and higher diffraction orders. Full-wave FEM simulations are used to verify the validity of obtained results.
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