研究目的

The problem or phenomenon addressed in this study is the homogenization of time-harmonic Maxwell’s equations in a periodic, layered structure made of two-dimensional (2D) metallic sheets immersed in a heterogeneous and in principle anisotropic dielectric medium. The goal is the rigorous derivation of the effective dielectric permittivity of the system from the solution of a local cell problem via suitable averages.

研究成果

The study concludes with the rigorous derivation of the effective dielectric permittivity of the system from the solution of a local cell problem via suitable averages. The effective permittivity and cell problem express a bulk average from the host dielectric and a surface average germane to the 2D material (metallic layer). The implications of this analysis in the modeling of plasmonic crystals are discussed, including the design of plasmonic crystals that exhibit no refraction (epsilon-near-zero effect).

研究不足

The technical and application constraints of the experiments include the assumption that the bulk material surrounding the metallic sheets is slightly lossy, which amounts to the addition of a small, positive imaginary part to the dielectric permittivity εd. Potential areas for optimization include extending the analysis to more general settings, such as tensorial parameters εd and σ d, and non-planar sheets.