Homogenization of plasmonic crystals: Seeking the epsilon-near-zero effect
This work provides a theoretical foundation for designing plasmonic crystals with epsilon-near-zero effect, but is incremental as it extends existing homogenization methods.
The authors derive homogenized Maxwell's equations for periodically arranged conducting sheets in a heterogeneous dielectric host, aiming to enable epsilon-near-zero propagation. The work generalizes previous Bloch-wave approaches and highlights the role of a vector-valued corrector field for surface waves.
By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell's equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic dielectric host. This structure is motivated by the need to design plasmonic crystals that enable the propagation of electromagnetic waves with no phase delay (epsilon-near-zero effect). Our microscopic model incorporates the surface conductivity of the two-dimensional (2D) material of each sheet and a corresponding line charge density through a line conductivity along possible edges of the sheets. Our analysis generalizes averaging principles inherent in previous Bloch-wave approaches. We investigate physical implications of our findings. In particular, we emphasize the role of the vector-valued corrector field, which expresses microscopic modes of surface waves on the 2D material. We demonstrate how our homogenization procedure may set the foundation for computational investigations of: effective optical responses of reasonably general geometries, and complicated design problems in the plasmonics of 2D materials.