Homogenization of plasmonic crystals: seeking the epsilon-near-zero effect

Area of Science:

• Condensed Matter Physics
• Electromagnetism
• Materials Science

Background:

• Periodic structures of conducting sheets are key for novel electromagnetic phenomena.
• Designing plasmonic crystals requires understanding wave propagation in complex dielectric environments.
• The epsilon-near-zero (ENZ) effect allows for unique wave manipulation, crucial for advanced optical devices.

Purpose of the Study:

• To derive and investigate homogenized Maxwell's equations for periodically arranged conducting material sheets.
• To incorporate surface and line conductivity of two-dimensional (2D) materials into a microscopic model.
• To generalize existing averaging principles for Bloch-wave approaches in heterogeneous and anisotropic media.

Main Methods:

• Asymptotic analysis to derive homogenized equations.
• Numerical simulations to investigate the derived system.
• Incorporation of surface conductivity and line conductivity for 2D materials.
• Generalization of averaging principles for complex host materials.

Main Results:

• A system of homogenized Maxwell's equations for the described composite structure.
• Identification of the role of the vector-valued corrector field in describing surface wave modes.
• Demonstration of a foundation for computational investigations of effective optical responses.
• Insights into the design of plasmonic crystals with ENZ properties.

Conclusions:

• The derived homogenized equations provide a powerful tool for analyzing electromagnetic wave propagation in 2D material-based plasmonic crystals.
• The method facilitates the design of materials with tailored optical responses, particularly for ENZ applications.
• This work lays the groundwork for advanced computational studies in 2D material plasmonics and metamaterial design.