Dynamic Effective Medium Theory for Two-Dimensional Non-Magnetic Metamaterial Lattices using Multipole Expansion

TL;DR

This paper develops a dynamic effective medium theory for 2D non-magnetic metamaterials using multipole expansion, enabling accurate homogenization beyond static limits for optical nanorod lattices.

Contribution

It introduces a multipole-based formulation for dynamic homogenization of 2D metamaterials, extending beyond quasi-static approximations.

Findings

Reverts to known static formulas in the quasistatic limit.

Provides a method to compute Bloch modes based on lattice geometry.

Useful for homogenizing nanorod metamaterials in optical applications.

Abstract

We present a formulation for deriving effective medium properties of infinitely periodic two-dimensional metamaterial lattice structures beyond the static and quasi-static limits. We utilize the multipole expansions, where the polarization currents associated with the supported Bloch modes are expressed via the electric dipole, magnetic dipole, and electric quadrupole moments per unit length. We then propose a method to calculate the Bloch modes based on the lattice geometry and individual unit element structure. The results revert to well-known formulas in the quasistatic limit and are useful for the homogenization of nanorod-type metamaterials which are frequently used in optical applications.