Networks of sign-changing metamaterials: existence and spectral properties

TL;DR

This paper investigates the spectral properties and resonances of networks composed of materials with positive and negative parameters, revealing geometry-dependent behaviors and effects of boundary conditions.

Contribution

It provides new insights into the spectral behavior of sign-changing metamaterial networks, highlighting the influence of network geometry and boundary conditions on resonances.

Findings

Resonant values depend specifically on network geometry.

Boundary conditions significantly affect the spectral properties.

Resonances are linked to plasmonic phenomena in composite networks.

Abstract

We study composite assemblages of dielectrics and metamaterials with respectively positive and negative material parameters. In the continuum case, for a scalar equation, such media may exhibit so-called plasmonic resonances for certain values of the (negative) conductivity in the metamaterial. This work investigates such resonances, and the associated eigenfunctions, in the case of composite conducting networks. Unlike the continuous media, we show a surprising specific dependence on the geometry of the network of the resonant values. We also study how the problem is affected by the choice of boundary conditions on the external nodes of the structure.