Compact Localized States in Engineered Flat-Band $\cal PT$ Metamaterials

TL;DR

This paper analytically demonstrates how flat, dispersionless bands and localized states can be engineered in one-dimensional $ ext{PT}$ symmetric metamaterials with split-ring resonators, without relying on geometrical effects.

Contribution

It introduces a method to create flat bands and localized states in $ ext{PT}$ metamaterials by tuning coupling parameters, not geometry, and confirms their stability through simulations.

Findings

Flat bands arise from parameter tuning, not geometry.

Existence of stable, two-site localized eigenmodes.

Localized modes can be formed from single-site excitations.

Abstract

The conditions leading to flat dispersionless frequency bands in truly one-dimensional parity-time ($\cal PT$) symmetric metamaterials comprising split-ring resonators (SRRs) arranged in a binary pattern are obtained analytically. In this paradigmatic system, in which the SRRs are coupled through both electric and magnetic dipole-dipole forces, flat-bands may arise from tailoring its natural parameters (such as, e.g., the coupling coefficients between SRRs) and not from geometrical effects. For sets of parameters which values are tailored to flatten the upper band of the spectrum, the solution of the corresponding quadratic eigenvalue problem reveals the existence of compact, two-site localized eigenmodes. Numerical simulations confirm the existence and the dynamic stability of such modes, which can be formed through the evolution of single-site initial excitations without disorder or nonlinearity.