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Compact Localized States in Engineered Flat-Band Metamaterials.

N Lazarides^1,2, G P Tsironis^1,2

¹Department of Physics, University of Crete, P. O. Box 2208, 71003 Heraklion, Greece.

Scientific Reports

|March 22, 2019

Summary

Researchers analytically found conditions for flat bands in 1D parity-time symmetric metamaterials. Tailoring natural parameters, not geometry, creates localized eigenmodes, confirmed by simulations.

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Area of Science:

Condensed Matter Physics
Metamaterials Science
Photonics

Background:

One-dimensional (1D) metamaterials offer unique electromagnetic properties.
Parity-time (PT) symmetry in metamaterials enables novel phenomena like flat bands.
Split-ring resonators (SRRs) are fundamental building blocks for metamaterials.

Purpose of the Study:

To analytically determine the conditions for achieving flat dispersionless frequency bands in 1D PT-symmetric metamaterials.
To investigate the role of natural parameter tuning versus geometrical effects in band flattening.
To identify and characterize the emergent eigenmodes associated with these flat bands.

Main Methods:

Analytical derivation of conditions for flat bands in a binary-patterned SRR chain.
Coupling analysis considering electric and magnetic dipole-dipole interactions.
Quadratic eigenvalue problem solution to reveal eigenmode properties.
Numerical simulations to validate analytical predictions and assess mode stability.

Main Results:

Flat bands in 1D PT-symmetric metamaterials arise from tuning natural parameters, not geometry.
Tailoring specific parameters leads to the formation of compact, two-site localized eigenmodes.
Numerical simulations confirm the existence and dynamic stability of these localized modes.
Localized modes can evolve from single-site excitations without disorder or nonlinearity.

Conclusions:

The study provides an analytical framework for designing 1D PT-symmetric metamaterials with flat bands.
Compact, two-site localized eigenmodes are a key consequence of parameter-tailored flat bands.
These findings open avenues for novel applications in wave manipulation and signal processing using metamaterials.