Universal Route for the Emergence of Exceptional Points in PT-Symmetric Metamaterials with Unfolding Spectral Symmetries

TL;DR

This paper presents a universal method for creating exceptional points in PT-symmetric metamaterials with fractal spectral symmetries, enabling advanced control of elastic waves and sensitive sensing applications.

Contribution

It introduces a universal route for exceptional point formation in PT-symmetric metamaterials with fractal spectra, demonstrated across various complex structures.

Findings

Exceptional points form scale-free fractal patterns.

The formation of EPs is governed by spectral fractal dimension.

Universal design principles for elastic metamaterials are established.

Abstract

We introduce a class of Parity-Time symmetric elastodynamic metamaterials (Ed-MetaMater) whose Hermitian counterpart exhibits a frequency spectrum with unfolding (fractal) symmetries. Our study reveals a scale-free formation of exceptional points (EP) whose density is dictated by the fractal dimension of their Hermitian spectra. Demonstrated in a quasi-periodic Aubry-Harper, a geometric H-tree-fractal, and an aperiodic Fibonacci Ed-MetaMater, the universal route for EP-formation is established via a coupled mode theory model with controllable fractal spectrum. This universality will enable the rational design of novel Ed-MetaMater for hypersensitive sensing and elastic wave control.