Exceptional points and scattering of discrete mechanical metamaterials

TL;DR

This paper investigates the properties and implications of exceptional points in discrete mechanical metamaterials, focusing on their effects on wave scattering, symmetry, and potential for novel wave control applications.

Contribution

It provides a fundamental analysis of exceptional points in discrete models, highlighting their impact on scattering behavior and symmetry considerations in mechanical metamaterials.

Findings

EPs can be tuned to achieve bi-directional transparency.

Symmetry considerations influence the existence and nature of EPs.

Complex stiffness modeling reveals control over wave reflection at EPs.

Abstract

Exceptional points (EPs) are complex singularities of parametric linear operators where two or more eigenvalues and eigenvectors coalesce. EPs are attracting increasing interest in mechanical metamaterials due to their strong potentials for wave filtering, cloaking, and sensing applications. This work studies the band topology and scattering behaviors near EPs, using discrete models of metamaterial (MM) systems. The questions of existence of EPs and their physical manifestations will be addressed with particular focus on symmetry considerations and scattering behavior. Discrete mass-spring models with adjustable parameters are used here to elucidate the EP-related phenomena in a fundamental form. The transfer and scattering matrices are analyzed to provide practical insights on the restrictions associated with reciprocity and fundamental symmetries. By including complex stiffness in frequency domain as a representation of non-conservative mechanical loss or gain, the MM arrays can be tuned to achieve bi-directional transparency or one-way reflection when operating at the EPs. This analytical study will contribute to the understandings of EPs in mechanical context and the design of micro-structured media for novel applications.