# Anomalous energy transport in laminates with exceptional points

## TL;DR

This paper investigates unusual energy transport phenomena in elastic laminates, revealing modes that attenuate and propagate simultaneously, and demonstrating exceptional points leading to metamaterial effects like negative refraction and beam steering.

## Contribution

It uncovers the existence of exceptional points in in-plane elastic waves in laminates, enabling novel metamaterial behaviors not seen in anti-plane shear wave models.

## Key findings

- Modes that attenuate and propagate simultaneously
- Existence of exceptional points where modes coalesce
- Negative refraction and beam steering observed near these points

## Abstract

Recent interest in metamaterials has led to a renewed study of wave mechanics in different branches of physics. Elastodynamics involves a special intricacy, owing to a coupling between the volumetric and shear parts of the elastic waves. Through a study of in-plane waves traversing periodic laminates, we here show that this coupling can result with unusual energy transport. We find that the corresponding frequency spectrum contains modes which simultaneously attenuate and propagate, and demonstrate that these modes coalesce to purely propagating modes at exceptional points, a property that was recently reported in parity-time symmetric systems. We show that the laminate exhibits metamaterial features near these points, such as negative refraction, and beam steering and splitting. While negative refraction in laminates has been demonstrated before by considering pure shear waves impinging an interface with multiple layers, here we realize it for coupled waves impinging a simple single-layer interface. This feature, together with the appearance of exceptional points, are absent from the model problem of anti-plane shear waves which have no volumetric part, and hence from the mathematically identical electromagnetic waves. Our work further paves the way for applications such as asymmetric mode switches, by encircling exceptional points in a tangible, purely elastic apparatus.