Anomalous energy transport in laminates with exceptional 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.

Linking Scalar Elastodynamics and Non-Hermitian Quantum Mechanics

“…Despite the huge difference in the length scale that the two theories were developed for, fascinating realizations of quantum phenomena were demonstrated using macroscopic systems in recent years [2]. Examples include the Hall effect [3,4], geometric phase [5], and negative refraction [6][7][8][9][10]. Special attention is given to extraordinary transport properties based on PT symmetry [11][12][13][14][15][16][17][18], which corresponds to the commutativity of an operator with combined parity-time reversal operators.…”

Exploring Metamaterials’ Structures Through the Relaxed Micromorphic Model: Switching an Acoustic Screen Into an Acoustic Absorber

“…When considering the dynamical behavior of mechanical metamaterials, things become, if possible, even more impressive, given the unusual responses that such metamaterials can provide when coming in contact with elastic waves (Deymier, 2013;Hussein et al, 2014;Barchiesi et al, 2019). It is today possible to find researchers working on metamaterials exhibiting band-gaps (Liu et al, 2000;Wang et al, 2014;Zhu et al, 2015;Bilal et al, 2018;El Sherbiny and Placidi, 2018;Celli et al, 2019;Goh and Kallivokas, 2019;Koutsianitis et al, 2019), cloaking (Norris et al, 2014;Bückmann et al, 2015;Misseroni et al, 2016;Misseroni et al, 2019), focusing (Guenneau et al, 2007;Cummer et al, 2016), channelling (Kaina et al, 2017;Tallarico et al, 2017;Wang et al, 2018;Bordiga et al, 2019;Miniaci et al, 2019), negative refraction (Zhu et al, 2015;Srivastava, 2016;Willis, 2016;Bordiga et al, 2019;Lustig et al, 2019;Morini et al, 2019), etc., as soon as they interact with mechanical waves.…”

Flexural wave absorption by lossy gradient elastic metasurface

“…Fortunately, similar methods (Willis, 2016;Srivastava, 2016), which are also called mode-coupling methods for consistency, had been used in elastic waves to study negative refraction of anti-plane shear waves at a plane interface between a homogeneous elastic half-space and a layered periodic composite. Recently, these methods (Lustig et al, 2019;Lustig and Shmuel (2018); Mokhtari et al, 2019;Mokhtari et al, 2020) had been extended to study the scattering of in-plane elastic waves.…”