Parity-Time Symmetry and Exceptional Points for Flexural-Gravity Waves in Buoyant Thin-Plates

Mohamed Farhat,Pai-Yen Chen,Sebastien Guenneau,Ying Wu

doi:10.3390/cryst10111039

Abstract

We derive and apply a transfer matrix method (M-matrix) coupling liquid surface waves and flexural-gravity waves in buoyant thin elastic plates. We analyze the scattering matrix (S-matrix) formalism for such waves propagating within a Fabry-Perot like system, which are solutions of a sixth order partial differential equation (PDE) supplied with adequate boundary conditions. We develop a parity-time (PT)-symmetry theory and its applications to thin elastic floating plates. The sixth order PDE governing the propagation of these waves leads to six by six M and S matrices, and results in specific physical properties of the PT-symmetric elastic plate systems. We show the effect of geometry and gain/loss on the asymmetric propagation of flexural-gravity waves, as well as a Fano-like line-shape of the reflection signature. Importantly, we show the possibility of obtaining coherent perfect absorber-laser (CPAL) using simple thin structures.

Highlights

Wave propagation in complex media is a vibrant research topic that spans a multidisciplinary spectrum, ranging from electromagnetism, acoustics, elastodynamics, hydro-dynamics, and matter waves [1,2]
We have shown that P T -symmetry breaking resulting in exceptional point (EP) can be generalized to the peculiar situation of coupled liquid surface water (LSW) and FG waves
The scattering of flexural-gravity waves propagating in layered buoyant thin-plates was analytically studied by means of the transfer matrix and scattering matrix formalism, and was subsequently analyzed

Summary

Introduction

Wave propagation in complex media is a vibrant research topic that spans a multidisciplinary spectrum, ranging from electromagnetism, acoustics, elastodynamics, hydro-dynamics, and matter waves [1,2]. One such example of interest in this realm is metamaterials and metasurfaces that consist of resonant elements (three-dimensional (3D) and 2D, respectively). The field of solid-state electronics has grown thanks to semiconductor materials [16]. These crystalline media (e.g., Si or GaAs) allow for the control and/or storage of electrons. The extension of semiconductors to the realms of waves (electromagnetic, acousto-elastic, etc.) [17,18] is expected to revolutionize the control of wave propagation

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