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

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.

Citation
Farhat, M., Guenneau, S., Chen, P.-Y., & Wu, Y. (2020). Parity-Time Symmetry and Exceptional Points for Flexural-Gravity Waves in Buoyant Thin-Plates. Crystals, 10(11), 1039. doi:10.3390/cryst10111039

Acknowledgements
This research was funded by King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Grant No. OSR-2016-CRG5-2950 and KAUST Baseline Research Fund BAS/1/1626-01-01.

Publisher
MDPI AG

Journal
Crystals

DOI
10.3390/cryst10111039

Additional Links
https://www.mdpi.com/2073-4352/10/11/1039

Permanent link to this record