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.
Bibliographical noteKAUST Repository Item: Exported on 2020-11-18
Acknowledged KAUST grant number(s): BAS/1/1626-01-01, OSR-2016-CRG5-2950
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.