This project, an international collaboration with Prof. Fotis Diakonos from the University of Athens and Prof. Peter Schmelcher from University of Hamburg is about the implementation of the concept of complete local symmetry in lossy acoustic waveguides and scattering setups. The existence of a spatially invariant current is shown theoretically and observed experimentally despite the presence of losses,. We demonstrated how this invariant current leads to the generalization of the Bloch and parity theorems for lossy systems defining a mapping of the pressure field between symmetry related spatial domains. Using experimental data we verified this mapping with remarkable accuracy. For the performed experiment we employed a construction technique based on local symmetries which allows the design of setups with prescribed perfect transmission resonances in the lossless case. Our results revealed the fundamental role of symmetries in restricted spatial domains and clearly indicate that completely locally symmetric devices constitute a promising class of setups, regarding the manipulation of wave propagation.
(a),(b) Pictures of the experimental setup. (c) Schematic of the experimental setup. (d) δ-barrier correspondence of the acoustic structure in the low frequency regime. U1,U2 correspond to the strength of the δ-barrier potential and D1, D2 to the domains of the reflection symmetry decomposition of the waveguide