Invariant currents in lossy acoustic waveguides with complete local symmetry

TL;DR

This paper demonstrates that invariant currents can exist in lossy acoustic waveguides with complete local symmetry, leading to generalized theorems and precise control of wave propagation despite losses.

Contribution

It introduces the concept of complete local symmetry in lossy acoustic systems and experimentally verifies invariant currents and their implications for wave manipulation.

Findings

Invariant currents exist in lossy systems with local symmetry

Generalized Bloch and parity theorems apply to lossy waveguides

Design techniques enable perfect transmission resonances

Abstract

We implement the concept of complete local symmetry in lossy acoustic waveguides. Despite the presence of losses, the existence of a spatially invariant current is shown theoretically and observed experimentally. We demonstrate 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 verify this mapping with remarkable accuracy. For the performed experiment we employ a construction technique based on local symmetries which allows the design of setups with prescribed perfect transmission resonances in the lossless case. Our results reveal 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.