  The goal of this work is to design an acoustic mode converter. More
precisely, the wave number is chosen so that two modes can propagate. We
explain how to construct geometries such that the energy of the modes is
completely transmitted and additionally the mode 1 is converted into the mode 2
and conversely. To proceed, we work in a symmetric waveguide made of two
branches connected by two thin ligaments whose lengths and positions are
carefully tuned. The approach is based on asymptotic analysis for thin
ligaments around resonance lengths. We also provide numerical results to
illustrate the theory.
