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Communications in Mathematical Sciences
Volume 20 (2022)
Design of a mode converter using thin resonant ligaments
Pages: 425 – 445
The goal of this work is to design an acoustic mode converter. The wave number is fixed 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.
acoustic waveguide, mode converter, asymptotic analysis, thin ligament, scattering coefficients, complex resonance
2010 Mathematics Subject Classification
35B40, 35J05, 35Q60, 41A60, 78A40, 78M35
The research of S.A. Nazarov was supported by the grant No. 17-11-01003 of the Russian Science Foundation.
Received 13 February 2021
Accepted 18 July 2021
Published 28 January 2022