Communications in Mathematical Sciences

Volume 20 (2022)

Number 2

Design of a mode converter using thin resonant ligaments

Pages: 425 – 445

DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n2.a6

Authors

Lucas Chesnel (INRIA / Centre de mathématiques appliquées, École Polytechnique, Institut Polytechnique de Paris, Palaiseau, France)

Jérémy Heleine (INRIA / Centre de mathématiques appliquées, École Polytechnique, Institut Polytechnique de Paris, Palaiseau, France)

Sergei A. Nazarov (Laboratory of Mathematical Methods in Mechanics of Materials, IPME RAS, St.Petersburg, Russia)

Abstract

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.

Keywords

acoustic waveguide, mode converter, asymptotic analysis, thin ligament, scattering coefficients, complex resonance

2010 Mathematics Subject Classification

35B40, 35J05, 35Q60, 41A60, 78A40, 78M35

Full Text (PDF format)

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