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Localization of exceptional points and modal branch tracking for acoustic waveguides applications

Abstract : For applications dealing with dissipative acoustic waveguides strong modal attenuation are often achieved close to exceptional points (EP). These EP correspond to a particular tuning of certain design parameters which render the associated eigenvalue problem degenerate where both eigenvalues, i.e. the wavenumber, and eigenvectors of a pair of guided modes coalesce. These non-Hermitian degeneracies have raised considerable attention in the scientific community as these can have a great impact in a variety of physical problems. Here, a new algorithm is proposed to quickly explore the parametric space and to locate EPs. The method requires the computation of successive derivatives of two selected eigenpairs with respect to the parameter so that, after recombination, regular functions can be constructed. This algebraic manipulation permits the EP localization, using standard root-finding algorithms and the computation of the associated Puiseux series up to an arbitrary order, useful to follow modal branches. Examples related to the acousic propagation in straight ducts with absorbing walls and in periodic guiding structures are given to illustrate the versatility of the proposed method and its ability to handle large size matrices arising from finite element discretization techniques.
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https://hal.archives-ouvertes.fr/hal-03221405
Contributor : Claude Inserra <>
Submitted on : Thursday, May 20, 2021 - 11:10:43 AM
Last modification on : Friday, May 21, 2021 - 3:42:08 AM

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Benoit Nennig, Emmanuel Perrey-Debain, Martin Ghienne. Localization of exceptional points and modal branch tracking for acoustic waveguides applications. eForum Acusticum 2020, Dec 2020, Lyon, France. pp.401-402, ⟨10.48465/fa.2020.0589⟩. ⟨hal-03221405⟩

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