Localisation of eigenfunctions and increased dissipation in irregular resonators. Applications to wave absorption.

Bernard Sapoval
École Polytechnique
Condensed Matter Physics

First observed on fractal drums and fractal acoustic cavities, localization of Helmholtz eigenmodes has been found to exist whatever the shape and characteristic sizes of a cavity with an irregular geometry. This is true both for shallow electromagnetic cavities and shallow acoustical cavities. More irregular structures induce a global decrease of the existence surface or participation ratios of the eigenmodes. These irregular cavities present efficient damping properties and there is a specific enhancement of the dissipation for those modes that are localized near the cavity boundaries by what we call “frontier localization”. In a different manner, in cavities partially filled with an irregular shaped absorbing material, there appears a new type of localization, “astride localization”, for modes which exist in both regions absorbing and non-absorbing regions. It is these modes that are specifically efficient in dissipating the energy of waves reaching irregular absorbing structures.

Presentation (PowerPoint File)

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