Scattering resonances in unbounded transmission problems with sign-changing coefficient

Camille Carvalho (1, 2) , Zoïs Moitier (3)

1 UC Merced - University of California [Merced]
2 INSA Lyon - Institut National des Sciences Appliquées de Lyon
3 KIT - Karlsruhe Institute of Technology

It is well-known that classical optical cavities can exhibit localized phenomena associated to scattering resonances (using the Black Box Scattering Theory), leading to numerical instabilities in approximating the solution. Those localized phenomena concentrate at the inner boundary of the cavity and are called whispering gallery modes. In this paper we investigate scattering resonances for unbounded transmission problems with sign-changing coefficient (corresponding to optical cavities with negative optical propertie(s), for example made of metamaterials). Due to the change of sign of optical properties, previous results cannot be applied directly, and interface phenomena at the metamaterial-dielectric interface (such as the so-called surface plasmons) emerge. We establish the existence of scattering resonances for arbitrary two-dimensional smooth metamaterial cavities. The proof relies on an asymptotic characterization of the resonances, and extending the Black Box Scattering Theory to problems with sign-changing coefficient. Our asymptotic analysis reveals that, depending on the metamaterial's properties, scattering resonances situated closed to the real axis are associated to surface plasmons. Examples for several metamaterial cavities are provided.

Mots clés: Helmholtz equation; Scattering resonances; Sign-changing coefficient; Asymptotic expansions

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Optique [physics.optics]

Camille Carvalho, Zoïs Moitier. Scattering resonances in unbounded transmission problems with sign-changing coefficient. 2022. ⟨hal-02965993v2⟩