Maxwell's equations with hypersingularities at a conical plasmonic tip

Dhia, Anne‐Sophie Bonnet‐Ben; Chesnel, Lucas; Rihani, Mahran

doi:10.1016/j.matpur.2022.03.001

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2022

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“…Other types of singularities in 2D have also been considered [7]. Much less is known for 3D domains, but analogous results for smooth conical singularities have been considered in [5] and [20], and for edges in [39]. The plasmonic problem has also been investigated numerically for some regular polyhedra [19,48].…”

Section: Introductionmentioning

confidence: 99%

The quasi-static plasmonic problem for polyhedra

León-Contreras

Perfekt

2022

Math. Ann.

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We characterize the essential spectrum of the plasmonic problem for polyhedra in $${\mathbb {R}}^3$$ R 3 . The description is particularly simple for convex polyhedra and permittivities $$\epsilon < - 1$$ ϵ < - 1 . The plasmonic problem is interpreted as a spectral problem through a boundary integral operator, the direct value of the double layer potential, also known as the Neumann–Poincaré operator. We therefore study the spectral structure of the double layer potential for polyhedral cones and polyhedra.

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