On Ventcel-type transmission conditions for a Helmholtz problem with a non-uniform thin layer

Abstract

We study the asymptotic behaviour of the electric field in the transverse magnetic (TM) mode, propagating in a material composed of a two-dimensional object surrounded by a thin layer of non-constant thickness and embedded in an ambient medium. Using an asymptotic expansion of the solution u ε to the Helmholtz problem, we derive Ventcel-type transmission conditions on the limit interface Γ modelling the effect of the thin layer with accuracy up to O(ε 2 ).