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In this work we derive a WKB expansion for the electromagnetic fieldssolution of the time-harmonic Maxwell equations set in a domain with a thinlayer. As a by-product of this expansion we obtain new second order asymptoticmodels with generalized impedance transmission conditions that turn out todepend on the mean curvature of the boundary of the subdomain surrounded by thethin layer. We show that these models can be easily integrated in finiteelement methods by developing mixed variational formulations. One applicationof this work concerns the computation of the electromagnetic field inbiological cells.

Wentzel--Kramers--Brillouin Expansions and Generalized Impedance  Transmission Conditions for Thin-Layer Problems in Electromagnetism with  Application to Biological Cells