Generalized Impedance Boundary Conditions for Thin Dielectric Coatings with Variable Thickness

We derive so-called Generalized Impedance Boundary Conditions (GIBC) that model thin dielectric coatings with variable width. We treat the 2-D electromagnetic problem for both TM and TE polarizations. The expressions of the GIBCs are explicited up to the third order (with respect to the coating width). The order of convergence is numerically validated through various numerical examples. A particular attention is given to the cases where the inner boundary has corner singularities