A solution to the electromagnetic scattering of a transverse magnetic
plane wave due to a perfectly conducting elliptic cylinder coated by a
lossless, nonmagnetic, and elliptic multilayer dielectric is proposed
. Despite the lack of orthogonality of the eigenfunctions of the held
inside different layers, an efficient recursive procedure for the comp
utation of the solution is devised. It is based on series expansions o
f the fields in terms of Mathieu functions and on a Galerkin approach.
An outline of the procedure is given, and some numerical results, con
cerning both the field quantities and the radar cross section per unit
length, are provided.