The formal solution to the electromagnetic scattering by a dielectric multi
layer, infinite cylinder, of elliptic crass section is proposed in the case
of line-source illumination. The solution is obtained through a recursive
procedure in which the coefficients of the eigenfunctions of the elliptic c
ylinder in each dielectric layer are efficiently computed and matched in th
e external layer to the incident field expanded in terms of Mathieu functio
ns. The mathematical formulation is provided, together with a number of che
cks and comparison examples. (C) 2000 John Wiley & Sons, Inc.