Surface polaritons on an elliptic cylinder

The dispersion relation for surface polaritons propagating on the symmetry axis of an elliptic cylinder is derived. By solving Maxwell's equations, a set of two transcendental equations corresponding to the dispersion relation of the surface polaritons is obtained. It is shown that, in general, even and odd solutions are coupled except in the electrostatic limit and that the existence of an eccentricity introduces additional modes when compared with results for a circular cylinder. Numerical results are obtained by considering a metallic elliptic cylinder surrounded by a vacuum.