  We consider the interaction of an electromagnetic field with a left-handed
sphere, i.e., with a sphere fabricated from a left-handed material, in the
framework of complex angular momentum techniques. We emphasize more
particularly, from a semiclassical point of view, the resonant aspects of the
problem linked to the existence of surface polaritons. We prove that the
long-lived resonant modes can be classified into distinct families, each family
being generated by one surface polariton propagating close to the sphere
surface and we physically describe all the surface polaritons by providing, for
each one, its dispersion relation and its damping. This can be achieved by
noting that each surface polariton corresponds to a particular Regge pole of
the electric part (TM) or the magnetic part (TE) of the $S$ matrix of the
sphere. Moreover, for both polarizations, we find that there exists a
particular surface polariton which corresponds, in the large radius limit, to
that supported by the plane interface. There also exists, for both
polarizations, an infinite family of surface polaritons of whispering gallery
type having no analogs in the plane interface case and specific to left-handed
materials. They present a "left-handed behavior" (phase and group velocities
are opposite) as well as a very weak damping. They could be very useful in the
context of plasmonics or cavity quantum electrodynamics.
