  We present a theory for the cloaking of arbitrarily-shaped objects and
demonstrate electromagnetic scattering-cancellation through designed
homogeneous coatings. First, in the small-particle limit, we expand the dipole
moment of a coated object in terms of its resonant modes. By zeroing the
numerator of the resulting rational function, we accurately predict the
permittivity values of the coating layer that abates the total scattered power.
Then, we extend the applicability of the method beyond the small-particle
limit, deriving the radiation corrections of the scattering-cancellation
permittivity within a perturbation approach. Our method permits the design of
invisibility cloaks for irregularly-shaped devices such as complex sensors and
detectors.
