  Resonant modes determine the response of electromagnetic devices, including
dielectric and plasmonic resonators. Relying on the degrees of freedom that
metamaterials provide, this contribution shows how to design, at will, the
resonant modes of a dielectric object placed in an unbounded space.
Specifically, the proposed method returns in analytical form the spatial
distribution of the dielectric susceptibility tensor for which the object
exhibits resonances at prescribed frequencies and spatial distribution of the
polarization. Together with the synthesis of the material, two key concepts are
introduced: the controlled tunability of the resonant modes and the number of
essential modes, i.e. the number of modes that uniquely characterize the
spatial distribution of the dielectric susceptibility. Moreover, this approach
can be applied to design the resonant modes of any system where the
constitutive relationship is linear and local.
