  We analyse mathematically the imaging modality using electromagnetic
nanoparticles as contrast agent. This method uses the electromagnetic fields,
collected before and after injecting electromagnetic nanoparticles, to
reconstruct the electrical permittivity. The particularity here is that these
nanoparticles have high contrast electric or magnetic properties compared to
the background media. First, we introduce the concept of electric (or magnetic)
nanoparticles to describe the particles, of relative diameter $\delta$
(relative to the size of the imaging domain), having relative electric
permittivity (or relative magnetic permeability) of order $\delta^{-\alpha}$
with a certain $\alpha>0$, as $0<\delta<<1$. Examples of such material, used in
the imaging community, are discussed. Second, we derive the asymptotic
expansion of the electromagnetic fields due to such singular contrasts. We
consider here the scalar electromagnetic model. Using these expansions, we
extract the values of the total fields inside the domain of imaging from the
scattered fields measured before and after injecting the nanoparticles. From
these total fields, we derive the values of the electric permittivity at the
expense of numerical differentiations.
