  This paper is concerned with the inverse problem of reconstructing a small
object from far field measurements by using the field interaction with a
plasmonic particle which can be viewed as a passive sensor. It is a follow-up
of the work [H. Ammari et al., Reconstructing fine details of small objects by
using plasmonic spectroscopic data, SIAM J. Imag. Sci., to appear], where the
intermediate interaction regime was considered. In that regime, it was shown
that the presence of the target object induces small shifts to the resonant
frequencies of the plasmonic particle. These shifts, which can be determined
from the far field data, encodes the contracted generalized polarization
tensors of the target object, from which one can perform reconstruction beyond
the usual resolution limit. The main argument is based on perturbation theory.
However, the same argument is no longer applicable in the strong interaction
regime as considered in this paper due to the large shift induced by strong
field interaction between the particles. We develop a novel technique based on
conformal mapping theory to overcome this difficulty. The key is to design a
conformal mapping which transforms the two particle system into a shell-core
structure, in which the inner dielectric core corresponds to the target object.
We show that a perturbation argument can be used to analyze the shift in the
resonant frequencies due to the presence of the inner dielectric core. This
shift also encodes information of the contracted polarization tensors of the
core, from which one can reconstruct its shape, and hence the target object.
Our theoretical findings are supplemented by a variety of numerical results
based on an efficient optimal control algorithm. The results of this paper make
the mathematical foundation for plasmonic sensing complete.
