Summary: ENHANCED RESOLUTION IN STRUCTURED MEDIA
HABIB AMMARI, ERIC BONNETIER, AND YVES CAPDEBOSCQ
Abstract. The aim of this paper is to prove that we can achieve a resolution enhancement
in detecting a target inclusion if it is surrounded by an appropriate structured medium. The
physical notions of resolution and focal spot are revisited. Indeed, the resolution enhancement
is estimated in terms of the material parameters of the structured medium.
In this paper, we consider the problem of imaging a target inclusion in a structured medium.
We rigorously prove that the structured medium can improve the resolution in imaging the target
from far-field measurements. Indeed, we precisely quantify the resolution enhancement in terms
of the material parameters and the geometry of the structured medium.
Our mathematical analysis connects to a series of experiments recently performed by the group
of M. Fink . In these experiments, one studies the response to electromagnetic excitations
with wavelength , of a row of stick antennas placed on a metallic plane. The spacing between
the antennas is /30. The group of antennas is surrounded by a network of thin conducting rods,
that occupies a bounded region in space. The spacing between these thin scatterers is of the order
As one of the antennas radiates at frequency , the signal is recorded by an array of transducers,
far from the region occupied by the antennas and the scatterers (at a distance of about 10). The
signal is then time reversed and re-emitted by the transducers.