  The problem of reconstructing the spatial support of an extended radiating
electric current source density in a lossy dielectric medium from transient
boundary measurements of the electric fields is studied. A time reversal
algorithm is proposed to localize a source density from loss-less wave-field
measurements. Further, in order to recover source densities in a lossy medium,
we first build attenuation operators thereby relating loss-less waves with
lossy ones. Then based on asymptotic expansions of attenuation operators with
respect to attenuation parameter, we propose two time reversal strategies for
localization. The losses in electromagnetic wave propagation are incorporated
using the Debye's complex permittivity, which is well-adopted for low
frequencies (radio and microwave) associated with polarization in dielectrics.
