  The time domain linear sampling method (TD-LSM) solves inverse scattering
problems using time domain data by creating an indicator function for the
support of the unknown scatterer. It involves only solving a linear integral
equation called the near-field equation using different data from sampling
points that probe the domain where the scatterer is located. To date, the
method has been used for the acoustic wave equation and has been tested for
several different types of scatterers, i.e. sound hard, impedance, and
penetrable, and for waveguides. In this paper, we extend the TD-LSM to the time
dependent Maxwell's system with impedance boundary conditions - a similar
analysis handles the case of a perfect electric conductor (PEC). We provide an
analysis that supports the use of the TD-LSM for this problem, and preliminary
numerical tests of the algorithm. Our analysis relies on the Laplace transform
approach previously used for the acoustic wave equation. This is the first
application of the TD-LSM in electromagnetism.
