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The time domain linear sampling method (TD-LSM) solves inverse scatteringproblems using time domain data by creating an indicator function for thesupport of the unknown scatterer. It involves only solving a linear integralequation called the near-field equation using different data from samplingpoints that probe the domain where the scatterer is located. To date, themethod has been used for the acoustic wave equation and has been tested forseveral different types of scatterers, i.e. sound hard, impedance, andpenetrable, and for waveguides. In this paper, we extend the TD-LSM to the timedependent Maxwell's system with impedance boundary conditions - a similaranalysis handles the case of a perfect electric conductor (PEC). We provide ananalysis that supports the use of the TD-LSM for this problem, and preliminarynumerical tests of the algorithm. Our analysis relies on the Laplace transformapproach previously used for the acoustic wave equation. This is the firstapplication of the TD-LSM in electromagnetism.

The Time Domain Linear Sampling Method for determining the shape of multiple scatterers using electromagnetic waves