  In this paper, a perfectly matched layer (PML) method is proposed to solve
the time-domain electromagnetic scattering problems in 3D effectively. The PML
problem is defined in a spherical layer and derived by using the Laplace
transform and real coordinate stretching in the frequency domain. The
well-posedness and the stability estimate of the PML problem are first proved
based on the Laplace transform and the energy method. The exponential
convergence of the PML method is then established in terms of the thickness of
the layer and the PML absorbing parameter. As far as we know, this is the first
convergence result for the time-domain PML method for the three-dimensional
Maxwell equations. Our proof is mainly based on the stability estimates of
solutions of the truncated PML problem and the exponential decay estimates of
the stretched dyadic Green's function for the Maxwell equations in the free
space.
