  The goal of this work is to study the electromagnetic scattering problem of
time-domain Maxwell's equations in an unbounded structure. An exact transparent
boundary condition is developed to reformulate the scattering problem into an
initial-boundary value problem in an infinite rectangular slab. The
well-posedness and stability are established for the reduced problem. Our proof
is based on the method of energy, the Lax--Milgram lemma, and the inversion
theorem of the Laplace transform. Moreover, a priori estimates with explicit
dependence on the time are achieved for the electric field by directly studying
the time-domain Maxwell equations.
