Well-posedness and stability of Time-domain Electromagnetic scattering problem in chiral structures

This work investigates electromagnetic plane wave propagation within chiral structures. The medium inside the structure is chiral and heterogeneous. Wave propagation in such chiral media is generally governed by Maxwell's equations coupled with the Drude-Born-Fedorov constitutive equations. In this paper, an exact transparent boundary condition is developed to reformulate the scattering problem into an initial-boundary value problem posed on an infinite rectangular slab. Well-posedness and stability are established for the reduced problem. Our proof relies on the energy method, the Lax-Milgram lemma, and the inversion theorem of the Laplace transform. Furthermore, a priori estimates with explicit time dependence for the electric field are obtained by directly analyzing the time-domain Maxwell's equations.