  In this work, we propose staggered FDTD schemes based on the correction
function method (CFM) to discretize Maxwell's equations with embedded perfect
electric conductor (PEC) boundary conditions. The CFM uses a minimization
procedure to compute a correction to a given FD scheme in the vicinity of the
embedded boundary to retain its order. The minimization problem associated with
CFM approaches is analyzed in the context of Maxwell's equations with embedded
boundaries. In order to obtain a well-posed problem, we propose fictitious
interface conditions to fulfill the lack of information, namely the surface
current and charge density, on the embedded boundary. Fictitious interfaces can
induce some issues for long time simulations and therefore the penalization
coefficient associated with fictitious interface conditions must be chosen
small enough. We introduce CFM-FDTD schemes based on the well-known Yee scheme
and a fourth-order staggered FDTD scheme. Long time simulations and convergence
studies are performed in 2-D for various geometries of the embedded boundary.
CFM-FDTD schemes have shown high-order convergence.
