A sequence of absorbing boundary conditions for Maxwell’s equations

Following the scheme developed by Engquist and Majda [Math Comp. 31 (1977) 629] for first-order systems, we derive a theoretical perfectly absorbing nonlocal boundary condition for Maxwell’s equations at a flat outer boundary. This condition can be approximated to any desired order by a differential equation on the boundary, and a sequence of such equations is developed here in terms of tangential derivatives of the electromagnetic fields at the boundary. The resulting set of equations, comprising Maxwell’s equations in the interior together with any of the local boundary conditions, is shown to admit no exponentially growing solutions, and questions of their well-posedness are addressed.