Remarks on the Huygens absorbing boundary conditions for electromagnetics

The Huygens absorbing boundary conditions (ABCs) are promising new implementations of operator ABCs. They have certain advantageous features which are lacked in other operator ABCs. Under certain conditions and with the Huygens ABCs, the transmitted wave depends solely upon the second derivative with respect to time or upon the double integral of the incident wave. For such cases and for problems with a Dirichlet boundary condition, the overall reflection is not unique. Two new examples of the Huygens ABCs are given for such cases. For each example and with a FDTD scheme the newly derived reflection is less than that which has been studied by Bérenger [J.-P. Bérenger, On the Huygens absorbing boundary conditions for electromagnetics, J. Comput. Phys. 226 (2007) 354–378].