A simple stackable re-radiating boundary condition (rRBC) for FDTD

The fundamental properties of a new re-radiating boundary condition (rRBC) for terminating the grid in the finite-difference time-domain (FDTD) method are examined. It is shown that because it is based on the field teleportation principle of [M.E. Watts et al., February-March 2003], this rRBC generates exact negative copies of the outgoing time-domain fields in FDTD, independently of the angle of incidence, polarization, field impedance, or material properties. The effect of the rRBC is to differentiate the outgoing signal and reduce it approximately by a factor of 10 in the time domain. Several rRBC boundaries can be stacked, one after the other, to continually decrease the level of the outgoing signal. Termination of the rRBC stack with a one cell Huygen's condition further reduces the signal, and minimizes the integration feedback as the faint echoes cross backwards through the rRBCs. It is shown that the net result is a boundary that is more efficient than a PML of similar total thickness (especially at shallow angles of incidence) and is trivial to program, requiring no special treatment for corners or material properties.