Absorbing boundary conditions in the context of the hybrid ray-FDTD moving window solution

The hybrid ray-FDTD moving window scheme has been presented for the propagation of electromagnetic pulses in homogeneous and inhomogeneous media. This method has been cast in the Lagrange formulation, where the field equations have been transformed into a moving frame. Compared with the stationary formulation, the moving frame equations exhibit different characteristics in terms of both numerical dispersion and absorbing boundary conditions. It has been shown that the wavepacket-tracking Lagrangian formulation reduces the effects of numerical dispersion compared with the stationary frame. In this paper, the moving frame formulation is extended to 3D and applied to track a propagating wavepacket (pulsed beam). We derive both the numerical dispersion relations and the stability conditions using a unified approach. Boundary conditions for the moving frame scheme are derived by diagonalizing the field equations, identifying the backward propagating and stationary eigenfunctions as the basic two independent unknowns and imposing numerical absorption or specification upon them.