FDTD lattice termination with periodic boundary conditions

The potential of periodic boundary conditions to provide an alternative method for terminating finite-difference time-domain lattices, instead of absorbing boundary conditions or perfectly matched layers, is examined in this paper. Employing a recent combination of the sine-cosine technique with the array-scanning method, a large number of problems of interest can be efficiently terminated at periodic boundaries, which effectively act as absorbers. Hence, a unified treatment of inhomogeneous, dispersive and conductive media, each of which requires a reformulation of the perfectly matched layer, is attained, with an excellent performance that is not compromised by the close proximity of a source to the boundary. In addition, while the reflectivity of perfectly matched layers increases when the refractive index of the working volume is a non-analytic function, the proposed approach is not affected. The presence of non-periodic boundary conditions can still be accounted for by hybrid periodic/absorbing terminations.