A 1D multipoint auxiliary propagator (1D-MAP) for sourcing plane waves for FDTD

Although having larger leakage errors, the IFA auxiliary grid has its merits in easy implementation and low memory cost. Attracted by these practical advantages, we therefore develop a ID multipoint auxiliary propagator (ID-MAP) that is derived directly from the corresponding 2D/3D dispersion relation. The ID-MAP evaluates a field value explicitly in the time-domain, and has an identical dispersive relation for the auxiliary propagator and the 2D/3D domain with no numerical approximation. Therefore, in practice, the ID-MAP achieves no leakage errors for TFSF (total-field scattered-field) implementations.