Analytic analysis of the CP-FDTD and C-FDTD methods for offset planar boundaries

A locally-conformal FDTD scheme, known as the conformal FDTD (C-FDTD) method, has been introduced previously to model perfect electric conductors (PECs) that do not align with the grill. This scheme is arguably the simplest conformal scheme to date since the electric field update equations are unchanged and there are only minor changes made to the update equations for magnetic field nodes adjacent to the PEC boundary. Unlike for the contour path FDTD (CP-FDTD) method, no nearest-neighbour approximation is used. We derive the reflection coefficient for the C-FDTD and CP-FDTD methods for TM/sub x/, illumination of planar boundaries that are aligned with, but offset from, the grid. A similar analysis holds for TE/sub x/, illumination.