A study of numerical reflections caused by FDTD mesh refinements in 1D and 2D

A study of FDTD solutions on variable and subgridded meshes is presented. The effect of numerical reflections previously known from simulation practice is mathematically confirmed. It is shown that the magnitude of reflections can be accurately predicted by combining the numerical dispersion relations in the two mesh subregions, Snell's law, and electric field continuity condition. The theory is validated for the 2D TE modes at normal and oblique incidence.