Analysis of the accuracy of the numerical reflection coefficient of the finite-difference time-domain method at planar material interfaces

This paper presents a rigorous analysis of the numerical error of the reflection coefficient of the finite-difference time-domain (FDTD) algorithm at planar material boundaries. The derived expressions show that the numerical reflection depends on a large number of parameters, such as the grid resolution and the time step, the frequency, the angle, and the polarization of the incident wave. In conclusion, the FDTD algorithm does not accurately fulfill the boundary conditions for the continuity of the fields. The theoretical findings enable the detailed characterization of the field behavior in the grid at material interfaces. The numerical total reflection and the Brewster angle are studied as well as the discretization influences on the specific absorption rate (SAR).