Modeling of Sloped Interfaces on a Yee Grid

To represent material boundaries in the finite-difference time-domain or frequency-domain method, effective cell permittivity ε_eff can be introduced for each grid cell crossed by material interface. In this paper we revisit the derivation of tensorial ε_eff for a sloped interface, and describe possible interpolation schemes for coupling of different effective electric field and induction components near the interface. We put the resulting non-symmetric and symmetrized effective permittivity matrices to numerical tests in the frequency domain. For very-high-contrast interfaces the symmetrized schemes perform worse than simple staircasing while non-symmetrized interpolation retains the second-order convergence.