FDTD Stability Analysis of Metasurface GSTCs with Normal Surface Polarizations

Generalized Sheet Transition Conditions (GSTC) with tangential and normal susceptibility components in time domain are formulated as a state-space equation, which allows the poles of the system to be conveniently determined by simply finding the eigenvalues of the state matrix. The GSTC is then time-discretized based on trapezoidal rule, and formulated into discrete-time state-space form. The impact of the normal susceptibility component, and its associated oblique incidence on the numerical stability is discussed here by finding the numerical poles from the discrete-time state-space formulation.