Spectral analysis of finite difference models of open structures in time and frequency domain

We present an analysis of extended, FDTD-like methods which is based on the eigenvalues of the iteration matrix. For a stable update scheme these eigenvalues must lie within the unit circle, and this kind of analysis is applied to systems with radiation losses. For small models, it is possible to compute the eigenvalues numerically and to compare them to the spectrum of the corresponding time-continuous formulation. This allows to assess the accuracy and stability properties of different implementation variants.