Spectral stability of PML implementations in time domain for resonators with radiation losses

We discuss some stability problems of Perfectly Matched Layer implementations in time domain, which are applied to resonant structures. The spectral stability of the update matrix for different implementations is analyzed. One of them produces unstable eigenvalues if time steps close to the CFL limit are used. For small time steps, the derivation of both schemes is consistent. Finally, a more realistic setup of an optical cavity is examined, where the same behavior is observed.