Time-domain spectral considerations for electromagnetic waves in layered media

The response of a continuously layered medium to a pulsed source is evaluated by using the classical Sommerfeld-Weyl spectral representation. A contrast-source integral equation for the time-normalized wavenumber spectral constituent is derived. For certain values of the normalized wavenumber, this equation cannot be solved by a stable time-domain algorithm. The instabilities correspond to the occurrence of guided-wave modes in the symmetry direction of the layered structure.