In a previous paper; a surface impedance formalism was given. Its appl
ication to interfaces modelling between homogeneous and frequency depe
ndent media, was of great interest in the finite difference time-domai
n (FDTD) codes. In this paper, an extension of the method to dispel si
ve media is presented. Applying this formalism to lossless Debye mediu
m, the analytical expressions of the time-domain surface impedances ar
e given. The implementation in a FDTD code permits then a numerical ve
rification of the results in relation to the Fresnel method.