The application of Fourier analysis to study leaky waves has the advantage
of simplicity, but it is not dear why the complex roots of the dispersion r
elations represent leaky waves, nor how the leakage occurs. We investigate
the different kinds of leakage that can occur in a three layer plasma, and
to which Fouler pseudomodes they are associated. We find four basic mechani
sms, called "surface mode...", "single interface...", "trapped wave..." and
"lost insulation leakage". These mechanisms appear in pure form only near
certain limiting cases, in which the parameters of the problem take some sp
ecial values. As soon as the parameters depart significantly from the limit
ing values, the behavior of the leaky wave complicates and mixtures of the
mechanisms occur, in varying amounts. In consequence different points of th
e same complex branch of the spectrum may correspond to different mechanism
s. All the complex branches of the spectrum correspond to leaky waves, but
in general it is not possible to classify them according to type of leakage
, except close to a limiting case. Since in a three layer configuration the
re are many of these, the spectrum of leaky waves is very complicated.