  We study the massless limit of the Klein-Gordon (K-G) equation in 1+1
dimensions with static complex potentials as an attempt to give an alternative,
but equivalent, representation of plane electromagnetic (em) wave propagation
in active medium. In the case of dispersionless em medium, the analogy dictates
that the potential in the K-G equation is complex and energy-dependent. In the
non-relativistic domain we study an analogous inertial system by considering
wave packet propagation through a complex potential barrier and solve the
time-independent Schrodinger equation with a potential that has the same energy
dependence as that of the K-G equation. The behavior of these solutions is
compared with those found elsewhere in the literature for the propagation of
electromagnetic plane waves in a uniform active medium with complex dielectric
constant. Our study concluded that the discrepancy between the time dependent
and stationary results is due to the energy poles crossing the real axis in the
complex energy plane. It was demonstrated unambiguously that there is a
frequency (energy) and size dependent gain threshold above which the stationary
results become unstable. This threshold corresponds to the value of the gain at
which the pole crosses the real axis.
