  We report in this paper the analytical and numerical results on the effect of
amplification on the transmission and reflection coefficient of a periodic
one-dimensional Kronig-Penney lattice. A qualitative agreement is found with
the tight-binding model where the transmission and reflection increase for
small lengths before strongly oscillating with a maximum at a certain length.
For larger lengths the transmission decays exponentially with the same rate as
in the growing region while the reflection saturates at a high value. However,
the maximum transmission (and reflection) moves to larger lengths and diverges
in the limit of vanishing amplification instead of going to unity. In very
large samples, it is anticipated that the presence of disorder and the
associated length scale will limit this uninhibited growth in amplification.
Also, there are other interesting competitive effects between disorder and
localization giving rise to some nonmonotonic behavior in the peak of
transmission.
