  We study transmission and reflection properties of a perfectly amplifying as
well as absorbing medium analytically by using the tight binding equation.
Different expressions for transmittance and reflectance are obtained for even
and odd values of the sample length which is the origin of their oscillatory
behavior. In a weak amplifying medium, a cross-over length scale exists below
which transmittance and reflectance increase exponentially and above which
transmittance decays exponentially while the reflectance gets saturated.
Depending on amplification transmittance and reflectance show singular behavior
at the cross-over length. In a weak absorbing medium we do not find any
cross-over length scale. The transmission coefficient behaves similar to that
in an amplifying medium in the asymptotic limit. In a strong
amplifying/absorbing medium, the transmission coefficient decays exponentially
in the large length limit. In both weak as well as strong absorbing media the
logarithm of the reflection coefficient shows the same behavior as obtained in
an amplifying medium but with opposite sign.
