  Perturbation theory is applied to one-dimensional scattering systems
consisting of a general class of inhomogeneous and isotropic slabs having size
$L$ described by the relative permittivity $\varepsilon(z) = 1 + \alpha
\chi(z)$, where $\chi(z)$ is the electric susceptibility and $\alpha$ the
perturbation parameter. The transmitted and reflected amplitudes are shown to
be written as Born series in powers of $\alpha$ and Pad\'e approximants are
used to obtain analytical results with a high and arbitrary degree of accuracy.
The approach is very general and can handle oblique incidence. Examples are
given for the transmission and reflection amplitudes of plane waves interacting
with Hermitian and non-Hermitian structures with known and unknown exact
solutions.
