  The concept of the energy gap is a fundamental characteristic of the band
structure of a material and it determines its physical properties. Formally the
energy gap appears in the dispersion relation $E_k$, where the vector $k$ is
determined on the whole momentum space. However, today the {\it gapped momentum
materials} are in the focus of research in which the so-called {\it momentum or
$k$-gap} can emerge, i.e. some lacunae of momentum space are excluded from the
domain of the function $E_k$. One of such examples present the non-Hermitian
systems. Within the random phase approximation we study the dielectric
properties of the momentum gapped materials in one, two and three dimensions
for both cases of zero and finite temperatures. We find the corresponding
plasmon modes and determine the unusual behavior of the appropriate dispersion
relations for each dimensionality. Based on these findings we evaluate the
absorption coefficient of gapped momentum media and provide some numerical
estimations of its value for the practical applications.
