  Dielectric responses of a multi-component plasma are investigated at finite
temperature considering the case of optically generated carriers in a wurtzite
GaN. The effective dielectric function and polarizability functions $\Pi_c
(q,\omega)$ are determined such that they satisfy the Dyson equations of the
effective interactions among plasma components. The behavior of plasma
component-resolved electronic polarizability functions and the effective
dielectric function of the plasma are examined including the effects of dynamic
screening at finite temperature. Spectral analysis of the dielectric response
functions are performed and their dynamic and nonlocal (finite-$q$) behaviors
are explored. Our result shows that, for a multi-component plasma of high
carrier densities, the well-defined optic plasmonic modes are clearly seen well
outside the single particle excitation continuum of lighter mass electrons and
that the additional low frequency acoustic plasmonic branch is located outside
single particle excitation continuum of doubly degenerate heavier mass A-holes.
The contribution of the heavier mass species to dressed $\Pi_c (q,\omega)$ is
very similar to the case of bare $\Pi_c^0 (q,\omega)$.
  \pacs{72.20.Ht, 71.38.-k, 61.85.+p} \keywords{Hot carriers, Multi-component
plasma, Dielectric response, Dielectric function, Polarizability functions,
wurtzite GaN}
