  We investigate the nontrivial characteristics of modulational instability
(MI) in a system of Bragg gratings with saturable nonlinearity. We also
introduce an equal amount of gain and loss into the existing system which gives
rise to an additional degree of freedom, thanks to the concept of $\cal PT$-
symmetry. We obtain the nonlinear dispersion relation of the saturable model
and discover that such dispersion relations for both the conventional and $\cal
PT$- symmetric cases contradict with the conventional Kerr and saturable
systems by not displaying the typical signature of loop formation in either the
upper branch or lower branch of the curve drawn against the wavenumber and
detuning parameter. We then employ a standard linear stability analysis in
order to study the MI dynamics of the continuous waves perturbed by an
infinitesimal perturbation. The main objective of this paper is twofold. We
first investigate the dynamics of the MI gain spectrum at the top and bottom of
the photonic bandgap followed by a comprehensive analysis carried out in the
anomalous and normal dispersion regimes. As a result, this perturbed system
driven by the saturable nonlinearity and gain/loss yields a variety of
instability spectra, which include the conventional side bands, monotonically
increasing gain, the emergence of a single spectrum in either of the Stokes
wavenumber region, and so on. In particular, we observe a remarkably peculiar
spectrum, which is caused predominantly by the system parameter though the
perturbation wavenumber boosts the former. We also address the impact of all
the physical parameters considered in the proposed model which include coupling
coefficient, dispersion parameter, and saturable nonlinearity on the phenomenon
of MI for different $\cal PT$- symmetric regimes ranging from unbroken to
broken one in greater detail.
