  We study fundamental optical gap solitons in the model of a fiber Bragg
grating (BG), which is subjected to a periodic modulation of the local
reflectivity, giving rise to a supergrating. In addition, the local refractive
index is also periodically modulated with the same period. It is known that the
supergrating opens an infinite system of new bandgaps in the BG's spectrum. We
use a combination of analytical and computational methods to show that each
emerging bandgap is filled with gap solitons (GSs), including asymmetric ones
and bound states of the GSs. In particular, bifurcations of the GSs created by
the supergrating are studied in terms of a geometric analysis.
