Families of solitons in Bragg supergratings

► We study gap solitons (GSs) in supergratings by analytical and computational methods. ► Periodic modulations of the local reflectivity and refractive index are considered. ► The Melnikov and averaging methods are used in the theory. ► New bandgaps filled with GSs are shown to be opened by the supergrating. ► Bifurcations of GSs are also discussed by a geometric approach.