A highly unusual pattern of strong multiple resonances for bulk electromagnetic waves is predicted and analysed numerically in thick periodic holographic gratings in a slab with the mean permittivity that is larger than that of the surrounding media. This pattern is shown to exist in the geometry of grazing-angle scattering (GAS), that is when the scattered wave (+1 diffracted order) in the slab propagates almost parallel to the slab (grating) boundaries. The predicted resonances are demonstrated to be unrelated to resonant generation of the conventional guided modes of the slab. Their physical explanation is associated with resonant generation of a completely new type of eigenmodes in a thick slab with a periodic grating. These new slab eigenmodes are generically related to the grating; they do not exist if the grating amplitude is zero. The field structure of these eigenmodes and their dependence on structural and wave parameters is analysed. The results are extended to the case of GAS of guided modes in a slab with a periodic groove array of small corrugation amplitude and small variations in the mean thickness of the slab at the array boundaries.
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