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The resonance relation for a parametrically modulated dielectric slab is derived. For such a slab, it is found that two types of resonance may arise: one results in a time-growing field everywhere in space and the other results in a surface wave that may grow along the interface between air and the dielectric slab. The effect of frequency-coupling on the resonance condition is carefully studied and may be explained by use of an expression for the approximation of two-frequencies coupling. (Author)