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[en] We demonstrate that the optical response of a periodically modulated dynamic slab exhibits infinite resonances for frequencies ω=(Ω/2)(2l+1), namely, odd multiples of one-half of the modulating frequency Ω of the dielectric function ε(t). These frequencies coincide partially with the usual condition of parametric amplification. However, the resonances occur only for certain normalized slab thicknesses LR. These resonances follow from detailed numerical studies based on our recent paper [Zurita-Sanchez, Halevi, and Cervantes-Gonzalez, Phys. Rev. A 79, 053821 (2009)]. As the thickness L nearly matches a resonance thickness LR, the amplitudes of counterpropagating modes in the slab obey a condition implying that both have the same modulus and their phases match a condition related to LR and the bulk wave vectors. When this condition is met, the electric field profile inside the slab is a superposition of standing waves with odd and even symmetries, and the reflection and transmission coefficients can reach great values and become infinite at exact resonance. Numerical simulations of the optical response are shown for a sinusoidal ε(t) with either moderate or strong modulation. As expected, as the modulation strength increases, higher-order harmonics ω-nΩ (n=0,±1,±2,...) become more noticeable, and short-wavelength bulk modes contribute significantly. However, we found that, regardless of the excitation frequency ω=(Ω/2)(2l+1), the dominant spectral component of the generated fields is Ω/2. Also, as the excitation frequency increases, the parity of the standing waves is conserved.