Parametric resonances in a temporal photonic crystal slab

We have studied resonances in a dynamic slab whose permittivity and/or permeability are periodic functions of time, namely, a temporal photonic crystal. We find strong and narrow resonances for frequencies that are equal to $1/2$ or $3/2$, etc. of the modulation frequency provided that a certain geometric parameter (proportional to the slab thickness and to the modulation frequency) assumes values such that the electric field in the slab is either symmetric or antisymmetric with respect to the slab center. These resonances turn out to be absent whenever the electric and magnetic modulations are in phase and have equal strengths, that is, when there are no band gaps between k bands. The resonance peaks appear for all the modulation harmonics and are superimposed on Fabry-P\'erot--like background oscillations. For not very strong modulations, the resonances can be described in terms of the relative impedance of the slab and a parameter that expresses the modulation strength.