Pulse propagation through a slab with time-periodic dielectric function ε(t)

We describe pulse propagation through a slab with periodic dielectric function ε(t), thus extending our previous investigation for monochromatic incidence [Phys. Rev. A 79, 053821 (2009)]. Based on the concepts of phase and group delays, we prove that, for an incident quasi-monochromatic pulse, the transmitted pulse can be expressed as a superposition of partial pulses that are exact replicas of the incident pulse and that exit the slab with a time delay. These partial pulses have harmonic carrier frequencies ω c - nΩ (n is an integer, ω c is the carrier frequency of the incident pulse, and Ω = 2π/T is the slab modulation frequency). We find numerically that these partial pulses can be fast (peak velocity vn > c or vn < 0) or slow (vn << c). Further, we investigate the peak velocity v p of the outcoming pulse for several cases. We find that this peak velocity v p and the partial peak velocities vn do not diverge--as occurs to the group velocity v g of the bulk dynamic-periodic medium when ω c = Ω/2. We expect that these results could be verified in the microwave regime [see Halevi et al., Proc. SPIE 8095, 80950I (2011)].