The role of the time delay in the reflection and transmission of ultrashort electromagnetic pulses on a system of parallel current sheets

The reflection and transmission of a few-cycle laser pulse impinging on two parallel thin metal layers have been analyzed. The two layers, with a thickness much smaller than the skin depth of the incoming radiation field, are represented by current sheets embedded in three dielectrics, all with different index of refraction. The dynamics of the surface currents and the scattered radiation field are described by the coupled system of Maxwell-Lorentz equations. When applying the plane wave modeling assumptions, these reduce to a hybrid system of two delay differential equations for the electron motion in the layers and a recurrence relation for the scattered field. The solution is given as the limit of a singularly perturbed system and the effects of the time delay on the dynamics is analyzed.