External light control of three-dimensional ultrashort far-infrared pulses in an inhomogeneous array of carbon nanotubes

We present a study of the propagation of three-dimensional (3D) bipolar electromagnetic ultrashort pulses in an inhomogeneous array of semiconductor carbon nanotubes (CNTs) in the presence of a control high-frequency (HF) electric field. The inhomogeneity is present in the form of a layer with an increased concentration of conduction electrons, which acts as a barrier for the propagation of ultrashort electromagnetic pulses through the CNT array. The dynamics of the pulse is described by a nonlinear equation for the vector potential of the electromagnetic field (it takes the form of a 3D generalization of the sine-Gordon equation), derived from the Maxwell's equations and averaged over the period of the HF control field. By means of systematic simulations, we demonstrate that, depending on the amplitude and frequency of the HF control, the ultrashort pulse approaching the barrier layer either passes it or bounces back. The layer's transmissivity for the incident pulse is significantly affected by the amplitude and frequency of the HF control field, with the reflection coefficient nearly vanishing in intervals that make up a discrete set of transparency windows, which resembles the effect of the electromagnetically induced transparency. Having passed the barrier, the ultrashort pulse continues to propagate, keeping its spatiotemporal integrity. The results may be used for the design of soliton valves, with the transmissivity of the soliton stream accurately controlled by the HF field.