Stabilization of ultrashort pulses by external pumping in an array of carbon nanotubes subject to piezoelectric effects

Abstract

We study the combined effects of electromagnetic pumping and piezoelectric damping on the propagation of ultrashort pulses in carbon nanotubes. Based on Maxwell’s equations, an effective equation is obtained for the vector potential of the electromagnetic field, which takes into account both the dissipation of the pulse field associated with piezoelectric effects due to the oscillations of the heavy nuclei of the medium and the pumping from an external electromagnetic wave. Our analysis shows that, when the dissipative piezoelectric effects are properly compensated through external pumping, a stable propagation of the ultrashort pulses is achievable. Specifically, we demonstrate the stability of the steady-state form of the electromagnetic pulse at long time scales with variations in various system parameters, including the absorption coefficient of heavy ions as well as the initial pulse field distribution. In addition, the stability of the pulse with respect to angular perturbations—breaking the axisymmetry of the pulse distribution—is substantiated.