Collisions of three-dimensional bipolar optical solitons in an array of carbon nanotubes

We study interactions of extremely short three-dimensional bipolar electromagnetic pulses propagating towards each other in an array of semiconductor carbon nanotubes, along any direction perpendicular to their axes. The analysis provides a full account of the effects of the nonuniformity of the pulses’ fields along the axes. The evolution of the electromagnetic field and charge density in the sample is derived from the Maxwell’s equations and the continuity equation, respectively. In particular, we focus on indirect interaction of the pulses via the action of their fields on the electronic subsystem of the nanotube array. Changes in the shape of pulses in the course of their propagation and interaction are analyzed by calculating and visualizing the distribution of the electric field in the system. The numerical analysis reveals a possibility of stable post-collision propagation of pulses over distances much greater than their sizes

Propagation of three-dimensional bipolar ultrashort electromagnetic pulses in an inhomogeneous array of carbon nanotubes

We study the propagation of three-dimensional (3D) bipolar ultrashort electromagnetic pulses in an inhomogeneous array of semiconductor carbon nanotubes. The heterogeneity is represented by a planar region with an increased concentration of conduction electrons. The evolution of the electromagnetic field and electron concentration in the sample are governed by the Maxwell’s equations and continuity equation. In particular, nonuniformity of the electromagnetic field along the axis of the nanotubes is taken into account. We demonstrate that depending on values of the parameters of the electromagnetic pulse approaching the region with the higher electron concentration, the pulse is either reflected from the region or passes it. Specifically, our simulations demonstrate that after interacting with the higher-concentration area, the pulse can propagate steadily, without significant spreading. The possibility of such ultrashort electromagnetic pulses propagating in arrays of carbon nanotubes over distances significantly exceeding characteristic dimensions of the pulses makes it possible to consider them as 3D solitons

Asymptotic dynamics of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes

We study the propagation of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes at times much longer than the pulse duration, yet still shorter than the relaxation time in the system. The interaction of the electromagnetic field with the electronic subsystem of the medium is described by means of Maxwell’s equations, taking into account the field inhomogeneity along the nanotube axis beyond the approximation of slowly varying amplitudes and phases. A model is proposed for the analysis of the dynamics of an electromagnetic pulse in the form of an effective equation for the vector potential of the field. Our numerical analysis demonstrates the possibility of a satisfactory description of the evolution of the pulse field at large times by means of a three-dimensional generalization of the sine-Gordon and double sine-Gordon equations

Interaction of a two-dimensional electromagnetic pulse with an electron inhomogeneity in an array of carbon nanotubes in the presence of field inhomogeneity

In this study, we address the challenging problem of propagation of infrared electromagnetic two-dimensional bipolar pulses of extremely short duration in a heterogeneous array of semiconductor carbon nanotubes. Heterogeneity is defined here as a region of high electron density. The evolutions of the electromagnetic field and charge density in the sample are described by Maxwell’s equations and the continuity equation respectively, wherein the inhomogeneity of the field along the nanotube axis is integrated and incorporated into the modeling framework. Our numerical solution to this problem shows the possibility of a stable propagation of two-dimensional electromagnetic pulses through a heterogeneous array of carbon nanotubes. This propagation of electromagnetic pulses is accompanied by a redistribution of the electron density in the sample. For the first time to the best of our knowledge, this latter effect is fully accounted for in our study. Specifically, we demonstrate that depending on the initial speed of the electromagnetic pulse two possible outcomes might ensue: either (i) the pulse overcomes the region of increased electron concentration, or alternatively (ii) it is reflected therefrom. As a result, a near-infrared pulse is transmitted, while the long-wavelength infrared pulse is reflected, on an obstacle that is much smaller than its wavelength

2D electromagnetic breathers in carbon nanotubes

We study the propagation of two-dimensional bipolar electromagnetic pulses in an array of semiconducting carbon nanotubes. The electromagnetic field in such an array is described by Maxwell’s equations, reduced to a nonlinear wave equation. The initial field distribution is given in the form of the breather sine-Gordon equation, restricted by a Gaussian profile in a plane perpendicular to the direction of the momentum. The numerical solution of the wave equation shows the possibility of propagation of the electromagnetic breather in an array of nanotubes. We reveal the nature of the evolution of the breather’s shape and obtain the time dependence of its amplitude. We find that the breather, propagating in an array of nanotubes, is resistant to spreading and can travel a distance  ~10-3 ÷ 10-2 cm

Light bullet passing an array of carbon nanotubes with metallic mesh irregularities

We consider the propagation of 2D solitary electromagnetic waves and their scattering on a lattice of metallic inhomogeneities in the system of carbon nanotubes (CNTs). The electromagnetic field is considered on the basis of Maxwell equations, and the electronic system of carbon nanotubes is treated by the Boltzmann equation in relaxation time approximation. We numerically analyze the derived effective equation and reveal an increase of spectral composition of the last electromagnetic wave. Some possible practical applications of the discovered effect are discussed