Electromagnetic solitons in bundles of zigzag carbon nanotubes

The possibility of forming solitons in zigzag carbon nanotubes is investigated using the coupled equations for the classical function of the electron distribution and the Maxwell equations for an electromagnetic field. It is demonstrated that the solitons are generated as a result of correlated changes in the classical distribution function and the electric field induced by nonequilibrium electrons of a carbon nanotube. The effective equation describing the dynamics of the electromagnetic field is derived. The existence of solitons is confirmed by the results of numerical calculations. The characteristics of solitons are investigated as a function of the diameter of zigzag carbon nanotubes.     

Interaction of ultrashort light pulses with carbon nanotubes

The possibility of existence of electromagnetic solitons in carbon nanotubes is investigated on the basis of the coupled equations for the classical distribution function of electrons in such nanotubes and the Maxwell equations for electromagnetic fields. Solitons arise due to the matched change in the classical distribution function and the electric field formed by nonequilibrium electrons of a carbon nanotube. The data of numerical calculations, indicative of the existence of solitons, are reported.     

Electromagnetic solitons in carbon nanotubes at low temperatures

The propagation of a variable electromagnetic field in arrays of “zigzag” carbon nanotubes at low temperatures is considered. The electronic system of carbon nanotubes is analyzed using the Hamilton formalism with ignoring interactions with the phonon subsystem because the electromagnetic field pulse is extremely short. An effective equation for the amplitude of the electromagnetic field vector-potential was obtained. Solutions-analogues of solitons were revealed; these solutions corresponded to solitons for the cosine electronic subsystem dispersion law. The dependences of the nonlinear solutions obtained on problem parameters were analyzed.     

Collision of extremely short optical pulses in semiconductor carbon nanotubes

The interaction of extremely short optical pulses in semiconductor carbon nanotubes is discussed. An equation is derived for the dynamics of the electromagnetic field in a system of semiconductor carbon nanotubes at low temperatures, whose solutions are analogs to the solitons of the sine-Gordon equation. The behavior of extremely short optical pulses in semiconductor carbon nanotubes on collision is analyzed.     

Periodic current domains in a system of carbon nanotubes

The dynamics of propagation of periodic electromagnetic waves and the current induced by them in a system of carbon nanotubes is investigated. The study is performed on the basis of the analysis of the coupled equations for the classical distribution function of electrons in carbon nanotubes and the Maxwell equations for an electromagnetic field. An effective equation describing the electromagnetic field dynamics is obtained. Periodic changes in the form of an electromagnetic wave during its propagation are revealed. This effect is related to the energy exchange between periodic vibrations with different periods in the system under consideration. The corresponding regions of the current through carbon nanotubes form a regular periodic domain structure. The results of numerical calculations are reported, which make it possible to consider this effect at different problem parameters.     

Dissipative solitons in carbon nanotubes

The theoretical possibility of the existence of dissipative solitons in an array of carbon nanotubes when they are subjected to external uniform high-frequency electric field is discussed. An external alternating field is used for energy pumping of the electron subsystem, while a finite relaxation time leads to energy dissipation. The generation of a periodic sequence of electromagnetic pulses is revealed.     

Periodic current domains in bundles of carbon nanotubes

The dynamics of propagation of periodic electromagnetic waves and the related electric current in bundles of carbon nanotubes is studied. The study is based on an analysis of coupled equations for the classical electron distribution function in carbon nanotubes and the Maxwell equations for an electromagnetic field. An effective equation is obtained to describe the electromagnetic-field dynamics. Periodic changes are revealed in the shape of the electromagnetic wave propagating in a carbon medium. This effect is considered to be related to energy exchange between periodic oscillations having different periods. Certain regions of the current passing through carbon nanotubes form a periodic domain structure. The results of numerical calculations allow this effect to be analyzed as a function of the problem parameters.     

Two-dimensional electromagnetic breathers in an array of nanotubes with multilevel impurities

The propagation of a two-dimensional bipolar electromagnetic pulse in an array of semiconductor carbon nanotubes with multilevel impurities is studied. The electromagnetic field in the array of nanotubes is described by Maxwell’s equations reduced to a non-one-dimensional wave equation. The numerical solution to the wave equation demonstrates the possibility of the propagation of a two-dimensional electromagnetic breather in the array of nanotubes. The character of the evolution of the shape of the breather is elucidated, and the time dependence of the maximum intensity of its field is obtained. It is demonstrated that the introduction of multilevel impurities causes a significant change in the parameters, thereby providing an additional possibility for the stabilization of a laser pulse propagating in an array of semiconducting carbon nanotubes.     

Interaction of two-dimensional electromagnetic breathers in an array of carbon nanotubes

The propagation and interaction of two-dimensional bipolar electromagnetic pulses in an array of semiconducting carbon nanotubes have been investigated. The electromagnetic field in the array of carbon nanotubes has been described by the Maxwell’s equations reduced to the non-one-dimensional wave equation. The initial distribution of the field has been specified in the form of approaching breathers bounded by a Gaussian profile in the plane perpendicular to the pulse propagation direction. The numerical solution of the wave equation has revealed the possibility of stable propagation of breathers in the array of carbon nanotubes. It has been found that the interaction of electromagnetic breathers in the array of semiconducting carbon nanotubes has a character of quasi-elastic collisions.     

Dissipative solitons in carbon nanotubes

The possibility of analogs of dissipative solitons occurring in arrays of carbon nanotubes under the action of a high-frequency external uniform electric field on the array has been established theoretically. The electromagnetic field has been considered in terms of the Maxwell equations, and the conduction electrons in carbon nanotubes have been described by the Boltzmann kinetic equation in the relaxation-time approximation. The external ac electric field serves for energy pumping of the electronic subsystem, whereas a finite relaxation time leads to energy dissipation. The generation of a periodic sequence of electromagnetic pulses has been revealed. This sequence can be used for producing terahertz frequencies.     

Extremely short electromagnetic pulses in an array of carbon nanotubes with a longitudinal field inhomogeneity

The propagation of bipolar electromagnetic pulses in an array of semiconductor carbon nanotubes has been investigated. The inhomogeneity of the pulse field along the axis of the nanotubes has been taken into account for the first time. The evolution of the electromagnetic field and charge density in the sample has been described by the set of Maxwell’s equations and the continuity equation. The possibility of stable propagation of bipolar electromagnetic pulses occurring in an array of nanotubes has been demonstrated by numerical simulation. It has been shown that the propagation of the electromagnetic pulses induces the redistribution of the electron density in the sample.     

Two-dimensional unitary waves in a nonuniform block of carbon nanotubes

The propagation and scattering of two-dimensional unitary electromagnetic waves on metallic discontinuity in a block of carbon nanotubes is considered. The electromagnetic field was considered on the basis of Maxwell equations, and the electron system of carbon nanotubes was based on Boltzmann kinetic equations in an approximation of the relaxation time.     

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.     

Two-dimensional light bullets in an array of carbon nanotubes

The problem of the propagation of two-dimensional solitary electromagnetic waves in an array of carbon nanotubes has been considered. The electromagnetic field and the electron system of carbon nanotubes have been treated on the basis of the Maxwell’s equations and the Boltzmann kinetic equation in the relaxation-time approximation, respectively. The derived effective equation has been analyzed and the state of the electromagnetic field that is localized in two spatial dimensions has been found.     

Nonlinear waves and bistability in strong electromagnetic field driven molecular chains with optical-type vibration spectra

The possibility of electromagnetic field induced bistability and the existence of nonequilibrium “kinetic” solitons propagating along the molecular chain is shown. The phenomenon is due to selfconsistency of intramolecular kinetics with the dynamics of chain vibrations.     

Ultrashort optical pulses in carbon nanotubes and graphene with periodic impurities

The dispersion law for electrons has been derived by the Green’s function method using the Anderson periodic model, which has been proposed to describe the electron subsystem in carbon nanotubes and graphene with impurities. The combined dynamics of electrons and an electromagnetic field has been considered in the low-temperature limit, and the effective equation describing the propagation of ultrashort optical pulses has been obtained. The solutions to this equation as functions of the parameters of the problem have been presented.     

Dynamics of ultimately short electromagnetic pulses in chiral carbon nanotubes

The wave equation for the electromagnetic field propagating in chiral carbon nanotubes has been analyzed. The phenomenological equation similar to the sine-Gordon equation has been derived. The dynamics of the electromagnetic pulse has been investigated.     

Propagation of vector solitons in a quasi-resonant medium with stark deformation of quantum states

The nonlinear dynamics of a vector two-component optical pulse propagating in quasi-resonance conditions in a medium of nonsymmetric quantum objects is investigated for Stark splitting of quantum energy levels by an external electric field. We consider the case when the ordinary component of the optical pulse induces ?? transitions, while the extraordinary component induces the ?? transition and shifts the frequencies of the allowed transitions due to the dynamic Stark effect. It is found that under Zakharov-Benney resonance conditions, the propagation of the optical pulse is accompanied by generation of an electromagnetic pulse in the terahertz band and is described by the vector generalization of the nonlinear Yajima-Oikawa system. It is shown that this system (as well as its formal generalization with an arbitrary number of optical components) is integrable by the inverse scattering transformation method. The corresponding Darboux transformations are found for obtaining multisoliton solutions. The influence of transverse effects on the propagation of vector solitons is investigated. The conditions under which transverse dynamics leads to self-focusing (defocusing) of solitons are determined.