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Consideration of periodically alternating arrays of noninteracting carbon nanotubes with the metal type of conductivity as elements of the quantum layer heterostructures (quantum wells), which will play the role of the active field, is suggested. From the earlier obtained results based on the models of the elementary cell, it follows that the system in the neighborhood of the Dirac points at the presence of the longitudinal electric field will have equidistant spectrum. The eigenvalues of the energies do not depending on the longitudinal electric field. The two-component eigenfunctions do not depend on the longitudinal electric field. The amplification of the generation terahertz radiation by the analogy with the cascade lasers in the multilevel medium, based on the system of the noninteracting metallic carbon, is considered. If concentration of the nanotubes is 10 7 cm -2 then the output power per unit area will be about Q $ n 0 k 0 hxJ k =e % 8 W=cm 2 . The wavelength of the terahertz radiation is 65 lm.

Electron properties of semiconducting zigzag carbon nanotubes (CNTs) can be described by two uncoupled Dirac equations of dimension (1+1) for the particle with nonzero mass. The solutions of these equations are two charge-neutral Majorana fields. An analogous equation is obtained for the carbon chains. We use the approach, wherein wavefunction of charged particle is represented as the production of a rapidly oscillating exponent and the slowly varying function amplitude depending on the longitudinal coordinate.

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Theoretical investigation and computer simulation of the evolution of terahertz (THz) radiation in a two-level resonance gain medium was carried out on the basis of Maxwell–Bloch equations, using the slowly varying amplitude approximation. The gain medium is based on a system of noninteracting parallel-oriented metallic carbon nanotubes and nanoribbons. Considering the Maxwell–Garnett theory (MGT), the effective dielectric function (EDF) of the medium was obtained. Due to the large nanotube dipole moment (or large value of oscillator strength) not only THz radiation occurs, but also a totality of periodic pulses generation. Results of simulation totally coincide with the theoretical ones. The equation for the phase by analogy with the self-induced transparency (SIT), taking into account the dissipative processes, was obtained. The obtained equation describes a mathematical pendulum, where friction force is proportional to the velocity and directed to the opposite of particle movement. The friction leads to the fact that the pendulum makes a full rotation around the axis or decays, depending on the absorption properties of a gain medium. It was shown that at the certain properties of a gain medium, the equation coincides with the well-known Sine-Gordon equation. It was obtained, that at the initial pumping [Formula: see text] m[Formula: see text] and at the volume fraction of nanoparticles about 10[Formula: see text], the stationary value of radiation energy in a resonator is about 1 J/m3.