Nonlinear interaction of electromagnetic waves with chiral carbon nanotubes. Helical parametrization

摘要

The parametrization scheme for carbon nanotubes (CNTs) — helical parametrization — has been developed, where the crystalline structure of non-zigzag (n_1,n_2) CNTs is described as a set of n_2 double helices, and the electron energy spectrum of the CNTs consists of n_2 different helicoidal branches. The parametrization scheme is shown to be natural and more convenient for analyzing the electromagnetic response properties of chiral CNTs. Bloch equations for the density matrix have been obtained and adapted for the helical parametrization that allows studying the interaction between chiral CNTs and electromagnetic fields with arbitrary polarization and spatial structure. As an example, the spectra of high-order harmonics in chiral CNTs have been evaluated from the Bloch equations.