Curvature effect on polarization of light emitted from chiral carbon nanotubes

We investigate that effect of the curvature on induced hybridization and modification of emission profiles for each chiral's index single-wall carbon nanotubes (SWCNTs). According to the Schwinger two particle pair state method, we provide an analytical expression by calculating polar of spot intensity as a function of the polar angle. The emission profiles for indirect transition have an asymmetric shape as a function of the electron wave vector of the axis direction kt and depend on the chiral index. Here we show polarization-dependent, given analytically by expanding the matrix element into the scalar product of the light polarization vector and the dipole vector. These scalar products having a maximum value depend on the summation of phase factors of spinors of electrons in the conduction band Φc and valence band Φv. In the case of direct transition, dipole vector tube axis is maximum at the phase summation of Φc and Φv is 0 or 2π. In contrast, the maximum dipole vector circumference is obtained at the phase summation of π for the case of indirect transition. We can predict a strong emission peak and emission profiles which can be used to identify optical transitions in an individual SWCNT with different chiral indices experimentally.