We report ab initio calculations of electronic and the linear optical properties of a (4,1) chiral carbon nanotube, using the full-potential linear augmented plane-wave (FP-LAPW) method. The dielectric tensor is derived within the randomphase approximation (RPA). All optical spectra, such as: dielectric function, absorption coefficient, optical conductivity, extinction coefficient, loss function, sum rule, reflectivity, and the refractive index have been calculated for both electric field polarizations, parallel and perpendicular to the tube axis. It is revealed that the optical spectra are anisotropic along these two polarizations. For the parallel polarization, adding the intraband transition contributions, will change the optical spectra of a (4,1) nanotube significantly. The calculated optical gap, Eg, electronic dielectric constant, e(1), and the refractive index, n, in the parallel polarization are obtained as 2.6 eV, 1.98, and 1.4, respectively. The results show that for small diameter of SWCNTs the chirality has a strong effect on their optical spectra. Adding the intraband transition contributions showed that the dielectric function has singularity at zero frequency, due to the metallic behavior of a (4,1) chiral nanotube.

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