Chirality-dependent absorption and third-order polarizability spectra in open single-wall carbon nanotubes

The optimized configurations and electronic structures have been obtained based on the density-functional theory for finite open single-walled carbon nanotubes of (4,4) and (5,5). The calculated results show that the bond lengths, bond angles, and charge distributions at the tube ends are significantly different from those at the tube wall. Then, the electronic absorption spectra of the two tubes are calculated by the time-dependent density-functional theory. The evidences show agreement between the theoretical and available experimental results. A strong and wide absorption band occurs for the case of light polarized parallel to the tube axis; a weak absorption and large transparent range appear as the case of light polarized perpendicular to the tube axis. Finally, the dynamic third-order optical polarizabilities in the three optical processes are obtained in terms of the sum-over-states method combined with the above-mentioned method. It is found that the anisotropy of the polarizabilities is larger for the (4,4) than (5,5) tube, and the tube with a larger axial length and smaller diameter has a larger third-order optical polarizabilities at nonresonant frequencies. The largest third-order polarizability is in the direction of both the polarized light and basic light along with the tube axis, and two photon excitation states make main contributions to the polarizabilities of the (4,4) and (5,5) tubes.