Optical properties of carbon nanotubes

Abstract

Using the extended Hubbard model and sum-over-state method, we have calculated the linear polarizability $\ensuremath{\alpha}$ and the third-order nonlinear polarizability $\ensuremath{\gamma}$ for carbon nanotubes with finite lengths. We find that the chiral symmetry of nanotubes with finite length has a great effect on their optical properties. For example, the finite length $(n,m)$ tubes with $n\ensuremath{-}m$ being not a multiple of 3, will have smaller $\ensuremath{\alpha}$ and much smaller $\ensuremath{\gamma}$ values than other finite length tubes.