Design of single-walled carbon nanotubes with a large two-photon absorption cross section

Resonant enhancements of the two-photon absorption cross sections $\ensuremath{\delta}$ have been investigated for different types of seven single-walled carbon nanotubes. The obtained results show that the $\ensuremath{\delta}$ values increase as degree of curvature decreases, that is, $\ensuremath{\delta}$ values increase as $n$ increase for $(n,n)$ tubes ($n=3$,4,5). The $\ensuremath{\delta}$ values linearly vary with the lengths for the $(n,m)$ of $m\ensuremath{\ne}n$ tubes. The origination of a large two-photon absorption cross section has been discussed and it is ascribed to the dispersion effect of tube radius and large $\ensuremath{\pi}$-electron delocalizations in fine open carbon nanotubes.