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

Resonant enhancements of the two-photon absorption cross sections $\delta$ have been investigated for different types of seven single-walled carbon nanotubes. The obtained results show that the $\delta$ values increase as degree of curvature decreases, that is, $\delta$ values increase as $n$ increase for $(n,n)$ tubes ($n=3$,4,5). The $\delta$ values linearly vary with the lengths for the $(n,m)$ of $m\ne n$ 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 $\pi$-electron delocalizations in fine open carbon nanotubes.

Figure 1

The configuration of nanotubes: (a) $(5,5)∕80$, (b) $(4,2)∕72$, (c) $(6,0)∕72$.

Figure 2

The calculated two-photon absorption cross section of SWCN’s at tube axial direction based on TDDFT at B3LYP/3-21G level combined with SOS method.

Figure 3

The plots of $\mathrm{lm}(-;,,-)$ values vs. number of two-photon states at the character wavelength for the studied SWCN’s.

Figure 4

Scheme of the calculated energy levels and transition dipole moments (in eV and a.u. unit, respectively) at three state models for $\left(n,n\right)$ tubes.

Figure 5

The orbitals contributing mostly to one-photon state and two-photon resonant states of $(4,4)∕64$ tube.