Theoretical modelling of nonlinear refraction and two-photon absorption in single-wall carbon nanotube bundles

The nonlinear refractive index n2 and the two-photon absorption coefficient α2 are calculated for a bundle of diameter-distributed and aligned single-wall carbon nanotubes. The dispersion of the nanotube circumference length is shown to have important effects on the resonant behaviour of both quantities under consideration, giving rise to a strong broadening, intensity decrease, and `red' shift of the position of the positive and negative resonant peaks in the n2(ω) and α2(ω) spectra. It is predicted that a relatively large refractive-index change (~ 1 cm2 GW-1) from a positive to a negative peak value produced by a relatively small variation of pump frequency can be achieved for real samples of carbon nanotubes in the frequency range where they are almost transparent. The results indicate that carbon nanotubes are a promising novel class of nanoscale materials that could be used in practical optical switching applications.