Third-order optical nonlinearity of semiconductor carbon nanotubes: third harmonic generation

Within the framework of a two-band model of the electronic structure of sem iconductor carbon nanotubes (CNs) we have studied the third-order nonlinear optical susceptibility chi(THG)((3))(omega) responsible for the effect of the third harmonic generation. We have obtained a theoretical expression fo r chi(THG)((3))(omega) which takes into account the contributions to the su sceptibility due to purely interband transitions of pi-electrons and combin ed intraband-interband motion of the latter. A. detailed analysis of the di spersion dependence of chi(THG)((3))(omega) has been carried out in a wide range of frequencies involving those which are much smaller than the bandga p energy and those equal to it by the order of magnitude. The nonlinear-opt ical spectra of chi(THG)((3))(omega) calculated numerically for nonchiral s ingle-shell nanotubes with different radii. The results show that at the ex pense of the increase of the radius of the nanotubes one can achieve a gian t enhancement of the power of radiation generated at the third harmonic fre quency in the three-photon resonance regime. It is also shown that the magn itude of the resonant optical susceptibility of CNs can exceed the resonanc e values of chi(THG)((3)) for the fullerenes C-60 and C-70 by several order s. The results obtained allow us to give a positive prognostic estimate of CNs as a new class of materials for nonlinear optics. (C) 1999 Elsevier Sci ence S.A. All rights reserved.