Theoretical study of third-order nonlinear optical response of semiconductor carbon nanotubes

We present a theoretical study of the nonlinear-optical properties of single-shell semiconductor carbon nanotubes (CNs) within a simple model based on the two-band approximation of their electronic structure. By use of the Genkin-Mednis approach, we have calculated the nonlinear-optical spectra of the susceptibility of chi((3))(omega) for the following third-order polarization effects: the third harmonic generation, the intensity-dependent index of refraction, the two-photon absorption and the DC Kerr effect. It is found that in off-resonant conditions the susceptibility chi((3))(0) shows a four-power dependence on the tubule radius and can reach values typical of bulk III-V semiconductor compounds with the strongest nonlinear optical properties. The optical spectra of chi((3))(omega) under the three-photon resonance regime have revealed considerable enhancement of the radiation power generated at a third-harmonic frequency. Our results show that in CNs the nonlinear index of refraction as large as 2 x 10(-8) cm(2) W-1 can be achieved in a region where the two-photon absorption is small. The change of the refractive index of CNs of the order of 10(-11)E(0)(2) (V-2 cm(-2)) was found to be induced by a uniform static electric field E-0 applied along the CNs axis. It is concluded that carbon nanotubes present a considerable interest in view of their possible utilization in a variety of nonlinear optical devices. (C) 1998 Elsevier Science B.V. All rights reserved.