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

Abstract

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 χ (3)( ω) 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 χ (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 χ (3)( ω) 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 2×10 −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.