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

With the tight-binding model of semiconductor carbon nanotubes, the third-order nonlinearity of carbon nanotubes has been studied theoretically by using the two-band approximation. Taking the contribution of pure interband transition of π-electron and combined intraband–interband motion into account, a spectrum of χTHG(3) has been obtained. The results show that for a typical semiconductor carbon nanotube the off-resonant magnitude of |χTHG(3)| reaches 10−7–10−8 esu and |χTHG(3)| value at three-photon resonant peak 10−5 esu. The nonlinear susceptibility χTHG(3) strongly depends on the nanotubes geometry and considerably increases with the increasing radii of carbon nanotubes. In addition, it is found that the third-order nonlinear susceptibility of carbon nanotubes obeys 1/Δg6 law.