Enhancements of third-order nonlinear optical response in excited state of the fullerenes ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$

Dynamic third-order nonlinear polarizabilities of three optical processes of third-harmonic generation, electric-field-induced second-harmonic generation, and degenerate four-wave mixing have been calculated at the both ground and excited states in ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ fullerenes in terms of the sum-over-states formula. The transition moment elements and the transition energies in this formula are obtained using the intermediate neglect of differential overlap and single- and double-excitation configuration interaction method. The calculated third-order polarizabilities show a dispersion behavior with different from ground state and a strong enhancement of third-order nonlinear optical response in the first excited singlet state. The calculated nonresonant susceptibilities ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}(-\omega ;\omega ,\omega ,-\omega )$ of this excited state reach the magnitude of ${10}^{-10}\mathrm{esu}$ for ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ films.