Second-harmonic generation and linear electro-optical coefficients of   SiC polytypes and nanotubes
  The second-order nonlinear optical susceptibility ($\chi_{abc}^{(2)}$) and linear electro-optical coefficient ($r_{abc}$) of a large number of single-walled zigzag, armchair and chiral SiC nanotubes (SiC-NTs) as well as bulk SiC polytypes (2H-, 4H-, 6H- and 3C-SiC) and single graphitic SiC sheet have been calculated from first-principles. The calculations are based on density functional theory in the local density approximation and highly accurate full-potential projector augmented-wave method is used. Both the zigzag and chiral SiC-NTs are found to exhibit large second-order nonlinear optical behavior with the $\chi_{abc}^{(2)}$ and $r_{abc}$ coefficients being up to ten-times larger than that of bulk SiC polytypes, and also being up to thirteen-times larger than the counterparts of the corresponding BN-NTs, indicating that SiC-NTs are promising materials for nonlinear optical and opto-electric applications. The prominant features in the spectra of $\chi_{abc}^{(2)}(-2\omega,\omega,\omega)$ of the SiC-NTs are correlated with the features in the linear optical dielectric function $\epsilon (\omega)$ in terms of single-photon and two-photon resonances. 
I. J. Wu and G. Y. Guo