  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.
