  We theoretically discuss the physical origin of the dielectric constants
[{\epsilon}({\omega})] and second harmonic generation coefficients
[\{chi}(2)({\omega})] of the ABA-stacked two-dimensional graphene-like silicon
carbide (2D-SiC) with the number of layers up to 5. It is found that the
intensities of the pronounced peaks of both {\epsilon}({\omega}) and
\{chi}(2)({\omega}) exhibit a clear layer number dependence. For the light
polarization parallel to the 2DSiC plane, the monolayer SiC (ML-SiC) and
multilayer SiC (MuL-SiC) have very similar pronounced peak positions of
{\epsilon}({\omega}), which are attributed to the {\pi}->{\pi}* and
{\sigma}->{\sigma}* transitions. However, for the light polarization
perpendicular to the 2D-SiC plane, a characteristic peak is found for the
MuL-SiC at about 4.0 eV, except that the allowed {\pi}->{\sigma}* and
{\sigma}->{\pi}* transition peaks are found for both ML-SiC and MuL-SiC in the
high-energy region (> 8 eV). This characteristic peak is attributed to the
interlayer {\pi}->{\pi}* transition which does not exist for the ML-SiC, and at
this peak position, the ML-SiC has a weak dark exciton based on the mBJ
calculation within the Bethe-Salpeter equation framework. For
\{chi}(2)({\omega}), the single-particle transition channels based on the
three-band terms dominate the second harmonic generation process of both ML-SiC
and MuL-SiC and determine the size and sign of \{chi}(2)({\omega}). In the
ultraviolet visible region, the purely interband motion and intraband motion of
electrons competitively determine the size and sign of \{chi}(2)({\omega}). For
the light polarization perpendicular to the 2D-SiC plane, the intraband motion
of electrons modulated more dramatically the interband motion than for that
parallel to the 2D-SiC plane.
