Thin SiC films, grown on Si by substitution of C into Si on Si substrates with and without a SiGe buffer layer, have been investigated with optical techniques. The formation of SiC domains leads to strong green and blue photoluminescence from stacking faults and surface oxides. Introduction of a 10-nm-thick SiGe buffer layer leads to improved crystallinity as evidenced by X-ray diffraction and optical second-harmonic generation (SHG). Nonlinear optical azimuthal rotational spectra demonstrate the presence of cubic SiC in the film. Furthermore, angle-of-incidence scans are consistent with simulations based on a film with cubic symmetry which demonstrates that the cubic phase dominates the SiC film. Growth on vicinal Si(111) leads to a SiC film with the same c_1v symmetry as the substrate, demonstrating that the lattice planes of the SiC film follow those of the Si substrate. Spatially resolved SHG scans show structures that are related to the underlying structure of the Si interface resulting from the growth process.