  LMTO calculations are presented for the frequency dependent second harmonic
generation (SHG) in the polytypes 2H, 4H, 6H, 15R and 3C of SiC. All
independent tensor components are calculated. The spectral features and the
ratios of the 333 to 311 tensorial components are studied as a function of the
degree of hexagonality. The relationship to the linear optical response and the
underlying band structure are investigated. SHG is suggested to be a sensitive
tool for investigating the near band edge interband excitations.
