  A comprehensive analysis of second harmonic generation (SHG) in a diatomic
zincblende crystal based on the Simplified Bond Hyperpolarizability Model
(SBHM), Group Theory (GT) is presented. The third rank tensor between the two
approaches are compared and applied to reproduce rotational anisotropy (RA) SHG
experimental result.It is well known that such a crystal is noncentrosymmetric,
therefore the second harmonic generation source is dominated by bulk dipoles
with a SHG polarization $P_{BD}=\chi_{ijk}^{(2)}E(\omega)E(\omega)$. We show
that the SBHM previously applied to mono crystal system such as Silicon can
also be applied to an atomic cell containing two different atoms e.g. GaAs by
introducing an effective hyperpolarizability
$\alpha_{2GaAs}=\left(\alpha_{2Ga}-\alpha_{2As}\right)$ . Comparison with GT
yields the same third rank tensor for a $T_d$ point group corresponding to bulk
tetrahedral structure. Interestingly, SBHM gives good agreement with RASHG
experiment of GaAs using only one single fitting parameter when Fresnel
analysis is also incorporated in the model.
