  Second-harmonic-generation (SHG) in centrosymmetric material such as Si(111)
is usually understood either from the phenomenology theory or more recently
using the Simplified Bond-Hyperpolarizability Model (SBHM) [G. D. Powell, J. F.
Wang, and D. E. Aspnes, Phys. Rev. B 65, 205320/1 (2002)]. Although SBHM is
derived from a classical point of view, it has the advantage over the former
that it gives-especially for lower symmetry systems- a clear physical picture
and a more efficient explanation of how nonlinearity is generated. In this
paper we provide a step-by-step description of the SBHM in Si(111) for the
linear and second harmonic case. We present a SHG experiment of Si(111) and
show how it can be modelled by summing up the contribution of the fields
produced by the anharmonic motion along the bonds.
