  In the currently accepted models of the nonlinear optics, the nonlinear
radiation was treated as the result of an infinitesimally thin polarization
sheet layer, and a three layer model was generally employed. The direct
consequence of this approach is that an apriori dielectric constant, which
still does not have a clear definition, has to be assigned to this polarization
layer. Because the Second Harmonic Generation (SHG) and the Sum-Frequency
Generation vibrational Spectroscopy (SFG-VS) have been proven as the sensitive
probes for interfaces with the submonolayer coverage, the treatment based on
the more realistic discrete induced dipole model needs to be developed. Here we
show that following the molecular optics theory approach the SHG, as well as
the SFG-VS, radiation from the monolayer or submonolayer at an interface can be
rigorously treated as the radiation from an induced dipole lattice at the
interface. In this approach, the introduction of the polarization sheet is no
longer necessary. Therefore, the ambiguity of the unaccounted dielectric
constant of the polarization layer is no longer an issue. Moreover, the
anisotropic two dimensional microscopic local field factors can be explicitly
expressed with the linear polarizability tensors of the interfacial molecules.
Based on the planewise dipole sum rule in the molecular monolayer, crucial
experimental tests of this microscopic treatment with SHG and SFG-VS are
discussed. Many puzzles in the literature of surface SHG and SFG spectroscopy
studies can also be understood or resolved in this framework. This new
treatment may provide a solid basis for the quantitative analysis in the
surface SHG and SFG studies.
