Treatment of Linear and Nonlinear Dielectric Property of Molecular Monolayer and Submonolayer with Microscopic Dipole Lattice Model: I. Second Harmonic Generation and Sum-Frequency Generation

Abstract

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.