Microscopic molecular optics theory of surface second harmonic generation and sum-frequency generation spectroscopy based on the discrete dipole lattice model

The aim of this work is to present a coherent description of the microscopic theory of surface nonlinear optical spectroscopy for solving practical problems in understanding the details of the molecular interface. We review the related issues and show that by following microscopic molecular optics theory, second harmonic generation (SHG), as well as sum-frequency generation vibrational spectroscopy (SFG-VS), radiation from a monolayer or submonolayer can be rigorously treated as the radiation from an induced dipole lattice at the interface. In this approach, the introduction of an infinitesimally thin polarization sheet as in macroscopic theory with the Maxwell equations and the boundary conditions is no longer necessary. As a direct consequence, the ambiguity of the unaccounted dielectric constant of the interfacial layer is no longer an issue. Moreover, the anisotropic two-dimensional microscopic local field factors can be explicitly defined with the linear polarizability tensors of the interfacial molecules. Based on the planewise dipole sum rule in the molecular monolayer, experimental tests of this microscopic treatment with SHG and SFG-VS are discussed