Sum frequency generation from partially ordered media and interfaces: a polarization analysis

The theory of sum frequency generation (SFG) is treated within a molecular quantum electrodynamical framework and applied to an ensemble of partially oriented molecules, for lucid analysis of the SFG intensity dependence on beam polarization and molecular symmetry. By expanding the orientational distribution function in terms of an infinite set of Legendre polynomials, it is shown that the observed SFG intensity may be followed in terms of a finite set of distinct contributions. For a time-dependent distribution, each contribution has unique temporal characteristics which may be separated experimentally by manipulation of the laser beam and detection geometry. Specific configurations required for complete separation of the different terms are given. The theory is further developed for partially oriented molecules, within thin films or adsorbed onto surfaces. Consideration is also given to the effect of temperature variation, which should open new avenues for the elucidation of molecular orientation in such media.