Interference effects in the sum frequency generation spectra of thin organic films. I. Theoretical modeling and simulation

Abstract

A general theoretical calculation is described for predicting the interference effect in the sum frequency generation (SFG) spectra from a model thin-film system as a function of film thickness. The calculations were carried out for a three-layer thin film consisting of an organic monolayer, a dielectric thin film of variable thickness, and a gold substrate. This system comprises two sources of SFG, namely, a resonant contribution from the monolayer/dielectric film interface and a nonresonant contribution from the dielectric film/gold interface. The calculation shows that both the spectral intensity and the shape of the SFG spectra vary significantly with the thickness of the dielectric layer due to interference effects in the thin film. The intensity changes at a particular frequency were explained in terms of the changes in the local field factors ($L$ factors) as a function of the dielectric film thickness. The $L$ factor for each beam changes periodically with the thickness of the dielectric film. However, the combined $L$ factor for the three beams shows complicated thickness dependent features and no clear periodicity was found. On the other hand, if the susceptibilities of both the resonant and nonresonant terms are fixed, changes in the spectral shape will be mainly due to changes in the phase differences between the two terms with the film thickness. The interference behavior also depends strongly on the polarization combinations of the sum frequency, visible, and infrared beams. A general method is provided for predicting changes in the spectral shapes at different film thicknesses by taking into account the relative intensities and phases of the SFG signals from the two interfaces. The model calculation provides important insights for understanding the nonlinear optical responses from any thin-film system and is an essential tool for quantitatively revealing the nonlinear susceptibilities, which are directly related to the actual structure of the interfacial molecules from the observed SFG spectra after quantitative removal of the $L$ factors.