A perturbation theory approach was developed for predicting the vibrational and electronic second-order nonlinear optical (NLO) polarizabilities of materials and macromolecules comprised of many coupled chromophores, with an emphasis on common protein secondary structural motifs. The polarization-dependent NLO properties of electronic and vibrational transitions in assemblies of amide chromophores comprising the polypeptide backbones of proteins were found to be accurately recovered in quantum chemical calculations by treating the coupling between adjacent oscillators perturbatively. A novel diagrammatic approach was developed to provide an intuitive visual means of interpreting the results of the perturbation theory calculations. Using this approach, the chiral and achiral polarization-dependent electronic SHG, isotropic SFG, and vibrational SFG nonlinear optical activities of protein structures were predicted and interpreted within the context of simple orientational models.

The theoretical framework for nonlinear optical Stokes ellipsometry (NOSE) is developed as a faster alternative to previous nonlinear optical ellipsometry (NOE) techniques. NOE is the determination of the complex-valued elements within the Jones χ (n) tensor, from which all experimental observables in a given configuration can be predicted. By replacing the moving optics with a photoelastic modulator (PEM) operating at 50 kHz and employing a high repetition rate laser, full ellipsometric detection of the χ (2) tensor can in theory be performed in as little as 20 μs. Two complementary models were developed to analyze the proposed instrumental setup for NOSE. The first more general approach is based on a regression analysis method, which was compared to a second explicit analytical model valid for a particular experimental configuration. Additionally, the rigor of the regression analysis method against noise was investigated.

A data analysis and visualization program was developed to assist in the interpretation of second-order nonlinear optical (NLO) processes, including vibrational sum-frequency generation and electronically resonant second harmonic generation. A novel diagrammatic approach allows concise visual representations of the resonant NLO molecular response. By mapping the predicted NLO response as a function of molecular orientation, molecular modeling results can be combined with experimental measurements for orientational analysis. A method is developed and implemented to predict the nonlinear optical properties of the amide backbones in complete proteins with known structures. NLOPredict is available for most computer operating systems from http://sda.iu.edu/nlopredict/.

Second harmonic generation (SHG) has developed into a powerful tool for characterizing oriented thin films, surfaces, and interfaces. Furthermore, the nonlinear optical nature of wave-mixing processes typically results in the generation of a coherent signal beam with a well-defined polarization state. This coherence offers unique opportunities for the extraction of detailed molecular and surface properties from polarization analysis. In previous studies, nonlinear optical ellipsometry (NOE) has been developed as a means to retain sign and phase information between the different nonzero χ (2) tensor elements present in a given sample. However, those previous methods and related approaches for polarization analysis have all relied on the physical movement of optical elements to perform the analysis. The time required to physically move the appropriate optical elements ultimately dictates the fastest analysis time possible in a given technique. Such long acquisition times have limited NOE analyses to systems exhibiting excellent photostability and have precluded the feasibility of NOE imaging. Development of nonlinear optical Stokes ellipsometry (NOSE) was shown to address many of these problems. By increasing the repetition rate of the laser system and replacing previously slow rotating polarization optics with a rapid photoelastic modulator, the acquisition time with full polarization analysis was reduced from several hours to less than a second. This technique was validated against established NOE techniques using z-cut quartz as a reference sample and then demonstrated on a dye thin film. Additionally, an orientation analysis of the thin film was performed. These studies resulted in an order of magnitude improvement in precision relative to previous NOE techniques, while simultaneously accompanied by a reduction in acquisition time of more than four orders of magnitude.

The application of nonlinear optical Stokes ellipsometry (NOSE) coupled with principal component analysis (PCA) is demonstrated for the chemically selective analysis of molecular monolayers. NOSE allows for rapid polarization measurements of nonlinear optical materials and thin surface films, which in turn benefits from comparably fast data analysis approaches. PCA combined with linear curve fitting techniques greatly reduce the analysis time relative to nonlinear curve fitting. NOSE-PCA is first validated with studies of z-cut quartz, followed by analysis of four thin dye films with similar nonlinear optical properties. The high precision of NOSE measurements combined with the rapid analysis time enabled chemical discrimination between different dyes and the practical realization of NOSE microscopy.