Uniaxial systems represent the next lowest symmetry below isotropic and are ubiquitous. The objective of the present work is to present a systematic foundation for interpreting polarization-dependent four-wave mixing measurements of oriented and aligned assemblies. Orientational averages connecting the molecular frame to the macroscopic frame in uniaxial assemblies were derived for several common molecular symmetry groups for coherent anti-Stokes Raman spectroscopy (CARS) measurements, coherent anti-Stokes two-photon spectroscopy (CATS) probing electronic transitions, resonant two-photon absorption (2PA), and traditional Raman measurements. First, the complete set of orientational averages connecting the molecular and macroscopic frames was compiled for the most general case of C1 molecular symmetry. Then, the orientational averages of a select few commonly occurring molecular symmetry groups (Cs, C2, C2v, and C3v) were explored in greater detail to illustrate the approach and to facilitate the interpretation of routine experimental measurements. One outcome of this analysis is the prediction of efficient electric dipole-allowed chiral-specific four-wave mixing in uniaxially oriented media.

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/.

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