Orientational correlation functions and polarization selectivity for nonlinear spectroscopy of isotropic media. I. Third order

The contribution of orientational relaxation to the tensor components of the third-order nonlinear polarization is evaluated for off-resonance Raman and dipole resonant experiments in the perturbative limit. Orientational correlation functions are calculated within the model of orientational diffusion for all third-order tensor components relevant to isotropic media. General expressions for polarization geometries that are selective to particular components of the signal, i.e., magic angles, are derived for collinear and crossed-beam excitation geometries. It is shown that although limited selectivity exists for Raman spectroscopies, no combination of polarizations will give complete selectivity to the isotropic, anisotropic, or nonresonant contributions to the Raman polarizability tensor. For resonant spectroscopies, the four-time correlation function that describes the orientational polarization decay can be written as the product of three two-time correlation functions. While magic angles for orientational relaxation will exist for experiments that probe population dynamics, such as pump–probe and transient grating spectroscopies, orientational relaxation cannot be removed from coherence experiments such as the photon echo.