Third-order susceptibility tensors of partially ordered systems

The general problem of averaging a microscopic third-order susceptibility tensor over a distribution of orientations is discussed. For the common case in which the distribution is uniform under rotation about one axis, the patterns of the macroscopic tensors for degenerate four-wave mixing, third harmonic generation, CARS, and nondegenerate four-wave mixing are given. Comparison of measurements involving variations in the polarizations and propagation directions of the fields can lead to the determination of the orientation distribution if the microscopic tensor is known.