Symmetry Analysis of Tensors Using Mathematica

William Martin McClain
Wayne State University

Cartesian tensors describe the optical polarization properties of nonlinear optical effects in molecules. Two-index tensors describe two-photon absorption; three-index tensors describe three-photon (two-in, one-out) scattering processes, etc. The symmetry of the molecule and the symmetries of the molecular states impart specific symmetries to the tensor. These may be determined experimentally using linear and circular polarized laser beams, even if the molecule is orientationally averaged in the liquid or gaseous state. Mathematica packages and programs for determining such tensor symmetries will be presented.