Symmetries of the static electric field induced optical effects in rarefied fluids

The expression for the energy of a molecule in a static electric field is investigated in terms of the irreducible spherical polarizability tensors. The symmetries of its dependence upon the molecular orientation is discussed in detail. The case of the various molecular point groups and the usual approximations are analyzed. The generalized Langevin functions, which describe the thermodynamical averaging over the molecular orientations in a fluid at equilibrium, are calculated exactly and their properties are discussed for the case where molecular correlations can be neglected (i.e., for rarefied fluids). The use of the formalism is illustrated by its application to two well known electro-optical effects; the Kerr effect and the static field induced second harmonic generation.