An algorithm for the nonlinear optical susceptibilities of dipolar molecules, and an application to third harmonic generation

It is well known that a simple transformation of the electric dipole interaction provides a convenient means for ascertaining the effects of permanent dipoles on the optical behaviour of systems with a response dominated by two energy levels. By establishing the general validity of the procedure for parametric processes such as harmonic generation, it is shown how the detailed structure of the optical susceptibilities associated with arbitrary forms of optical nonlinearity can be ascertained by an algorithmic method, based on a novel interpretation of the relevant quantum electrodynamical Feynman diagrams. Application of the algorithm to second and third harmonic generation illustrates its usefulness and simplicity, whilst also providing new results and revealing features, related to the role of permanent dipoles, which have not hitherto been apparent.