The role of longitudinal polarization in surface second harmonic generation

Use of the classical polarization concept is deeply entrenched in standard nonlinear optics. Nonetheless it establishes a framework for the formulation of theory which is not directly amenable to the resolution of certain kinds of question. In particular, it can obscure the difference between coherent and incoherent optical response. This has been forcefully illustrated by recent controversy over the issue of second harmonic generation involving surfaces or interfaces of isotropic fluids. It is the purpose of this paper, by formulating a theory cast directly in terms of the observable, the harmonic intensity, to resolve the issue. Through a unified treatment of both coherent and incoherent contributions to the second harmonic, it is unequivocally demonstrated that any signal classically associated with longitudinal polarization is necessarily incoherent.