Causal vs. Noncausal Description of Nonlinear Wave Mixing; Resolving the Damping-Sign Controversy

Frequency-domain nonlinear wave mixing processes may be described either using response functions whereby the signal is generated after all interactions with the incoming fields, or in terms of scattering amplitudes where all fields are treated symetrically with no specific time ordering. Closed Green's function expressions derived for the two types of signals have different analytical properties. The recent controversy regarding the sign of radiative damping in the linear (Kramers Heisenberg) formula is put in a broader context.