Quantum electrodynamics furnishes a new type of representation for the characterisation of nonlinear optical processes. The treatment elicits the detailed role and interplay of specific quantum channels, information that is not afforded by other methods. Following an illustrative application to the case of Rayleigh scattering, the method is applied to second and third harmonic generation. Derivations are given of parameters that quantify the various quantum channels and their interferences; the results are illustrated graphically. With given examples, it is shown in some systems that optical nonlinearity owes its origin to an isolated channel, or a small group of channels. © 2009 World Scientific Publishing Company.