Non-linear processes to result from multipole interactions between molecules and electromagnetic fields

A compact and at the same time general tensor formalism adapted to the theoretical prediction of a wide range of non-linear processes due in general to multipole interactions between atomic or molecular systems and electromagnetic fields is proposed. Recurring to a semi-classical method, the expectation values of the 2 n -pole induced electric moment P e ( n ) and 2 n -pole magnetic moment P m ( n ) for a transition k → l are computed explicitly to within the third order of quantum-mechanical perturbation theory approximation. The formalism is demonstrated with regard to its utility and simplicity on the example of electric and magnetic multipole light scattering with multiharmonic frequencies ω kl + ω 1 + ω 2 +... + ω r .