Second harmonic generation theory for a helical macromolecule with high sensitivity to structural disorder

Microscopic theory for the second harmonic generation in a helical molecular system is developed in the minimal coupling representation including non-local interaction effects. At the second order to the field we find a compact expression which combines dipolar, quadrupolar and magnetic contributions. A detailed derivation of the response is performed to specifically isolate the quadratic coupling terms, which we denote as the K coupling. Applying the theory to a helical macromolecule we find that the dipolar and quadrupolar contributions reflect the symmetry properties of the system and its homogeneity, while the K coupling contribution reveals inhomogeneities of the system.