A general class of multipolar molecules is introduced in the context of quadratic nonlinear optics by way of extension of the more specific cases of dipolar and octupolar molecules. An adequate irreducible tensor formalism permits us to define rotationally invariant molecular features that couple to corresponding field tensor components, thereby enabling us to account for a variety of coherent and noncoherent processes such as harmonic light (hyper-Rayleigh) scattering, coherent second-harmonic generation in electrically poled media, and the recently proposed optical poling scheme. Experiments in both harmonic light scattering in solution (for some multipolar molecules) and optical poling (in Disperse Red 1–methyl methacrylate thin films) are analyzed in light of this model. A general tensorial permutation lemma of broad validity allows nonlinear light–matter interactions to be condensed in a statistical medium in compact rotationally invariant expressions: The main tensorial symmetry features for both molecular susceptibility and read–write field polarization tensors that jointly drive these interactions are clearly revealed.
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