Molecular engineering implications of rotational invariance in quadratic nonlinear optics: From dipolar to octupolar molecules and materials

Abstract

Molecules and assemblies therefrom with strictly vanishing multipolar‐like tensorial susceptibilities of given orders are defined in general, following group theoretical prescriptions. This approach leads, in the case of quadratic nonlinear optical properties, to a new class of molecules with strictly vanishing dipole moments and dipolar components of the quadratic hyperpolarizability tensor β. The remaining nonvanishing irreducible β component, referred to as the octupolar component, had not been previously considered in the perspective of molecular engineering and optimization, as proposed in this work. The adequate tensorial framework for depicting such an approach is derived for the various point‐symmetry classes and a vectorial representation introduced to depict the full anisotropic nature of nonlinear polarizabilities. It permits a more general and adequate scaling of molecules and materials in terms of their efficiencies, while previous molecular classifications, strongly biased by the electric field second‐harmonic (EFISH) solution experiment, focus almost exclusively on the dipolar component of β. Various molecular engineering routes meant at enhancing the octupolar β component are proposed and illustrated by specific examples. The molecular quantum implications of the existence of octupolar nonlinearities are discussed with three‐level systems shown to replace the inadequate traditional two‐level model. Finally, identical tensorial symmetry considerations, applied consistently to molecular assemblies (χ(2)susceptibility) and interacting light beam (F (2) cubic field tensor) evidence the relevance of circularly polarized beams to probe octupolar assemblies, the ellipticity of the outgoing beam in the case of second‐harmonic generation depending on the ratio of the octupolar over dipolar susceptibility components.