From Octupoles to Octupoling and from EFISH to MEFISH
The promotion of individual molecular tensor properties at a larger ensemble scale remains a key issue in nonlinear optics that can be addressed by adequate tailoring of an externally applied electric potential. It has been abundantly addressed in the case of dipolar molecules under the earlier Langevin-Kielich-Benoit frame, all the way to its subsequent implementation in the realm of quadratic nonlinear optics and there from, into a wealth of more applied electro-optic device applications. In contrast, the issue of non-dipolar molecules, such as octupoles and more generally that of multipolar molecules, had been left aside, whereas the latter are being recognized as the more general pool of candidate nonlinear molecules. We have therefore developed a conceptual frame to further guide practical implementations of general electric field induced multipoling configurations that potentially enable to generalize the earlier dipolar orientation schemes.
Based on the relevant irreducible representation of tensors at molecular scales and up, multipoling configurations are proposed to promote at the required statistically averaged cell level any individual irreducible component of a molecular tensor property of interest, based on the consideration of adequately defined electric potential boundary conditions. We define here 2-D and 3-D irreducible components of the externally applied electrostatic potential that can be coupled to any molecular tensor property of interest via a multipolar charge moment of the same tensor rank. We show that three basic tensors, namely the targeted molecular property tensor, the multipolar tensor, and the applied voltage distribution tensor contribute to the multipoling process. A central result in this work is the establishment of a general coupling rule which is prerequisite to multipoling, and imposes that those three tensors jointly exhibit a nonvanishing component upon projection into the same J-labeled irreducible tensor subspace. Analytical expressions for orientation averages of molecular tensors are then provided in the general case, assuming the validity of a linear approximation to the Maxwell-Boltzmann canonical distribution. Further integration over all spatial configurations within the entire “multipoling” cell (or “MEFISH” cell, for Multipolar Electric Field Induced Second Harmonic) leads to fully analytical averaged expressions of the molecular tensors. Whether isolated or organized in arrays, electrode patterns are shown to follow a discretized approximation to the well-known spherical harmonics, thereby generalizing the simpler bipolar capacitor design for dipolar orientation. General cell electrode design rules are being defined towards actual implementation of multipoling and orders of magnitude for achievable multipoling efficiencies are estimated, pointing-out the interest of a nanotechnology route towards multipolar electrode design.
Keywords: Electric field induced second-harmonic generation, octupoles, multipoles, nonlinear molecules, guest-host systems, electrodes.