Molecular Tensor Analysis of Third-Harmonic Scattering in Liquids

Abstract

Third-harmonic scattering is a nonlinear optical process that involves the molecular second-hyperpolarizability, γ. This work presents a rigorous quantum electrodynamical analysis of the scattering process, involving a partially index-symmetric construction of the fourth-rank γ tensor-dispensing with the Kleinman symmetry condition. To account for stochastic molecular rotation in fluids, methods of isotropic averaging must be employed to relate the molecular properties to accessible experimental quantities such as depolarization ratio. A complete eighth-rank tensor rotational average yields results for observable third-harmonic scattering rates, cast as a function of the natural-invariant γ components, and the polarization geometry of the experiment. Decomposing the tensor γ into irreducible weights allows specific predictions to be made for each molecular point group, allowing greater discrimination between the results for different molecular symmetries.

Harmonic light scattering study reveals structured clusters upon the supramolecular aggregation of regioregular poly(3-alkylthiophene)

“…SHS and THS are both nonlinear scattering techniques that require illumination of the sample in solution with a high-power laser. In contrast to linear scattering where photons scattered at the same frequency are detected, SHS and THS are processes for which scattering occurs at the double and triple frequency, respectively 37,[51][52][53][54][55] . The scattered intensity for SHS (I 2ω ) and THS (I 3ω ) depends on the square and cube of the incident intensity (I ω ), respectively.…”

Symmetries, Conserved Properties, Tensor Representations, and Irreducible Forms in Molecular Quantum Electrodynamics

“…The essential flaws and general inapplicability of Kleinman symmetry were in fact quickly pointed out by Wagnière [118]. Recent work on third harmonic scattering has again shown that emphatic differences arise, according to whether or not full index symmetry is assumed [119]. As a corollary to all such cases, however, it is of interest that in a specific case where all the photons involved in the interaction have identical polarization, then, for the same reasons discussed in Section 6, the results will indeed be consistent with Kleinman symmetry.…”

Third harmonic scattering in liquids

“…Contributions from irreducible parts of the γ tensor of all rank are included in the isotropic average of the squared γ tensor, γ 2 , appearing in the final expression. 4 The analogous calculation for second harmonic scattering (HRS) mediated by the first hyperpolarizability tensor β gives…”

“…For direct THS, the isotropic average of the squared γ tensor γ 2 has contributions from the irreducible parts of γ with ranks 0, 1, 2, 3, and 4, producing polarized and depolarized THS, and non-zero THS for circular polarized incident light. 2,4 In the most general case, the following relation holds for direct THS at 90 • scattering angle: 4…”

“…THS has only recently been explored as an experimental technique to measure the molecular second hyperpolarizability tensor γ αβγδ (−3ω; ω, ω, ω). [1][2][3][4] It is considered to be analogous to the lower-order incoherent second harmonic scattering (SHS) process, also called hyper-Rayleigh scattering (HRS), which is widely used to measure the molecular first hyperpolarizability tensor β αβγ (−2ω; ω, ω). [5][6][7][8] The advantages of incoherent scattering measurements over coherent wave mixing and harmonic generation techniques are potential access to more hyperpolarizability tensor components by polarization analysis and great experimental simplicity.…”