Spectral Broadening of Elastic Second-Harmonic Light Scattering in Liquids

Abstract

The spectral width of "elastic" second-harmonic light scattering has been measured for a number of liquids. The broadening arises principally from rotational molecular motions and, ignoring possible nonadditive molecule-molecule interactions, the spectrum is shown to be related to the Fourier transform of the orientation-dependent pair distribution function $G(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}, \stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}, t)$. An irreducible spherical-tensor representation is employed. It is shown that a totally symmetric nonlinear-susceptibility tensor produces elastic harmonic light scattering characterized by just the first- and third-degree spherical elements of $G(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}, \stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}, t)$ and that the corresponding spectra may be independently determined. For Brownian orientational motion, these comprise Lorentzians whose widths are related to the tensorial orientational-diffusion coefficient. For isotropic orientational diffusion, the widths are in the ratio 1: 6. Dielectric-relaxation and depolarized Rayleigh scattering also relate to $G(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}, \stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}, t)$, and the results of all three experiments are compared. In no instance was isotropic orientational diffusion found to be a satisfactory model. A more extended study was made of carbon tetrachloride. Evidence was found both for nonadditive response and for coherent effects resulting from short-range orientational ordering. The extremely weak signals - often less than one photoevent per laser firing - necessitated development of a reliable high-repetition-rate $Q$-switched ruby laser and use of electronic data-accumulation techniques.