Measurements of Nonlinear Light Scattering

Double‐quantum light scattering by a system of molecules is discussed in this paper. Expressions have been obtained for the scattered light intensity considering both the coherent and incoherent contributions. In that coherent contributions are also considered in this treatment, it goes beyond the scope of previous studies. It is shown that, for molecules of low symmetry, elliptically polarized light must be used in order to determine five independent quadratic forms in the 18 symmetric components (βijk+βikj). According to the present results, the apparent discrepancy between the observed value of ⅓ for the depolarization ratio for CCl4 and the value to be expected from theory may be due to the fact that the coherent contribution had been neglected in previous theoretical considerations. In general, orientational correlation is essential if there is to be appreciable contribution from coherent scattering. For macromolecules, this constitutes a major difference between single‐ and double‐quantum scattering...

Double‐Quantum Light Scattering by Molecules

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.

Spectral Broadening of Elastic Second-Harmonic Light Scattering in Liquids

Hyper-Raman scattering by vibrational excitations in crystals, glasses and liquids

The dipole moment induced by a radiation field may be expanded in terms of the electric field vector. The third‐ and fourth‐rank tensors in this expansion, β and γ, respectively, correspond to three‐ and four‐photon Raman effects. Diagrammatic perturbation theory is used to obtain explicit quantum‐mechanical expressions for the β and γ tensors. Selection rules for the symmetric γ tensor and for the nonsymmetric β and γ tensors are then calculated for the important molecular point groups. The results are compared with those for the ordinary Raman effect, and conditions necessary for the observation of nonlinear effects are discussed.

Selection Rules for Three- and Four-Photon Raman Interactions

: It may become possible to observe the third-order process of radiation in the strong electromagnetic field of a laser beam with two photons absorbed and a third one emitted during a transition between energy levels of a material system. This process is analogous to the ordinary Raman effect, in which only two photons are involved. A theoretical analysis is given and the conclusion reached that with a beam intensity of 0.1 MW/sq cm, the vibrational Raman spectrum of molecules or crystals may be obtained by the three-photon process. It is shown that this effect actually offers a new spectroscopic method. Its importance lies in the difference of the selection rule of this effect and that of the infrared absorption and the ordinary Raman effect. It is also pointed out that the stimulated radiation of three-photon Raman effect may be realized when pumped with a powerful laser beam. (Author)

Yin-yuan Li

Papers

Raman effect of multiple radiation process and its applications in spectroscopy