Quantum theory of coherent hyper-Raman scattering from isotropic materials

The fully quantum mechanical theory of coherent hyper-Raman scattering is developed. In this scattering process, which has previously been proposed, two laser beams of wave vectors and frequencies k1 and ω1 and k2 and ω2, respectively, impinge upon the sample to produce a scattered beam characterized by a wave vector k3=4k1−k2 and a frequency ω3=4ω1−ω2. An expression for the rate of scattering from a gas is derived, and several polarization experiments are discussed. It is shown that the selection rules for coherent hyper-Raman scattering are identical to those for the spontaneous hyper-Raman process. A relation between the coherent hyper-Raman spectrum and a correlation function of the hyperpolarizability is obtained. The coherent hyper-Raman process, though not yet observed in the laboratory, may afford an improved way of obtaining hyper-Raman spectra. This process bears the same relation to spontaneous hyper-Raman scattering as the coherent Raman process does to spontaneous Raman scattering, and it should display similar advantages, viz., a higher signal to noise ratio and a resolution limited only by the laser linewidth.