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 ω₁and 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.