Enhanced stimulated Raman scattering and general three-boson parametric instabilities

A recent theory of stimulated Raman scattering explained a Stokes-intensity-enhanced gain that had been observed but that was not predicted by earlier theories. It is shown that in the earlier golden-rule analyses (perturbation-theory treatment of occupation numbers $n$) the enhancement was lost by neglecting the increase of the vibrational amplitudes above their thermal-equilibrium values. Even though the probability of an individual ion or molecule being excited is small, the occupation number of the phonon in the Raman process is large. In the previous mode-amplitude analyses, the enhancement was lost in the method of linearizing the nonlinear differential equations. By solving these same mode-amplitude equations for the $n\text{'}\mathrm{s}$ without using the previous linearization scheme, the enhancement is obtained and the equivalence of the mode-amplitude and golden-rule boson-occupation-number results is demonstrated explicitly. The analysis shows explicitly that the loss of phase information in using the boson occupation numbers does not cause the loss of enhancement. The results are applicable to other three-boson splitting processes that are important in ferromagnetism, phonon interactions, plasma instabilities, and device physics.