Theory of the Stimulated Raman and Related Effects

A simple description of the stimulated Raman emission of Stokes radiation, and of the induced absorption found by Stoicheff at the anti‐Stokes frequency, is based on the semiclassical theory of radiation. This theory gives the well‐known formulas for absorption and stimulated emission when carried to the first order in the time‐dependent perturbation due to the interaction of the light beam with the molecules. If there are two light beams of frequencies ω_L and ω, the second‐order perturbation may be associated with stimulated emission at the Stokes frequency ω=ω₋₁=ω_L—ω_R and with induced absorption at the anti‐Stokes frequency ω=ω₁=ω_L+ω_R, where ω_L is the laser frequency and ω_R a Raman‐active vibrational frequency; in both cases, there is a molecular transition to the excited vibrational state. The highly directional and very sharp anti‐Stokes emission at ω₁ arises from the conversion by molecules in intense beams at ω_L and ω₋₁ of two ω_L photons into an ω₋₁, ω₁ pair. Like spontaneous emission from excited states, the production of this anti‐Stokes radiation requires the full quantum theory of radiation for an adequate description. The emission of ω₁ and the observed directional absorption of ω₋₁ due to the reverse conversion ω₋₁+ω₁→2ω_L are explained. The anti‐Stokes emission is proportional to the Stokes intensity and to the square of that of the laser, and to the square of the molecular number density; its sharpness is due to the absence of a molecular transition. The generation of photon pairs ω_−n+ω_n, where ω_n=ω_L+nω_R, can occur for all values of n, but it is most efficient for n=1, due to resonance in the appropriate molecular hyperpolarizability and to the intensity of the Stokes beam at ω₋₁.