THEORY OF STIMULATED RAMAN EFFECT

The matrix element describing the fourth-order process in which two photons are simultaneously scattered by a molecule is calculated with the help of time-ordered graphs. The two incident and two scattered photons are assumed to have different frequencies; only dipole allowed transitions are considered; and the initial and final molecular levels are taken to be the same. In the special case where the incident photons have the same frequency, the result of Buckingham [J. Chem. Phys. 43, 25 (1965)] is recovered. The scattered photons have a continuous spectrum sharply peaked around the Stokes and anti-Stokes frequencies. If two incident photons excite a higher molecular level, the continuum is enhanced, leading to the possibility of antiresonances near the Stokes and anti-Stokes frequencies.