Generation of Stokes and Anti-Stokes Radiation in Raman Media

A three-dimensional analysis of stimulated Raman emission is presented for a medium through which a cylindrical laser beam passes. The buildup of the Stokes radiation from the spontaneous fluctuations in the Raman medium is considered. A generalization of the fluctuation-dissipation theorem is derived relating the current-current fluctuations at the Stokes frequency to the laser-induced (negative) conductance at this frequency. The anti-Stokes radiation is treated as arising from the interaction of the laser field and the molecular vibrations accompanying the Stokes radiation. The anti-Stokes radiation emerges in a narrow cone around the familiar phase-matching direction given by ${\mathbf{\beta }}_{-}=2\mathrm{}{\mathbf{k}}_L-{\mathbf{\beta }}_{+}$, where ${\mathbf{\beta }}_{-}$ and ${\mathbf{\beta }}_{+}$ are the (real parts of the) propagation constants of Stokes and anti-Stokes waves in the medium, and ${\mathbf{k}}_L$ is the laser propagation vector. The angular width of the anti-Stokes radiation cone is evaluated.