Multiple pass stimulated Raman conversion with pump depletion

In this work we derive an analytical expression for the efficiency of stimulated Raman conversion applicable to Gaussian pump and Stokes beams in a multiple-pass cell. Pump depletion and mirror reflectivity are taken into account. The result provides a simple expression for calculating the conversion efficiency versus the number of passes through a Raman cell. It is especially useful in the design of multiple-pass cells for infrared Raman conversion in which the gain is low and many passes are required.