We demonstrate that the frequency conversion in the cascaded processes can be mapped uniquely to an associated three-wave mixing processes in adiabatic evolution. After solving the coupling wave equations of three-wave mixing processes, we immediately find the solutions of the corresponding cascaded coupled equations. Furthermore, we introduce a rather simple model, which displays the main features of the optical stimulated Raman adiabatic passage (STIRAP) but allows for analytic evaluation of all quantities. It performs two simultaneous three-wave mixing processes efficiently and without significant generation of an intermediate frequency. At last, we consider in detail the effects of the phase mismatch to the optical STIRAP efficiency, which show that the analytic bounds are seen to describe the transfer region very accurately.

• Received 16 April 2013

DOI:https://doi.org/10.1103/PhysRevA.88.023806